49.445 * [progress]: [Phase 1 of 3] Setting up. 0.003 * * * [progress]: [1/2] Preparing points 0.218 * * * [progress]: [2/2] Setting up program. 0.223 * [progress]: [Phase 2 of 3] Improving. 0.223 * * * * [progress]: [ 1 / 1 ] simplifiying candidate # 0.223 * [simplify]: Simplifying: (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 0.223 * * [simplify]: iteration 0: 13 enodes 0.227 * * [simplify]: iteration 1: 31 enodes 0.233 * * [simplify]: iteration 2: 62 enodes 0.245 * * [simplify]: iteration 3: 124 enodes 0.279 * * [simplify]: iteration 4: 328 enodes 0.540 * * [simplify]: iteration 5: 970 enodes 0.931 * * [simplify]: iteration 6: 2026 enodes 1.422 * * [simplify]: iteration complete: 2026 enodes 1.422 * * [simplify]: Extracting #0: cost 1 inf + 0 1.423 * * [simplify]: Extracting #1: cost 86 inf + 0 1.424 * * [simplify]: Extracting #2: cost 311 inf + 1 1.428 * * [simplify]: Extracting #3: cost 435 inf + 46 1.433 * * [simplify]: Extracting #4: cost 405 inf + 4118 1.445 * * [simplify]: Extracting #5: cost 293 inf + 28237 1.477 * * [simplify]: Extracting #6: cost 140 inf + 129132 1.521 * * [simplify]: Extracting #7: cost 9 inf + 256512 1.581 * * [simplify]: Extracting #8: cost 0 inf + 265066 1.635 * * [simplify]: Extracting #9: cost 0 inf + 265063 1.680 * * [simplify]: Extracting #10: cost 0 inf + 264810 1.733 * [simplify]: Simplified to: (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) 1.745 * * [progress]: iteration 1 / 4 1.745 * * * [progress]: picking best candidate 1.757 * * * * [pick]: Picked # 1.757 * * * [progress]: localizing error 1.795 * * * [progress]: generating rewritten candidates 1.795 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1) 1.811 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1) 1.835 * * * * [progress]: [ 3 / 3 ] rewriting at (2) 1.884 * * * [progress]: generating series expansions 1.884 * * * * [progress]: [ 1 / 3 ] generating series at (2 1) 1.885 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1.885 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1.885 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1.885 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1.885 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1.885 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1.885 * [taylor]: Taking taylor expansion of 1/2 in k 1.885 * [backup-simplify]: Simplify 1/2 into 1/2 1.885 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 1.885 * [taylor]: Taking taylor expansion of 1/2 in k 1.885 * [backup-simplify]: Simplify 1/2 into 1/2 1.885 * [taylor]: Taking taylor expansion of k in k 1.885 * [backup-simplify]: Simplify 0 into 0 1.885 * [backup-simplify]: Simplify 1 into 1 1.885 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 1.885 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 1.885 * [taylor]: Taking taylor expansion of 2 in k 1.885 * [backup-simplify]: Simplify 2 into 2 1.885 * [taylor]: Taking taylor expansion of (* n PI) in k 1.885 * [taylor]: Taking taylor expansion of n in k 1.885 * [backup-simplify]: Simplify n into n 1.885 * [taylor]: Taking taylor expansion of PI in k 1.885 * [backup-simplify]: Simplify PI into PI 1.885 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.885 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1.886 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1.886 * [backup-simplify]: Simplify (* 1/2 0) into 0 1.886 * [backup-simplify]: Simplify (- 0) into 0 1.886 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 1.886 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1.887 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1.887 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1.887 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1.887 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1.887 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1.887 * [taylor]: Taking taylor expansion of 1/2 in n 1.887 * [backup-simplify]: Simplify 1/2 into 1/2 1.887 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 1.887 * [taylor]: Taking taylor expansion of 1/2 in n 1.887 * [backup-simplify]: Simplify 1/2 into 1/2 1.887 * [taylor]: Taking taylor expansion of k in n 1.887 * [backup-simplify]: Simplify k into k 1.887 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.887 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.887 * [taylor]: Taking taylor expansion of 2 in n 1.887 * [backup-simplify]: Simplify 2 into 2 1.887 * [taylor]: Taking taylor expansion of (* n PI) in n 1.887 * [taylor]: Taking taylor expansion of n in n 1.887 * [backup-simplify]: Simplify 0 into 0 1.887 * [backup-simplify]: Simplify 1 into 1 1.887 * [taylor]: Taking taylor expansion of PI in n 1.887 * [backup-simplify]: Simplify PI into PI 1.887 * [backup-simplify]: Simplify (* 0 PI) into 0 1.887 * [backup-simplify]: Simplify (* 2 0) into 0 1.888 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.889 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1.890 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.890 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 1.890 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1.890 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1.891 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.892 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1.893 * [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))))) 1.893 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1.893 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1.893 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1.893 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1.893 * [taylor]: Taking taylor expansion of 1/2 in n 1.893 * [backup-simplify]: Simplify 1/2 into 1/2 1.893 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 1.893 * [taylor]: Taking taylor expansion of 1/2 in n 1.893 * [backup-simplify]: Simplify 1/2 into 1/2 1.893 * [taylor]: Taking taylor expansion of k in n 1.893 * [backup-simplify]: Simplify k into k 1.893 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.893 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.893 * [taylor]: Taking taylor expansion of 2 in n 1.893 * [backup-simplify]: Simplify 2 into 2 1.893 * [taylor]: Taking taylor expansion of (* n PI) in n 1.893 * [taylor]: Taking taylor expansion of n in n 1.893 * [backup-simplify]: Simplify 0 into 0 1.893 * [backup-simplify]: Simplify 1 into 1 1.893 * [taylor]: Taking taylor expansion of PI in n 1.893 * [backup-simplify]: Simplify PI into PI 1.894 * [backup-simplify]: Simplify (* 0 PI) into 0 1.894 * [backup-simplify]: Simplify (* 2 0) into 0 1.895 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.896 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1.896 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.896 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 1.896 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1.896 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1.897 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.898 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1.899 * [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))))) 1.899 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1.899 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1.899 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1.899 * [taylor]: Taking taylor expansion of 1/2 in k 1.899 * [backup-simplify]: Simplify 1/2 into 1/2 1.899 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 1.899 * [taylor]: Taking taylor expansion of 1/2 in k 1.899 * [backup-simplify]: Simplify 1/2 into 1/2 1.899 * [taylor]: Taking taylor expansion of k in k 1.899 * [backup-simplify]: Simplify 0 into 0 1.899 * [backup-simplify]: Simplify 1 into 1 1.899 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1.899 * [taylor]: Taking taylor expansion of (log n) in k 1.899 * [taylor]: Taking taylor expansion of n in k 1.899 * [backup-simplify]: Simplify n into n 1.899 * [backup-simplify]: Simplify (log n) into (log n) 1.899 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 1.899 * [taylor]: Taking taylor expansion of (* 2 PI) in k 1.899 * [taylor]: Taking taylor expansion of 2 in k 1.899 * [backup-simplify]: Simplify 2 into 2 1.899 * [taylor]: Taking taylor expansion of PI in k 1.899 * [backup-simplify]: Simplify PI into PI 1.899 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 1.900 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.900 * [backup-simplify]: Simplify (* 1/2 0) into 0 1.901 * [backup-simplify]: Simplify (- 0) into 0 1.901 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 1.902 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.903 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1.904 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1.905 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1.906 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.907 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1.909 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1.910 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1.910 * [backup-simplify]: Simplify (- 0) into 0 1.911 * [backup-simplify]: Simplify (+ 0 0) into 0 1.912 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.913 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1.915 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.915 * [taylor]: Taking taylor expansion of 0 in k 1.915 * [backup-simplify]: Simplify 0 into 0 1.915 * [backup-simplify]: Simplify 0 into 0 1.916 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.917 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 1.919 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1.919 * [backup-simplify]: Simplify (+ 0 0) into 0 1.920 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1.920 * [backup-simplify]: Simplify (- 1/2) into -1/2 1.921 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 1.923 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1.926 * [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))))))) 1.929 * [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))))))) 1.931 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.932 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.935 * [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 1.937 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1.937 * [backup-simplify]: Simplify (- 0) into 0 1.937 * [backup-simplify]: Simplify (+ 0 0) into 0 1.939 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.941 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1.944 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.944 * [taylor]: Taking taylor expansion of 0 in k 1.944 * [backup-simplify]: Simplify 0 into 0 1.944 * [backup-simplify]: Simplify 0 into 0 1.944 * [backup-simplify]: Simplify 0 into 0 1.946 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.947 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1.951 * [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 1.951 * [backup-simplify]: Simplify (+ 0 0) into 0 1.952 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1.953 * [backup-simplify]: Simplify (- 0) into 0 1.953 * [backup-simplify]: Simplify (+ 0 0) into 0 1.954 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1.956 * [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))))) 1.959 * [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))))) 1.966 * [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))))) 1.966 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1.966 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1.966 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1.966 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1.966 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1.966 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1.966 * [taylor]: Taking taylor expansion of 1/2 in k 1.966 * [backup-simplify]: Simplify 1/2 into 1/2 1.966 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1.966 * [taylor]: Taking taylor expansion of 1/2 in k 1.966 * [backup-simplify]: Simplify 1/2 into 1/2 1.966 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.966 * [taylor]: Taking taylor expansion of k in k 1.966 * [backup-simplify]: Simplify 0 into 0 1.966 * [backup-simplify]: Simplify 1 into 1 1.967 * [backup-simplify]: Simplify (/ 1 1) into 1 1.967 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1.967 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 1.967 * [taylor]: Taking taylor expansion of 2 in k 1.967 * [backup-simplify]: Simplify 2 into 2 1.967 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.967 * [taylor]: Taking taylor expansion of PI in k 1.967 * [backup-simplify]: Simplify PI into PI 1.967 * [taylor]: Taking taylor expansion of n in k 1.967 * [backup-simplify]: Simplify n into n 1.967 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.967 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1.967 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1.967 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 1.967 * [backup-simplify]: Simplify (- 1/2) into -1/2 1.968 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 1.968 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1.968 * [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)))) 1.968 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1.968 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1.968 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1.968 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1.968 * [taylor]: Taking taylor expansion of 1/2 in n 1.968 * [backup-simplify]: Simplify 1/2 into 1/2 1.968 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1.968 * [taylor]: Taking taylor expansion of 1/2 in n 1.968 * [backup-simplify]: Simplify 1/2 into 1/2 1.968 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.968 * [taylor]: Taking taylor expansion of k in n 1.968 * [backup-simplify]: Simplify k into k 1.968 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.968 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1.968 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.968 * [taylor]: Taking taylor expansion of 2 in n 1.968 * [backup-simplify]: Simplify 2 into 2 1.968 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.968 * [taylor]: Taking taylor expansion of PI in n 1.968 * [backup-simplify]: Simplify PI into PI 1.968 * [taylor]: Taking taylor expansion of n in n 1.968 * [backup-simplify]: Simplify 0 into 0 1.968 * [backup-simplify]: Simplify 1 into 1 1.969 * [backup-simplify]: Simplify (/ PI 1) into PI 1.969 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 1.970 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.970 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1.970 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1.970 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1.971 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1.971 * [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))) 1.972 * [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)))) 1.972 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1.972 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1.972 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1.972 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1.972 * [taylor]: Taking taylor expansion of 1/2 in n 1.972 * [backup-simplify]: Simplify 1/2 into 1/2 1.972 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1.972 * [taylor]: Taking taylor expansion of 1/2 in n 1.972 * [backup-simplify]: Simplify 1/2 into 1/2 1.972 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.972 * [taylor]: Taking taylor expansion of k in n 1.972 * [backup-simplify]: Simplify k into k 1.972 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.972 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1.972 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.972 * [taylor]: Taking taylor expansion of 2 in n 1.973 * [backup-simplify]: Simplify 2 into 2 1.973 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.973 * [taylor]: Taking taylor expansion of PI in n 1.973 * [backup-simplify]: Simplify PI into PI 1.973 * [taylor]: Taking taylor expansion of n in n 1.973 * [backup-simplify]: Simplify 0 into 0 1.973 * [backup-simplify]: Simplify 1 into 1 1.973 * [backup-simplify]: Simplify (/ PI 1) into PI 1.973 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 1.974 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.974 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1.974 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1.974 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1.975 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1.976 * [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))) 1.977 * [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)))) 1.977 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1.977 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1.977 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1.977 * [taylor]: Taking taylor expansion of 1/2 in k 1.977 * [backup-simplify]: Simplify 1/2 into 1/2 1.977 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1.977 * [taylor]: Taking taylor expansion of 1/2 in k 1.977 * [backup-simplify]: Simplify 1/2 into 1/2 1.977 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.977 * [taylor]: Taking taylor expansion of k in k 1.977 * [backup-simplify]: Simplify 0 into 0 1.977 * [backup-simplify]: Simplify 1 into 1 1.977 * [backup-simplify]: Simplify (/ 1 1) into 1 1.977 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1.977 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 1.977 * [taylor]: Taking taylor expansion of (* 2 PI) in k 1.977 * [taylor]: Taking taylor expansion of 2 in k 1.977 * [backup-simplify]: Simplify 2 into 2 1.977 * [taylor]: Taking taylor expansion of PI in k 1.977 * [backup-simplify]: Simplify PI into PI 1.983 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 1.984 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.984 * [taylor]: Taking taylor expansion of (log n) in k 1.984 * [taylor]: Taking taylor expansion of n in k 1.984 * [backup-simplify]: Simplify n into n 1.984 * [backup-simplify]: Simplify (log n) into (log n) 1.985 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 1.985 * [backup-simplify]: Simplify (- 1/2) into -1/2 1.985 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 1.985 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.986 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1.987 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1.987 * [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)))) 1.988 * [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)))) 1.989 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.989 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 1.990 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1.990 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.991 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1.991 * [backup-simplify]: Simplify (- 0) into 0 1.991 * [backup-simplify]: Simplify (+ 0 0) into 0 1.992 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1.993 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1.994 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1.994 * [taylor]: Taking taylor expansion of 0 in k 1.994 * [backup-simplify]: Simplify 0 into 0 1.994 * [backup-simplify]: Simplify 0 into 0 1.994 * [backup-simplify]: Simplify 0 into 0 1.995 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.996 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1.997 * [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 1.998 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.998 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1.998 * [backup-simplify]: Simplify (- 0) into 0 1.999 * [backup-simplify]: Simplify (+ 0 0) into 0 1.999 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.000 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 2.004 * [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 2.004 * [taylor]: Taking taylor expansion of 0 in k 2.004 * [backup-simplify]: Simplify 0 into 0 2.004 * [backup-simplify]: Simplify 0 into 0 2.004 * [backup-simplify]: Simplify 0 into 0 2.004 * [backup-simplify]: Simplify 0 into 0 2.006 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.007 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.013 * [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 2.013 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.014 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 2.015 * [backup-simplify]: Simplify (- 0) into 0 2.015 * [backup-simplify]: Simplify (+ 0 0) into 0 2.017 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.018 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 2.019 * [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 2.019 * [taylor]: Taking taylor expansion of 0 in k 2.019 * [backup-simplify]: Simplify 0 into 0 2.019 * [backup-simplify]: Simplify 0 into 0 2.020 * [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))))) 2.021 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 2.021 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 2.021 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 2.021 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 2.021 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 2.021 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.021 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.021 * [taylor]: Taking taylor expansion of 1/2 in k 2.021 * [backup-simplify]: Simplify 1/2 into 1/2 2.021 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.021 * [taylor]: Taking taylor expansion of k in k 2.021 * [backup-simplify]: Simplify 0 into 0 2.021 * [backup-simplify]: Simplify 1 into 1 2.021 * [backup-simplify]: Simplify (/ 1 1) into 1 2.021 * [taylor]: Taking taylor expansion of 1/2 in k 2.021 * [backup-simplify]: Simplify 1/2 into 1/2 2.021 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 2.021 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 2.021 * [taylor]: Taking taylor expansion of -2 in k 2.021 * [backup-simplify]: Simplify -2 into -2 2.021 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.021 * [taylor]: Taking taylor expansion of PI in k 2.021 * [backup-simplify]: Simplify PI into PI 2.021 * [taylor]: Taking taylor expansion of n in k 2.021 * [backup-simplify]: Simplify n into n 2.021 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.021 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 2.021 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 2.022 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.022 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.022 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 2.022 * [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))) 2.022 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.022 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.022 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.022 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.022 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.022 * [taylor]: Taking taylor expansion of 1/2 in n 2.022 * [backup-simplify]: Simplify 1/2 into 1/2 2.022 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.022 * [taylor]: Taking taylor expansion of k in n 2.022 * [backup-simplify]: Simplify k into k 2.022 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.022 * [taylor]: Taking taylor expansion of 1/2 in n 2.022 * [backup-simplify]: Simplify 1/2 into 1/2 2.022 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.022 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.022 * [taylor]: Taking taylor expansion of -2 in n 2.022 * [backup-simplify]: Simplify -2 into -2 2.022 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.022 * [taylor]: Taking taylor expansion of PI in n 2.022 * [backup-simplify]: Simplify PI into PI 2.022 * [taylor]: Taking taylor expansion of n in n 2.022 * [backup-simplify]: Simplify 0 into 0 2.023 * [backup-simplify]: Simplify 1 into 1 2.023 * [backup-simplify]: Simplify (/ PI 1) into PI 2.023 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.024 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.024 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.024 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.025 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.025 * [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))) 2.026 * [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)))) 2.026 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.026 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.026 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.026 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.026 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.026 * [taylor]: Taking taylor expansion of 1/2 in n 2.026 * [backup-simplify]: Simplify 1/2 into 1/2 2.026 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.026 * [taylor]: Taking taylor expansion of k in n 2.026 * [backup-simplify]: Simplify k into k 2.026 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.026 * [taylor]: Taking taylor expansion of 1/2 in n 2.026 * [backup-simplify]: Simplify 1/2 into 1/2 2.026 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.026 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.026 * [taylor]: Taking taylor expansion of -2 in n 2.026 * [backup-simplify]: Simplify -2 into -2 2.026 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.026 * [taylor]: Taking taylor expansion of PI in n 2.027 * [backup-simplify]: Simplify PI into PI 2.027 * [taylor]: Taking taylor expansion of n in n 2.027 * [backup-simplify]: Simplify 0 into 0 2.027 * [backup-simplify]: Simplify 1 into 1 2.027 * [backup-simplify]: Simplify (/ PI 1) into PI 2.027 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.028 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.028 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.028 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.029 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.030 * [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))) 2.030 * [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)))) 2.030 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 2.030 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 2.030 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.030 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.030 * [taylor]: Taking taylor expansion of 1/2 in k 2.030 * [backup-simplify]: Simplify 1/2 into 1/2 2.030 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.030 * [taylor]: Taking taylor expansion of k in k 2.030 * [backup-simplify]: Simplify 0 into 0 2.031 * [backup-simplify]: Simplify 1 into 1 2.031 * [backup-simplify]: Simplify (/ 1 1) into 1 2.031 * [taylor]: Taking taylor expansion of 1/2 in k 2.031 * [backup-simplify]: Simplify 1/2 into 1/2 2.031 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 2.031 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 2.031 * [taylor]: Taking taylor expansion of (* -2 PI) in k 2.031 * [taylor]: Taking taylor expansion of -2 in k 2.031 * [backup-simplify]: Simplify -2 into -2 2.031 * [taylor]: Taking taylor expansion of PI in k 2.031 * [backup-simplify]: Simplify PI into PI 2.031 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.032 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.032 * [taylor]: Taking taylor expansion of (log n) in k 2.032 * [taylor]: Taking taylor expansion of n in k 2.032 * [backup-simplify]: Simplify n into n 2.032 * [backup-simplify]: Simplify (log n) into (log n) 2.032 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.032 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.032 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.033 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 2.034 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 2.035 * [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)))) 2.035 * [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)))) 2.036 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.036 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.037 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 2.037 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.038 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.038 * [backup-simplify]: Simplify (+ 0 0) into 0 2.039 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.039 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 2.041 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.041 * [taylor]: Taking taylor expansion of 0 in k 2.041 * [backup-simplify]: Simplify 0 into 0 2.041 * [backup-simplify]: Simplify 0 into 0 2.041 * [backup-simplify]: Simplify 0 into 0 2.041 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.042 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.044 * [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 2.044 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.045 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.045 * [backup-simplify]: Simplify (+ 0 0) into 0 2.046 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.048 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 2.050 * [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 2.050 * [taylor]: Taking taylor expansion of 0 in k 2.050 * [backup-simplify]: Simplify 0 into 0 2.050 * [backup-simplify]: Simplify 0 into 0 2.050 * [backup-simplify]: Simplify 0 into 0 2.050 * [backup-simplify]: Simplify 0 into 0 2.052 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.053 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.059 * [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 2.059 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.060 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 2.061 * [backup-simplify]: Simplify (+ 0 0) into 0 2.062 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.063 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 2.065 * [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 2.065 * [taylor]: Taking taylor expansion of 0 in k 2.065 * [backup-simplify]: Simplify 0 into 0 2.065 * [backup-simplify]: Simplify 0 into 0 2.065 * [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))))) 2.066 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1) 2.066 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) 2.066 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 2.066 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.066 * [taylor]: Taking taylor expansion of 2 in n 2.066 * [backup-simplify]: Simplify 2 into 2 2.066 * [taylor]: Taking taylor expansion of (* n PI) in n 2.066 * [taylor]: Taking taylor expansion of n in n 2.066 * [backup-simplify]: Simplify 0 into 0 2.066 * [backup-simplify]: Simplify 1 into 1 2.066 * [taylor]: Taking taylor expansion of PI in n 2.066 * [backup-simplify]: Simplify PI into PI 2.066 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.066 * [taylor]: Taking taylor expansion of 2 in n 2.066 * [backup-simplify]: Simplify 2 into 2 2.066 * [taylor]: Taking taylor expansion of (* n PI) in n 2.066 * [taylor]: Taking taylor expansion of n in n 2.066 * [backup-simplify]: Simplify 0 into 0 2.066 * [backup-simplify]: Simplify 1 into 1 2.066 * [taylor]: Taking taylor expansion of PI in n 2.066 * [backup-simplify]: Simplify PI into PI 2.066 * [backup-simplify]: Simplify (* 0 PI) into 0 2.067 * [backup-simplify]: Simplify (* 2 0) into 0 2.067 * [backup-simplify]: Simplify 0 into 0 2.068 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.069 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.069 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.070 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.070 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 2.070 * [backup-simplify]: Simplify 0 into 0 2.071 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.072 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.072 * [backup-simplify]: Simplify 0 into 0 2.073 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.073 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.074 * [backup-simplify]: Simplify 0 into 0 2.074 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.075 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 2.075 * [backup-simplify]: Simplify 0 into 0 2.076 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.077 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 2.077 * [backup-simplify]: Simplify 0 into 0 2.078 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.079 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.079 * [backup-simplify]: Simplify 0 into 0 2.080 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 2.080 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) 2.080 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 2.080 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.080 * [taylor]: Taking taylor expansion of 2 in n 2.080 * [backup-simplify]: Simplify 2 into 2 2.080 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.080 * [taylor]: Taking taylor expansion of PI in n 2.080 * [backup-simplify]: Simplify PI into PI 2.080 * [taylor]: Taking taylor expansion of n in n 2.080 * [backup-simplify]: Simplify 0 into 0 2.080 * [backup-simplify]: Simplify 1 into 1 2.081 * [backup-simplify]: Simplify (/ PI 1) into PI 2.081 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.081 * [taylor]: Taking taylor expansion of 2 in n 2.081 * [backup-simplify]: Simplify 2 into 2 2.081 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.081 * [taylor]: Taking taylor expansion of PI in n 2.081 * [backup-simplify]: Simplify PI into PI 2.081 * [taylor]: Taking taylor expansion of n in n 2.081 * [backup-simplify]: Simplify 0 into 0 2.081 * [backup-simplify]: Simplify 1 into 1 2.081 * [backup-simplify]: Simplify (/ PI 1) into PI 2.081 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.082 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.082 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.083 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.083 * [backup-simplify]: Simplify 0 into 0 2.085 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.086 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.086 * [backup-simplify]: Simplify 0 into 0 2.087 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.087 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.087 * [backup-simplify]: Simplify 0 into 0 2.088 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.089 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.089 * [backup-simplify]: Simplify 0 into 0 2.090 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.092 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.092 * [backup-simplify]: Simplify 0 into 0 2.093 * [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 2.095 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.095 * [backup-simplify]: Simplify 0 into 0 2.095 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 2.096 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n)) 2.096 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 2.096 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.096 * [taylor]: Taking taylor expansion of -2 in n 2.096 * [backup-simplify]: Simplify -2 into -2 2.096 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.096 * [taylor]: Taking taylor expansion of PI in n 2.096 * [backup-simplify]: Simplify PI into PI 2.096 * [taylor]: Taking taylor expansion of n in n 2.096 * [backup-simplify]: Simplify 0 into 0 2.096 * [backup-simplify]: Simplify 1 into 1 2.097 * [backup-simplify]: Simplify (/ PI 1) into PI 2.097 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.097 * [taylor]: Taking taylor expansion of -2 in n 2.097 * [backup-simplify]: Simplify -2 into -2 2.097 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.097 * [taylor]: Taking taylor expansion of PI in n 2.097 * [backup-simplify]: Simplify PI into PI 2.097 * [taylor]: Taking taylor expansion of n in n 2.097 * [backup-simplify]: Simplify 0 into 0 2.097 * [backup-simplify]: Simplify 1 into 1 2.097 * [backup-simplify]: Simplify (/ PI 1) into PI 2.098 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.098 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.099 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.100 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.100 * [backup-simplify]: Simplify 0 into 0 2.101 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.102 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.102 * [backup-simplify]: Simplify 0 into 0 2.103 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.104 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.104 * [backup-simplify]: Simplify 0 into 0 2.105 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.106 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.106 * [backup-simplify]: Simplify 0 into 0 2.107 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.108 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.108 * [backup-simplify]: Simplify 0 into 0 2.108 * [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 2.109 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.109 * [backup-simplify]: Simplify 0 into 0 2.110 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 2.110 * * * * [progress]: [ 3 / 3 ] generating series at (2) 2.110 * [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)))) 2.110 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 2.110 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 2.110 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.110 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.110 * [taylor]: Taking taylor expansion of k in k 2.110 * [backup-simplify]: Simplify 0 into 0 2.110 * [backup-simplify]: Simplify 1 into 1 2.111 * [backup-simplify]: Simplify (/ 1 1) into 1 2.111 * [backup-simplify]: Simplify (sqrt 0) into 0 2.112 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.112 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 2.112 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 2.112 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 2.112 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 2.112 * [taylor]: Taking taylor expansion of 1/2 in k 2.112 * [backup-simplify]: Simplify 1/2 into 1/2 2.112 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 2.112 * [taylor]: Taking taylor expansion of 1/2 in k 2.112 * [backup-simplify]: Simplify 1/2 into 1/2 2.112 * [taylor]: Taking taylor expansion of k in k 2.112 * [backup-simplify]: Simplify 0 into 0 2.112 * [backup-simplify]: Simplify 1 into 1 2.112 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 2.112 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 2.112 * [taylor]: Taking taylor expansion of 2 in k 2.112 * [backup-simplify]: Simplify 2 into 2 2.112 * [taylor]: Taking taylor expansion of (* n PI) in k 2.112 * [taylor]: Taking taylor expansion of n in k 2.112 * [backup-simplify]: Simplify n into n 2.112 * [taylor]: Taking taylor expansion of PI in k 2.112 * [backup-simplify]: Simplify PI into PI 2.112 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.112 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 2.112 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 2.113 * [backup-simplify]: Simplify (* 1/2 0) into 0 2.113 * [backup-simplify]: Simplify (- 0) into 0 2.113 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.113 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 2.113 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 2.113 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 2.113 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.113 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.113 * [taylor]: Taking taylor expansion of k in n 2.114 * [backup-simplify]: Simplify k into k 2.114 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.114 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 2.114 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.114 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 2.114 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 2.114 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 2.114 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 2.114 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 2.114 * [taylor]: Taking taylor expansion of 1/2 in n 2.114 * [backup-simplify]: Simplify 1/2 into 1/2 2.114 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 2.114 * [taylor]: Taking taylor expansion of 1/2 in n 2.114 * [backup-simplify]: Simplify 1/2 into 1/2 2.114 * [taylor]: Taking taylor expansion of k in n 2.114 * [backup-simplify]: Simplify k into k 2.114 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 2.114 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.114 * [taylor]: Taking taylor expansion of 2 in n 2.114 * [backup-simplify]: Simplify 2 into 2 2.114 * [taylor]: Taking taylor expansion of (* n PI) in n 2.114 * [taylor]: Taking taylor expansion of n in n 2.114 * [backup-simplify]: Simplify 0 into 0 2.114 * [backup-simplify]: Simplify 1 into 1 2.114 * [taylor]: Taking taylor expansion of PI in n 2.114 * [backup-simplify]: Simplify PI into PI 2.114 * [backup-simplify]: Simplify (* 0 PI) into 0 2.115 * [backup-simplify]: Simplify (* 2 0) into 0 2.116 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.116 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.117 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.117 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 2.117 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 2.117 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 2.118 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.119 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 2.120 * [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))))) 2.120 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 2.120 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.120 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.120 * [taylor]: Taking taylor expansion of k in n 2.120 * [backup-simplify]: Simplify k into k 2.120 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.120 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 2.120 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.120 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 2.120 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 2.120 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 2.120 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 2.120 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 2.120 * [taylor]: Taking taylor expansion of 1/2 in n 2.120 * [backup-simplify]: Simplify 1/2 into 1/2 2.120 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 2.120 * [taylor]: Taking taylor expansion of 1/2 in n 2.120 * [backup-simplify]: Simplify 1/2 into 1/2 2.120 * [taylor]: Taking taylor expansion of k in n 2.120 * [backup-simplify]: Simplify k into k 2.120 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 2.120 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.120 * [taylor]: Taking taylor expansion of 2 in n 2.120 * [backup-simplify]: Simplify 2 into 2 2.120 * [taylor]: Taking taylor expansion of (* n PI) in n 2.120 * [taylor]: Taking taylor expansion of n in n 2.120 * [backup-simplify]: Simplify 0 into 0 2.120 * [backup-simplify]: Simplify 1 into 1 2.120 * [taylor]: Taking taylor expansion of PI in n 2.120 * [backup-simplify]: Simplify PI into PI 2.120 * [backup-simplify]: Simplify (* 0 PI) into 0 2.121 * [backup-simplify]: Simplify (* 2 0) into 0 2.122 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.123 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.123 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.123 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 2.123 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 2.123 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 2.124 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.125 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 2.126 * [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))))) 2.127 * [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))) 2.127 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 2.127 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 2.127 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 2.127 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 2.127 * [taylor]: Taking taylor expansion of 1/2 in k 2.127 * [backup-simplify]: Simplify 1/2 into 1/2 2.127 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 2.127 * [taylor]: Taking taylor expansion of 1/2 in k 2.127 * [backup-simplify]: Simplify 1/2 into 1/2 2.127 * [taylor]: Taking taylor expansion of k in k 2.127 * [backup-simplify]: Simplify 0 into 0 2.127 * [backup-simplify]: Simplify 1 into 1 2.127 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 2.127 * [taylor]: Taking taylor expansion of (log n) in k 2.127 * [taylor]: Taking taylor expansion of n in k 2.127 * [backup-simplify]: Simplify n into n 2.127 * [backup-simplify]: Simplify (log n) into (log n) 2.127 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.127 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.127 * [taylor]: Taking taylor expansion of 2 in k 2.127 * [backup-simplify]: Simplify 2 into 2 2.127 * [taylor]: Taking taylor expansion of PI in k 2.127 * [backup-simplify]: Simplify PI into PI 2.127 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.128 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.128 * [backup-simplify]: Simplify (* 1/2 0) into 0 2.128 * [backup-simplify]: Simplify (- 0) into 0 2.129 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.129 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.130 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 2.131 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 2.131 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.131 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.131 * [taylor]: Taking taylor expansion of k in k 2.131 * [backup-simplify]: Simplify 0 into 0 2.131 * [backup-simplify]: Simplify 1 into 1 2.131 * [backup-simplify]: Simplify (/ 1 1) into 1 2.131 * [backup-simplify]: Simplify (sqrt 0) into 0 2.132 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.133 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 2.133 * [backup-simplify]: Simplify 0 into 0 2.133 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.134 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 2.135 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.135 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 2.136 * [backup-simplify]: Simplify (- 0) into 0 2.136 * [backup-simplify]: Simplify (+ 0 0) into 0 2.137 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.137 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 2.139 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.139 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 2.139 * [taylor]: Taking taylor expansion of 0 in k 2.139 * [backup-simplify]: Simplify 0 into 0 2.140 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.140 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.141 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.142 * [backup-simplify]: Simplify (+ 0 0) into 0 2.142 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 2.142 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.143 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.144 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2.146 * [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))))))) 2.148 * [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))))))) 2.149 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 2.150 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.150 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.152 * [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 2.153 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 2.153 * [backup-simplify]: Simplify (- 0) into 0 2.153 * [backup-simplify]: Simplify (+ 0 0) into 0 2.154 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.155 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.157 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.157 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.157 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 2.158 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) 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 (- (+ (* 1 (/ 0 1)))) into 0 2.161 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.162 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.162 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.164 * [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 2.164 * [backup-simplify]: Simplify (+ 0 0) into 0 2.165 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 2.165 * [backup-simplify]: Simplify (- 0) into 0 2.166 * [backup-simplify]: Simplify (+ 0 0) into 0 2.167 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.170 * [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))))) 2.175 * [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)))))))) 2.181 * [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)))))))) 2.182 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.183 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.186 * [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 2.187 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 2.187 * [backup-simplify]: Simplify (- 0) into 0 2.187 * [backup-simplify]: Simplify (+ 0 0) into 0 2.188 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.189 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 2.192 * [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 2.192 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.193 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 2.195 * [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 2.195 * [taylor]: Taking taylor expansion of 0 in k 2.195 * [backup-simplify]: Simplify 0 into 0 2.195 * [backup-simplify]: Simplify 0 into 0 2.195 * [backup-simplify]: Simplify 0 into 0 2.196 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.200 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.203 * [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 2.204 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.208 * [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 2.208 * [backup-simplify]: Simplify (+ 0 0) into 0 2.209 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 2.209 * [backup-simplify]: Simplify (- 0) into 0 2.209 * [backup-simplify]: Simplify (+ 0 0) into 0 2.211 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 2.215 * [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))))))) 2.225 * [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)))))))))))))) 2.232 * [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)))))))))))))) 2.245 * [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)))))))))))))))))))))) 2.246 * [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))))) 2.246 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 2.246 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 2.246 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.246 * [taylor]: Taking taylor expansion of k in k 2.246 * [backup-simplify]: Simplify 0 into 0 2.246 * [backup-simplify]: Simplify 1 into 1 2.247 * [backup-simplify]: Simplify (sqrt 0) into 0 2.248 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.248 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 2.248 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 2.248 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 2.248 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.248 * [taylor]: Taking taylor expansion of 1/2 in k 2.248 * [backup-simplify]: Simplify 1/2 into 1/2 2.248 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.248 * [taylor]: Taking taylor expansion of 1/2 in k 2.249 * [backup-simplify]: Simplify 1/2 into 1/2 2.249 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.249 * [taylor]: Taking taylor expansion of k in k 2.249 * [backup-simplify]: Simplify 0 into 0 2.249 * [backup-simplify]: Simplify 1 into 1 2.249 * [backup-simplify]: Simplify (/ 1 1) into 1 2.249 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 2.249 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 2.249 * [taylor]: Taking taylor expansion of 2 in k 2.249 * [backup-simplify]: Simplify 2 into 2 2.249 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.249 * [taylor]: Taking taylor expansion of PI in k 2.249 * [backup-simplify]: Simplify PI into PI 2.249 * [taylor]: Taking taylor expansion of n in k 2.249 * [backup-simplify]: Simplify n into n 2.249 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.249 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 2.249 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 2.250 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.250 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.251 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.251 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 2.251 * [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)))) 2.251 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 2.251 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.251 * [taylor]: Taking taylor expansion of k in n 2.251 * [backup-simplify]: Simplify k into k 2.251 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.251 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.251 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.251 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.251 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.251 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.251 * [taylor]: Taking taylor expansion of 1/2 in n 2.251 * [backup-simplify]: Simplify 1/2 into 1/2 2.251 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.251 * [taylor]: Taking taylor expansion of 1/2 in n 2.252 * [backup-simplify]: Simplify 1/2 into 1/2 2.252 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.252 * [taylor]: Taking taylor expansion of k in n 2.252 * [backup-simplify]: Simplify k into k 2.252 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.252 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.252 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.252 * [taylor]: Taking taylor expansion of 2 in n 2.252 * [backup-simplify]: Simplify 2 into 2 2.252 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.252 * [taylor]: Taking taylor expansion of PI in n 2.252 * [backup-simplify]: Simplify PI into PI 2.252 * [taylor]: Taking taylor expansion of n in n 2.252 * [backup-simplify]: Simplify 0 into 0 2.252 * [backup-simplify]: Simplify 1 into 1 2.252 * [backup-simplify]: Simplify (/ PI 1) into PI 2.253 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.254 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.254 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.254 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.254 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.256 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.257 * [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))) 2.258 * [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)))) 2.258 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 2.258 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.258 * [taylor]: Taking taylor expansion of k in n 2.258 * [backup-simplify]: Simplify k into k 2.258 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.258 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.258 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.258 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.258 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.259 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.259 * [taylor]: Taking taylor expansion of 1/2 in n 2.259 * [backup-simplify]: Simplify 1/2 into 1/2 2.259 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.259 * [taylor]: Taking taylor expansion of 1/2 in n 2.259 * [backup-simplify]: Simplify 1/2 into 1/2 2.259 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.259 * [taylor]: Taking taylor expansion of k in n 2.259 * [backup-simplify]: Simplify k into k 2.259 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.259 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.259 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.259 * [taylor]: Taking taylor expansion of 2 in n 2.259 * [backup-simplify]: Simplify 2 into 2 2.259 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.259 * [taylor]: Taking taylor expansion of PI in n 2.259 * [backup-simplify]: Simplify PI into PI 2.259 * [taylor]: Taking taylor expansion of n in n 2.259 * [backup-simplify]: Simplify 0 into 0 2.259 * [backup-simplify]: Simplify 1 into 1 2.260 * [backup-simplify]: Simplify (/ PI 1) into PI 2.260 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.261 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.261 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.261 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.261 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.263 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.264 * [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))) 2.266 * [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)))) 2.267 * [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)) 2.267 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 2.267 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 2.267 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 2.267 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.267 * [taylor]: Taking taylor expansion of 1/2 in k 2.267 * [backup-simplify]: Simplify 1/2 into 1/2 2.267 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.267 * [taylor]: Taking taylor expansion of 1/2 in k 2.267 * [backup-simplify]: Simplify 1/2 into 1/2 2.267 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.267 * [taylor]: Taking taylor expansion of k in k 2.267 * [backup-simplify]: Simplify 0 into 0 2.267 * [backup-simplify]: Simplify 1 into 1 2.268 * [backup-simplify]: Simplify (/ 1 1) into 1 2.268 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 2.268 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.268 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.268 * [taylor]: Taking taylor expansion of 2 in k 2.268 * [backup-simplify]: Simplify 2 into 2 2.268 * [taylor]: Taking taylor expansion of PI in k 2.268 * [backup-simplify]: Simplify PI into PI 2.268 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.269 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.269 * [taylor]: Taking taylor expansion of (log n) in k 2.269 * [taylor]: Taking taylor expansion of n in k 2.269 * [backup-simplify]: Simplify n into n 2.269 * [backup-simplify]: Simplify (log n) into (log n) 2.270 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.270 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.270 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.270 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.271 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 2.271 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 2.272 * [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)))) 2.272 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.272 * [taylor]: Taking taylor expansion of k in k 2.272 * [backup-simplify]: Simplify 0 into 0 2.272 * [backup-simplify]: Simplify 1 into 1 2.272 * [backup-simplify]: Simplify (sqrt 0) into 0 2.273 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.274 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 2.274 * [backup-simplify]: Simplify 0 into 0 2.275 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.275 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.279 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.279 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.279 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.279 * [backup-simplify]: Simplify (- 0) into 0 2.280 * [backup-simplify]: Simplify (+ 0 0) into 0 2.281 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.281 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 2.282 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.283 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 2.283 * [taylor]: Taking taylor expansion of 0 in k 2.283 * [backup-simplify]: Simplify 0 into 0 2.283 * [backup-simplify]: Simplify 0 into 0 2.284 * [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)))))) 2.285 * [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)))))) 2.286 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.286 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.288 * [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 2.289 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.289 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.290 * [backup-simplify]: Simplify (- 0) into 0 2.290 * [backup-simplify]: Simplify (+ 0 0) into 0 2.292 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.294 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 2.296 * [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 2.297 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 2.299 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 2.299 * [taylor]: Taking taylor expansion of 0 in k 2.299 * [backup-simplify]: Simplify 0 into 0 2.299 * [backup-simplify]: Simplify 0 into 0 2.299 * [backup-simplify]: Simplify 0 into 0 2.302 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.304 * [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)))))) 2.305 * [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)))))) 2.307 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.308 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.314 * [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 2.315 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.316 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 2.316 * [backup-simplify]: Simplify (- 0) into 0 2.317 * [backup-simplify]: Simplify (+ 0 0) into 0 2.318 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.320 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 2.323 * [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 2.324 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 2.326 * [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 2.326 * [taylor]: Taking taylor expansion of 0 in k 2.327 * [backup-simplify]: Simplify 0 into 0 2.327 * [backup-simplify]: Simplify 0 into 0 2.327 * [backup-simplify]: Simplify 0 into 0 2.327 * [backup-simplify]: Simplify 0 into 0 2.331 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.333 * [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)))))) 2.335 * [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)))))) 2.339 * [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)))))))) 2.340 * [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))) 2.340 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 2.340 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 2.340 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 2.340 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 2.340 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 2.340 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.340 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.340 * [taylor]: Taking taylor expansion of 1/2 in k 2.341 * [backup-simplify]: Simplify 1/2 into 1/2 2.341 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.341 * [taylor]: Taking taylor expansion of k in k 2.341 * [backup-simplify]: Simplify 0 into 0 2.341 * [backup-simplify]: Simplify 1 into 1 2.341 * [backup-simplify]: Simplify (/ 1 1) into 1 2.341 * [taylor]: Taking taylor expansion of 1/2 in k 2.341 * [backup-simplify]: Simplify 1/2 into 1/2 2.341 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 2.341 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 2.341 * [taylor]: Taking taylor expansion of -2 in k 2.341 * [backup-simplify]: Simplify -2 into -2 2.341 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.341 * [taylor]: Taking taylor expansion of PI in k 2.341 * [backup-simplify]: Simplify PI into PI 2.341 * [taylor]: Taking taylor expansion of n in k 2.341 * [backup-simplify]: Simplify n into n 2.341 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.341 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 2.342 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 2.342 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.342 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.343 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 2.343 * [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))) 2.343 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.343 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.343 * [taylor]: Taking taylor expansion of -1 in k 2.343 * [backup-simplify]: Simplify -1 into -1 2.343 * [taylor]: Taking taylor expansion of k in k 2.343 * [backup-simplify]: Simplify 0 into 0 2.343 * [backup-simplify]: Simplify 1 into 1 2.343 * [backup-simplify]: Simplify (/ -1 1) into -1 2.344 * [backup-simplify]: Simplify (sqrt 0) into 0 2.345 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.345 * [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)))) 2.345 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 2.345 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.345 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.345 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.345 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.345 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.345 * [taylor]: Taking taylor expansion of 1/2 in n 2.346 * [backup-simplify]: Simplify 1/2 into 1/2 2.346 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.346 * [taylor]: Taking taylor expansion of k in n 2.346 * [backup-simplify]: Simplify k into k 2.346 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.346 * [taylor]: Taking taylor expansion of 1/2 in n 2.346 * [backup-simplify]: Simplify 1/2 into 1/2 2.346 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.346 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.346 * [taylor]: Taking taylor expansion of -2 in n 2.346 * [backup-simplify]: Simplify -2 into -2 2.346 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.346 * [taylor]: Taking taylor expansion of PI in n 2.346 * [backup-simplify]: Simplify PI into PI 2.346 * [taylor]: Taking taylor expansion of n in n 2.346 * [backup-simplify]: Simplify 0 into 0 2.346 * [backup-simplify]: Simplify 1 into 1 2.346 * [backup-simplify]: Simplify (/ PI 1) into PI 2.347 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.348 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.348 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.348 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.349 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.351 * [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))) 2.352 * [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)))) 2.352 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.352 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.352 * [taylor]: Taking taylor expansion of -1 in n 2.352 * [backup-simplify]: Simplify -1 into -1 2.352 * [taylor]: Taking taylor expansion of k in n 2.352 * [backup-simplify]: Simplify k into k 2.352 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.352 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.352 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.352 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.354 * [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))) 2.354 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 2.354 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.354 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.354 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.354 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.354 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.354 * [taylor]: Taking taylor expansion of 1/2 in n 2.354 * [backup-simplify]: Simplify 1/2 into 1/2 2.354 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.354 * [taylor]: Taking taylor expansion of k in n 2.354 * [backup-simplify]: Simplify k into k 2.354 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.354 * [taylor]: Taking taylor expansion of 1/2 in n 2.354 * [backup-simplify]: Simplify 1/2 into 1/2 2.354 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.354 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.354 * [taylor]: Taking taylor expansion of -2 in n 2.354 * [backup-simplify]: Simplify -2 into -2 2.354 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.354 * [taylor]: Taking taylor expansion of PI in n 2.354 * [backup-simplify]: Simplify PI into PI 2.354 * [taylor]: Taking taylor expansion of n in n 2.354 * [backup-simplify]: Simplify 0 into 0 2.355 * [backup-simplify]: Simplify 1 into 1 2.355 * [backup-simplify]: Simplify (/ PI 1) into PI 2.356 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.357 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.357 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.357 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.358 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.359 * [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))) 2.361 * [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)))) 2.361 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.361 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.361 * [taylor]: Taking taylor expansion of -1 in n 2.361 * [backup-simplify]: Simplify -1 into -1 2.361 * [taylor]: Taking taylor expansion of k in n 2.361 * [backup-simplify]: Simplify k into k 2.361 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.361 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.361 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.361 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.362 * [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))) 2.363 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 2.363 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 2.363 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 2.363 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.363 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.363 * [taylor]: Taking taylor expansion of 1/2 in k 2.363 * [backup-simplify]: Simplify 1/2 into 1/2 2.363 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.363 * [taylor]: Taking taylor expansion of k in k 2.363 * [backup-simplify]: Simplify 0 into 0 2.363 * [backup-simplify]: Simplify 1 into 1 2.363 * [backup-simplify]: Simplify (/ 1 1) into 1 2.363 * [taylor]: Taking taylor expansion of 1/2 in k 2.363 * [backup-simplify]: Simplify 1/2 into 1/2 2.363 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 2.363 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 2.363 * [taylor]: Taking taylor expansion of (* -2 PI) in k 2.363 * [taylor]: Taking taylor expansion of -2 in k 2.363 * [backup-simplify]: Simplify -2 into -2 2.363 * [taylor]: Taking taylor expansion of PI in k 2.363 * [backup-simplify]: Simplify PI into PI 2.364 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.365 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.365 * [taylor]: Taking taylor expansion of (log n) in k 2.365 * [taylor]: Taking taylor expansion of n in k 2.365 * [backup-simplify]: Simplify n into n 2.365 * [backup-simplify]: Simplify (log n) into (log n) 2.366 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.366 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.366 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.367 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 2.368 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 2.369 * [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)))) 2.370 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.370 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.370 * [taylor]: Taking taylor expansion of -1 in k 2.370 * [backup-simplify]: Simplify -1 into -1 2.370 * [taylor]: Taking taylor expansion of k in k 2.370 * [backup-simplify]: Simplify 0 into 0 2.370 * [backup-simplify]: Simplify 1 into 1 2.370 * [backup-simplify]: Simplify (/ -1 1) into -1 2.370 * [backup-simplify]: Simplify (sqrt 0) into 0 2.372 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.373 * [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))))) 2.374 * [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))))) 2.376 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.376 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.378 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 2.378 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.379 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.379 * [backup-simplify]: Simplify (+ 0 0) into 0 2.381 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.381 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 2.383 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.383 * [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 2.384 * [taylor]: Taking taylor expansion of 0 in k 2.384 * [backup-simplify]: Simplify 0 into 0 2.384 * [backup-simplify]: Simplify 0 into 0 2.384 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.386 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.388 * [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)))))) 2.388 * [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)))))) 2.389 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.390 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.392 * [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 2.392 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.392 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.393 * [backup-simplify]: Simplify (+ 0 0) into 0 2.393 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.394 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 2.396 * [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 2.396 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.396 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 2.397 * [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 2.397 * [taylor]: Taking taylor expansion of 0 in k 2.397 * [backup-simplify]: Simplify 0 into 0 2.397 * [backup-simplify]: Simplify 0 into 0 2.397 * [backup-simplify]: Simplify 0 into 0 2.398 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.400 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.405 * [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)))))) 2.406 * [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)))))) 2.408 * [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))))))))))) 2.408 * * * [progress]: simplifying candidates 2.408 * * * * [progress]: [ 1 / 445 ] simplifiying candidate # 2.409 * * * * [progress]: [ 2 / 445 ] simplifiying candidate # 2.409 * * * * [progress]: [ 3 / 445 ] simplifiying candidate # 2.409 * * * * [progress]: [ 4 / 445 ] simplifiying candidate # 2.409 * * * * [progress]: [ 5 / 445 ] simplifiying candidate # 2.409 * * * * [progress]: [ 6 / 445 ] simplifiying candidate # 2.409 * * * * [progress]: [ 7 / 445 ] simplifiying candidate # 2.409 * * * * [progress]: [ 8 / 445 ] simplifiying candidate # 2.409 * * * * [progress]: [ 9 / 445 ] simplifiying candidate # 2.409 * * * * 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2.413 * * * * [progress]: [ 57 / 445 ] simplifiying candidate # 2.413 * * * * [progress]: [ 58 / 445 ] simplifiying candidate # 2.413 * * * * [progress]: [ 59 / 445 ] simplifiying candidate # 2.413 * * * * [progress]: [ 60 / 445 ] simplifiying candidate # 2.413 * * * * [progress]: [ 61 / 445 ] simplifiying candidate # 2.413 * * * * [progress]: [ 62 / 445 ] simplifiying candidate # 2.413 * * * * [progress]: [ 63 / 445 ] simplifiying candidate # 2.413 * * * * [progress]: [ 64 / 445 ] simplifiying candidate # 2.413 * * * * [progress]: [ 65 / 445 ] simplifiying candidate # 2.414 * * * * [progress]: [ 66 / 445 ] simplifiying candidate # 2.414 * * * * [progress]: [ 67 / 445 ] simplifiying candidate #real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))> 2.414 * * * * [progress]: [ 68 / 445 ] simplifiying candidate # 2.414 * * * * [progress]: [ 69 / 445 ] simplifiying candidate # 2.414 * * * * [progress]: [ 70 / 445 ] simplifiying candidate # 2.414 * * * * [progress]: [ 71 / 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* * [progress]: [ 87 / 445 ] simplifiying candidate #real (real->posit16 (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))> 2.415 * * * * [progress]: [ 88 / 445 ] simplifiying candidate # 2.415 * * * * [progress]: [ 89 / 445 ] simplifiying candidate # 2.415 * * * * [progress]: [ 90 / 445 ] simplifiying candidate # 2.415 * * * * [progress]: [ 91 / 445 ] simplifiying candidate # 2.415 * * * * [progress]: [ 92 / 445 ] simplifiying candidate # 2.415 * * * * [progress]: [ 93 / 445 ] simplifiying candidate # 2.415 * * * * [progress]: [ 94 / 445 ] simplifiying candidate # 2.415 * * * * [progress]: [ 95 / 445 ] simplifiying candidate # 2.416 * * * * [progress]: [ 96 / 445 ] simplifiying candidate # 2.416 * * * * [progress]: [ 97 / 445 ] simplifiying candidate # 2.416 * * * * [progress]: [ 98 / 445 ] simplifiying candidate # 2.416 * * * * [progress]: [ 99 / 445 ] simplifiying candidate # 2.416 * * * * [progress]: [ 100 / 445 ] simplifiying candidate # 2.416 * * * * [progress]: [ 101 / 445 ] 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candidate # 2.442 * * * * [progress]: [ 438 / 445 ] simplifiying candidate # 2.442 * * * * [progress]: [ 439 / 445 ] simplifiying candidate # 2.442 * * * * [progress]: [ 440 / 445 ] simplifiying candidate # 2.442 * * * * [progress]: [ 441 / 445 ] simplifiying candidate # 2.442 * * * * [progress]: [ 442 / 445 ] simplifiying candidate # 2.442 * * * * [progress]: [ 443 / 445 ] simplifiying candidate # 2.443 * * * * [progress]: [ 444 / 445 ] simplifiying candidate # 2.443 * * * * [progress]: [ 445 / 445 ] simplifiying candidate # 2.450 * [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) 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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))))))))))) 2.465 * * [simplify]: iteration 0: 695 enodes 2.726 * * [simplify]: iteration 1: 1526 enodes 3.107 * * [simplify]: iteration 2: 2001 enodes 3.549 * * [simplify]: iteration complete: 2001 enodes 3.549 * * [simplify]: Extracting #0: cost 233 inf + 0 3.551 * * [simplify]: Extracting #1: cost 515 inf + 1 3.557 * * [simplify]: Extracting #2: cost 739 inf + 1881 3.561 * * [simplify]: Extracting #3: cost 804 inf + 11914 3.574 * * [simplify]: Extracting #4: cost 562 inf + 88070 3.609 * * [simplify]: Extracting #5: cost 346 inf + 180910 3.666 * * [simplify]: Extracting #6: cost 193 inf + 273665 3.742 * * [simplify]: Extracting #7: cost 60 inf + 356856 3.815 * * [simplify]: Extracting #8: cost 23 inf + 387667 3.882 * * [simplify]: Extracting #9: cost 23 inf + 390493 3.972 * * [simplify]: Extracting #10: cost 15 inf + 395110 4.054 * * [simplify]: Extracting #11: cost 10 inf + 400340 4.124 * * [simplify]: Extracting #12: cost 4 inf + 408621 4.226 * * [simplify]: Extracting #13: cost 0 inf + 415390 4.311 * * [simplify]: Extracting #14: cost 0 inf + 415265 4.426 * * [simplify]: Extracting #15: cost 0 inf + 415190 4.525 * [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))) 4.644 * * * [progress]: adding candidates to table 11.385 * * [progress]: iteration 2 / 4 11.385 * * * [progress]: picking best candidate 11.437 * * * * [pick]: Picked # 11.437 * * * [progress]: localizing error 11.485 * * * [progress]: generating rewritten candidates 11.485 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 11.517 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 11.527 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 11.562 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 11.629 * * * [progress]: generating series expansions 11.629 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 11.630 * [backup-simplify]: Simplify (pow (* (* 2 PI) n) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) 11.630 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0 11.630 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 11.630 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 11.630 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 11.630 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k 11.630 * [taylor]: Taking taylor expansion of 1/2 in k 11.631 * [backup-simplify]: Simplify 1/2 into 1/2 11.631 * [taylor]: Taking taylor expansion of (- 1 k) in k 11.631 * [taylor]: Taking taylor expansion of 1 in k 11.631 * [backup-simplify]: Simplify 1 into 1 11.631 * [taylor]: Taking taylor expansion of k in k 11.631 * [backup-simplify]: Simplify 0 into 0 11.631 * [backup-simplify]: Simplify 1 into 1 11.631 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 11.631 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 11.631 * [taylor]: Taking taylor expansion of 2 in k 11.631 * [backup-simplify]: Simplify 2 into 2 11.631 * [taylor]: Taking taylor expansion of (* n PI) in k 11.631 * [taylor]: Taking taylor expansion of n in k 11.631 * [backup-simplify]: Simplify n into n 11.631 * [taylor]: Taking taylor expansion of PI in k 11.631 * [backup-simplify]: Simplify PI into PI 11.631 * [backup-simplify]: Simplify (* n PI) into (* n PI) 11.631 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 11.631 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 11.632 * [backup-simplify]: Simplify (- 0) into 0 11.632 * [backup-simplify]: Simplify (+ 1 0) into 1 11.632 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.633 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 11.633 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 11.633 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 11.633 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 11.633 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 11.633 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n 11.633 * [taylor]: Taking taylor expansion of 1/2 in n 11.633 * [backup-simplify]: Simplify 1/2 into 1/2 11.633 * [taylor]: Taking taylor expansion of (- 1 k) in n 11.633 * [taylor]: Taking taylor expansion of 1 in n 11.633 * [backup-simplify]: Simplify 1 into 1 11.633 * [taylor]: Taking taylor expansion of k in n 11.633 * [backup-simplify]: Simplify k into k 11.633 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.633 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.633 * [taylor]: Taking taylor expansion of 2 in n 11.633 * [backup-simplify]: Simplify 2 into 2 11.633 * [taylor]: Taking taylor expansion of (* n PI) in n 11.633 * [taylor]: Taking taylor expansion of n in n 11.633 * [backup-simplify]: Simplify 0 into 0 11.633 * [backup-simplify]: Simplify 1 into 1 11.633 * [taylor]: Taking taylor expansion of PI in n 11.633 * [backup-simplify]: Simplify PI into PI 11.634 * [backup-simplify]: Simplify (* 0 PI) into 0 11.634 * [backup-simplify]: Simplify (* 2 0) into 0 11.636 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.638 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.639 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.639 * [backup-simplify]: Simplify (- k) into (- k) 11.639 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k) 11.639 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 11.641 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.642 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 11.644 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 11.644 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 11.644 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 11.644 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 11.644 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n 11.644 * [taylor]: Taking taylor expansion of 1/2 in n 11.644 * [backup-simplify]: Simplify 1/2 into 1/2 11.644 * [taylor]: Taking taylor expansion of (- 1 k) in n 11.644 * [taylor]: Taking taylor expansion of 1 in n 11.644 * [backup-simplify]: Simplify 1 into 1 11.644 * [taylor]: Taking taylor expansion of k in n 11.644 * [backup-simplify]: Simplify k into k 11.644 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.644 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.644 * [taylor]: Taking taylor expansion of 2 in n 11.644 * [backup-simplify]: Simplify 2 into 2 11.644 * [taylor]: Taking taylor expansion of (* n PI) in n 11.644 * [taylor]: Taking taylor expansion of n in n 11.644 * [backup-simplify]: Simplify 0 into 0 11.644 * [backup-simplify]: Simplify 1 into 1 11.644 * [taylor]: Taking taylor expansion of PI in n 11.644 * [backup-simplify]: Simplify PI into PI 11.645 * [backup-simplify]: Simplify (* 0 PI) into 0 11.645 * [backup-simplify]: Simplify (* 2 0) into 0 11.647 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.649 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.650 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.650 * [backup-simplify]: Simplify (- k) into (- k) 11.651 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k) 11.651 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 11.652 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.653 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 11.655 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 11.655 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k 11.655 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k 11.655 * [taylor]: Taking taylor expansion of 1/2 in k 11.655 * [backup-simplify]: Simplify 1/2 into 1/2 11.655 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k 11.655 * [taylor]: Taking taylor expansion of (- 1 k) in k 11.655 * [taylor]: Taking taylor expansion of 1 in k 11.655 * [backup-simplify]: Simplify 1 into 1 11.655 * [taylor]: Taking taylor expansion of k in k 11.655 * [backup-simplify]: Simplify 0 into 0 11.655 * [backup-simplify]: Simplify 1 into 1 11.655 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 11.655 * [taylor]: Taking taylor expansion of (log n) in k 11.655 * [taylor]: Taking taylor expansion of n in k 11.655 * [backup-simplify]: Simplify n into n 11.655 * [backup-simplify]: Simplify (log n) into (log n) 11.655 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 11.655 * [taylor]: Taking taylor expansion of (* 2 PI) in k 11.655 * [taylor]: Taking taylor expansion of 2 in k 11.655 * [backup-simplify]: Simplify 2 into 2 11.655 * [taylor]: Taking taylor expansion of PI in k 11.655 * [backup-simplify]: Simplify PI into PI 11.656 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.657 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.658 * [backup-simplify]: Simplify (- 0) into 0 11.658 * [backup-simplify]: Simplify (+ 1 0) into 1 11.659 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.660 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI))) 11.661 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 11.662 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 11.664 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 11.665 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.666 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 11.668 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.668 * [backup-simplify]: Simplify (- 0) into 0 11.669 * [backup-simplify]: Simplify (+ 0 0) into 0 11.669 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0 11.676 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.677 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 11.679 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.679 * [taylor]: Taking taylor expansion of 0 in k 11.679 * [backup-simplify]: Simplify 0 into 0 11.679 * [backup-simplify]: Simplify 0 into 0 11.680 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 11.681 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 11.683 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.683 * [backup-simplify]: Simplify (+ 0 0) into 0 11.683 * [backup-simplify]: Simplify (- 1) into -1 11.684 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.685 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n))) 11.688 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 11.691 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 11.694 * [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))))))) 11.695 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 11.696 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 11.700 * [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 11.701 * [backup-simplify]: Simplify (- 0) into 0 11.701 * [backup-simplify]: Simplify (+ 0 0) into 0 11.702 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0 11.704 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.705 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 11.708 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.708 * [taylor]: Taking taylor expansion of 0 in k 11.708 * [backup-simplify]: Simplify 0 into 0 11.708 * [backup-simplify]: Simplify 0 into 0 11.708 * [backup-simplify]: Simplify 0 into 0 11.710 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 11.711 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 11.715 * [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 11.715 * [backup-simplify]: Simplify (+ 0 0) into 0 11.716 * [backup-simplify]: Simplify (- 0) into 0 11.716 * [backup-simplify]: Simplify (+ 0 0) into 0 11.719 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 11.721 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 11.726 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 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))))) 11.731 * [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))))) 11.741 * [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))))) 11.742 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) 11.742 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0 11.742 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 11.742 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 11.742 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 11.742 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 11.742 * [taylor]: Taking taylor expansion of 1/2 in k 11.742 * [backup-simplify]: Simplify 1/2 into 1/2 11.742 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 11.742 * [taylor]: Taking taylor expansion of 1 in k 11.742 * [backup-simplify]: Simplify 1 into 1 11.742 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.742 * [taylor]: Taking taylor expansion of k in k 11.742 * [backup-simplify]: Simplify 0 into 0 11.742 * [backup-simplify]: Simplify 1 into 1 11.743 * [backup-simplify]: Simplify (/ 1 1) into 1 11.743 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 11.743 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 11.743 * [taylor]: Taking taylor expansion of 2 in k 11.743 * [backup-simplify]: Simplify 2 into 2 11.743 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.743 * [taylor]: Taking taylor expansion of PI in k 11.743 * [backup-simplify]: Simplify PI into PI 11.743 * [taylor]: Taking taylor expansion of n in k 11.743 * [backup-simplify]: Simplify n into n 11.743 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.743 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 11.743 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 11.744 * [backup-simplify]: Simplify (- 1) into -1 11.744 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.744 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2 11.745 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 11.745 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 11.745 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 11.745 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.745 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.745 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 11.745 * [taylor]: Taking taylor expansion of 1/2 in n 11.745 * [backup-simplify]: Simplify 1/2 into 1/2 11.745 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 11.745 * [taylor]: Taking taylor expansion of 1 in n 11.745 * [backup-simplify]: Simplify 1 into 1 11.745 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.745 * [taylor]: Taking taylor expansion of k in n 11.745 * [backup-simplify]: Simplify k into k 11.745 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.745 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.745 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.745 * [taylor]: Taking taylor expansion of 2 in n 11.745 * [backup-simplify]: Simplify 2 into 2 11.745 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.745 * [taylor]: Taking taylor expansion of PI in n 11.745 * [backup-simplify]: Simplify PI into PI 11.745 * [taylor]: Taking taylor expansion of n in n 11.745 * [backup-simplify]: Simplify 0 into 0 11.745 * [backup-simplify]: Simplify 1 into 1 11.746 * [backup-simplify]: Simplify (/ PI 1) into PI 11.746 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.748 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.748 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.748 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 11.748 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 11.749 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.751 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 11.752 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 11.752 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 11.752 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.752 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.752 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 11.752 * [taylor]: Taking taylor expansion of 1/2 in n 11.752 * [backup-simplify]: Simplify 1/2 into 1/2 11.752 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 11.752 * [taylor]: Taking taylor expansion of 1 in n 11.752 * [backup-simplify]: Simplify 1 into 1 11.752 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.752 * [taylor]: Taking taylor expansion of k in n 11.752 * [backup-simplify]: Simplify k into k 11.752 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.752 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.752 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.752 * [taylor]: Taking taylor expansion of 2 in n 11.753 * [backup-simplify]: Simplify 2 into 2 11.753 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.753 * [taylor]: Taking taylor expansion of PI in n 11.753 * [backup-simplify]: Simplify PI into PI 11.753 * [taylor]: Taking taylor expansion of n in n 11.753 * [backup-simplify]: Simplify 0 into 0 11.753 * [backup-simplify]: Simplify 1 into 1 11.753 * [backup-simplify]: Simplify (/ PI 1) into PI 11.754 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.755 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.755 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.755 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 11.755 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 11.756 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.758 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 11.759 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 11.759 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k 11.759 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k 11.759 * [taylor]: Taking taylor expansion of 1/2 in k 11.759 * [backup-simplify]: Simplify 1/2 into 1/2 11.759 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k 11.759 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 11.759 * [taylor]: Taking taylor expansion of 1 in k 11.759 * [backup-simplify]: Simplify 1 into 1 11.759 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.759 * [taylor]: Taking taylor expansion of k in k 11.759 * [backup-simplify]: Simplify 0 into 0 11.759 * [backup-simplify]: Simplify 1 into 1 11.760 * [backup-simplify]: Simplify (/ 1 1) into 1 11.760 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 11.760 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 11.760 * [taylor]: Taking taylor expansion of (* 2 PI) in k 11.760 * [taylor]: Taking taylor expansion of 2 in k 11.760 * [backup-simplify]: Simplify 2 into 2 11.760 * [taylor]: Taking taylor expansion of PI in k 11.760 * [backup-simplify]: Simplify PI into PI 11.761 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.762 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.762 * [taylor]: Taking taylor expansion of (log n) in k 11.762 * [taylor]: Taking taylor expansion of n in k 11.762 * [backup-simplify]: Simplify n into n 11.762 * [backup-simplify]: Simplify (log n) into (log n) 11.763 * [backup-simplify]: Simplify (- 1) into -1 11.763 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.763 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 11.764 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 11.765 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) 11.767 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) 11.768 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 11.769 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 11.770 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.771 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 11.773 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.773 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.773 * [backup-simplify]: Simplify (- 0) into 0 11.774 * [backup-simplify]: Simplify (+ 0 0) into 0 11.774 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0 11.776 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.777 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 11.779 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.779 * [taylor]: Taking taylor expansion of 0 in k 11.779 * [backup-simplify]: Simplify 0 into 0 11.779 * [backup-simplify]: Simplify 0 into 0 11.779 * [backup-simplify]: Simplify 0 into 0 11.780 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.781 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 11.785 * [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 11.785 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.785 * [backup-simplify]: Simplify (- 0) into 0 11.786 * [backup-simplify]: Simplify (+ 0 0) into 0 11.787 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0 11.788 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.790 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 11.792 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.792 * [taylor]: Taking taylor expansion of 0 in k 11.792 * [backup-simplify]: Simplify 0 into 0 11.792 * [backup-simplify]: Simplify 0 into 0 11.792 * [backup-simplify]: Simplify 0 into 0 11.792 * [backup-simplify]: Simplify 0 into 0 11.794 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.795 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.801 * [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 11.801 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.802 * [backup-simplify]: Simplify (- 0) into 0 11.802 * [backup-simplify]: Simplify (+ 0 0) into 0 11.803 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0 11.805 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.807 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 11.810 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 11.810 * [taylor]: Taking taylor expansion of 0 in k 11.810 * [backup-simplify]: Simplify 0 into 0 11.810 * [backup-simplify]: Simplify 0 into 0 11.811 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) 11.812 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) 11.812 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0 11.812 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 11.812 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 11.812 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 11.812 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 11.812 * [taylor]: Taking taylor expansion of 1/2 in k 11.812 * [backup-simplify]: Simplify 1/2 into 1/2 11.812 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 11.812 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.812 * [taylor]: Taking taylor expansion of k in k 11.812 * [backup-simplify]: Simplify 0 into 0 11.812 * [backup-simplify]: Simplify 1 into 1 11.813 * [backup-simplify]: Simplify (/ 1 1) into 1 11.813 * [taylor]: Taking taylor expansion of 1 in k 11.813 * [backup-simplify]: Simplify 1 into 1 11.813 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 11.813 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 11.813 * [taylor]: Taking taylor expansion of -2 in k 11.813 * [backup-simplify]: Simplify -2 into -2 11.813 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.813 * [taylor]: Taking taylor expansion of PI in k 11.813 * [backup-simplify]: Simplify PI into PI 11.813 * [taylor]: Taking taylor expansion of n in k 11.813 * [backup-simplify]: Simplify n into n 11.813 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.813 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 11.813 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 11.814 * [backup-simplify]: Simplify (+ 1 0) into 1 11.814 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.814 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 11.814 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 11.815 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 11.815 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 11.815 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 11.815 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 11.815 * [taylor]: Taking taylor expansion of 1/2 in n 11.815 * [backup-simplify]: Simplify 1/2 into 1/2 11.815 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 11.815 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.815 * [taylor]: Taking taylor expansion of k in n 11.815 * [backup-simplify]: Simplify k into k 11.815 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.815 * [taylor]: Taking taylor expansion of 1 in n 11.815 * [backup-simplify]: Simplify 1 into 1 11.815 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.815 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.815 * [taylor]: Taking taylor expansion of -2 in n 11.815 * [backup-simplify]: Simplify -2 into -2 11.815 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.815 * [taylor]: Taking taylor expansion of PI in n 11.815 * [backup-simplify]: Simplify PI into PI 11.815 * [taylor]: Taking taylor expansion of n in n 11.815 * [backup-simplify]: Simplify 0 into 0 11.815 * [backup-simplify]: Simplify 1 into 1 11.816 * [backup-simplify]: Simplify (/ PI 1) into PI 11.816 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.817 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.817 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 11.817 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 11.819 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.820 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 11.828 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 11.828 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 11.828 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 11.828 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 11.828 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 11.828 * [taylor]: Taking taylor expansion of 1/2 in n 11.828 * [backup-simplify]: Simplify 1/2 into 1/2 11.828 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 11.828 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.828 * [taylor]: Taking taylor expansion of k in n 11.828 * [backup-simplify]: Simplify k into k 11.828 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.828 * [taylor]: Taking taylor expansion of 1 in n 11.828 * [backup-simplify]: Simplify 1 into 1 11.828 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.828 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.828 * [taylor]: Taking taylor expansion of -2 in n 11.828 * [backup-simplify]: Simplify -2 into -2 11.829 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.829 * [taylor]: Taking taylor expansion of PI in n 11.829 * [backup-simplify]: Simplify PI into PI 11.829 * [taylor]: Taking taylor expansion of n in n 11.829 * [backup-simplify]: Simplify 0 into 0 11.829 * [backup-simplify]: Simplify 1 into 1 11.830 * [backup-simplify]: Simplify (/ PI 1) into PI 11.830 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.831 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.831 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 11.831 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 11.833 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.835 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 11.836 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 11.836 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k 11.836 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k 11.836 * [taylor]: Taking taylor expansion of 1/2 in k 11.836 * [backup-simplify]: Simplify 1/2 into 1/2 11.836 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k 11.836 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 11.836 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.836 * [taylor]: Taking taylor expansion of k in k 11.836 * [backup-simplify]: Simplify 0 into 0 11.836 * [backup-simplify]: Simplify 1 into 1 11.837 * [backup-simplify]: Simplify (/ 1 1) into 1 11.837 * [taylor]: Taking taylor expansion of 1 in k 11.837 * [backup-simplify]: Simplify 1 into 1 11.837 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 11.837 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 11.837 * [taylor]: Taking taylor expansion of (* -2 PI) in k 11.837 * [taylor]: Taking taylor expansion of -2 in k 11.837 * [backup-simplify]: Simplify -2 into -2 11.837 * [taylor]: Taking taylor expansion of PI in k 11.837 * [backup-simplify]: Simplify PI into PI 11.837 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.839 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.839 * [taylor]: Taking taylor expansion of (log n) in k 11.839 * [taylor]: Taking taylor expansion of n in k 11.839 * [backup-simplify]: Simplify n into n 11.839 * [backup-simplify]: Simplify (log n) into (log n) 11.839 * [backup-simplify]: Simplify (+ 1 0) into 1 11.839 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 11.840 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 11.842 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) 11.843 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 11.844 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 11.845 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 11.846 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.847 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 11.849 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 11.849 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.850 * [backup-simplify]: Simplify (+ 0 0) into 0 11.850 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0 11.852 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.853 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 11.855 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.855 * [taylor]: Taking taylor expansion of 0 in k 11.855 * [backup-simplify]: Simplify 0 into 0 11.855 * [backup-simplify]: Simplify 0 into 0 11.855 * [backup-simplify]: Simplify 0 into 0 11.856 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.857 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 11.861 * [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 11.861 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.862 * [backup-simplify]: Simplify (+ 0 0) into 0 11.863 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0 11.864 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.866 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 11.868 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.869 * [taylor]: Taking taylor expansion of 0 in k 11.869 * [backup-simplify]: Simplify 0 into 0 11.869 * [backup-simplify]: Simplify 0 into 0 11.869 * [backup-simplify]: Simplify 0 into 0 11.869 * [backup-simplify]: Simplify 0 into 0 11.870 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.871 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.878 * [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 11.878 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.878 * [backup-simplify]: Simplify (+ 0 0) into 0 11.879 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0 11.881 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.883 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 11.886 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 11.886 * [taylor]: Taking taylor expansion of 0 in k 11.886 * [backup-simplify]: Simplify 0 into 0 11.886 * [backup-simplify]: Simplify 0 into 0 11.887 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) 11.888 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 11.888 * [backup-simplify]: Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k)) 11.888 * [approximate]: Taking taylor expansion of (sqrt (/ 1 k)) in (k) around 0 11.888 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.888 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.888 * [taylor]: Taking taylor expansion of k in k 11.888 * [backup-simplify]: Simplify 0 into 0 11.888 * [backup-simplify]: Simplify 1 into 1 11.888 * [backup-simplify]: Simplify (/ 1 1) into 1 11.889 * [backup-simplify]: Simplify (sqrt 0) into 0 11.890 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.890 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.890 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.890 * [taylor]: Taking taylor expansion of k in k 11.890 * [backup-simplify]: Simplify 0 into 0 11.890 * [backup-simplify]: Simplify 1 into 1 11.891 * [backup-simplify]: Simplify (/ 1 1) into 1 11.891 * [backup-simplify]: Simplify (sqrt 0) into 0 11.892 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.892 * [backup-simplify]: Simplify 0 into 0 11.892 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.893 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 11.896 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.896 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.897 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.901 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.901 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.901 * [backup-simplify]: Simplify (+ (* +nan.0 (pow k 2)) (+ (* +nan.0 k) +nan.0)) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 11.901 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k) 11.901 * [approximate]: Taking taylor expansion of (sqrt k) in (k) around 0 11.901 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.901 * [taylor]: Taking taylor expansion of k in k 11.901 * [backup-simplify]: Simplify 0 into 0 11.901 * [backup-simplify]: Simplify 1 into 1 11.902 * [backup-simplify]: Simplify (sqrt 0) into 0 11.903 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.903 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.903 * [taylor]: Taking taylor expansion of k in k 11.903 * [backup-simplify]: Simplify 0 into 0 11.903 * [backup-simplify]: Simplify 1 into 1 11.904 * [backup-simplify]: Simplify (sqrt 0) into 0 11.905 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.905 * [backup-simplify]: Simplify 0 into 0 11.905 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.908 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.908 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.912 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.912 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.912 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (/ 1 k) 3)) (+ (* +nan.0 (pow (/ 1 k) 2)) (* +nan.0 (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 11.912 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 (- k)))) into (/ 1 (sqrt (/ -1 k))) 11.912 * [approximate]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in (k) around 0 11.912 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 11.912 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.912 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.912 * [taylor]: Taking taylor expansion of -1 in k 11.912 * [backup-simplify]: Simplify -1 into -1 11.912 * [taylor]: Taking taylor expansion of k in k 11.912 * [backup-simplify]: Simplify 0 into 0 11.912 * [backup-simplify]: Simplify 1 into 1 11.913 * [backup-simplify]: Simplify (/ -1 1) into -1 11.913 * [backup-simplify]: Simplify (sqrt 0) into 0 11.914 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.915 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 11.915 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 11.915 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.915 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.915 * [taylor]: Taking taylor expansion of -1 in k 11.915 * [backup-simplify]: Simplify -1 into -1 11.915 * [taylor]: Taking taylor expansion of k in k 11.915 * [backup-simplify]: Simplify 0 into 0 11.915 * [backup-simplify]: Simplify 1 into 1 11.915 * [backup-simplify]: Simplify (/ -1 1) into -1 11.916 * [backup-simplify]: Simplify (sqrt 0) into 0 11.917 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.917 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 11.917 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.918 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 11.921 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.923 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 11.923 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.924 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.928 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.931 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 11.932 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.933 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 11.933 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 11.933 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 11.933 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 11.933 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.934 * [taylor]: Taking taylor expansion of 2 in n 11.934 * [backup-simplify]: Simplify 2 into 2 11.934 * [taylor]: Taking taylor expansion of (* n PI) in n 11.934 * [taylor]: Taking taylor expansion of n in n 11.934 * [backup-simplify]: Simplify 0 into 0 11.934 * [backup-simplify]: Simplify 1 into 1 11.934 * [taylor]: Taking taylor expansion of PI in n 11.934 * [backup-simplify]: Simplify PI into PI 11.934 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.934 * [taylor]: Taking taylor expansion of 2 in n 11.934 * [backup-simplify]: Simplify 2 into 2 11.934 * [taylor]: Taking taylor expansion of (* n PI) in n 11.934 * [taylor]: Taking taylor expansion of n in n 11.934 * [backup-simplify]: Simplify 0 into 0 11.934 * [backup-simplify]: Simplify 1 into 1 11.934 * [taylor]: Taking taylor expansion of PI in n 11.934 * [backup-simplify]: Simplify PI into PI 11.934 * [backup-simplify]: Simplify (* 0 PI) into 0 11.935 * [backup-simplify]: Simplify (* 2 0) into 0 11.935 * [backup-simplify]: Simplify 0 into 0 11.936 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.938 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.938 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.939 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.939 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 11.939 * [backup-simplify]: Simplify 0 into 0 11.940 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 11.941 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 11.941 * [backup-simplify]: Simplify 0 into 0 11.942 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.942 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 11.943 * [backup-simplify]: Simplify 0 into 0 11.943 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.944 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 11.944 * [backup-simplify]: Simplify 0 into 0 11.945 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.946 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 11.946 * [backup-simplify]: Simplify 0 into 0 11.947 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 11.948 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 11.948 * [backup-simplify]: Simplify 0 into 0 11.949 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 11.949 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n)) 11.949 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 11.949 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.949 * [taylor]: Taking taylor expansion of 2 in n 11.949 * [backup-simplify]: Simplify 2 into 2 11.949 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.949 * [taylor]: Taking taylor expansion of PI in n 11.949 * [backup-simplify]: Simplify PI into PI 11.949 * [taylor]: Taking taylor expansion of n in n 11.949 * [backup-simplify]: Simplify 0 into 0 11.949 * [backup-simplify]: Simplify 1 into 1 11.950 * [backup-simplify]: Simplify (/ PI 1) into PI 11.950 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.950 * [taylor]: Taking taylor expansion of 2 in n 11.950 * [backup-simplify]: Simplify 2 into 2 11.950 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.950 * [taylor]: Taking taylor expansion of PI in n 11.950 * [backup-simplify]: Simplify PI into PI 11.950 * [taylor]: Taking taylor expansion of n in n 11.950 * [backup-simplify]: Simplify 0 into 0 11.950 * [backup-simplify]: Simplify 1 into 1 11.950 * [backup-simplify]: Simplify (/ PI 1) into PI 11.950 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.951 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.951 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.952 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 11.952 * [backup-simplify]: Simplify 0 into 0 11.953 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.953 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 11.953 * [backup-simplify]: Simplify 0 into 0 11.954 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.955 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.955 * [backup-simplify]: Simplify 0 into 0 11.956 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.956 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.956 * [backup-simplify]: Simplify 0 into 0 11.957 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.958 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.958 * [backup-simplify]: Simplify 0 into 0 11.964 * [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 11.965 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.965 * [backup-simplify]: Simplify 0 into 0 11.966 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 11.966 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (- n))) into (* -2 (/ PI n)) 11.966 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 11.966 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.966 * [taylor]: Taking taylor expansion of -2 in n 11.966 * [backup-simplify]: Simplify -2 into -2 11.966 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.966 * [taylor]: Taking taylor expansion of PI in n 11.966 * [backup-simplify]: Simplify PI into PI 11.966 * [taylor]: Taking taylor expansion of n in n 11.966 * [backup-simplify]: Simplify 0 into 0 11.966 * [backup-simplify]: Simplify 1 into 1 11.967 * [backup-simplify]: Simplify (/ PI 1) into PI 11.967 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.967 * [taylor]: Taking taylor expansion of -2 in n 11.967 * [backup-simplify]: Simplify -2 into -2 11.967 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.967 * [taylor]: Taking taylor expansion of PI in n 11.967 * [backup-simplify]: Simplify PI into PI 11.967 * [taylor]: Taking taylor expansion of n in n 11.967 * [backup-simplify]: Simplify 0 into 0 11.967 * [backup-simplify]: Simplify 1 into 1 11.967 * [backup-simplify]: Simplify (/ PI 1) into PI 11.968 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.968 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.969 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.969 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 11.969 * [backup-simplify]: Simplify 0 into 0 11.970 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.970 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 11.970 * [backup-simplify]: Simplify 0 into 0 11.971 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.972 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.972 * [backup-simplify]: Simplify 0 into 0 11.973 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.974 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.974 * [backup-simplify]: Simplify 0 into 0 11.974 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.975 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.975 * [backup-simplify]: Simplify 0 into 0 11.976 * [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 11.977 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.977 * [backup-simplify]: Simplify 0 into 0 11.977 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 11.977 * * * * [progress]: [ 4 / 4 ] generating series at (2) 11.978 * [backup-simplify]: Simplify (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) 11.978 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k n) around 0 11.978 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n 11.978 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 11.978 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 11.978 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 11.978 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n 11.978 * [taylor]: Taking taylor expansion of 1/2 in n 11.978 * [backup-simplify]: Simplify 1/2 into 1/2 11.978 * [taylor]: Taking taylor expansion of (- 1 k) in n 11.978 * [taylor]: Taking taylor expansion of 1 in n 11.978 * [backup-simplify]: Simplify 1 into 1 11.978 * [taylor]: Taking taylor expansion of k in n 11.978 * [backup-simplify]: Simplify k into k 11.978 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.978 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.978 * [taylor]: Taking taylor expansion of 2 in n 11.978 * [backup-simplify]: Simplify 2 into 2 11.978 * [taylor]: Taking taylor expansion of (* n PI) in n 11.978 * [taylor]: Taking taylor expansion of n in n 11.978 * [backup-simplify]: Simplify 0 into 0 11.978 * [backup-simplify]: Simplify 1 into 1 11.978 * [taylor]: Taking taylor expansion of PI in n 11.978 * [backup-simplify]: Simplify PI into PI 11.978 * [backup-simplify]: Simplify (* 0 PI) into 0 11.979 * [backup-simplify]: Simplify (* 2 0) into 0 11.980 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.981 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.981 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.981 * [backup-simplify]: Simplify (- k) into (- k) 11.981 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k) 11.981 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 11.982 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.983 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 11.984 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 11.984 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 11.984 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.984 * [taylor]: Taking taylor expansion of k in n 11.984 * [backup-simplify]: Simplify k into k 11.984 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.984 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 11.984 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.984 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 11.984 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k 11.984 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 11.984 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 11.984 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 11.984 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k 11.984 * [taylor]: Taking taylor expansion of 1/2 in k 11.984 * [backup-simplify]: Simplify 1/2 into 1/2 11.984 * [taylor]: Taking taylor expansion of (- 1 k) in k 11.984 * [taylor]: Taking taylor expansion of 1 in k 11.984 * [backup-simplify]: Simplify 1 into 1 11.984 * [taylor]: Taking taylor expansion of k in k 11.984 * [backup-simplify]: Simplify 0 into 0 11.984 * [backup-simplify]: Simplify 1 into 1 11.984 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 11.984 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 11.984 * [taylor]: Taking taylor expansion of 2 in k 11.984 * [backup-simplify]: Simplify 2 into 2 11.984 * [taylor]: Taking taylor expansion of (* n PI) in k 11.984 * [taylor]: Taking taylor expansion of n in k 11.984 * [backup-simplify]: Simplify n into n 11.984 * [taylor]: Taking taylor expansion of PI in k 11.984 * [backup-simplify]: Simplify PI into PI 11.984 * [backup-simplify]: Simplify (* n PI) into (* n PI) 11.984 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 11.984 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 11.985 * [backup-simplify]: Simplify (- 0) into 0 11.985 * [backup-simplify]: Simplify (+ 1 0) into 1 11.985 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.985 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 11.985 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 11.985 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.985 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.985 * [taylor]: Taking taylor expansion of k in k 11.985 * [backup-simplify]: Simplify 0 into 0 11.985 * [backup-simplify]: Simplify 1 into 1 11.986 * [backup-simplify]: Simplify (/ 1 1) into 1 11.986 * [backup-simplify]: Simplify (sqrt 0) into 0 11.987 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.987 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k 11.987 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 11.987 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 11.987 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 11.987 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k 11.987 * [taylor]: Taking taylor expansion of 1/2 in k 11.987 * [backup-simplify]: Simplify 1/2 into 1/2 11.987 * [taylor]: Taking taylor expansion of (- 1 k) in k 11.987 * [taylor]: Taking taylor expansion of 1 in k 11.987 * [backup-simplify]: Simplify 1 into 1 11.987 * [taylor]: Taking taylor expansion of k in k 11.987 * [backup-simplify]: Simplify 0 into 0 11.987 * [backup-simplify]: Simplify 1 into 1 11.987 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 11.987 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 11.987 * [taylor]: Taking taylor expansion of 2 in k 11.987 * [backup-simplify]: Simplify 2 into 2 11.987 * [taylor]: Taking taylor expansion of (* n PI) in k 11.987 * [taylor]: Taking taylor expansion of n in k 11.987 * [backup-simplify]: Simplify n into n 11.987 * [taylor]: Taking taylor expansion of PI in k 11.987 * [backup-simplify]: Simplify PI into PI 11.987 * [backup-simplify]: Simplify (* n PI) into (* n PI) 11.987 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 11.987 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 11.987 * [backup-simplify]: Simplify (- 0) into 0 11.988 * [backup-simplify]: Simplify (+ 1 0) into 1 11.988 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.988 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 11.988 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 11.988 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.988 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.988 * [taylor]: Taking taylor expansion of k in k 11.988 * [backup-simplify]: Simplify 0 into 0 11.988 * [backup-simplify]: Simplify 1 into 1 11.988 * [backup-simplify]: Simplify (/ 1 1) into 1 11.989 * [backup-simplify]: Simplify (sqrt 0) into 0 11.990 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.990 * [backup-simplify]: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0 11.990 * [taylor]: Taking taylor expansion of 0 in n 11.990 * [backup-simplify]: Simplify 0 into 0 11.990 * [backup-simplify]: Simplify 0 into 0 11.990 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 11.990 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 11.991 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 11.991 * [backup-simplify]: Simplify (- 1) into -1 11.991 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.992 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2 11.993 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 11.993 * [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))))) 11.993 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 11.993 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 11.993 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 11.993 * [taylor]: Taking taylor expansion of +nan.0 in n 11.993 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.993 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 11.993 * [taylor]: Taking taylor expansion of (sqrt 2) in n 11.993 * [taylor]: Taking taylor expansion of 2 in n 11.993 * [backup-simplify]: Simplify 2 into 2 11.993 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 11.994 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 11.994 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 11.994 * [taylor]: Taking taylor expansion of (* n PI) in n 11.994 * [taylor]: Taking taylor expansion of n in n 11.994 * [backup-simplify]: Simplify 0 into 0 11.994 * [backup-simplify]: Simplify 1 into 1 11.994 * [taylor]: Taking taylor expansion of PI in n 11.994 * [backup-simplify]: Simplify PI into PI 11.994 * [backup-simplify]: Simplify (* 0 PI) into 0 11.995 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.995 * [backup-simplify]: Simplify (sqrt 0) into 0 11.996 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 11.997 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 11.997 * [backup-simplify]: Simplify (* +nan.0 0) into 0 11.997 * [backup-simplify]: Simplify (- 0) into 0 11.997 * [backup-simplify]: Simplify 0 into 0 11.997 * [backup-simplify]: Simplify 0 into 0 11.998 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 12.000 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.000 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 12.001 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 12.002 * [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 12.002 * [backup-simplify]: Simplify (- 0) into 0 12.002 * [backup-simplify]: Simplify (+ 0 0) into 0 12.003 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0 12.003 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 12.004 * [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))) 12.004 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) 12.004 * [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 12.004 * [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 12.004 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 12.004 * [taylor]: Taking taylor expansion of +nan.0 in n 12.004 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.004 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 12.004 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 12.004 * [taylor]: Taking taylor expansion of (sqrt 2) in n 12.005 * [taylor]: Taking taylor expansion of 2 in n 12.005 * [backup-simplify]: Simplify 2 into 2 12.005 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 12.005 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 12.005 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 12.005 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 12.005 * [taylor]: Taking taylor expansion of 2 in n 12.005 * [backup-simplify]: Simplify 2 into 2 12.006 * [taylor]: Taking taylor expansion of (* n PI) in n 12.006 * [taylor]: Taking taylor expansion of n in n 12.006 * [backup-simplify]: Simplify 0 into 0 12.006 * [backup-simplify]: Simplify 1 into 1 12.006 * [taylor]: Taking taylor expansion of PI in n 12.006 * [backup-simplify]: Simplify PI into PI 12.006 * [backup-simplify]: Simplify (* 0 PI) into 0 12.006 * [backup-simplify]: Simplify (* 2 0) into 0 12.008 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.010 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 12.011 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.011 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 12.011 * [taylor]: Taking taylor expansion of (* n PI) in n 12.011 * [taylor]: Taking taylor expansion of n in n 12.011 * [backup-simplify]: Simplify 0 into 0 12.011 * [backup-simplify]: Simplify 1 into 1 12.011 * [taylor]: Taking taylor expansion of PI in n 12.011 * [backup-simplify]: Simplify PI into PI 12.012 * [backup-simplify]: Simplify (* 0 PI) into 0 12.013 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.013 * [backup-simplify]: Simplify (sqrt 0) into 0 12.015 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 12.015 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 12.015 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 12.015 * [taylor]: Taking taylor expansion of +nan.0 in n 12.015 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.015 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 12.015 * [taylor]: Taking taylor expansion of (sqrt 2) in n 12.015 * [taylor]: Taking taylor expansion of 2 in n 12.015 * [backup-simplify]: Simplify 2 into 2 12.015 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 12.016 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 12.016 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 12.016 * [taylor]: Taking taylor expansion of (* n PI) in n 12.016 * [taylor]: Taking taylor expansion of n in n 12.016 * [backup-simplify]: Simplify 0 into 0 12.016 * [backup-simplify]: Simplify 1 into 1 12.016 * [taylor]: Taking taylor expansion of PI in n 12.016 * [backup-simplify]: Simplify PI into PI 12.017 * [backup-simplify]: Simplify (* 0 PI) into 0 12.018 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.019 * [backup-simplify]: Simplify (sqrt 0) into 0 12.020 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 12.021 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.023 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 12.024 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 12.025 * [backup-simplify]: Simplify (* +nan.0 0) into 0 12.025 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 12.026 * [backup-simplify]: Simplify (* +nan.0 0) into 0 12.026 * [backup-simplify]: Simplify (- 0) into 0 12.027 * [backup-simplify]: Simplify (+ 0 0) into 0 12.027 * [backup-simplify]: Simplify (- 0) into 0 12.027 * [backup-simplify]: Simplify 0 into 0 12.030 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 12.036 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 12.040 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 12.042 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 12.042 * [backup-simplify]: Simplify 0 into 0 12.043 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.047 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.048 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.049 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 12.051 * [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 12.051 * [backup-simplify]: Simplify (- 0) into 0 12.051 * [backup-simplify]: Simplify (+ 0 0) into 0 12.053 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0 12.054 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 12.055 * [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))) 12.056 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (+ (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) +nan.0) (* (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) 12.056 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) in n 12.056 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))))) in n 12.056 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 12.056 * [taylor]: Taking taylor expansion of +nan.0 in n 12.056 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.056 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 12.056 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 12.056 * [taylor]: Taking taylor expansion of (sqrt 2) in n 12.056 * [taylor]: Taking taylor expansion of 2 in n 12.056 * [backup-simplify]: Simplify 2 into 2 12.056 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 12.056 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 12.056 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 12.056 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 12.056 * [taylor]: Taking taylor expansion of 2 in n 12.056 * [backup-simplify]: Simplify 2 into 2 12.056 * [taylor]: Taking taylor expansion of (* n PI) in n 12.057 * [taylor]: Taking taylor expansion of n in n 12.057 * [backup-simplify]: Simplify 0 into 0 12.057 * [backup-simplify]: Simplify 1 into 1 12.057 * [taylor]: Taking taylor expansion of PI in n 12.057 * [backup-simplify]: Simplify PI into PI 12.057 * [backup-simplify]: Simplify (* 0 PI) into 0 12.057 * [backup-simplify]: Simplify (* 2 0) into 0 12.058 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.059 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 12.060 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.060 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 12.060 * [taylor]: Taking taylor expansion of (* n PI) in n 12.060 * [taylor]: Taking taylor expansion of n in n 12.060 * [backup-simplify]: Simplify 0 into 0 12.060 * [backup-simplify]: Simplify 1 into 1 12.060 * [taylor]: Taking taylor expansion of PI in n 12.060 * [backup-simplify]: Simplify PI into PI 12.060 * [backup-simplify]: Simplify (* 0 PI) into 0 12.061 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.061 * [backup-simplify]: Simplify (sqrt 0) into 0 12.062 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 12.062 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))) in n 12.062 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))) in n 12.062 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 12.062 * [taylor]: Taking taylor expansion of +nan.0 in n 12.062 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.062 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 12.062 * [taylor]: Taking taylor expansion of (sqrt 2) in n 12.062 * [taylor]: Taking taylor expansion of 2 in n 12.062 * [backup-simplify]: Simplify 2 into 2 12.063 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 12.063 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 12.063 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 12.063 * [taylor]: Taking taylor expansion of (* n PI) in n 12.063 * [taylor]: Taking taylor expansion of n in n 12.063 * [backup-simplify]: Simplify 0 into 0 12.063 * [backup-simplify]: Simplify 1 into 1 12.063 * [taylor]: Taking taylor expansion of PI in n 12.063 * [backup-simplify]: Simplify PI into PI 12.063 * [backup-simplify]: Simplify (* 0 PI) into 0 12.064 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.065 * [backup-simplify]: Simplify (sqrt 0) into 0 12.065 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 12.065 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n 12.066 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 12.066 * [taylor]: Taking taylor expansion of +nan.0 in n 12.066 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.066 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 12.066 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 12.066 * [taylor]: Taking taylor expansion of (sqrt 2) in n 12.066 * [taylor]: Taking taylor expansion of 2 in n 12.066 * [backup-simplify]: Simplify 2 into 2 12.066 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 12.066 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 12.066 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 12.066 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 12.066 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 12.066 * [taylor]: Taking taylor expansion of 2 in n 12.066 * [backup-simplify]: Simplify 2 into 2 12.066 * [taylor]: Taking taylor expansion of (* n PI) in n 12.066 * [taylor]: Taking taylor expansion of n in n 12.066 * [backup-simplify]: Simplify 0 into 0 12.066 * [backup-simplify]: Simplify 1 into 1 12.066 * [taylor]: Taking taylor expansion of PI in n 12.066 * [backup-simplify]: Simplify PI into PI 12.067 * [backup-simplify]: Simplify (* 0 PI) into 0 12.067 * [backup-simplify]: Simplify (* 2 0) into 0 12.068 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.075 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 12.075 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.076 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.076 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 12.076 * [taylor]: Taking taylor expansion of (* n PI) in n 12.076 * [taylor]: Taking taylor expansion of n in n 12.076 * [backup-simplify]: Simplify 0 into 0 12.076 * [backup-simplify]: Simplify 1 into 1 12.076 * [taylor]: Taking taylor expansion of PI in n 12.076 * [backup-simplify]: Simplify PI into PI 12.077 * [backup-simplify]: Simplify (* 0 PI) into 0 12.078 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.078 * [backup-simplify]: Simplify (sqrt 0) into 0 12.079 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 12.080 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.081 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 12.082 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 12.082 * [backup-simplify]: Simplify (* +nan.0 0) into 0 12.082 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 12.082 * [backup-simplify]: Simplify (* +nan.0 0) into 0 12.083 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.084 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.085 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 12.086 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 12.087 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 12.088 * [backup-simplify]: Simplify (* +nan.0 0) into 0 12.088 * [backup-simplify]: Simplify (- 0) into 0 12.088 * [backup-simplify]: Simplify (+ 0 0) into 0 12.088 * [backup-simplify]: Simplify (- 0) into 0 12.089 * [backup-simplify]: Simplify (+ 0 0) into 0 12.089 * [backup-simplify]: Simplify (- 0) into 0 12.089 * [backup-simplify]: Simplify 0 into 0 12.090 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.091 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 12.093 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 12.095 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.097 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 12.099 * [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)))))))) 12.106 * [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)))))))) 12.109 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 12.115 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 12.119 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 12.128 * [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)))))))))) 12.137 * [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))))))) 12.145 * [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))))))) 12.146 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.151 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 12.152 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 12.158 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 12.166 * [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)))) 12.169 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 12.171 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 12.180 * [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))))))))))))) 12.181 * [backup-simplify]: Simplify (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) 12.181 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k n) around 0 12.181 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n 12.181 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 12.181 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 12.181 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 12.181 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 12.181 * [taylor]: Taking taylor expansion of 1/2 in n 12.181 * [backup-simplify]: Simplify 1/2 into 1/2 12.181 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 12.181 * [taylor]: Taking taylor expansion of 1 in n 12.181 * [backup-simplify]: Simplify 1 into 1 12.181 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.181 * [taylor]: Taking taylor expansion of k in n 12.181 * [backup-simplify]: Simplify k into k 12.181 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.181 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 12.181 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 12.181 * [taylor]: Taking taylor expansion of 2 in n 12.181 * [backup-simplify]: Simplify 2 into 2 12.181 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.181 * [taylor]: Taking taylor expansion of PI in n 12.181 * [backup-simplify]: Simplify PI into PI 12.181 * [taylor]: Taking taylor expansion of n in n 12.181 * [backup-simplify]: Simplify 0 into 0 12.181 * [backup-simplify]: Simplify 1 into 1 12.182 * [backup-simplify]: Simplify (/ PI 1) into PI 12.182 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.183 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.183 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.183 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 12.183 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 12.184 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.184 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 12.185 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 12.185 * [taylor]: Taking taylor expansion of (sqrt k) in n 12.185 * [taylor]: Taking taylor expansion of k in n 12.185 * [backup-simplify]: Simplify k into k 12.185 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 12.185 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 12.185 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k 12.185 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 12.185 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 12.185 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 12.185 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 12.185 * [taylor]: Taking taylor expansion of 1/2 in k 12.185 * [backup-simplify]: Simplify 1/2 into 1/2 12.185 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 12.185 * [taylor]: Taking taylor expansion of 1 in k 12.185 * [backup-simplify]: Simplify 1 into 1 12.185 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.185 * [taylor]: Taking taylor expansion of k in k 12.185 * [backup-simplify]: Simplify 0 into 0 12.185 * [backup-simplify]: Simplify 1 into 1 12.186 * [backup-simplify]: Simplify (/ 1 1) into 1 12.186 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 12.186 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 12.186 * [taylor]: Taking taylor expansion of 2 in k 12.186 * [backup-simplify]: Simplify 2 into 2 12.186 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.186 * [taylor]: Taking taylor expansion of PI in k 12.186 * [backup-simplify]: Simplify PI into PI 12.186 * [taylor]: Taking taylor expansion of n in k 12.186 * [backup-simplify]: Simplify n into n 12.186 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.186 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 12.186 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 12.186 * [backup-simplify]: Simplify (- 1) into -1 12.187 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.187 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2 12.187 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 12.187 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 12.187 * [taylor]: Taking taylor expansion of (sqrt k) in k 12.187 * [taylor]: Taking taylor expansion of k in k 12.187 * [backup-simplify]: Simplify 0 into 0 12.187 * [backup-simplify]: Simplify 1 into 1 12.187 * [backup-simplify]: Simplify (sqrt 0) into 0 12.188 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.188 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k 12.188 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 12.188 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 12.188 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 12.188 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 12.188 * [taylor]: Taking taylor expansion of 1/2 in k 12.188 * [backup-simplify]: Simplify 1/2 into 1/2 12.188 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 12.188 * [taylor]: Taking taylor expansion of 1 in k 12.188 * [backup-simplify]: Simplify 1 into 1 12.188 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.188 * [taylor]: Taking taylor expansion of k in k 12.188 * [backup-simplify]: Simplify 0 into 0 12.188 * [backup-simplify]: Simplify 1 into 1 12.189 * [backup-simplify]: Simplify (/ 1 1) into 1 12.189 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 12.189 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 12.189 * [taylor]: Taking taylor expansion of 2 in k 12.189 * [backup-simplify]: Simplify 2 into 2 12.189 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.189 * [taylor]: Taking taylor expansion of PI in k 12.189 * [backup-simplify]: Simplify PI into PI 12.189 * [taylor]: Taking taylor expansion of n in k 12.189 * [backup-simplify]: Simplify n into n 12.189 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.189 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 12.189 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 12.195 * [backup-simplify]: Simplify (- 1) into -1 12.195 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.196 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2 12.196 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 12.196 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 12.196 * [taylor]: Taking taylor expansion of (sqrt k) in k 12.196 * [taylor]: Taking taylor expansion of k in k 12.196 * [backup-simplify]: Simplify 0 into 0 12.196 * [backup-simplify]: Simplify 1 into 1 12.196 * [backup-simplify]: Simplify (sqrt 0) into 0 12.197 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.197 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 0) into 0 12.197 * [taylor]: Taking taylor expansion of 0 in n 12.197 * [backup-simplify]: Simplify 0 into 0 12.197 * [backup-simplify]: Simplify 0 into 0 12.198 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 12.198 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 12.198 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 12.198 * [taylor]: Taking taylor expansion of +nan.0 in n 12.198 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.198 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 12.198 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 12.198 * [taylor]: Taking taylor expansion of 1/2 in n 12.198 * [backup-simplify]: Simplify 1/2 into 1/2 12.198 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 12.198 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 12.198 * [taylor]: Taking taylor expansion of 1 in n 12.198 * [backup-simplify]: Simplify 1 into 1 12.198 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.198 * [taylor]: Taking taylor expansion of k in n 12.198 * [backup-simplify]: Simplify k into k 12.198 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.198 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 12.198 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 12.198 * [taylor]: Taking taylor expansion of 2 in n 12.198 * [backup-simplify]: Simplify 2 into 2 12.198 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.198 * [taylor]: Taking taylor expansion of PI in n 12.198 * [backup-simplify]: Simplify PI into PI 12.198 * [taylor]: Taking taylor expansion of n in n 12.198 * [backup-simplify]: Simplify 0 into 0 12.198 * [backup-simplify]: Simplify 1 into 1 12.198 * [backup-simplify]: Simplify (/ PI 1) into PI 12.199 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.199 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.200 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.200 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 12.200 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.201 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 12.202 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 12.203 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 12.203 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 12.204 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 12.205 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 12.205 * [backup-simplify]: Simplify 0 into 0 12.207 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.207 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 12.208 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 12.208 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 12.208 * [taylor]: Taking taylor expansion of +nan.0 in n 12.208 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.208 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 12.208 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 12.208 * [taylor]: Taking taylor expansion of 1/2 in n 12.208 * [backup-simplify]: Simplify 1/2 into 1/2 12.208 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 12.208 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 12.208 * [taylor]: Taking taylor expansion of 1 in n 12.208 * [backup-simplify]: Simplify 1 into 1 12.208 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.208 * [taylor]: Taking taylor expansion of k in n 12.208 * [backup-simplify]: Simplify k into k 12.208 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.208 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 12.208 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 12.208 * [taylor]: Taking taylor expansion of 2 in n 12.208 * [backup-simplify]: Simplify 2 into 2 12.208 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.208 * [taylor]: Taking taylor expansion of PI in n 12.208 * [backup-simplify]: Simplify PI into PI 12.208 * [taylor]: Taking taylor expansion of n in n 12.208 * [backup-simplify]: Simplify 0 into 0 12.208 * [backup-simplify]: Simplify 1 into 1 12.208 * [backup-simplify]: Simplify (/ PI 1) into PI 12.209 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.209 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.209 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.209 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 12.210 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.211 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 12.212 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 12.212 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 12.213 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 12.214 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 12.215 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 12.215 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.216 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 12.217 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 12.217 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.217 * [backup-simplify]: Simplify (- 0) into 0 12.217 * [backup-simplify]: Simplify (+ 0 0) into 0 12.218 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.219 * [backup-simplify]: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 12.220 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0 12.222 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.223 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0 12.223 * [backup-simplify]: Simplify (- 0) into 0 12.223 * [backup-simplify]: Simplify 0 into 0 12.223 * [backup-simplify]: Simplify 0 into 0 12.225 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.226 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 12.226 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 12.226 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 12.226 * [taylor]: Taking taylor expansion of +nan.0 in n 12.226 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.226 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 12.226 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 12.226 * [taylor]: Taking taylor expansion of 1/2 in n 12.226 * [backup-simplify]: Simplify 1/2 into 1/2 12.226 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 12.226 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 12.226 * [taylor]: Taking taylor expansion of 1 in n 12.226 * [backup-simplify]: Simplify 1 into 1 12.226 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.226 * [taylor]: Taking taylor expansion of k in n 12.226 * [backup-simplify]: Simplify k into k 12.226 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.226 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 12.226 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 12.226 * [taylor]: Taking taylor expansion of 2 in n 12.226 * [backup-simplify]: Simplify 2 into 2 12.226 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.226 * [taylor]: Taking taylor expansion of PI in n 12.226 * [backup-simplify]: Simplify PI into PI 12.226 * [taylor]: Taking taylor expansion of n in n 12.226 * [backup-simplify]: Simplify 0 into 0 12.226 * [backup-simplify]: Simplify 1 into 1 12.227 * [backup-simplify]: Simplify (/ PI 1) into PI 12.227 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.228 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.228 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.228 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 12.229 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.229 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 12.230 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 12.231 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 12.232 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 12.232 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 12.234 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 12.236 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))) 12.237 * [backup-simplify]: Simplify (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) 12.237 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (k n) around 0 12.237 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n 12.237 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 12.237 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 12.237 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 12.237 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 12.237 * [taylor]: Taking taylor expansion of 1/2 in n 12.237 * [backup-simplify]: Simplify 1/2 into 1/2 12.237 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 12.237 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.237 * [taylor]: Taking taylor expansion of k in n 12.237 * [backup-simplify]: Simplify k into k 12.237 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.237 * [taylor]: Taking taylor expansion of 1 in n 12.237 * [backup-simplify]: Simplify 1 into 1 12.237 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 12.237 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.237 * [taylor]: Taking taylor expansion of -2 in n 12.237 * [backup-simplify]: Simplify -2 into -2 12.237 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.237 * [taylor]: Taking taylor expansion of PI in n 12.237 * [backup-simplify]: Simplify PI into PI 12.237 * [taylor]: Taking taylor expansion of n in n 12.237 * [backup-simplify]: Simplify 0 into 0 12.237 * [backup-simplify]: Simplify 1 into 1 12.238 * [backup-simplify]: Simplify (/ PI 1) into PI 12.238 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.239 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.239 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 12.239 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 12.240 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.240 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 12.241 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 12.241 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 12.241 * [taylor]: Taking taylor expansion of (/ -1 k) in n 12.241 * [taylor]: Taking taylor expansion of -1 in n 12.241 * [backup-simplify]: Simplify -1 into -1 12.241 * [taylor]: Taking taylor expansion of k in n 12.241 * [backup-simplify]: Simplify k into k 12.241 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 12.241 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 12.241 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 12.241 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 12.242 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) 12.242 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k 12.242 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 12.242 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 12.242 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 12.242 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 12.242 * [taylor]: Taking taylor expansion of 1/2 in k 12.242 * [backup-simplify]: Simplify 1/2 into 1/2 12.242 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 12.242 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.242 * [taylor]: Taking taylor expansion of k in k 12.242 * [backup-simplify]: Simplify 0 into 0 12.242 * [backup-simplify]: Simplify 1 into 1 12.243 * [backup-simplify]: Simplify (/ 1 1) into 1 12.243 * [taylor]: Taking taylor expansion of 1 in k 12.243 * [backup-simplify]: Simplify 1 into 1 12.243 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 12.243 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 12.243 * [taylor]: Taking taylor expansion of -2 in k 12.243 * [backup-simplify]: Simplify -2 into -2 12.243 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.243 * [taylor]: Taking taylor expansion of PI in k 12.243 * [backup-simplify]: Simplify PI into PI 12.243 * [taylor]: Taking taylor expansion of n in k 12.243 * [backup-simplify]: Simplify n into n 12.243 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.243 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 12.243 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 12.243 * [backup-simplify]: Simplify (+ 1 0) into 1 12.243 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.244 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 12.244 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 12.244 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.244 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.244 * [taylor]: Taking taylor expansion of -1 in k 12.244 * [backup-simplify]: Simplify -1 into -1 12.244 * [taylor]: Taking taylor expansion of k in k 12.244 * [backup-simplify]: Simplify 0 into 0 12.244 * [backup-simplify]: Simplify 1 into 1 12.244 * [backup-simplify]: Simplify (/ -1 1) into -1 12.244 * [backup-simplify]: Simplify (sqrt 0) into 0 12.245 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.245 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) 12.245 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k 12.245 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 12.245 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 12.245 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 12.245 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 12.245 * [taylor]: Taking taylor expansion of 1/2 in k 12.245 * [backup-simplify]: Simplify 1/2 into 1/2 12.245 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 12.246 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.246 * [taylor]: Taking taylor expansion of k in k 12.246 * [backup-simplify]: Simplify 0 into 0 12.246 * [backup-simplify]: Simplify 1 into 1 12.246 * [backup-simplify]: Simplify (/ 1 1) into 1 12.246 * [taylor]: Taking taylor expansion of 1 in k 12.246 * [backup-simplify]: Simplify 1 into 1 12.246 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 12.246 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 12.246 * [taylor]: Taking taylor expansion of -2 in k 12.246 * [backup-simplify]: Simplify -2 into -2 12.246 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.246 * [taylor]: Taking taylor expansion of PI in k 12.246 * [backup-simplify]: Simplify PI into PI 12.246 * [taylor]: Taking taylor expansion of n in k 12.246 * [backup-simplify]: Simplify n into n 12.246 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.246 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 12.246 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 12.246 * [backup-simplify]: Simplify (+ 1 0) into 1 12.247 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.247 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 12.247 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 12.247 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.247 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.247 * [taylor]: Taking taylor expansion of -1 in k 12.247 * [backup-simplify]: Simplify -1 into -1 12.247 * [taylor]: Taking taylor expansion of k in k 12.247 * [backup-simplify]: Simplify 0 into 0 12.247 * [backup-simplify]: Simplify 1 into 1 12.247 * [backup-simplify]: Simplify (/ -1 1) into -1 12.247 * [backup-simplify]: Simplify (sqrt 0) into 0 12.248 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.248 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) 12.249 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 12.249 * [taylor]: Taking taylor expansion of +nan.0 in n 12.249 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.249 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 12.249 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 12.249 * [taylor]: Taking taylor expansion of 1/2 in n 12.249 * [backup-simplify]: Simplify 1/2 into 1/2 12.249 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 12.249 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 12.249 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.249 * [taylor]: Taking taylor expansion of -2 in n 12.249 * [backup-simplify]: Simplify -2 into -2 12.249 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.249 * [taylor]: Taking taylor expansion of PI in n 12.249 * [backup-simplify]: Simplify PI into PI 12.249 * [taylor]: Taking taylor expansion of n in n 12.249 * [backup-simplify]: Simplify 0 into 0 12.249 * [backup-simplify]: Simplify 1 into 1 12.249 * [backup-simplify]: Simplify (/ PI 1) into PI 12.250 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.251 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.251 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 12.251 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.251 * [taylor]: Taking taylor expansion of k in n 12.251 * [backup-simplify]: Simplify k into k 12.251 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.251 * [taylor]: Taking taylor expansion of 1 in n 12.251 * [backup-simplify]: Simplify 1 into 1 12.253 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.253 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 12.254 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 12.255 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 12.256 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 12.258 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 12.259 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 12.260 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 12.263 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.264 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) 12.264 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 12.264 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 12.264 * [taylor]: Taking taylor expansion of +nan.0 in n 12.264 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.264 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 12.264 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 12.264 * [taylor]: Taking taylor expansion of 1/2 in n 12.264 * [backup-simplify]: Simplify 1/2 into 1/2 12.264 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 12.264 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 12.264 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.264 * [taylor]: Taking taylor expansion of -2 in n 12.264 * [backup-simplify]: Simplify -2 into -2 12.265 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.265 * [taylor]: Taking taylor expansion of PI in n 12.265 * [backup-simplify]: Simplify PI into PI 12.265 * [taylor]: Taking taylor expansion of n in n 12.265 * [backup-simplify]: Simplify 0 into 0 12.265 * [backup-simplify]: Simplify 1 into 1 12.265 * [backup-simplify]: Simplify (/ PI 1) into PI 12.266 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.267 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.267 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 12.267 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.267 * [taylor]: Taking taylor expansion of k in n 12.267 * [backup-simplify]: Simplify k into k 12.267 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.267 * [taylor]: Taking taylor expansion of 1 in n 12.267 * [backup-simplify]: Simplify 1 into 1 12.268 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.268 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 12.269 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 12.270 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 12.271 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 12.272 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 12.272 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 12.273 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 12.274 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.274 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.274 * [backup-simplify]: Simplify (+ 0 0) into 0 12.275 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.275 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 12.276 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 12.277 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0 12.278 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0 12.279 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.280 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0 12.281 * [backup-simplify]: Simplify 0 into 0 12.281 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.284 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.285 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) 12.285 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 12.285 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 12.285 * [taylor]: Taking taylor expansion of +nan.0 in n 12.285 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.285 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 12.285 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 12.285 * [taylor]: Taking taylor expansion of 1/2 in n 12.285 * [backup-simplify]: Simplify 1/2 into 1/2 12.285 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 12.285 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 12.285 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.285 * [taylor]: Taking taylor expansion of -2 in n 12.285 * [backup-simplify]: Simplify -2 into -2 12.285 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.285 * [taylor]: Taking taylor expansion of PI in n 12.285 * [backup-simplify]: Simplify PI into PI 12.285 * [taylor]: Taking taylor expansion of n in n 12.285 * [backup-simplify]: Simplify 0 into 0 12.285 * [backup-simplify]: Simplify 1 into 1 12.285 * [backup-simplify]: Simplify (/ PI 1) into PI 12.286 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.286 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.286 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 12.286 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.286 * [taylor]: Taking taylor expansion of k in n 12.286 * [backup-simplify]: Simplify k into k 12.286 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.286 * [taylor]: Taking taylor expansion of 1 in n 12.286 * [backup-simplify]: Simplify 1 into 1 12.287 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.287 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 12.288 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 12.289 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 12.289 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 12.290 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 12.297 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 12.298 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 12.300 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 12.300 * * * [progress]: simplifying candidates 12.300 * * * * [progress]: [ 1 / 196 ] simplifiying candidate # 12.301 * * * * [progress]: [ 2 / 196 ] simplifiying candidate # 12.301 * * * * [progress]: [ 3 / 196 ] simplifiying candidate # 12.301 * * * * [progress]: [ 4 / 196 ] simplifiying candidate # 12.301 * * * * [progress]: [ 5 / 196 ] simplifiying candidate # 12.301 * * * * [progress]: [ 6 / 196 ] simplifiying candidate # 12.301 * * * * [progress]: [ 7 / 196 ] simplifiying candidate # 12.301 * * * * [progress]: [ 8 / 196 ] simplifiying candidate # 12.301 * * * * [progress]: [ 9 / 196 ] simplifiying candidate # 12.301 * * * * [progress]: [ 10 / 196 ] simplifiying candidate # 12.301 * * * * [progress]: [ 11 / 196 ] simplifiying candidate # 12.301 * * * * [progress]: [ 12 / 196 ] simplifiying candidate # 12.301 * * * * [progress]: [ 13 / 196 ] simplifiying candidate # 12.301 * * * * [progress]: [ 14 / 196 ] simplifiying candidate # 12.301 * * * * [progress]: [ 15 / 196 ] simplifiying candidate # 12.301 * * * * [progress]: [ 16 / 196 ] simplifiying candidate # 12.301 * * * * [progress]: [ 17 / 196 ] simplifiying candidate # 12.301 * * * * [progress]: [ 18 / 196 ] simplifiying candidate # 12.302 * * * * [progress]: [ 19 / 196 ] simplifiying candidate # 12.302 * * * * [progress]: [ 20 / 196 ] simplifiying candidate # 12.302 * * * * [progress]: [ 21 / 196 ] simplifiying candidate # 12.302 * * * * [progress]: [ 22 / 196 ] simplifiying candidate # 12.302 * * * * [progress]: [ 23 / 196 ] simplifiying candidate # 12.302 * * * * [progress]: [ 24 / 196 ] simplifiying candidate # 12.302 * * * * [progress]: [ 25 / 196 ] simplifiying candidate # 12.302 * * * * [progress]: [ 26 / 196 ] simplifiying candidate # 12.302 * * * * [progress]: [ 27 / 196 ] simplifiying candidate # 12.302 * * * * [progress]: [ 28 / 196 ] simplifiying candidate # 12.302 * * * * [progress]: [ 29 / 196 ] simplifiying candidate # 12.302 * * * * [progress]: [ 30 / 196 ] simplifiying candidate # 12.302 * * * * [progress]: [ 31 / 196 ] simplifiying candidate # 12.302 * * * * [progress]: [ 32 / 196 ] simplifiying candidate # 12.302 * * * * [progress]: [ 33 / 196 ] simplifiying candidate # 12.303 * * * * [progress]: [ 34 / 196 ] simplifiying candidate # 12.303 * * * * [progress]: [ 35 / 196 ] simplifiying candidate # 12.303 * * * * [progress]: [ 36 / 196 ] simplifiying candidate # 12.303 * * * * [progress]: [ 37 / 196 ] simplifiying candidate # 12.303 * * * * [progress]: [ 38 / 196 ] simplifiying candidate # 12.303 * * * * [progress]: [ 39 / 196 ] simplifiying candidate # 12.303 * * * * [progress]: [ 40 / 196 ] simplifiying candidate # 12.303 * * * * [progress]: [ 41 / 196 ] simplifiying candidate # 12.303 * * * * [progress]: [ 42 / 196 ] simplifiying candidate #real (real->posit16 (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))> 12.303 * * * * [progress]: [ 43 / 196 ] simplifiying candidate # 12.303 * * * * [progress]: [ 44 / 196 ] simplifiying candidate # 12.303 * * * * [progress]: [ 45 / 196 ] simplifiying candidate # 12.303 * * * * [progress]: [ 46 / 196 ] simplifiying candidate # 12.303 * * * * [progress]: [ 47 / 196 ] simplifiying candidate # 12.303 * * * * [progress]: [ 48 / 196 ] simplifiying candidate # 12.304 * * * * [progress]: [ 49 / 196 ] simplifiying candidate # 12.304 * * * * [progress]: [ 50 / 196 ] simplifiying candidate # 12.304 * * * * [progress]: [ 51 / 196 ] simplifiying candidate # 12.304 * * * * [progress]: [ 52 / 196 ] simplifiying candidate # 12.304 * * * * [progress]: [ 53 / 196 ] simplifiying candidate # 12.304 * * * * [progress]: [ 54 / 196 ] simplifiying candidate # 12.304 * * * * [progress]: [ 55 / 196 ] simplifiying candidate # 12.304 * * * * [progress]: [ 56 / 196 ] simplifiying candidate # 12.304 * * * * [progress]: [ 57 / 196 ] simplifiying candidate # 12.304 * * * * [progress]: [ 58 / 196 ] simplifiying candidate # 12.304 * * * * [progress]: [ 59 / 196 ] simplifiying candidate # 12.304 * * * * [progress]: [ 60 / 196 ] simplifiying candidate # 12.304 * * * * [progress]: [ 61 / 196 ] simplifiying candidate # 12.304 * * * * [progress]: [ 62 / 196 ] simplifiying candidate # 12.304 * * * * [progress]: [ 63 / 196 ] simplifiying candidate # 12.304 * * * * [progress]: [ 64 / 196 ] simplifiying candidate # 12.305 * * * * [progress]: [ 65 / 196 ] simplifiying candidate # 12.305 * * * * [progress]: [ 66 / 196 ] simplifiying candidate # 12.305 * * * * [progress]: [ 67 / 196 ] simplifiying candidate # 12.305 * * * * [progress]: [ 68 / 196 ] simplifiying candidate # 12.305 * * * * [progress]: [ 69 / 196 ] simplifiying candidate # 12.305 * * * * [progress]: [ 70 / 196 ] simplifiying candidate # 12.305 * * * * [progress]: [ 71 / 196 ] simplifiying candidate # 12.305 * * * * [progress]: [ 72 / 196 ] simplifiying candidate # 12.305 * * * * [progress]: [ 73 / 196 ] simplifiying candidate # 12.305 * * * * [progress]: [ 74 / 196 ] simplifiying candidate # 12.305 * * * * [progress]: [ 75 / 196 ] simplifiying candidate # 12.305 * * * * [progress]: [ 76 / 196 ] simplifiying candidate # 12.305 * * * * [progress]: [ 77 / 196 ] simplifiying candidate # 12.305 * * * * [progress]: [ 78 / 196 ] simplifiying candidate # 12.306 * * * * [progress]: [ 79 / 196 ] simplifiying candidate # 12.306 * * * * [progress]: [ 80 / 196 ] simplifiying candidate # 12.306 * * * * [progress]: [ 81 / 196 ] simplifiying candidate # 12.306 * * * * [progress]: [ 82 / 196 ] simplifiying candidate # 12.306 * * * * [progress]: [ 83 / 196 ] simplifiying candidate # 12.306 * * * * [progress]: [ 84 / 196 ] simplifiying candidate # 12.306 * * * * [progress]: [ 85 / 196 ] simplifiying candidate # 12.306 * * * * [progress]: [ 86 / 196 ] simplifiying candidate # 12.306 * * * * [progress]: [ 87 / 196 ] simplifiying candidate # 12.306 * * * * [progress]: [ 88 / 196 ] simplifiying candidate # 12.306 * * * * [progress]: [ 89 / 196 ] simplifiying candidate # 12.306 * * * * [progress]: [ 90 / 196 ] simplifiying candidate #real (real->posit16 (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> 12.306 * * * * [progress]: [ 91 / 196 ] simplifiying candidate # 12.306 * * * * [progress]: [ 92 / 196 ] simplifiying candidate # 12.306 * * * * [progress]: [ 93 / 196 ] simplifiying candidate # 12.306 * * * * [progress]: [ 94 / 196 ] simplifiying candidate # 12.307 * * * * [progress]: [ 95 / 196 ] simplifiying candidate # 12.307 * * * * [progress]: [ 96 / 196 ] simplifiying candidate # 12.307 * * * * [progress]: [ 97 / 196 ] simplifiying candidate # 12.307 * * * * [progress]: [ 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candidate # 12.308 * * * * [progress]: [ 113 / 196 ] simplifiying candidate # 12.308 * * * * [progress]: [ 114 / 196 ] simplifiying candidate # 12.308 * * * * [progress]: [ 115 / 196 ] simplifiying candidate # 12.308 * * * * [progress]: [ 116 / 196 ] simplifiying candidate # 12.308 * * * * [progress]: [ 117 / 196 ] simplifiying candidate # 12.308 * * * * [progress]: [ 118 / 196 ] simplifiying candidate # 12.308 * * * * [progress]: [ 119 / 196 ] simplifiying candidate # 12.308 * * * * [progress]: [ 120 / 196 ] simplifiying candidate # 12.308 * * * * [progress]: [ 121 / 196 ] simplifiying candidate # 12.308 * * * * [progress]: [ 122 / 196 ] simplifiying candidate # 12.308 * * * * [progress]: [ 123 / 196 ] simplifiying candidate # 12.308 * * * * [progress]: [ 124 / 196 ] simplifiying candidate # 12.308 * * * * [progress]: [ 125 / 196 ] simplifiying candidate # 12.308 * * * * [progress]: [ 126 / 196 ] simplifiying candidate # 12.309 * * * * [progress]: [ 127 / 196 ] simplifiying candidate 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[progress]: [ 187 / 196 ] simplifiying candidate # 12.313 * * * * [progress]: [ 188 / 196 ] simplifiying candidate # 12.313 * * * * [progress]: [ 189 / 196 ] simplifiying candidate # 12.313 * * * * [progress]: [ 190 / 196 ] simplifiying candidate # 12.313 * * * * [progress]: [ 191 / 196 ] simplifiying candidate # 12.313 * * * * [progress]: [ 192 / 196 ] simplifiying candidate # 12.313 * * * * [progress]: [ 193 / 196 ] simplifiying candidate # 12.313 * * * * [progress]: [ 194 / 196 ] simplifiying candidate # 12.313 * * * * [progress]: [ 195 / 196 ] simplifiying candidate # 12.313 * * * * [progress]: [ 196 / 196 ] simplifiying candidate # 12.317 * [simplify]: Simplifying: (expm1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (log1p (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) (* 1 (/ (- 1 k) 2)) (* 1 (/ (- 1 k) 2)) (* 1 (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)) (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1)) (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (sqrt 2))) (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) 1)) (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2 PI) n) (/ 1 (sqrt 2))) (pow (* (* 2 PI) n) (/ 1 1)) (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2))) (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) 1)) (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (sqrt 2))) (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) 1)) (pow (* (* 2 PI) n) (/ 1 (* 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(/ (/ (- 1 k) 2) 2))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) 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(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 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (- (+ (* +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 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 12.324 * * [simplify]: iteration 0: 353 enodes 12.522 * * [simplify]: iteration 1: 953 enodes 12.816 * * [simplify]: iteration 2: 2008 enodes 13.249 * * [simplify]: iteration complete: 2008 enodes 13.250 * * [simplify]: Extracting #0: cost 104 inf + 0 13.251 * * [simplify]: Extracting #1: cost 342 inf + 3 13.255 * * [simplify]: Extracting #2: cost 595 inf + 6426 13.274 * * [simplify]: Extracting #3: cost 498 inf + 44851 13.303 * * [simplify]: Extracting #4: cost 327 inf + 117446 13.339 * * [simplify]: Extracting #5: cost 105 inf + 204125 13.411 * * [simplify]: Extracting #6: cost 39 inf + 236512 13.485 * * [simplify]: Extracting #7: cost 14 inf + 246398 13.561 * * [simplify]: Extracting #8: cost 0 inf + 255087 13.637 * * [simplify]: Extracting #9: cost 0 inf + 253447 13.719 * [simplify]: Simplified to: (expm1 (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (log1p (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (* (/ (- 1 k) 2) (log (* (* 2 n) PI))) (* (/ (- 1 k) 2) (log (* (* 2 n) PI))) (* (/ (- 1 k) 2) (log (* (* 2 n) PI))) (* (/ (- 1 k) 2) (log (* (* 2 n) PI))) (/ (- 1 k) 2) (/ (- 1 k) 2) (/ (- 1 k) 2) (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)) (pow (* (* 2 n) PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (pow (* (* 2 n) PI) (sqrt (/ (- 1 k) 2))) (pow (* (* 2 n) PI) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2)))) (pow (* (* 2 n) PI) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (pow (* (* 2 n) PI) (* (cbrt (- 1 k)) (cbrt (- 1 k)))) (pow (* (* 2 n) PI) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2 n) PI) (/ (sqrt (- 1 k)) (sqrt 2))) (pow (* (* 2 n) PI) (sqrt (- 1 k))) (pow (* (* 2 n) PI) (/ (/ 1 (cbrt 2)) (cbrt 2))) (pow (* (* 2 n) PI) (/ 1 (sqrt 2))) (* (* 2 n) PI) (pow (* (* 2 n) PI) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2 n) PI) (/ (+ 1 (sqrt k)) (sqrt 2))) (pow (* (* 2 n) PI) (+ 1 (sqrt k))) (pow (* (* 2 n) PI) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2 n) PI) (/ (+ 1 (sqrt k)) (sqrt 2))) (pow (* (* 2 n) PI) (+ 1 (sqrt k))) (pow (* (* 2 n) PI) (/ (/ 1 (cbrt 2)) (cbrt 2))) (pow (* (* 2 n) PI) (/ 1 (sqrt 2))) (* (* 2 n) PI) (* (* 2 n) PI) (pow (* (* 2 n) PI) (- 1 k)) (pow (* PI 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)) (* (/ (- 1 k) 2) (log (* (* 2 n) PI))) (exp (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (* (cbrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 n) PI) (/ (- 1 k) 2)))) (cbrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (pow (pow (* (* 2 n) PI) (/ (- 1 k) 2)) 3) (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (pow (* (* 2 n) PI) (/ (- 1 k) 4)) (pow (* (* 2 n) PI) (/ (- 1 k) 4)) (real->posit16 (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (expm1 (/ 1 (sqrt k))) (log1p (/ 1 (sqrt k))) -1/2 -1 -1/2 (- (log (sqrt k))) (- (log (sqrt k))) (- (log (sqrt k))) (- (log (sqrt k))) (exp (/ 1 (sqrt k))) (/ (/ 1 k) (sqrt k)) (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (cbrt (/ 1 (sqrt k))) (* (/ (/ 1 (sqrt k)) (sqrt k)) (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k))) -1 (- (sqrt k)) (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) 1 (/ 1 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) 1 (/ 1 (sqrt k)) (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) 1 (/ 1 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) 1 (/ 1 (sqrt k)) (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) 1 (/ 1 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) 1 (/ 1 (sqrt k)) (/ 1 (sqrt k)) (sqrt k) (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1 (sqrt (sqrt k))) 1 (/ 1 (sqrt (sqrt k))) 1 (sqrt k) (sqrt k) (sqrt k) (real->posit16 (/ 1 (sqrt k))) (expm1 (* (* 2 n) PI)) (log1p (* (* 2 n) PI)) (* (* 2 n) PI) (* (* 2 n) PI) (log (* (* 2 n) PI)) (log (* (* 2 n) PI)) (log (* (* 2 n) PI)) (exp (* (* 2 n) PI)) (* (* (* 8 (* PI PI)) PI) (* (* n n) n)) (* (* (* PI 2) (* PI 2)) (* (* PI 2) (* (* n n) n))) (* (cbrt (* (* 2 n) PI)) (cbrt (* (* 2 n) PI))) (cbrt (* (* 2 n) PI)) (* (* (* (* 2 n) PI) (* (* 2 n) PI)) (* (* 2 n) PI)) (sqrt (* (* 2 n) PI)) (sqrt (* (* 2 n) PI)) (* 2 (* PI (* (cbrt n) (cbrt n)))) (* (* PI 2) (sqrt n)) (* PI 2) (* n PI) (real->posit16 (* (* 2 n) PI)) (expm1 (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt k))) (log1p (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt k))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (- (log (sqrt k)))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (- (log (sqrt k)))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (- (log (sqrt k)))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (- (log (sqrt k)))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (- (log (sqrt k)))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (- (log (sqrt k)))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (- (log (sqrt k)))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (- (log (sqrt k)))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (- (log (sqrt k)))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (- (log (sqrt k)))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (- (log (sqrt k)))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (- (log (sqrt k)))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (- (log (sqrt k)))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (- (log (sqrt k)))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (- (log (sqrt k)))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (- (log (sqrt k)))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (- (log (sqrt k)))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (- (log (sqrt k)))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (- (log (sqrt k)))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (- (log (sqrt k)))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (- (log (sqrt k)))) (exp (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (pow (* (* 2 n) PI) (/ (- 1 k) 2)) 3) (* (sqrt k) k)) (* (pow (pow (* (* 2 n) PI) (/ (- 1 k) 2)) 3) (* (/ (/ 1 (sqrt k)) (sqrt k)) (/ 1 (sqrt k)))) (* (cbrt (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt k))) (pow (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt k)) 3) (sqrt (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt k))) (sqrt (* (* 2 n) PI)) (* (pow (* (* 2 n) PI) (/ k 2)) (sqrt k)) (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2)))) (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2)))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 n) PI) (/ (- 1 k) 4))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 n) PI) (/ (- 1 k) 4))) (/ (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (/ (* (cbrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 n) PI) (/ (- 1 k) 2)))) (sqrt k)) (/ (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (sqrt k)) (/ 1 (sqrt k)) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 4)) (sqrt k)) (* (cbrt (/ 1 (sqrt k))) (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (cbrt (sqrt k))) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt (cbrt k))) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (cbrt (sqrt k))) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt (cbrt k))) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (cbrt (sqrt k))) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt (cbrt k))) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt k)) (/ (sqrt (* (* 2 n) PI)) (sqrt k)) (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (real->posit16 (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt k))) (fma (* 1/4 (log (* PI 2))) (* (* (exp (* 1/2 (log (* (* 2 n) PI)))) (log n)) (* k k)) (- (fma (* 1/8 (exp (* 1/2 (log (* (* 2 n) PI))))) (* (* (* k k) (log n)) (log n)) (fma (* 1/8 (* (log (* PI 2)) (log (* PI 2)))) (* (exp (* 1/2 (log (* (* 2 n) PI)))) (* k k)) (exp (* 1/2 (log (* (* 2 n) PI)))))) (* 1/2 (* k (+ (* (exp (* 1/2 (log (* (* 2 n) PI)))) (log n)) (* (log (* PI 2)) (exp (* 1/2 (log (* (* 2 n) PI)))))))))) (exp (* 1/2 (* (log (* (* 2 n) PI)) (- 1 k)))) (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n))))) (- (+ (- (* +nan.0 (* k k)) +nan.0) (* +nan.0 k))) (+ (/ (- +nan.0) (* k k)) (- (/ +nan.0 k) (/ +nan.0 (* (* k k) k)))) (+ (/ (- +nan.0) (* k k)) (- (/ +nan.0 k) +nan.0)) (* (* 2 n) PI) (* (* 2 n) PI) (* (* 2 n) PI) (+ (- (* (* (* (* n PI) k) (sqrt 2)) +nan.0)) (+ (- (* (* +nan.0 (sqrt 2)) (* n PI)) (* (* (* (* (* n PI) k) (sqrt 2)) (log (* PI 2))) +nan.0)) (* (* +nan.0 (sqrt 2)) (- (* (* n PI) (* (log n) k)) (* (* n PI) (* n PI)))))) (+ (* (- (/ (exp (* 1/2 (* (log (* (* 2 n) PI)) (- 1 k)))) k)) +nan.0) (- (* +nan.0 (/ (exp (* 1/2 (* (log (* (* 2 n) PI)) (- 1 k)))) (* k k))) (* (/ +nan.0 (* k k)) (/ (exp (* 1/2 (* (log (* (* 2 n) PI)) (- 1 k)))) k)))) (- (- (/ (* (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n))))) +nan.0) k) (- (/ (* (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n))))) +nan.0) (* k k)) (* (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n))))) +nan.0)))) 13.740 * * * [progress]: adding candidates to table 15.891 * * [progress]: iteration 3 / 4 15.891 * * * [progress]: picking best candidate 15.939 * * * * [pick]: Picked # 15.939 * * * [progress]: localizing error 15.981 * * * [progress]: generating rewritten candidates 15.981 * * * * [progress]: [ 1 / 3 ] rewriting at (2 2) 15.997 * * * * [progress]: [ 2 / 3 ] rewriting at (2 2 1) 16.022 * * * * [progress]: [ 3 / 3 ] rewriting at (2) 16.047 * * * [progress]: generating series expansions 16.047 * * * * [progress]: [ 1 / 3 ] generating series at (2 2) 16.048 * [backup-simplify]: Simplify (pow (* (* 2 PI) n) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) 16.048 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0 16.048 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 16.048 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 16.048 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 16.048 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k 16.048 * [taylor]: Taking taylor expansion of 1/2 in k 16.048 * [backup-simplify]: Simplify 1/2 into 1/2 16.048 * [taylor]: Taking taylor expansion of (- 1 k) in k 16.048 * [taylor]: Taking taylor expansion of 1 in k 16.048 * [backup-simplify]: Simplify 1 into 1 16.048 * [taylor]: Taking taylor expansion of k in k 16.048 * [backup-simplify]: Simplify 0 into 0 16.048 * [backup-simplify]: Simplify 1 into 1 16.048 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 16.048 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 16.048 * [taylor]: Taking taylor expansion of 2 in k 16.048 * [backup-simplify]: Simplify 2 into 2 16.048 * [taylor]: Taking taylor expansion of (* n PI) in k 16.048 * [taylor]: Taking taylor expansion of n in k 16.049 * [backup-simplify]: Simplify n into n 16.049 * [taylor]: Taking taylor expansion of PI in k 16.049 * [backup-simplify]: Simplify PI into PI 16.049 * [backup-simplify]: Simplify (* n PI) into (* n PI) 16.049 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 16.049 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 16.049 * [backup-simplify]: Simplify (- 0) into 0 16.049 * [backup-simplify]: Simplify (+ 1 0) into 1 16.049 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 16.050 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 16.050 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 16.050 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 16.050 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 16.050 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 16.050 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n 16.050 * [taylor]: Taking taylor expansion of 1/2 in n 16.050 * [backup-simplify]: Simplify 1/2 into 1/2 16.050 * [taylor]: Taking taylor expansion of (- 1 k) in n 16.050 * [taylor]: Taking taylor expansion of 1 in n 16.050 * [backup-simplify]: Simplify 1 into 1 16.050 * [taylor]: Taking taylor expansion of k in n 16.050 * [backup-simplify]: Simplify k into k 16.050 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 16.050 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 16.050 * [taylor]: Taking taylor expansion of 2 in n 16.050 * [backup-simplify]: Simplify 2 into 2 16.050 * [taylor]: Taking taylor expansion of (* n PI) in n 16.050 * [taylor]: Taking taylor expansion of n in n 16.050 * [backup-simplify]: Simplify 0 into 0 16.050 * [backup-simplify]: Simplify 1 into 1 16.050 * [taylor]: Taking taylor expansion of PI in n 16.050 * [backup-simplify]: Simplify PI into PI 16.050 * [backup-simplify]: Simplify (* 0 PI) into 0 16.051 * [backup-simplify]: Simplify (* 2 0) into 0 16.052 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.052 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 16.053 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 16.053 * [backup-simplify]: Simplify (- k) into (- k) 16.053 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k) 16.053 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 16.054 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 16.055 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 16.055 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 16.055 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 16.056 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 16.056 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 16.056 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n 16.056 * [taylor]: Taking taylor expansion of 1/2 in n 16.056 * [backup-simplify]: Simplify 1/2 into 1/2 16.056 * [taylor]: Taking taylor expansion of (- 1 k) in n 16.056 * [taylor]: Taking taylor expansion of 1 in n 16.056 * [backup-simplify]: Simplify 1 into 1 16.056 * [taylor]: Taking taylor expansion of k in n 16.056 * [backup-simplify]: Simplify k into k 16.056 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 16.056 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 16.056 * [taylor]: Taking taylor expansion of 2 in n 16.056 * [backup-simplify]: Simplify 2 into 2 16.056 * [taylor]: Taking taylor expansion of (* n PI) in n 16.056 * [taylor]: Taking taylor expansion of n in n 16.056 * [backup-simplify]: Simplify 0 into 0 16.056 * [backup-simplify]: Simplify 1 into 1 16.056 * [taylor]: Taking taylor expansion of PI in n 16.056 * [backup-simplify]: Simplify PI into PI 16.056 * [backup-simplify]: Simplify (* 0 PI) into 0 16.056 * [backup-simplify]: Simplify (* 2 0) into 0 16.057 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.058 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 16.059 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 16.059 * [backup-simplify]: Simplify (- k) into (- k) 16.059 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k) 16.059 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 16.060 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 16.061 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 16.061 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 16.061 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k 16.061 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k 16.061 * [taylor]: Taking taylor expansion of 1/2 in k 16.061 * [backup-simplify]: Simplify 1/2 into 1/2 16.061 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k 16.061 * [taylor]: Taking taylor expansion of (- 1 k) in k 16.061 * [taylor]: Taking taylor expansion of 1 in k 16.061 * [backup-simplify]: Simplify 1 into 1 16.061 * [taylor]: Taking taylor expansion of k in k 16.061 * [backup-simplify]: Simplify 0 into 0 16.061 * [backup-simplify]: Simplify 1 into 1 16.061 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 16.062 * [taylor]: Taking taylor expansion of (log n) in k 16.062 * [taylor]: Taking taylor expansion of n in k 16.062 * [backup-simplify]: Simplify n into n 16.062 * [backup-simplify]: Simplify (log n) into (log n) 16.062 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 16.062 * [taylor]: Taking taylor expansion of (* 2 PI) in k 16.062 * [taylor]: Taking taylor expansion of 2 in k 16.062 * [backup-simplify]: Simplify 2 into 2 16.062 * [taylor]: Taking taylor expansion of PI in k 16.062 * [backup-simplify]: Simplify PI into PI 16.062 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 16.063 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 16.063 * [backup-simplify]: Simplify (- 0) into 0 16.063 * [backup-simplify]: Simplify (+ 1 0) into 1 16.064 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 16.064 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI))) 16.065 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 16.066 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 16.066 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 16.067 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 16.068 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 16.069 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 16.069 * [backup-simplify]: Simplify (- 0) into 0 16.069 * [backup-simplify]: Simplify (+ 0 0) into 0 16.070 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0 16.071 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 16.072 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 16.074 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0 16.074 * [taylor]: Taking taylor expansion of 0 in k 16.074 * [backup-simplify]: Simplify 0 into 0 16.074 * [backup-simplify]: Simplify 0 into 0 16.075 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 16.076 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 16.078 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 16.078 * [backup-simplify]: Simplify (+ 0 0) into 0 16.078 * [backup-simplify]: Simplify (- 1) into -1 16.079 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.080 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n))) 16.082 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 16.085 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 16.088 * [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))))))) 16.089 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 16.090 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 16.093 * [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 16.093 * [backup-simplify]: Simplify (- 0) into 0 16.094 * [backup-simplify]: Simplify (+ 0 0) into 0 16.094 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0 16.096 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 16.097 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 16.099 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 16.099 * [taylor]: Taking taylor expansion of 0 in k 16.099 * [backup-simplify]: Simplify 0 into 0 16.099 * [backup-simplify]: Simplify 0 into 0 16.099 * [backup-simplify]: Simplify 0 into 0 16.101 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 16.104 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 16.107 * [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 16.108 * [backup-simplify]: Simplify (+ 0 0) into 0 16.108 * [backup-simplify]: Simplify (- 0) into 0 16.109 * [backup-simplify]: Simplify (+ 0 0) into 0 16.111 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 16.113 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 16.117 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 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))))) 16.122 * [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))))) 16.131 * [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))))) 16.131 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) 16.131 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0 16.131 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 16.131 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 16.131 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 16.131 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 16.131 * [taylor]: Taking taylor expansion of 1/2 in k 16.131 * [backup-simplify]: Simplify 1/2 into 1/2 16.131 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 16.131 * [taylor]: Taking taylor expansion of 1 in k 16.131 * [backup-simplify]: Simplify 1 into 1 16.131 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.131 * [taylor]: Taking taylor expansion of k in k 16.131 * [backup-simplify]: Simplify 0 into 0 16.132 * [backup-simplify]: Simplify 1 into 1 16.132 * [backup-simplify]: Simplify (/ 1 1) into 1 16.132 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 16.132 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 16.132 * [taylor]: Taking taylor expansion of 2 in k 16.132 * [backup-simplify]: Simplify 2 into 2 16.132 * [taylor]: Taking taylor expansion of (/ PI n) in k 16.132 * [taylor]: Taking taylor expansion of PI in k 16.132 * [backup-simplify]: Simplify PI into PI 16.132 * [taylor]: Taking taylor expansion of n in k 16.132 * [backup-simplify]: Simplify n into n 16.132 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 16.132 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 16.132 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 16.132 * [backup-simplify]: Simplify (- 1) into -1 16.133 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.133 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2 16.133 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 16.133 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 16.133 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 16.133 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 16.133 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 16.133 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 16.133 * [taylor]: Taking taylor expansion of 1/2 in n 16.133 * [backup-simplify]: Simplify 1/2 into 1/2 16.133 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 16.133 * [taylor]: Taking taylor expansion of 1 in n 16.133 * [backup-simplify]: Simplify 1 into 1 16.133 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.133 * [taylor]: Taking taylor expansion of k in n 16.133 * [backup-simplify]: Simplify k into k 16.133 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.133 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 16.133 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 16.133 * [taylor]: Taking taylor expansion of 2 in n 16.133 * [backup-simplify]: Simplify 2 into 2 16.133 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.133 * [taylor]: Taking taylor expansion of PI in n 16.133 * [backup-simplify]: Simplify PI into PI 16.133 * [taylor]: Taking taylor expansion of n in n 16.133 * [backup-simplify]: Simplify 0 into 0 16.133 * [backup-simplify]: Simplify 1 into 1 16.134 * [backup-simplify]: Simplify (/ PI 1) into PI 16.134 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 16.135 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 16.135 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 16.135 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 16.135 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 16.136 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 16.136 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 16.137 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 16.137 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 16.137 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 16.137 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 16.137 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 16.137 * [taylor]: Taking taylor expansion of 1/2 in n 16.137 * [backup-simplify]: Simplify 1/2 into 1/2 16.137 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 16.137 * [taylor]: Taking taylor expansion of 1 in n 16.137 * [backup-simplify]: Simplify 1 into 1 16.137 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.137 * [taylor]: Taking taylor expansion of k in n 16.137 * [backup-simplify]: Simplify k into k 16.137 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.137 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 16.137 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 16.137 * [taylor]: Taking taylor expansion of 2 in n 16.137 * [backup-simplify]: Simplify 2 into 2 16.137 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.137 * [taylor]: Taking taylor expansion of PI in n 16.138 * [backup-simplify]: Simplify PI into PI 16.138 * [taylor]: Taking taylor expansion of n in n 16.138 * [backup-simplify]: Simplify 0 into 0 16.138 * [backup-simplify]: Simplify 1 into 1 16.138 * [backup-simplify]: Simplify (/ PI 1) into PI 16.138 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 16.139 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 16.139 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 16.139 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 16.139 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 16.140 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 16.141 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 16.141 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 16.141 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k 16.141 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k 16.141 * [taylor]: Taking taylor expansion of 1/2 in k 16.141 * [backup-simplify]: Simplify 1/2 into 1/2 16.141 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k 16.141 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 16.141 * [taylor]: Taking taylor expansion of 1 in k 16.142 * [backup-simplify]: Simplify 1 into 1 16.142 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.142 * [taylor]: Taking taylor expansion of k in k 16.142 * [backup-simplify]: Simplify 0 into 0 16.142 * [backup-simplify]: Simplify 1 into 1 16.142 * [backup-simplify]: Simplify (/ 1 1) into 1 16.142 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 16.142 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 16.142 * [taylor]: Taking taylor expansion of (* 2 PI) in k 16.142 * [taylor]: Taking taylor expansion of 2 in k 16.142 * [backup-simplify]: Simplify 2 into 2 16.142 * [taylor]: Taking taylor expansion of PI in k 16.142 * [backup-simplify]: Simplify PI into PI 16.142 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 16.143 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 16.143 * [taylor]: Taking taylor expansion of (log n) in k 16.143 * [taylor]: Taking taylor expansion of n in k 16.143 * [backup-simplify]: Simplify n into n 16.143 * [backup-simplify]: Simplify (log n) into (log n) 16.143 * [backup-simplify]: Simplify (- 1) into -1 16.144 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.144 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 16.144 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 16.145 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) 16.151 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) 16.152 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 16.153 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 16.153 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 16.154 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 16.155 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 16.155 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 16.155 * [backup-simplify]: Simplify (- 0) into 0 16.156 * [backup-simplify]: Simplify (+ 0 0) into 0 16.156 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0 16.157 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 16.158 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 16.159 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 16.159 * [taylor]: Taking taylor expansion of 0 in k 16.159 * [backup-simplify]: Simplify 0 into 0 16.159 * [backup-simplify]: Simplify 0 into 0 16.159 * [backup-simplify]: Simplify 0 into 0 16.160 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.160 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 16.163 * [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 16.163 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.163 * [backup-simplify]: Simplify (- 0) into 0 16.164 * [backup-simplify]: Simplify (+ 0 0) into 0 16.165 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0 16.166 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 16.168 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 16.170 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 16.170 * [taylor]: Taking taylor expansion of 0 in k 16.170 * [backup-simplify]: Simplify 0 into 0 16.170 * [backup-simplify]: Simplify 0 into 0 16.170 * [backup-simplify]: Simplify 0 into 0 16.170 * [backup-simplify]: Simplify 0 into 0 16.172 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.173 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 16.179 * [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 16.179 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.179 * [backup-simplify]: Simplify (- 0) into 0 16.180 * [backup-simplify]: Simplify (+ 0 0) into 0 16.181 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0 16.183 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 16.185 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 16.187 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 16.187 * [taylor]: Taking taylor expansion of 0 in k 16.187 * [backup-simplify]: Simplify 0 into 0 16.188 * [backup-simplify]: Simplify 0 into 0 16.189 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) 16.190 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) 16.190 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0 16.190 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 16.190 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 16.190 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 16.190 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 16.190 * [taylor]: Taking taylor expansion of 1/2 in k 16.190 * [backup-simplify]: Simplify 1/2 into 1/2 16.190 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 16.190 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.190 * [taylor]: Taking taylor expansion of k in k 16.190 * [backup-simplify]: Simplify 0 into 0 16.190 * [backup-simplify]: Simplify 1 into 1 16.190 * [backup-simplify]: Simplify (/ 1 1) into 1 16.190 * [taylor]: Taking taylor expansion of 1 in k 16.190 * [backup-simplify]: Simplify 1 into 1 16.190 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 16.190 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 16.190 * [taylor]: Taking taylor expansion of -2 in k 16.191 * [backup-simplify]: Simplify -2 into -2 16.191 * [taylor]: Taking taylor expansion of (/ PI n) in k 16.191 * [taylor]: Taking taylor expansion of PI in k 16.191 * [backup-simplify]: Simplify PI into PI 16.191 * [taylor]: Taking taylor expansion of n in k 16.191 * [backup-simplify]: Simplify n into n 16.191 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 16.191 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 16.191 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 16.191 * [backup-simplify]: Simplify (+ 1 0) into 1 16.192 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 16.192 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 16.192 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 16.192 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 16.192 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 16.192 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 16.192 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 16.192 * [taylor]: Taking taylor expansion of 1/2 in n 16.192 * [backup-simplify]: Simplify 1/2 into 1/2 16.192 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 16.192 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.192 * [taylor]: Taking taylor expansion of k in n 16.192 * [backup-simplify]: Simplify k into k 16.192 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.193 * [taylor]: Taking taylor expansion of 1 in n 16.193 * [backup-simplify]: Simplify 1 into 1 16.193 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 16.193 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 16.193 * [taylor]: Taking taylor expansion of -2 in n 16.193 * [backup-simplify]: Simplify -2 into -2 16.193 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.193 * [taylor]: Taking taylor expansion of PI in n 16.193 * [backup-simplify]: Simplify PI into PI 16.193 * [taylor]: Taking taylor expansion of n in n 16.193 * [backup-simplify]: Simplify 0 into 0 16.193 * [backup-simplify]: Simplify 1 into 1 16.193 * [backup-simplify]: Simplify (/ PI 1) into PI 16.194 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 16.195 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 16.195 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 16.195 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 16.197 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 16.198 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 16.199 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 16.199 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 16.199 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 16.199 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 16.199 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 16.199 * [taylor]: Taking taylor expansion of 1/2 in n 16.199 * [backup-simplify]: Simplify 1/2 into 1/2 16.200 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 16.200 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.200 * [taylor]: Taking taylor expansion of k in n 16.200 * [backup-simplify]: Simplify k into k 16.200 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.200 * [taylor]: Taking taylor expansion of 1 in n 16.200 * [backup-simplify]: Simplify 1 into 1 16.200 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 16.200 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 16.200 * [taylor]: Taking taylor expansion of -2 in n 16.200 * [backup-simplify]: Simplify -2 into -2 16.200 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.200 * [taylor]: Taking taylor expansion of PI in n 16.200 * [backup-simplify]: Simplify PI into PI 16.200 * [taylor]: Taking taylor expansion of n in n 16.200 * [backup-simplify]: Simplify 0 into 0 16.200 * [backup-simplify]: Simplify 1 into 1 16.201 * [backup-simplify]: Simplify (/ PI 1) into PI 16.201 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 16.202 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 16.203 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 16.203 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 16.204 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 16.206 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 16.207 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 16.207 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k 16.207 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k 16.207 * [taylor]: Taking taylor expansion of 1/2 in k 16.207 * [backup-simplify]: Simplify 1/2 into 1/2 16.207 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k 16.207 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 16.207 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.207 * [taylor]: Taking taylor expansion of k in k 16.207 * [backup-simplify]: Simplify 0 into 0 16.207 * [backup-simplify]: Simplify 1 into 1 16.208 * [backup-simplify]: Simplify (/ 1 1) into 1 16.208 * [taylor]: Taking taylor expansion of 1 in k 16.208 * [backup-simplify]: Simplify 1 into 1 16.208 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 16.208 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 16.208 * [taylor]: Taking taylor expansion of (* -2 PI) in k 16.208 * [taylor]: Taking taylor expansion of -2 in k 16.208 * [backup-simplify]: Simplify -2 into -2 16.208 * [taylor]: Taking taylor expansion of PI in k 16.208 * [backup-simplify]: Simplify PI into PI 16.209 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 16.210 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 16.210 * [taylor]: Taking taylor expansion of (log n) in k 16.210 * [taylor]: Taking taylor expansion of n in k 16.210 * [backup-simplify]: Simplify n into n 16.210 * [backup-simplify]: Simplify (log n) into (log n) 16.211 * [backup-simplify]: Simplify (+ 1 0) into 1 16.211 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 16.212 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 16.213 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) 16.214 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 16.215 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 16.217 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 16.218 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 16.219 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 16.221 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 16.221 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 16.221 * [backup-simplify]: Simplify (+ 0 0) into 0 16.222 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0 16.223 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 16.224 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 16.226 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 16.226 * [taylor]: Taking taylor expansion of 0 in k 16.227 * [backup-simplify]: Simplify 0 into 0 16.227 * [backup-simplify]: Simplify 0 into 0 16.227 * [backup-simplify]: Simplify 0 into 0 16.228 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.229 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 16.232 * [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 16.233 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.233 * [backup-simplify]: Simplify (+ 0 0) into 0 16.234 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0 16.236 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 16.238 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 16.240 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 16.240 * [taylor]: Taking taylor expansion of 0 in k 16.240 * [backup-simplify]: Simplify 0 into 0 16.240 * [backup-simplify]: Simplify 0 into 0 16.240 * [backup-simplify]: Simplify 0 into 0 16.240 * [backup-simplify]: Simplify 0 into 0 16.242 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.243 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 16.249 * [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 16.250 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.250 * [backup-simplify]: Simplify (+ 0 0) into 0 16.251 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0 16.252 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 16.253 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 16.255 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 16.255 * [taylor]: Taking taylor expansion of 0 in k 16.255 * [backup-simplify]: Simplify 0 into 0 16.255 * [backup-simplify]: Simplify 0 into 0 16.256 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) 16.256 * * * * [progress]: [ 2 / 3 ] generating series at (2 2 1) 16.256 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 16.256 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 16.256 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 16.256 * [taylor]: Taking taylor expansion of 2 in n 16.256 * [backup-simplify]: Simplify 2 into 2 16.256 * [taylor]: Taking taylor expansion of (* n PI) in n 16.256 * [taylor]: Taking taylor expansion of n in n 16.256 * [backup-simplify]: Simplify 0 into 0 16.256 * [backup-simplify]: Simplify 1 into 1 16.256 * [taylor]: Taking taylor expansion of PI in n 16.256 * [backup-simplify]: Simplify PI into PI 16.257 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 16.257 * [taylor]: Taking taylor expansion of 2 in n 16.257 * [backup-simplify]: Simplify 2 into 2 16.257 * [taylor]: Taking taylor expansion of (* n PI) in n 16.257 * [taylor]: Taking taylor expansion of n in n 16.257 * [backup-simplify]: Simplify 0 into 0 16.257 * [backup-simplify]: Simplify 1 into 1 16.257 * [taylor]: Taking taylor expansion of PI in n 16.257 * [backup-simplify]: Simplify PI into PI 16.257 * [backup-simplify]: Simplify (* 0 PI) into 0 16.257 * [backup-simplify]: Simplify (* 2 0) into 0 16.257 * [backup-simplify]: Simplify 0 into 0 16.258 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.259 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 16.259 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 16.260 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 16.261 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 16.261 * [backup-simplify]: Simplify 0 into 0 16.261 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 16.262 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 16.262 * [backup-simplify]: Simplify 0 into 0 16.263 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 16.264 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 16.264 * [backup-simplify]: Simplify 0 into 0 16.265 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 16.265 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 16.265 * [backup-simplify]: Simplify 0 into 0 16.266 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 16.267 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 16.267 * [backup-simplify]: Simplify 0 into 0 16.269 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 16.270 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 16.270 * [backup-simplify]: Simplify 0 into 0 16.270 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 16.271 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n)) 16.271 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 16.271 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 16.271 * [taylor]: Taking taylor expansion of 2 in n 16.271 * [backup-simplify]: Simplify 2 into 2 16.271 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.271 * [taylor]: Taking taylor expansion of PI in n 16.271 * [backup-simplify]: Simplify PI into PI 16.271 * [taylor]: Taking taylor expansion of n in n 16.271 * [backup-simplify]: Simplify 0 into 0 16.271 * [backup-simplify]: Simplify 1 into 1 16.271 * [backup-simplify]: Simplify (/ PI 1) into PI 16.271 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 16.271 * [taylor]: Taking taylor expansion of 2 in n 16.271 * [backup-simplify]: Simplify 2 into 2 16.271 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.271 * [taylor]: Taking taylor expansion of PI in n 16.271 * [backup-simplify]: Simplify PI into PI 16.271 * [taylor]: Taking taylor expansion of n in n 16.271 * [backup-simplify]: Simplify 0 into 0 16.271 * [backup-simplify]: Simplify 1 into 1 16.271 * [backup-simplify]: Simplify (/ PI 1) into PI 16.272 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 16.272 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 16.273 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 16.273 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 16.273 * [backup-simplify]: Simplify 0 into 0 16.274 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.274 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 16.274 * [backup-simplify]: Simplify 0 into 0 16.275 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.632 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 16.632 * [backup-simplify]: Simplify 0 into 0 16.634 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.635 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 16.635 * [backup-simplify]: Simplify 0 into 0 16.636 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.637 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 16.637 * [backup-simplify]: Simplify 0 into 0 16.638 * [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 16.639 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 16.639 * [backup-simplify]: Simplify 0 into 0 16.639 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 16.640 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (- n))) into (* -2 (/ PI n)) 16.640 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 16.640 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 16.640 * [taylor]: Taking taylor expansion of -2 in n 16.640 * [backup-simplify]: Simplify -2 into -2 16.640 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.640 * [taylor]: Taking taylor expansion of PI in n 16.640 * [backup-simplify]: Simplify PI into PI 16.640 * [taylor]: Taking taylor expansion of n in n 16.640 * [backup-simplify]: Simplify 0 into 0 16.640 * [backup-simplify]: Simplify 1 into 1 16.640 * [backup-simplify]: Simplify (/ PI 1) into PI 16.640 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 16.640 * [taylor]: Taking taylor expansion of -2 in n 16.640 * [backup-simplify]: Simplify -2 into -2 16.640 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.640 * [taylor]: Taking taylor expansion of PI in n 16.640 * [backup-simplify]: Simplify PI into PI 16.640 * [taylor]: Taking taylor expansion of n in n 16.640 * [backup-simplify]: Simplify 0 into 0 16.641 * [backup-simplify]: Simplify 1 into 1 16.641 * [backup-simplify]: Simplify (/ PI 1) into PI 16.641 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 16.642 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 16.643 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 16.643 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 16.643 * [backup-simplify]: Simplify 0 into 0 16.644 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.645 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 16.645 * [backup-simplify]: Simplify 0 into 0 16.645 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.646 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 16.646 * [backup-simplify]: Simplify 0 into 0 16.647 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.648 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 16.648 * [backup-simplify]: Simplify 0 into 0 16.648 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.649 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 16.649 * [backup-simplify]: Simplify 0 into 0 16.650 * [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 16.651 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 16.651 * [backup-simplify]: Simplify 0 into 0 16.651 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 16.651 * * * * [progress]: [ 3 / 3 ] generating series at (2) 16.652 * [backup-simplify]: Simplify (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) 16.652 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k n) around 0 16.652 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n 16.652 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 16.652 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 16.652 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 16.652 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n 16.652 * [taylor]: Taking taylor expansion of 1/2 in n 16.652 * [backup-simplify]: Simplify 1/2 into 1/2 16.652 * [taylor]: Taking taylor expansion of (- 1 k) in n 16.652 * [taylor]: Taking taylor expansion of 1 in n 16.652 * [backup-simplify]: Simplify 1 into 1 16.652 * [taylor]: Taking taylor expansion of k in n 16.652 * [backup-simplify]: Simplify k into k 16.652 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 16.652 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 16.652 * [taylor]: Taking taylor expansion of 2 in n 16.652 * [backup-simplify]: Simplify 2 into 2 16.652 * [taylor]: Taking taylor expansion of (* n PI) in n 16.652 * [taylor]: Taking taylor expansion of n in n 16.652 * [backup-simplify]: Simplify 0 into 0 16.652 * [backup-simplify]: Simplify 1 into 1 16.652 * [taylor]: Taking taylor expansion of PI in n 16.652 * [backup-simplify]: Simplify PI into PI 16.652 * [backup-simplify]: Simplify (* 0 PI) into 0 16.653 * [backup-simplify]: Simplify (* 2 0) into 0 16.654 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.655 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 16.655 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 16.655 * [backup-simplify]: Simplify (- k) into (- k) 16.655 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k) 16.655 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 16.656 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 16.657 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 16.658 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 16.658 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 16.658 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.658 * [taylor]: Taking taylor expansion of k in n 16.658 * [backup-simplify]: Simplify k into k 16.658 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.658 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 16.658 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 16.658 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 16.658 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k 16.658 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 16.658 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 16.658 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 16.658 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k 16.658 * [taylor]: Taking taylor expansion of 1/2 in k 16.658 * [backup-simplify]: Simplify 1/2 into 1/2 16.658 * [taylor]: Taking taylor expansion of (- 1 k) in k 16.658 * [taylor]: Taking taylor expansion of 1 in k 16.658 * [backup-simplify]: Simplify 1 into 1 16.658 * [taylor]: Taking taylor expansion of k in k 16.658 * [backup-simplify]: Simplify 0 into 0 16.658 * [backup-simplify]: Simplify 1 into 1 16.658 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 16.658 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 16.658 * [taylor]: Taking taylor expansion of 2 in k 16.658 * [backup-simplify]: Simplify 2 into 2 16.658 * [taylor]: Taking taylor expansion of (* n PI) in k 16.658 * [taylor]: Taking taylor expansion of n in k 16.658 * [backup-simplify]: Simplify n into n 16.658 * [taylor]: Taking taylor expansion of PI in k 16.658 * [backup-simplify]: Simplify PI into PI 16.658 * [backup-simplify]: Simplify (* n PI) into (* n PI) 16.658 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 16.658 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 16.659 * [backup-simplify]: Simplify (- 0) into 0 16.659 * [backup-simplify]: Simplify (+ 1 0) into 1 16.659 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 16.659 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 16.659 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 16.659 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 16.659 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.659 * [taylor]: Taking taylor expansion of k in k 16.659 * [backup-simplify]: Simplify 0 into 0 16.659 * [backup-simplify]: Simplify 1 into 1 16.660 * [backup-simplify]: Simplify (/ 1 1) into 1 16.660 * [backup-simplify]: Simplify (sqrt 0) into 0 16.661 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 16.661 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k 16.661 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 16.661 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 16.661 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 16.661 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k 16.661 * [taylor]: Taking taylor expansion of 1/2 in k 16.661 * [backup-simplify]: Simplify 1/2 into 1/2 16.661 * [taylor]: Taking taylor expansion of (- 1 k) in k 16.661 * [taylor]: Taking taylor expansion of 1 in k 16.661 * [backup-simplify]: Simplify 1 into 1 16.661 * [taylor]: Taking taylor expansion of k in k 16.661 * [backup-simplify]: Simplify 0 into 0 16.661 * [backup-simplify]: Simplify 1 into 1 16.661 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 16.661 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 16.661 * [taylor]: Taking taylor expansion of 2 in k 16.661 * [backup-simplify]: Simplify 2 into 2 16.661 * [taylor]: Taking taylor expansion of (* n PI) in k 16.661 * [taylor]: Taking taylor expansion of n in k 16.661 * [backup-simplify]: Simplify n into n 16.661 * [taylor]: Taking taylor expansion of PI in k 16.661 * [backup-simplify]: Simplify PI into PI 16.661 * [backup-simplify]: Simplify (* n PI) into (* n PI) 16.661 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 16.661 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 16.662 * [backup-simplify]: Simplify (- 0) into 0 16.662 * [backup-simplify]: Simplify (+ 1 0) into 1 16.662 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 16.662 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 16.662 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 16.662 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 16.662 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.662 * [taylor]: Taking taylor expansion of k in k 16.662 * [backup-simplify]: Simplify 0 into 0 16.662 * [backup-simplify]: Simplify 1 into 1 16.663 * [backup-simplify]: Simplify (/ 1 1) into 1 16.663 * [backup-simplify]: Simplify (sqrt 0) into 0 16.664 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 16.664 * [backup-simplify]: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0 16.664 * [taylor]: Taking taylor expansion of 0 in n 16.664 * [backup-simplify]: Simplify 0 into 0 16.664 * [backup-simplify]: Simplify 0 into 0 16.664 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 16.665 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 16.665 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 16.665 * [backup-simplify]: Simplify (- 1) into -1 16.666 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.666 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2 16.666 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 16.667 * [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))))) 16.667 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 16.667 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 16.667 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 16.667 * [taylor]: Taking taylor expansion of +nan.0 in n 16.667 * [backup-simplify]: Simplify +nan.0 into +nan.0 16.667 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 16.667 * [taylor]: Taking taylor expansion of (sqrt 2) in n 16.667 * [taylor]: Taking taylor expansion of 2 in n 16.667 * [backup-simplify]: Simplify 2 into 2 16.667 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 16.668 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 16.668 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 16.668 * [taylor]: Taking taylor expansion of (* n PI) in n 16.668 * [taylor]: Taking taylor expansion of n in n 16.668 * [backup-simplify]: Simplify 0 into 0 16.668 * [backup-simplify]: Simplify 1 into 1 16.668 * [taylor]: Taking taylor expansion of PI in n 16.668 * [backup-simplify]: Simplify PI into PI 16.668 * [backup-simplify]: Simplify (* 0 PI) into 0 16.669 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.669 * [backup-simplify]: Simplify (sqrt 0) into 0 16.670 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 16.670 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 16.670 * [backup-simplify]: Simplify (* +nan.0 0) into 0 16.671 * [backup-simplify]: Simplify (- 0) into 0 16.671 * [backup-simplify]: Simplify 0 into 0 16.671 * [backup-simplify]: Simplify 0 into 0 16.671 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 16.673 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 16.674 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 16.675 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 16.676 * [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 16.677 * [backup-simplify]: Simplify (- 0) into 0 16.677 * [backup-simplify]: Simplify (+ 0 0) into 0 16.678 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0 16.679 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 16.680 * [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))) 16.681 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) 16.681 * [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 16.681 * [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 16.681 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 16.681 * [taylor]: Taking taylor expansion of +nan.0 in n 16.681 * [backup-simplify]: Simplify +nan.0 into +nan.0 16.681 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 16.681 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 16.681 * [taylor]: Taking taylor expansion of (sqrt 2) in n 16.681 * [taylor]: Taking taylor expansion of 2 in n 16.681 * [backup-simplify]: Simplify 2 into 2 16.681 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 16.682 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 16.682 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 16.682 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 16.682 * [taylor]: Taking taylor expansion of 2 in n 16.682 * [backup-simplify]: Simplify 2 into 2 16.682 * [taylor]: Taking taylor expansion of (* n PI) in n 16.682 * [taylor]: Taking taylor expansion of n in n 16.682 * [backup-simplify]: Simplify 0 into 0 16.682 * [backup-simplify]: Simplify 1 into 1 16.682 * [taylor]: Taking taylor expansion of PI in n 16.682 * [backup-simplify]: Simplify PI into PI 16.683 * [backup-simplify]: Simplify (* 0 PI) into 0 16.683 * [backup-simplify]: Simplify (* 2 0) into 0 16.685 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.686 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 16.688 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 16.688 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 16.688 * [taylor]: Taking taylor expansion of (* n PI) in n 16.688 * [taylor]: Taking taylor expansion of n in n 16.688 * [backup-simplify]: Simplify 0 into 0 16.688 * [backup-simplify]: Simplify 1 into 1 16.688 * [taylor]: Taking taylor expansion of PI in n 16.688 * [backup-simplify]: Simplify PI into PI 16.688 * [backup-simplify]: Simplify (* 0 PI) into 0 16.690 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.691 * [backup-simplify]: Simplify (sqrt 0) into 0 16.692 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 16.692 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 16.692 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 16.692 * [taylor]: Taking taylor expansion of +nan.0 in n 16.692 * [backup-simplify]: Simplify +nan.0 into +nan.0 16.692 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 16.692 * [taylor]: Taking taylor expansion of (sqrt 2) in n 16.692 * [taylor]: Taking taylor expansion of 2 in n 16.692 * [backup-simplify]: Simplify 2 into 2 16.693 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 16.693 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 16.694 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 16.694 * [taylor]: Taking taylor expansion of (* n PI) in n 16.694 * [taylor]: Taking taylor expansion of n in n 16.694 * [backup-simplify]: Simplify 0 into 0 16.694 * [backup-simplify]: Simplify 1 into 1 16.694 * [taylor]: Taking taylor expansion of PI in n 16.694 * [backup-simplify]: Simplify PI into PI 16.694 * [backup-simplify]: Simplify (* 0 PI) into 0 16.696 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.696 * [backup-simplify]: Simplify (sqrt 0) into 0 16.697 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 16.699 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 16.700 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 16.703 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 16.703 * [backup-simplify]: Simplify (* +nan.0 0) into 0 16.704 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 16.704 * [backup-simplify]: Simplify (* +nan.0 0) into 0 16.705 * [backup-simplify]: Simplify (- 0) into 0 16.705 * [backup-simplify]: Simplify (+ 0 0) into 0 16.706 * [backup-simplify]: Simplify (- 0) into 0 16.706 * [backup-simplify]: Simplify 0 into 0 16.709 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 16.715 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 16.718 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 16.721 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 16.721 * [backup-simplify]: Simplify 0 into 0 16.722 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.726 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 16.727 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 16.729 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 16.732 * [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 16.733 * [backup-simplify]: Simplify (- 0) into 0 16.733 * [backup-simplify]: Simplify (+ 0 0) into 0 16.734 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0 16.736 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 16.738 * [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))) 16.739 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (+ (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) +nan.0) (* (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) 16.739 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) in n 16.739 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))))) in n 16.739 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 16.739 * [taylor]: Taking taylor expansion of +nan.0 in n 16.739 * [backup-simplify]: Simplify +nan.0 into +nan.0 16.739 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 16.739 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 16.739 * [taylor]: Taking taylor expansion of (sqrt 2) in n 16.739 * [taylor]: Taking taylor expansion of 2 in n 16.739 * [backup-simplify]: Simplify 2 into 2 16.740 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 16.741 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 16.741 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 16.741 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 16.741 * [taylor]: Taking taylor expansion of 2 in n 16.741 * [backup-simplify]: Simplify 2 into 2 16.741 * [taylor]: Taking taylor expansion of (* n PI) in n 16.741 * [taylor]: Taking taylor expansion of n in n 16.741 * [backup-simplify]: Simplify 0 into 0 16.741 * [backup-simplify]: Simplify 1 into 1 16.741 * [taylor]: Taking taylor expansion of PI in n 16.741 * [backup-simplify]: Simplify PI into PI 16.742 * [backup-simplify]: Simplify (* 0 PI) into 0 16.742 * [backup-simplify]: Simplify (* 2 0) into 0 16.744 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.746 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 16.747 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 16.747 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 16.747 * [taylor]: Taking taylor expansion of (* n PI) in n 16.747 * [taylor]: Taking taylor expansion of n in n 16.747 * [backup-simplify]: Simplify 0 into 0 16.747 * [backup-simplify]: Simplify 1 into 1 16.747 * [taylor]: Taking taylor expansion of PI in n 16.747 * [backup-simplify]: Simplify PI into PI 16.747 * [backup-simplify]: Simplify (* 0 PI) into 0 16.749 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.750 * [backup-simplify]: Simplify (sqrt 0) into 0 16.751 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 16.751 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))) in n 16.751 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))) in n 16.751 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 16.751 * [taylor]: Taking taylor expansion of +nan.0 in n 16.752 * [backup-simplify]: Simplify +nan.0 into +nan.0 16.752 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 16.752 * [taylor]: Taking taylor expansion of (sqrt 2) in n 16.752 * [taylor]: Taking taylor expansion of 2 in n 16.752 * [backup-simplify]: Simplify 2 into 2 16.752 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 16.758 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 16.759 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 16.759 * [taylor]: Taking taylor expansion of (* n PI) in n 16.759 * [taylor]: Taking taylor expansion of n in n 16.759 * [backup-simplify]: Simplify 0 into 0 16.759 * [backup-simplify]: Simplify 1 into 1 16.759 * [taylor]: Taking taylor expansion of PI in n 16.759 * [backup-simplify]: Simplify PI into PI 16.760 * [backup-simplify]: Simplify (* 0 PI) into 0 16.761 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.762 * [backup-simplify]: Simplify (sqrt 0) into 0 16.763 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 16.763 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n 16.763 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 16.763 * [taylor]: Taking taylor expansion of +nan.0 in n 16.763 * [backup-simplify]: Simplify +nan.0 into +nan.0 16.764 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 16.764 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 16.764 * [taylor]: Taking taylor expansion of (sqrt 2) in n 16.764 * [taylor]: Taking taylor expansion of 2 in n 16.764 * [backup-simplify]: Simplify 2 into 2 16.764 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 16.765 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 16.765 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 16.765 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 16.765 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 16.765 * [taylor]: Taking taylor expansion of 2 in n 16.765 * [backup-simplify]: Simplify 2 into 2 16.765 * [taylor]: Taking taylor expansion of (* n PI) in n 16.765 * [taylor]: Taking taylor expansion of n in n 16.765 * [backup-simplify]: Simplify 0 into 0 16.765 * [backup-simplify]: Simplify 1 into 1 16.765 * [taylor]: Taking taylor expansion of PI in n 16.765 * [backup-simplify]: Simplify PI into PI 16.766 * [backup-simplify]: Simplify (* 0 PI) into 0 16.766 * [backup-simplify]: Simplify (* 2 0) into 0 16.768 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.769 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 16.771 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 16.772 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 16.772 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 16.772 * [taylor]: Taking taylor expansion of (* n PI) in n 16.772 * [taylor]: Taking taylor expansion of n in n 16.772 * [backup-simplify]: Simplify 0 into 0 16.772 * [backup-simplify]: Simplify 1 into 1 16.772 * [taylor]: Taking taylor expansion of PI in n 16.772 * [backup-simplify]: Simplify PI into PI 16.773 * [backup-simplify]: Simplify (* 0 PI) into 0 16.774 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.775 * [backup-simplify]: Simplify (sqrt 0) into 0 16.776 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 16.777 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 16.779 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 16.780 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 16.781 * [backup-simplify]: Simplify (* +nan.0 0) into 0 16.781 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 16.782 * [backup-simplify]: Simplify (* +nan.0 0) into 0 16.783 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 16.784 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 16.786 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 16.788 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 16.789 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 16.790 * [backup-simplify]: Simplify (* +nan.0 0) into 0 16.790 * [backup-simplify]: Simplify (- 0) into 0 16.790 * [backup-simplify]: Simplify (+ 0 0) into 0 16.791 * [backup-simplify]: Simplify (- 0) into 0 16.791 * [backup-simplify]: Simplify (+ 0 0) into 0 16.791 * [backup-simplify]: Simplify (- 0) into 0 16.792 * [backup-simplify]: Simplify 0 into 0 16.793 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 16.794 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 16.796 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 16.798 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 16.799 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 16.801 * [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)))))))) 16.805 * [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)))))))) 16.807 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 16.810 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 16.812 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 16.817 * [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)))))))))) 16.822 * [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))))))) 16.827 * [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))))))) 16.827 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 16.830 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 16.831 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 16.834 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 16.841 * [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)))) 16.846 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 16.848 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 16.857 * [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))))))))))))) 16.858 * [backup-simplify]: Simplify (* (pow (/ 1 k) -1/2) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) 16.858 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k n) around 0 16.858 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n 16.858 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 16.858 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 16.858 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 16.858 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 16.858 * [taylor]: Taking taylor expansion of 1/2 in n 16.858 * [backup-simplify]: Simplify 1/2 into 1/2 16.858 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 16.858 * [taylor]: Taking taylor expansion of 1 in n 16.858 * [backup-simplify]: Simplify 1 into 1 16.858 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.858 * [taylor]: Taking taylor expansion of k in n 16.858 * [backup-simplify]: Simplify k into k 16.858 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.858 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 16.858 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 16.858 * [taylor]: Taking taylor expansion of 2 in n 16.858 * [backup-simplify]: Simplify 2 into 2 16.858 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.858 * [taylor]: Taking taylor expansion of PI in n 16.858 * [backup-simplify]: Simplify PI into PI 16.858 * [taylor]: Taking taylor expansion of n in n 16.858 * [backup-simplify]: Simplify 0 into 0 16.858 * [backup-simplify]: Simplify 1 into 1 16.858 * [backup-simplify]: Simplify (/ PI 1) into PI 16.859 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 16.859 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 16.860 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 16.860 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 16.860 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 16.864 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 16.865 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 16.867 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 16.867 * [taylor]: Taking taylor expansion of (sqrt k) in n 16.867 * [taylor]: Taking taylor expansion of k in n 16.867 * [backup-simplify]: Simplify k into k 16.867 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 16.867 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 16.867 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k 16.867 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 16.867 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 16.867 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 16.867 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 16.867 * [taylor]: Taking taylor expansion of 1/2 in k 16.867 * [backup-simplify]: Simplify 1/2 into 1/2 16.867 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 16.867 * [taylor]: Taking taylor expansion of 1 in k 16.867 * [backup-simplify]: Simplify 1 into 1 16.867 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.867 * [taylor]: Taking taylor expansion of k in k 16.867 * [backup-simplify]: Simplify 0 into 0 16.867 * [backup-simplify]: Simplify 1 into 1 16.868 * [backup-simplify]: Simplify (/ 1 1) into 1 16.868 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 16.868 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 16.868 * [taylor]: Taking taylor expansion of 2 in k 16.868 * [backup-simplify]: Simplify 2 into 2 16.868 * [taylor]: Taking taylor expansion of (/ PI n) in k 16.868 * [taylor]: Taking taylor expansion of PI in k 16.868 * [backup-simplify]: Simplify PI into PI 16.868 * [taylor]: Taking taylor expansion of n in k 16.868 * [backup-simplify]: Simplify n into n 16.868 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 16.868 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 16.868 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 16.868 * [backup-simplify]: Simplify (- 1) into -1 16.869 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.869 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2 16.869 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 16.869 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 16.869 * [taylor]: Taking taylor expansion of (sqrt k) in k 16.869 * [taylor]: Taking taylor expansion of k in k 16.869 * [backup-simplify]: Simplify 0 into 0 16.869 * [backup-simplify]: Simplify 1 into 1 16.870 * [backup-simplify]: Simplify (sqrt 0) into 0 16.871 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 16.871 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k 16.871 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 16.871 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 16.871 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 16.871 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 16.871 * [taylor]: Taking taylor expansion of 1/2 in k 16.871 * [backup-simplify]: Simplify 1/2 into 1/2 16.871 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 16.871 * [taylor]: Taking taylor expansion of 1 in k 16.871 * [backup-simplify]: Simplify 1 into 1 16.871 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.871 * [taylor]: Taking taylor expansion of k in k 16.871 * [backup-simplify]: Simplify 0 into 0 16.871 * [backup-simplify]: Simplify 1 into 1 16.871 * [backup-simplify]: Simplify (/ 1 1) into 1 16.871 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 16.871 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 16.871 * [taylor]: Taking taylor expansion of 2 in k 16.871 * [backup-simplify]: Simplify 2 into 2 16.871 * [taylor]: Taking taylor expansion of (/ PI n) in k 16.871 * [taylor]: Taking taylor expansion of PI in k 16.871 * [backup-simplify]: Simplify PI into PI 16.871 * [taylor]: Taking taylor expansion of n in k 16.871 * [backup-simplify]: Simplify n into n 16.871 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 16.871 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 16.871 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 16.872 * [backup-simplify]: Simplify (- 1) into -1 16.872 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.872 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2 16.872 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 16.872 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 16.872 * [taylor]: Taking taylor expansion of (sqrt k) in k 16.872 * [taylor]: Taking taylor expansion of k in k 16.872 * [backup-simplify]: Simplify 0 into 0 16.872 * [backup-simplify]: Simplify 1 into 1 16.873 * [backup-simplify]: Simplify (sqrt 0) into 0 16.874 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 16.874 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 0) into 0 16.874 * [taylor]: Taking taylor expansion of 0 in n 16.874 * [backup-simplify]: Simplify 0 into 0 16.874 * [backup-simplify]: Simplify 0 into 0 16.874 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 16.874 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 16.874 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 16.874 * [taylor]: Taking taylor expansion of +nan.0 in n 16.874 * [backup-simplify]: Simplify +nan.0 into +nan.0 16.874 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 16.874 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 16.874 * [taylor]: Taking taylor expansion of 1/2 in n 16.874 * [backup-simplify]: Simplify 1/2 into 1/2 16.874 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 16.874 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 16.874 * [taylor]: Taking taylor expansion of 1 in n 16.874 * [backup-simplify]: Simplify 1 into 1 16.874 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.874 * [taylor]: Taking taylor expansion of k in n 16.874 * [backup-simplify]: Simplify k into k 16.874 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.874 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 16.874 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 16.874 * [taylor]: Taking taylor expansion of 2 in n 16.875 * [backup-simplify]: Simplify 2 into 2 16.875 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.875 * [taylor]: Taking taylor expansion of PI in n 16.875 * [backup-simplify]: Simplify PI into PI 16.875 * [taylor]: Taking taylor expansion of n in n 16.875 * [backup-simplify]: Simplify 0 into 0 16.875 * [backup-simplify]: Simplify 1 into 1 16.875 * [backup-simplify]: Simplify (/ PI 1) into PI 16.875 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 16.876 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 16.876 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 16.876 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 16.877 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 16.878 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 16.878 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 16.879 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 16.880 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 16.881 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 16.881 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 16.881 * [backup-simplify]: Simplify 0 into 0 16.883 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 16.884 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 16.884 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 16.884 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 16.884 * [taylor]: Taking taylor expansion of +nan.0 in n 16.884 * [backup-simplify]: Simplify +nan.0 into +nan.0 16.884 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 16.884 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 16.884 * [taylor]: Taking taylor expansion of 1/2 in n 16.884 * [backup-simplify]: Simplify 1/2 into 1/2 16.884 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 16.884 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 16.884 * [taylor]: Taking taylor expansion of 1 in n 16.884 * [backup-simplify]: Simplify 1 into 1 16.884 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.884 * [taylor]: Taking taylor expansion of k in n 16.884 * [backup-simplify]: Simplify k into k 16.884 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.884 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 16.884 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 16.884 * [taylor]: Taking taylor expansion of 2 in n 16.884 * [backup-simplify]: Simplify 2 into 2 16.884 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.884 * [taylor]: Taking taylor expansion of PI in n 16.884 * [backup-simplify]: Simplify PI into PI 16.884 * [taylor]: Taking taylor expansion of n in n 16.884 * [backup-simplify]: Simplify 0 into 0 16.884 * [backup-simplify]: Simplify 1 into 1 16.884 * [backup-simplify]: Simplify (/ PI 1) into PI 16.885 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 16.885 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 16.885 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 16.886 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 16.886 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 16.887 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 16.888 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 16.889 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 16.889 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 16.890 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 16.891 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 16.891 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 16.892 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 16.893 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 16.893 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 16.893 * [backup-simplify]: Simplify (- 0) into 0 16.893 * [backup-simplify]: Simplify (+ 0 0) into 0 16.894 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 16.895 * [backup-simplify]: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 16.896 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0 16.897 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 16.898 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0 16.898 * [backup-simplify]: Simplify (- 0) into 0 16.898 * [backup-simplify]: Simplify 0 into 0 16.898 * [backup-simplify]: Simplify 0 into 0 16.901 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 16.902 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 16.902 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 16.902 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 16.902 * [taylor]: Taking taylor expansion of +nan.0 in n 16.902 * [backup-simplify]: Simplify +nan.0 into +nan.0 16.902 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 16.902 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 16.902 * [taylor]: Taking taylor expansion of 1/2 in n 16.902 * [backup-simplify]: Simplify 1/2 into 1/2 16.902 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 16.902 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 16.902 * [taylor]: Taking taylor expansion of 1 in n 16.902 * [backup-simplify]: Simplify 1 into 1 16.902 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.902 * [taylor]: Taking taylor expansion of k in n 16.902 * [backup-simplify]: Simplify k into k 16.902 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.902 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 16.902 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 16.902 * [taylor]: Taking taylor expansion of 2 in n 16.902 * [backup-simplify]: Simplify 2 into 2 16.902 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.902 * [taylor]: Taking taylor expansion of PI in n 16.902 * [backup-simplify]: Simplify PI into PI 16.902 * [taylor]: Taking taylor expansion of n in n 16.902 * [backup-simplify]: Simplify 0 into 0 16.902 * [backup-simplify]: Simplify 1 into 1 16.902 * [backup-simplify]: Simplify (/ PI 1) into PI 16.903 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 16.904 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 16.904 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 16.904 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 16.905 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 16.906 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 16.907 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 16.908 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 16.909 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 16.910 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 16.912 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 16.914 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))) 16.915 * [backup-simplify]: Simplify (* (pow (/ 1 (- k)) -1/2) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) into (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) 16.915 * [approximate]: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in (k n) around 0 16.915 * [taylor]: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in n 16.915 * [taylor]: Taking taylor expansion of (sqrt (/ k -1)) in n 16.915 * [taylor]: Taking taylor expansion of (/ k -1) in n 16.915 * [taylor]: Taking taylor expansion of k in n 16.915 * [backup-simplify]: Simplify k into k 16.915 * [taylor]: Taking taylor expansion of -1 in n 16.915 * [backup-simplify]: Simplify -1 into -1 16.915 * [backup-simplify]: Simplify (/ k -1) into (* -1 k) 16.915 * [backup-simplify]: Simplify (sqrt (* -1 k)) into (sqrt (* -1 k)) 16.916 * [backup-simplify]: Simplify (- (/ 0 -1) (+ (* (* -1 k) (/ 0 -1)))) into 0 16.916 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (* -1 k)))) into 0 16.916 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 16.916 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 16.916 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 16.916 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 16.916 * [taylor]: Taking taylor expansion of 1/2 in n 16.916 * [backup-simplify]: Simplify 1/2 into 1/2 16.916 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 16.916 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.916 * [taylor]: Taking taylor expansion of k in n 16.916 * [backup-simplify]: Simplify k into k 16.916 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.916 * [taylor]: Taking taylor expansion of 1 in n 16.916 * [backup-simplify]: Simplify 1 into 1 16.916 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 16.916 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 16.916 * [taylor]: Taking taylor expansion of -2 in n 16.916 * [backup-simplify]: Simplify -2 into -2 16.916 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.916 * [taylor]: Taking taylor expansion of PI in n 16.916 * [backup-simplify]: Simplify PI into PI 16.916 * [taylor]: Taking taylor expansion of n in n 16.916 * [backup-simplify]: Simplify 0 into 0 16.916 * [backup-simplify]: Simplify 1 into 1 16.916 * [backup-simplify]: Simplify (/ PI 1) into PI 16.917 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 16.917 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 16.918 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 16.918 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 16.918 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 16.919 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 16.920 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 16.920 * [taylor]: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in k 16.920 * [taylor]: Taking taylor expansion of (sqrt (/ k -1)) in k 16.920 * [taylor]: Taking taylor expansion of (/ k -1) in k 16.920 * [taylor]: Taking taylor expansion of k in k 16.920 * [backup-simplify]: Simplify 0 into 0 16.920 * [backup-simplify]: Simplify 1 into 1 16.920 * [taylor]: Taking taylor expansion of -1 in k 16.920 * [backup-simplify]: Simplify -1 into -1 16.920 * [backup-simplify]: Simplify (/ 1 -1) into -1 16.921 * [backup-simplify]: Simplify (sqrt 0) into 0 16.921 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 16.922 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 16.922 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 16.922 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 16.922 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 16.922 * [taylor]: Taking taylor expansion of 1/2 in k 16.922 * [backup-simplify]: Simplify 1/2 into 1/2 16.922 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 16.922 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.922 * [taylor]: Taking taylor expansion of k in k 16.922 * [backup-simplify]: Simplify 0 into 0 16.922 * [backup-simplify]: Simplify 1 into 1 16.922 * [backup-simplify]: Simplify (/ 1 1) into 1 16.922 * [taylor]: Taking taylor expansion of 1 in k 16.922 * [backup-simplify]: Simplify 1 into 1 16.922 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 16.922 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 16.922 * [taylor]: Taking taylor expansion of -2 in k 16.922 * [backup-simplify]: Simplify -2 into -2 16.922 * [taylor]: Taking taylor expansion of (/ PI n) in k 16.922 * [taylor]: Taking taylor expansion of PI in k 16.922 * [backup-simplify]: Simplify PI into PI 16.922 * [taylor]: Taking taylor expansion of n in k 16.922 * [backup-simplify]: Simplify n into n 16.922 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 16.922 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 16.922 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 16.923 * [backup-simplify]: Simplify (+ 1 0) into 1 16.923 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 16.923 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 16.923 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 16.923 * [taylor]: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in k 16.923 * [taylor]: Taking taylor expansion of (sqrt (/ k -1)) in k 16.923 * [taylor]: Taking taylor expansion of (/ k -1) in k 16.923 * [taylor]: Taking taylor expansion of k in k 16.923 * [backup-simplify]: Simplify 0 into 0 16.923 * [backup-simplify]: Simplify 1 into 1 16.923 * [taylor]: Taking taylor expansion of -1 in k 16.923 * [backup-simplify]: Simplify -1 into -1 16.923 * [backup-simplify]: Simplify (/ 1 -1) into -1 16.924 * [backup-simplify]: Simplify (sqrt 0) into 0 16.924 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 16.924 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 16.924 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 16.925 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 16.925 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 16.925 * [taylor]: Taking taylor expansion of 1/2 in k 16.925 * [backup-simplify]: Simplify 1/2 into 1/2 16.925 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 16.925 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.925 * [taylor]: Taking taylor expansion of k in k 16.925 * [backup-simplify]: Simplify 0 into 0 16.925 * [backup-simplify]: Simplify 1 into 1 16.925 * [backup-simplify]: Simplify (/ 1 1) into 1 16.925 * [taylor]: Taking taylor expansion of 1 in k 16.925 * [backup-simplify]: Simplify 1 into 1 16.925 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 16.925 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 16.925 * [taylor]: Taking taylor expansion of -2 in k 16.925 * [backup-simplify]: Simplify -2 into -2 16.925 * [taylor]: Taking taylor expansion of (/ PI n) in k 16.925 * [taylor]: Taking taylor expansion of PI in k 16.925 * [backup-simplify]: Simplify PI into PI 16.925 * [taylor]: Taking taylor expansion of n in k 16.925 * [backup-simplify]: Simplify n into n 16.925 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 16.925 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 16.925 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 16.926 * [backup-simplify]: Simplify (+ 1 0) into 1 16.926 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 16.926 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 16.926 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 16.926 * [backup-simplify]: Simplify (* 0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) into 0 16.926 * [taylor]: Taking taylor expansion of 0 in n 16.926 * [backup-simplify]: Simplify 0 into 0 16.926 * [backup-simplify]: Simplify 0 into 0 16.927 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) 16.927 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 16.927 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 16.927 * [taylor]: Taking taylor expansion of +nan.0 in n 16.927 * [backup-simplify]: Simplify +nan.0 into +nan.0 16.927 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 16.927 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 16.927 * [taylor]: Taking taylor expansion of 1/2 in n 16.927 * [backup-simplify]: Simplify 1/2 into 1/2 16.927 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 16.927 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 16.927 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 16.927 * [taylor]: Taking taylor expansion of -2 in n 16.927 * [backup-simplify]: Simplify -2 into -2 16.927 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.927 * [taylor]: Taking taylor expansion of PI in n 16.927 * [backup-simplify]: Simplify PI into PI 16.927 * [taylor]: Taking taylor expansion of n in n 16.927 * [backup-simplify]: Simplify 0 into 0 16.927 * [backup-simplify]: Simplify 1 into 1 16.927 * [backup-simplify]: Simplify (/ PI 1) into PI 16.928 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 16.928 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 16.928 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 16.928 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.928 * [taylor]: Taking taylor expansion of k in n 16.928 * [backup-simplify]: Simplify k into k 16.928 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.928 * [taylor]: Taking taylor expansion of 1 in n 16.928 * [backup-simplify]: Simplify 1 into 1 16.929 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 16.929 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 16.930 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 16.931 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 16.932 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 16.933 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 16.934 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 16.935 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 16.935 * [backup-simplify]: Simplify 0 into 0 16.935 * [backup-simplify]: Simplify (- (/ 0 -1) (+ (* -1 (/ 0 -1)))) into 0 16.937 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 16.938 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) 16.938 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 16.938 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 16.938 * [taylor]: Taking taylor expansion of +nan.0 in n 16.938 * [backup-simplify]: Simplify +nan.0 into +nan.0 16.938 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 16.938 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 16.938 * [taylor]: Taking taylor expansion of 1/2 in n 16.938 * [backup-simplify]: Simplify 1/2 into 1/2 16.938 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 16.938 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 16.938 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 16.938 * [taylor]: Taking taylor expansion of -2 in n 16.938 * [backup-simplify]: Simplify -2 into -2 16.938 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.938 * [taylor]: Taking taylor expansion of PI in n 16.938 * [backup-simplify]: Simplify PI into PI 16.938 * [taylor]: Taking taylor expansion of n in n 16.938 * [backup-simplify]: Simplify 0 into 0 16.938 * [backup-simplify]: Simplify 1 into 1 16.938 * [backup-simplify]: Simplify (/ PI 1) into PI 16.939 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 16.939 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 16.939 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 16.939 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.939 * [taylor]: Taking taylor expansion of k in n 16.939 * [backup-simplify]: Simplify k into k 16.939 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.940 * [taylor]: Taking taylor expansion of 1 in n 16.940 * [backup-simplify]: Simplify 1 into 1 16.940 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 16.940 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 16.941 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 16.942 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 16.943 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 16.943 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 16.944 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 16.945 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 16.946 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 16.946 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 16.946 * [backup-simplify]: Simplify (+ 0 0) into 0 16.947 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 16.947 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 16.948 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 16.949 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0 16.950 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0 16.951 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 16.952 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0 16.952 * [backup-simplify]: Simplify (- 0) into 0 16.952 * [backup-simplify]: Simplify 0 into 0 16.952 * [backup-simplify]: Simplify 0 into 0 16.953 * [backup-simplify]: Simplify (- (/ 0 -1) (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 16.956 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 16.960 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) 16.961 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 16.961 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 16.961 * [taylor]: Taking taylor expansion of +nan.0 in n 16.961 * [backup-simplify]: Simplify +nan.0 into +nan.0 16.961 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 16.961 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 16.961 * [taylor]: Taking taylor expansion of 1/2 in n 16.961 * [backup-simplify]: Simplify 1/2 into 1/2 16.961 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 16.961 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 16.961 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 16.961 * [taylor]: Taking taylor expansion of -2 in n 16.961 * [backup-simplify]: Simplify -2 into -2 16.961 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.961 * [taylor]: Taking taylor expansion of PI in n 16.961 * [backup-simplify]: Simplify PI into PI 16.961 * [taylor]: Taking taylor expansion of n in n 16.961 * [backup-simplify]: Simplify 0 into 0 16.961 * [backup-simplify]: Simplify 1 into 1 16.962 * [backup-simplify]: Simplify (/ PI 1) into PI 16.962 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 16.963 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 16.963 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 16.963 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.963 * [taylor]: Taking taylor expansion of k in n 16.964 * [backup-simplify]: Simplify k into k 16.964 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.964 * [taylor]: Taking taylor expansion of 1 in n 16.964 * [backup-simplify]: Simplify 1 into 1 16.965 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 16.965 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 16.966 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 16.968 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 16.969 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 16.970 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 16.971 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 16.973 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 16.977 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k))))))) 16.977 * * * [progress]: simplifying candidates 16.977 * * * * [progress]: [ 1 / 118 ] simplifiying candidate # 16.978 * * * * [progress]: [ 2 / 118 ] simplifiying candidate # 16.978 * * * * [progress]: [ 3 / 118 ] simplifiying candidate # 16.978 * * * * [progress]: [ 4 / 118 ] simplifiying candidate # 16.978 * * * * [progress]: [ 5 / 118 ] simplifiying candidate # 16.978 * * * * [progress]: [ 6 / 118 ] simplifiying candidate # 16.978 * * * * [progress]: [ 7 / 118 ] simplifiying candidate # 16.978 * * * * [progress]: [ 8 / 118 ] simplifiying candidate # 16.978 * * * * [progress]: [ 9 / 118 ] simplifiying candidate # 16.978 * * * * [progress]: [ 10 / 118 ] simplifiying candidate # 16.978 * * * * [progress]: [ 11 / 118 ] simplifiying candidate # 16.978 * * * * [progress]: [ 12 / 118 ] simplifiying candidate # 16.978 * * * * [progress]: [ 13 / 118 ] simplifiying candidate # 16.978 * * * * [progress]: [ 14 / 118 ] simplifiying candidate # 16.979 * * * * [progress]: [ 15 / 118 ] simplifiying candidate # 16.979 * * * * [progress]: [ 16 / 118 ] simplifiying candidate # 16.979 * * * * [progress]: [ 17 / 118 ] simplifiying candidate # 16.979 * * * * [progress]: [ 18 / 118 ] simplifiying candidate # 16.979 * * * * [progress]: [ 19 / 118 ] simplifiying candidate # 16.979 * * * * [progress]: [ 20 / 118 ] simplifiying candidate # 16.979 * * * * [progress]: [ 21 / 118 ] simplifiying candidate # 16.979 * * * * [progress]: [ 22 / 118 ] simplifiying candidate # 16.979 * * * * [progress]: [ 23 / 118 ] simplifiying candidate # 16.979 * * * * [progress]: [ 24 / 118 ] simplifiying candidate # 16.979 * * * * [progress]: [ 25 / 118 ] simplifiying candidate # 16.979 * * * * [progress]: [ 26 / 118 ] simplifiying candidate # 16.979 * * * * [progress]: [ 27 / 118 ] simplifiying candidate # 16.979 * * * * [progress]: [ 28 / 118 ] simplifiying candidate # 16.980 * * * * [progress]: [ 29 / 118 ] simplifiying candidate # 16.980 * * * * [progress]: [ 30 / 118 ] simplifiying candidate # 16.980 * * * * [progress]: [ 31 / 118 ] simplifiying candidate # 16.980 * * * * [progress]: [ 32 / 118 ] simplifiying candidate # 16.980 * * * * [progress]: [ 33 / 118 ] simplifiying candidate # 16.980 * * * * [progress]: [ 34 / 118 ] simplifiying candidate # 16.980 * * * * [progress]: [ 35 / 118 ] simplifiying candidate # 16.980 * * * * [progress]: [ 36 / 118 ] simplifiying candidate # 16.980 * * * * [progress]: [ 37 / 118 ] simplifiying candidate # 16.980 * * * * [progress]: [ 38 / 118 ] simplifiying candidate # 16.980 * * * * [progress]: [ 39 / 118 ] simplifiying candidate # 16.980 * * * * [progress]: [ 40 / 118 ] simplifiying candidate # 16.980 * * * * [progress]: [ 41 / 118 ] simplifiying candidate # 16.980 * * * * [progress]: [ 42 / 118 ] simplifiying candidate #real (real->posit16 (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))> 16.980 * * * * [progress]: [ 43 / 118 ] simplifiying candidate # 16.980 * * * * [progress]: [ 44 / 118 ] simplifiying candidate # 16.980 * * * * [progress]: [ 45 / 118 ] simplifiying candidate # 16.981 * * * * [progress]: [ 46 / 118 ] simplifiying candidate # 16.981 * * * * [progress]: [ 47 / 118 ] simplifiying candidate # 16.981 * * * * [progress]: [ 48 / 118 ] simplifiying candidate # 16.981 * * * * [progress]: [ 49 / 118 ] simplifiying candidate # 16.981 * * * * [progress]: [ 50 / 118 ] simplifiying candidate # 16.981 * * * * [progress]: [ 51 / 118 ] simplifiying candidate # 16.981 * * * * [progress]: [ 52 / 118 ] simplifiying candidate # 16.981 * * * * [progress]: [ 53 / 118 ] simplifiying candidate # 16.981 * * * * [progress]: [ 54 / 118 ] simplifiying candidate # 16.981 * * * * [progress]: [ 55 / 118 ] simplifiying candidate # 16.981 * * * * [progress]: [ 56 / 118 ] simplifiying candidate # 16.981 * * * * [progress]: [ 57 / 118 ] simplifiying candidate # 16.981 * * * * [progress]: [ 58 / 118 ] simplifiying candidate # 16.981 * * * * [progress]: [ 59 / 118 ] simplifiying candidate # 16.981 * * * * [progress]: [ 60 / 118 ] simplifiying candidate # 16.982 * * * * [progress]: [ 61 / 118 ] simplifiying candidate # 16.982 * * * * [progress]: [ 62 / 118 ] simplifiying candidate #real (real->posit16 (* (* 2 PI) n))) (/ (- 1 k) 2))))> 16.982 * * * * [progress]: [ 63 / 118 ] simplifiying candidate # 16.982 * * * * [progress]: [ 64 / 118 ] simplifiying candidate # 16.982 * * * * [progress]: [ 65 / 118 ] simplifiying candidate # 16.982 * * * * [progress]: [ 66 / 118 ] simplifiying candidate # 16.982 * * * * [progress]: [ 67 / 118 ] simplifiying candidate # 16.982 * * * * [progress]: [ 68 / 118 ] simplifiying candidate # 16.982 * * * * [progress]: [ 69 / 118 ] simplifiying candidate # 16.982 * * * * [progress]: [ 70 / 118 ] simplifiying candidate # 16.982 * * * * [progress]: [ 71 / 118 ] simplifiying candidate # 16.982 * * * * [progress]: [ 72 / 118 ] simplifiying candidate # 16.982 * * * * [progress]: [ 73 / 118 ] simplifiying candidate # 16.982 * * * * [progress]: [ 74 / 118 ] simplifiying candidate # 16.982 * * * * [progress]: [ 75 / 118 ] simplifiying candidate # 16.983 * * * * [progress]: [ 76 / 118 ] simplifiying candidate # 16.983 * * * * [progress]: [ 77 / 118 ] simplifiying candidate # 16.983 * * * * [progress]: [ 78 / 118 ] simplifiying candidate # 16.983 * * * * [progress]: [ 79 / 118 ] simplifiying candidate # 16.983 * * * * [progress]: [ 80 / 118 ] simplifiying candidate # 16.983 * * * * [progress]: [ 81 / 118 ] simplifiying candidate # 16.983 * * * * [progress]: [ 82 / 118 ] simplifiying candidate # 16.983 * * * * [progress]: [ 83 / 118 ] simplifiying candidate # 16.983 * * * * [progress]: [ 84 / 118 ] simplifiying candidate # 16.983 * * * * [progress]: [ 85 / 118 ] simplifiying candidate # 16.983 * * * * [progress]: [ 86 / 118 ] simplifiying candidate # 16.983 * * * * [progress]: [ 87 / 118 ] simplifiying candidate # 16.983 * * * * [progress]: [ 88 / 118 ] simplifiying candidate # 16.983 * * * * [progress]: [ 89 / 118 ] simplifiying candidate # 16.983 * * * * [progress]: [ 90 / 118 ] simplifiying candidate # 16.984 * * * * [progress]: [ 91 / 118 ] simplifiying candidate # 16.984 * * * * [progress]: [ 92 / 118 ] simplifiying candidate # 16.984 * * * * [progress]: [ 93 / 118 ] simplifiying candidate # 16.984 * * * * [progress]: [ 94 / 118 ] simplifiying candidate # 16.984 * * * * [progress]: [ 95 / 118 ] simplifiying candidate # 16.984 * * * * [progress]: [ 96 / 118 ] simplifiying candidate # 16.984 * * * * [progress]: [ 97 / 118 ] simplifiying candidate # 16.984 * * * * [progress]: [ 98 / 118 ] simplifiying candidate # 16.984 * * * * [progress]: [ 99 / 118 ] simplifiying candidate # 16.984 * * * * [progress]: [ 100 / 118 ] simplifiying candidate # 16.984 * * * * [progress]: [ 101 / 118 ] simplifiying candidate # 16.984 * * * * [progress]: [ 102 / 118 ] simplifiying candidate # 16.984 * * * * [progress]: [ 103 / 118 ] simplifiying candidate # 16.984 * * * * [progress]: [ 104 / 118 ] simplifiying candidate # 16.984 * * * * [progress]: [ 105 / 118 ] simplifiying candidate # 16.985 * * * * [progress]: [ 106 / 118 ] simplifiying candidate # 16.985 * * * * [progress]: [ 107 / 118 ] simplifiying candidate # 16.985 * * * * [progress]: [ 108 / 118 ] simplifiying candidate #real (real->posit16 (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))> 16.985 * * * * [progress]: [ 109 / 118 ] simplifiying candidate # 16.985 * * * * [progress]: [ 110 / 118 ] simplifiying candidate # 16.985 * * * * [progress]: [ 111 / 118 ] simplifiying candidate # 16.985 * * * * [progress]: [ 112 / 118 ] simplifiying candidate # 16.985 * * * * [progress]: [ 113 / 118 ] simplifiying candidate # 16.985 * * * * [progress]: [ 114 / 118 ] simplifiying candidate # 16.985 * * * * [progress]: [ 115 / 118 ] simplifiying candidate # 16.985 * * * * [progress]: [ 116 / 118 ] simplifiying candidate # 16.985 * * * * [progress]: [ 117 / 118 ] simplifiying candidate # 16.985 * * * * [progress]: [ 118 / 118 ] simplifiying candidate # 16.988 * [simplify]: Simplifying: (expm1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (log1p (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) (* 1 (/ (- 1 k) 2)) (* 1 (/ (- 1 k) 2)) (* 1 (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)) (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1)) (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (sqrt 2))) (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) 1)) (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2 PI) n) (/ 1 (sqrt 2))) (pow (* (* 2 PI) n) (/ 1 1)) (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2))) (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) 1)) (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (sqrt 2))) (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) 1)) (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2 PI) n) (/ 1 (sqrt 2))) (pow (* (* 2 PI) n) (/ 1 1)) (pow (* (* 2 PI) n) 1) (pow (* (* 2 PI) n) (- 1 k)) (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (exp (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (real->posit16 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (expm1 (* (* 2 PI) n)) (log1p (* (* 2 PI) n)) (* (* 2 PI) n) (* (* 2 PI) n) (+ (+ (log 2) (log PI)) (log n)) (+ (log (* 2 PI)) (log n)) (log (* (* 2 PI) n)) (exp (* (* 2 PI) n)) (* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n)) (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n))) (cbrt (* (* 2 PI) n)) (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n)) (sqrt (* (* 2 PI) n)) (sqrt (* (* 2 PI) n)) (* (* 2 PI) (* (cbrt n) (cbrt n))) (* (* 2 PI) (sqrt n)) (* (* 2 PI) 1) (* PI n) (real->posit16 (* (* 2 PI) n)) (expm1 (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (log1p (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (+ (* (log k) -1/2) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2))) (+ (* (log k) -1/2) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2))) (+ (* (log k) -1/2) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) (+ (* (log k) -1/2) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) (+ (* (log k) -1/2) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (+ (* (log k) -1/2) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2))) (+ (* (log k) -1/2) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2))) (+ (* (log k) -1/2) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) (+ (* (log k) -1/2) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) (+ (* (log k) -1/2) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (+ (log (pow k -1/2)) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2))) (+ (log (pow k -1/2)) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2))) (+ (log (pow k -1/2)) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) (+ (log (pow k -1/2)) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) (+ (log (pow k -1/2)) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (log (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (exp (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (* (* (pow k -1/2) (pow k -1/2)) (pow k -1/2)) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (cbrt (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (* (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (pow (sqrt k) -1/2) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (pow (sqrt k) -1/2) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (pow (sqrt k) -1/2) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (pow (sqrt k) -1/2) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (sqrt (pow k -1/2)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (sqrt (pow k -1/2)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (sqrt (pow k -1/2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (sqrt (pow k -1/2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (pow k (/ -1/2 2)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (pow k (/ -1/2 2)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (pow k (/ -1/2 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (pow k (/ -1/2 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (pow k -1/2) (pow (* 2 PI) (/ (- 1 k) 2))) (* (pow k -1/2) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (* (pow k -1/2) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (pow k -1/2) 1) (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (pow (cbrt k) -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (pow (sqrt k) -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (cbrt (pow k -1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (sqrt (pow k -1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (pow k (/ -1/2 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (pow k -1/2) (pow (* (* 2 PI) n) (/ 1 2))) (real->posit16 (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (- (+ (* 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 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (- (+ (* +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 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k))))))) 16.992 * * [simplify]: iteration 0: 264 enodes 17.091 * * [simplify]: iteration 1: 732 enodes 17.341 * * [simplify]: iteration 2: 2000 enodes 17.851 * * [simplify]: iteration complete: 2000 enodes 17.851 * * [simplify]: Extracting #0: cost 79 inf + 0 17.852 * * [simplify]: Extracting #1: cost 360 inf + 0 17.855 * * [simplify]: Extracting #2: cost 709 inf + 2790 17.861 * * [simplify]: Extracting #3: cost 631 inf + 45138 17.877 * * [simplify]: Extracting #4: cost 406 inf + 156428 17.911 * * [simplify]: Extracting #5: cost 157 inf + 250754 17.977 * * [simplify]: Extracting #6: cost 37 inf + 309619 18.041 * * [simplify]: Extracting #7: cost 11 inf + 323599 18.104 * * [simplify]: Extracting #8: cost 0 inf + 330536 18.152 * * [simplify]: Extracting #9: cost 0 inf + 329726 18.210 * [simplify]: Simplified to: (expm1 (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (log1p (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (* (/ (- 1 k) 2) (log (* (* 2 n) PI))) (* (/ (- 1 k) 2) (log (* (* 2 n) PI))) (* (/ (- 1 k) 2) (log (* (* 2 n) PI))) (* (/ (- 1 k) 2) (log (* (* 2 n) PI))) (/ (- 1 k) 2) (/ (- 1 k) 2) (/ (- 1 k) 2) (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)) (pow (* (* 2 n) PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (pow (* (* 2 n) PI) (sqrt (/ (- 1 k) 2))) (pow (* (* 2 n) PI) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2)))) (pow (* (* 2 n) PI) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (pow (* (* 2 n) PI) (* (cbrt (- 1 k)) (cbrt (- 1 k)))) (pow (* (* 2 n) PI) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2))) (pow (* (* 2 n) PI) (/ (sqrt (- 1 k)) (sqrt 2))) (pow (* (* 2 n) PI) (sqrt (- 1 k))) (pow (* (* 2 n) PI) (/ (/ 1 (cbrt 2)) (cbrt 2))) (pow (* (* 2 n) PI) (/ 1 (sqrt 2))) (* (* 2 n) PI) (pow (* (* 2 n) PI) (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2 n) PI) (/ (+ (sqrt k) 1) (sqrt 2))) (pow (* (* 2 n) PI) (+ (sqrt k) 1)) (pow (* (* 2 n) PI) (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2 n) PI) (/ (+ (sqrt k) 1) (sqrt 2))) (pow (* (* 2 n) PI) (+ (sqrt k) 1)) (pow (* (* 2 n) PI) (/ (/ 1 (cbrt 2)) (cbrt 2))) (pow (* (* 2 n) PI) (/ 1 (sqrt 2))) (* (* 2 n) PI) (* (* 2 n) PI) (pow (* (* 2 n) PI) (- 1 k)) (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)) (* (/ (- 1 k) 2) (log (* (* 2 n) PI))) (exp (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (* (cbrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 n) PI) (/ (- 1 k) 2)))) (cbrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (* (* (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (pow (* (* 2 n) PI) (/ (- 1 k) 4)) (pow (* (* 2 n) PI) (/ (- 1 k) 4)) (real->posit16 (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (expm1 (* (* 2 n) PI)) (log1p (* (* 2 n) PI)) (* (* 2 n) PI) (* (* 2 n) PI) (log (* (* 2 n) PI)) (log (* (* 2 n) PI)) (log (* (* 2 n) PI)) (* (exp (* n PI)) (exp (* n PI))) (* (* (* (* (* 4 2) (* PI PI)) PI) (* n n)) n) (* (* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* n n)) n) (* (cbrt (* (* 2 n) PI)) (cbrt (* (* 2 n) PI))) (cbrt (* (* 2 n) PI)) (* (* (* 2 n) PI) (* (* (* 2 n) PI) (* (* 2 n) PI))) (sqrt (* (* 2 n) PI)) (sqrt (* (* 2 n) PI)) (* (* (* 2 PI) (cbrt n)) (cbrt n)) (* (sqrt n) (* 2 PI)) (* 2 PI) (* n PI) (real->posit16 (* (* 2 n) PI)) (expm1 (* (pow k -1/2) (pow (* (* 2 n) PI) (/ (- 1 k) 2)))) (log1p (* (pow k -1/2) (pow (* (* 2 n) PI) (/ (- 1 k) 2)))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (* -1/2 (log k))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (* -1/2 (log k))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (* -1/2 (log k))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (* -1/2 (log k))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (* -1/2 (log k))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (* -1/2 (log k))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (* -1/2 (log k))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (* -1/2 (log k))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (* -1/2 (log k))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (* -1/2 (log k))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (* -1/2 (log k))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (* -1/2 (log k))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (* -1/2 (log k))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (* -1/2 (log k))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (* -1/2 (log k))) (fma (log (* (* 2 n) PI)) (/ (- 1 k) 2) (* -1/2 (log k))) (exp (* (pow k -1/2) (pow (* (* 2 n) PI) (/ (- 1 k) 2)))) (* (* (* (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (* (pow k -1/2) (/ 1 k))) (* (cbrt (* (pow k -1/2) (pow (* (* 2 n) PI) (/ (- 1 k) 2)))) (cbrt (* (pow k -1/2) (pow (* (* 2 n) PI) (/ (- 1 k) 2))))) (cbrt (* (pow k -1/2) (pow (* (* 2 n) PI) (/ (- 1 k) 2)))) (* (* (* (pow k -1/2) (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (* (* (pow k -1/2) (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (pow k -1/2))) (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (sqrt (* (pow k -1/2) (pow (* (* 2 n) PI) (/ (- 1 k) 2)))) (sqrt (* (pow k -1/2) (pow (* (* 2 n) PI) (/ (- 1 k) 2)))) (* (pow (sqrt k) -1/2) (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2)))) (* (pow (sqrt k) -1/2) (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2)))) (* (pow (* (* 2 n) PI) (/ (- 1 k) 4)) (pow (sqrt k) -1/2)) (* (pow (* (* 2 n) PI) (/ (- 1 k) 4)) (pow (sqrt k) -1/2)) (* (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (sqrt (pow k -1/2))) (* (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (sqrt (pow k -1/2))) (* (pow (* (* 2 n) PI) (/ (- 1 k) 4)) (sqrt (pow k -1/2))) (* (pow (* (* 2 n) PI) (/ (- 1 k) 4)) (sqrt (pow k -1/2))) (* (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (pow k -1/4)) (* (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (pow k -1/4)) (* (pow k -1/4) (pow (* (* 2 n) PI) (/ (- 1 k) 4))) (* (pow k -1/4) (pow (* (* 2 n) PI) (/ (- 1 k) 4))) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow k -1/2)) (* (* (pow k -1/2) (cbrt (pow (* (* 2 n) PI) (/ (- 1 k) 2)))) (cbrt (pow (* (* 2 n) PI) (/ (- 1 k) 2)))) (* (pow k -1/2) (sqrt (pow (* (* 2 n) PI) (/ (- 1 k) 2)))) (pow k -1/2) (* (pow k -1/2) (pow (* (* 2 n) PI) (/ (- 1 k) 4))) (* (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (pow (cbrt k) -1/2)) (* (pow (sqrt k) -1/2) (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (* (pow k -1/2) (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (* (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (cbrt (pow k -1/2))) (* (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt (pow k -1/2))) (* (pow k -1/2) (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (* (pow k -1/4) (pow (* (* 2 n) PI) (/ (- 1 k) 2))) (* (pow k -1/2) (sqrt (* (* 2 n) PI))) (real->posit16 (* (pow k -1/2) (pow (* (* 2 n) PI) (/ (- 1 k) 2)))) (- (fma (* 1/4 (log (* 2 PI))) (* (exp (* 1/2 (log (* (* 2 n) PI)))) (* (log n) (* k k))) (fma (* 1/8 (exp (* 1/2 (log (* (* 2 n) PI))))) (* (* (log n) k) (* (log n) k)) (fma (* 1/8 (* (log (* 2 PI)) (log (* 2 PI)))) (* (* (exp (* 1/2 (log (* (* 2 n) PI)))) k) k) (exp (* 1/2 (log (* (* 2 n) PI))))))) (* 1/2 (* k (+ (* (exp (* 1/2 (log (* (* 2 n) PI)))) (log n)) (* (log (* 2 PI)) (exp (* 1/2 (log (* (* 2 n) PI))))))))) (exp (* (* 1/2 (- 1 k)) (log (* (* 2 n) PI)))) (exp (* (* 1/2 (- (log (* -2 PI)) (log (/ -1 n)))) (- 1 k))) (* (* 2 n) PI) (* (* 2 n) PI) (* (* 2 n) PI) (+ (* (* (* (* n PI) k) (sqrt 2)) (- +nan.0)) (fma (* +nan.0 (sqrt 2)) (* n PI) (+ (* (* (log (* 2 PI)) (* (* (* n PI) k) (sqrt 2))) (- +nan.0)) (* (* +nan.0 (sqrt 2)) (- (* (* n PI) (* (log n) k)) (* (* n PI) (* n PI))))))) (+ (* (- +nan.0) (/ (exp (* (* 1/2 (- 1 k)) (log (* (* 2 n) PI)))) k)) (* +nan.0 (- (/ (exp (* (* 1/2 (- 1 k)) (log (* (* 2 n) PI)))) (* k k)) (/ (exp (* (* 1/2 (- 1 k)) (log (* (* 2 n) PI)))) (* (* k k) k))))) (+ (* (/ (exp (* (* 1/2 (- (log (* -2 PI)) (log (/ -1 n)))) (- 1 k))) (* (* k k) k)) (- +nan.0)) (* +nan.0 (- (/ (exp (* (* 1/2 (- (log (* -2 PI)) (log (/ -1 n)))) (- 1 k))) (* k k)) (/ (exp (* (* 1/2 (- (log (* -2 PI)) (log (/ -1 n)))) (- 1 k))) k)))) 18.223 * * * [progress]: adding candidates to table 19.529 * * [progress]: iteration 4 / 4 19.529 * * * [progress]: picking best candidate 19.548 * * * * [pick]: Picked # 19.548 * * * [progress]: localizing error 19.575 * * * [progress]: generating rewritten candidates 19.575 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1 1) 19.611 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1) 19.631 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 19.647 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 20.090 * * * [progress]: generating series expansions 20.090 * * * * [progress]: [ 1 / 4 ] generating series at (2 1 1) 20.092 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 20.092 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 20.092 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 20.092 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 20.092 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 20.092 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 20.092 * [taylor]: Taking taylor expansion of 1/2 in k 20.092 * [backup-simplify]: Simplify 1/2 into 1/2 20.092 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 20.092 * [taylor]: Taking taylor expansion of 1/2 in k 20.092 * [backup-simplify]: Simplify 1/2 into 1/2 20.092 * [taylor]: Taking taylor expansion of k in k 20.092 * [backup-simplify]: Simplify 0 into 0 20.092 * [backup-simplify]: Simplify 1 into 1 20.092 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 20.092 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 20.092 * [taylor]: Taking taylor expansion of 2 in k 20.092 * [backup-simplify]: Simplify 2 into 2 20.092 * [taylor]: Taking taylor expansion of (* n PI) in k 20.092 * [taylor]: Taking taylor expansion of n in k 20.092 * [backup-simplify]: Simplify n into n 20.092 * [taylor]: Taking taylor expansion of PI in k 20.092 * [backup-simplify]: Simplify PI into PI 20.092 * [backup-simplify]: Simplify (* n PI) into (* n PI) 20.092 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 20.093 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 20.093 * [backup-simplify]: Simplify (* 1/2 0) into 0 20.094 * [backup-simplify]: Simplify (- 0) into 0 20.094 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 20.094 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 20.094 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 20.094 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 20.094 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 20.094 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 20.095 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 20.095 * [taylor]: Taking taylor expansion of 1/2 in n 20.095 * [backup-simplify]: Simplify 1/2 into 1/2 20.095 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 20.095 * [taylor]: Taking taylor expansion of 1/2 in n 20.095 * [backup-simplify]: Simplify 1/2 into 1/2 20.095 * [taylor]: Taking taylor expansion of k in n 20.095 * [backup-simplify]: Simplify k into k 20.095 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 20.095 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 20.095 * [taylor]: Taking taylor expansion of 2 in n 20.095 * [backup-simplify]: Simplify 2 into 2 20.095 * [taylor]: Taking taylor expansion of (* n PI) in n 20.095 * [taylor]: Taking taylor expansion of n in n 20.095 * [backup-simplify]: Simplify 0 into 0 20.095 * [backup-simplify]: Simplify 1 into 1 20.095 * [taylor]: Taking taylor expansion of PI in n 20.095 * [backup-simplify]: Simplify PI into PI 20.095 * [backup-simplify]: Simplify (* 0 PI) into 0 20.096 * [backup-simplify]: Simplify (* 2 0) into 0 20.098 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 20.099 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 20.100 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 20.100 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 20.100 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 20.100 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 20.102 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 20.103 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 20.104 * [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))))) 20.104 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 20.104 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 20.104 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 20.104 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 20.104 * [taylor]: Taking taylor expansion of 1/2 in n 20.104 * [backup-simplify]: Simplify 1/2 into 1/2 20.104 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 20.104 * [taylor]: Taking taylor expansion of 1/2 in n 20.105 * [backup-simplify]: Simplify 1/2 into 1/2 20.105 * [taylor]: Taking taylor expansion of k in n 20.105 * [backup-simplify]: Simplify k into k 20.105 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 20.105 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 20.105 * [taylor]: Taking taylor expansion of 2 in n 20.105 * [backup-simplify]: Simplify 2 into 2 20.105 * [taylor]: Taking taylor expansion of (* n PI) in n 20.105 * [taylor]: Taking taylor expansion of n in n 20.105 * [backup-simplify]: Simplify 0 into 0 20.105 * [backup-simplify]: Simplify 1 into 1 20.105 * [taylor]: Taking taylor expansion of PI in n 20.105 * [backup-simplify]: Simplify PI into PI 20.105 * [backup-simplify]: Simplify (* 0 PI) into 0 20.106 * [backup-simplify]: Simplify (* 2 0) into 0 20.107 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 20.109 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 20.110 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 20.111 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 20.111 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 20.111 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 20.112 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 20.113 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 20.114 * [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))))) 20.115 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 20.115 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 20.115 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 20.115 * [taylor]: Taking taylor expansion of 1/2 in k 20.115 * [backup-simplify]: Simplify 1/2 into 1/2 20.115 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 20.115 * [taylor]: Taking taylor expansion of 1/2 in k 20.115 * [backup-simplify]: Simplify 1/2 into 1/2 20.115 * [taylor]: Taking taylor expansion of k in k 20.115 * [backup-simplify]: Simplify 0 into 0 20.115 * [backup-simplify]: Simplify 1 into 1 20.115 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 20.115 * [taylor]: Taking taylor expansion of (log n) in k 20.115 * [taylor]: Taking taylor expansion of n in k 20.115 * [backup-simplify]: Simplify n into n 20.115 * [backup-simplify]: Simplify (log n) into (log n) 20.115 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 20.115 * [taylor]: Taking taylor expansion of (* 2 PI) in k 20.115 * [taylor]: Taking taylor expansion of 2 in k 20.115 * [backup-simplify]: Simplify 2 into 2 20.115 * [taylor]: Taking taylor expansion of PI in k 20.115 * [backup-simplify]: Simplify PI into PI 20.116 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 20.117 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 20.117 * [backup-simplify]: Simplify (* 1/2 0) into 0 20.118 * [backup-simplify]: Simplify (- 0) into 0 20.118 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 20.119 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 20.120 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 20.122 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 20.123 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 20.124 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 20.125 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 20.127 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 20.128 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 20.128 * [backup-simplify]: Simplify (- 0) into 0 20.128 * [backup-simplify]: Simplify (+ 0 0) into 0 20.130 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 20.131 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 20.133 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 20.133 * [taylor]: Taking taylor expansion of 0 in k 20.133 * [backup-simplify]: Simplify 0 into 0 20.133 * [backup-simplify]: Simplify 0 into 0 20.134 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 20.135 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 20.137 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 20.137 * [backup-simplify]: Simplify (+ 0 0) into 0 20.138 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 20.138 * [backup-simplify]: Simplify (- 1/2) into -1/2 20.139 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 20.140 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 20.144 * [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))))))) 20.147 * [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))))))) 20.149 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 20.150 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 20.153 * [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 20.154 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 20.155 * [backup-simplify]: Simplify (- 0) into 0 20.155 * [backup-simplify]: Simplify (+ 0 0) into 0 20.156 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 20.158 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 20.161 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 20.161 * [taylor]: Taking taylor expansion of 0 in k 20.161 * [backup-simplify]: Simplify 0 into 0 20.161 * [backup-simplify]: Simplify 0 into 0 20.161 * [backup-simplify]: Simplify 0 into 0 20.163 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 20.176 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 20.178 * [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 20.178 * [backup-simplify]: Simplify (+ 0 0) into 0 20.179 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 20.179 * [backup-simplify]: Simplify (- 0) into 0 20.179 * [backup-simplify]: Simplify (+ 0 0) into 0 20.180 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 20.183 * [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))))) 20.186 * [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))))) 20.192 * [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))))) 20.192 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 20.192 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 20.192 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 20.192 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 20.192 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 20.192 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 20.192 * [taylor]: Taking taylor expansion of 1/2 in k 20.192 * [backup-simplify]: Simplify 1/2 into 1/2 20.192 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 20.192 * [taylor]: Taking taylor expansion of 1/2 in k 20.192 * [backup-simplify]: Simplify 1/2 into 1/2 20.192 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.192 * [taylor]: Taking taylor expansion of k in k 20.192 * [backup-simplify]: Simplify 0 into 0 20.192 * [backup-simplify]: Simplify 1 into 1 20.193 * [backup-simplify]: Simplify (/ 1 1) into 1 20.193 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 20.193 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 20.193 * [taylor]: Taking taylor expansion of 2 in k 20.193 * [backup-simplify]: Simplify 2 into 2 20.193 * [taylor]: Taking taylor expansion of (/ PI n) in k 20.193 * [taylor]: Taking taylor expansion of PI in k 20.193 * [backup-simplify]: Simplify PI into PI 20.193 * [taylor]: Taking taylor expansion of n in k 20.193 * [backup-simplify]: Simplify n into n 20.193 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 20.193 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 20.193 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 20.193 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 20.194 * [backup-simplify]: Simplify (- 1/2) into -1/2 20.194 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 20.194 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 20.194 * [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)))) 20.194 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 20.194 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 20.194 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 20.194 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 20.194 * [taylor]: Taking taylor expansion of 1/2 in n 20.194 * [backup-simplify]: Simplify 1/2 into 1/2 20.194 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 20.194 * [taylor]: Taking taylor expansion of 1/2 in n 20.194 * [backup-simplify]: Simplify 1/2 into 1/2 20.194 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.194 * [taylor]: Taking taylor expansion of k in n 20.194 * [backup-simplify]: Simplify k into k 20.194 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.194 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 20.194 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 20.194 * [taylor]: Taking taylor expansion of 2 in n 20.194 * [backup-simplify]: Simplify 2 into 2 20.194 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.194 * [taylor]: Taking taylor expansion of PI in n 20.194 * [backup-simplify]: Simplify PI into PI 20.194 * [taylor]: Taking taylor expansion of n in n 20.194 * [backup-simplify]: Simplify 0 into 0 20.194 * [backup-simplify]: Simplify 1 into 1 20.195 * [backup-simplify]: Simplify (/ PI 1) into PI 20.195 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 20.196 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 20.196 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 20.196 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 20.196 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 20.197 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 20.197 * [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))) 20.198 * [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)))) 20.198 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 20.198 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 20.198 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 20.198 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 20.198 * [taylor]: Taking taylor expansion of 1/2 in n 20.198 * [backup-simplify]: Simplify 1/2 into 1/2 20.198 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 20.198 * [taylor]: Taking taylor expansion of 1/2 in n 20.198 * [backup-simplify]: Simplify 1/2 into 1/2 20.198 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.198 * [taylor]: Taking taylor expansion of k in n 20.198 * [backup-simplify]: Simplify k into k 20.198 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.198 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 20.198 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 20.198 * [taylor]: Taking taylor expansion of 2 in n 20.198 * [backup-simplify]: Simplify 2 into 2 20.198 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.198 * [taylor]: Taking taylor expansion of PI in n 20.198 * [backup-simplify]: Simplify PI into PI 20.198 * [taylor]: Taking taylor expansion of n in n 20.198 * [backup-simplify]: Simplify 0 into 0 20.198 * [backup-simplify]: Simplify 1 into 1 20.199 * [backup-simplify]: Simplify (/ PI 1) into PI 20.199 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 20.200 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 20.200 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 20.200 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 20.200 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 20.201 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 20.202 * [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))) 20.202 * [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)))) 20.202 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 20.202 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 20.202 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 20.202 * [taylor]: Taking taylor expansion of 1/2 in k 20.202 * [backup-simplify]: Simplify 1/2 into 1/2 20.202 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 20.202 * [taylor]: Taking taylor expansion of 1/2 in k 20.202 * [backup-simplify]: Simplify 1/2 into 1/2 20.202 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.203 * [taylor]: Taking taylor expansion of k in k 20.203 * [backup-simplify]: Simplify 0 into 0 20.203 * [backup-simplify]: Simplify 1 into 1 20.203 * [backup-simplify]: Simplify (/ 1 1) into 1 20.203 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 20.203 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 20.203 * [taylor]: Taking taylor expansion of (* 2 PI) in k 20.203 * [taylor]: Taking taylor expansion of 2 in k 20.203 * [backup-simplify]: Simplify 2 into 2 20.203 * [taylor]: Taking taylor expansion of PI in k 20.203 * [backup-simplify]: Simplify PI into PI 20.203 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 20.204 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 20.204 * [taylor]: Taking taylor expansion of (log n) in k 20.204 * [taylor]: Taking taylor expansion of n in k 20.204 * [backup-simplify]: Simplify n into n 20.204 * [backup-simplify]: Simplify (log n) into (log n) 20.204 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 20.205 * [backup-simplify]: Simplify (- 1/2) into -1/2 20.205 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 20.205 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 20.206 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 20.206 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 20.207 * [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)))) 20.208 * [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)))) 20.208 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 20.209 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 20.210 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 20.210 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 20.210 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 20.211 * [backup-simplify]: Simplify (- 0) into 0 20.211 * [backup-simplify]: Simplify (+ 0 0) into 0 20.212 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 20.213 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 20.214 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 20.214 * [taylor]: Taking taylor expansion of 0 in k 20.214 * [backup-simplify]: Simplify 0 into 0 20.214 * [backup-simplify]: Simplify 0 into 0 20.214 * [backup-simplify]: Simplify 0 into 0 20.216 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.216 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 20.220 * [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 20.220 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.221 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 20.222 * [backup-simplify]: Simplify (- 0) into 0 20.222 * [backup-simplify]: Simplify (+ 0 0) into 0 20.224 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 20.225 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 20.227 * [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 20.227 * [taylor]: Taking taylor expansion of 0 in k 20.227 * [backup-simplify]: Simplify 0 into 0 20.227 * [backup-simplify]: Simplify 0 into 0 20.227 * [backup-simplify]: Simplify 0 into 0 20.227 * [backup-simplify]: Simplify 0 into 0 20.229 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.230 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 20.235 * [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 20.235 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.236 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 20.236 * [backup-simplify]: Simplify (- 0) into 0 20.237 * [backup-simplify]: Simplify (+ 0 0) into 0 20.238 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 20.240 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 20.242 * [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 20.242 * [taylor]: Taking taylor expansion of 0 in k 20.242 * [backup-simplify]: Simplify 0 into 0 20.242 * [backup-simplify]: Simplify 0 into 0 20.243 * [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))))) 20.244 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 20.244 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 20.244 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 20.244 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 20.244 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 20.244 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 20.244 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 20.244 * [taylor]: Taking taylor expansion of 1/2 in k 20.244 * [backup-simplify]: Simplify 1/2 into 1/2 20.244 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.244 * [taylor]: Taking taylor expansion of k in k 20.244 * [backup-simplify]: Simplify 0 into 0 20.244 * [backup-simplify]: Simplify 1 into 1 20.245 * [backup-simplify]: Simplify (/ 1 1) into 1 20.245 * [taylor]: Taking taylor expansion of 1/2 in k 20.245 * [backup-simplify]: Simplify 1/2 into 1/2 20.245 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 20.245 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 20.245 * [taylor]: Taking taylor expansion of -2 in k 20.245 * [backup-simplify]: Simplify -2 into -2 20.245 * [taylor]: Taking taylor expansion of (/ PI n) in k 20.245 * [taylor]: Taking taylor expansion of PI in k 20.245 * [backup-simplify]: Simplify PI into PI 20.245 * [taylor]: Taking taylor expansion of n in k 20.245 * [backup-simplify]: Simplify n into n 20.245 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 20.245 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 20.245 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 20.246 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 20.246 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 20.246 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 20.246 * [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))) 20.246 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 20.246 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 20.246 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 20.247 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 20.247 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 20.247 * [taylor]: Taking taylor expansion of 1/2 in n 20.247 * [backup-simplify]: Simplify 1/2 into 1/2 20.247 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.247 * [taylor]: Taking taylor expansion of k in n 20.247 * [backup-simplify]: Simplify k into k 20.247 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.247 * [taylor]: Taking taylor expansion of 1/2 in n 20.247 * [backup-simplify]: Simplify 1/2 into 1/2 20.247 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 20.247 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 20.247 * [taylor]: Taking taylor expansion of -2 in n 20.247 * [backup-simplify]: Simplify -2 into -2 20.247 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.247 * [taylor]: Taking taylor expansion of PI in n 20.247 * [backup-simplify]: Simplify PI into PI 20.247 * [taylor]: Taking taylor expansion of n in n 20.247 * [backup-simplify]: Simplify 0 into 0 20.247 * [backup-simplify]: Simplify 1 into 1 20.247 * [backup-simplify]: Simplify (/ PI 1) into PI 20.248 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 20.249 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 20.249 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 20.249 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 20.250 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 20.251 * [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))) 20.252 * [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)))) 20.252 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 20.252 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 20.252 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 20.253 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 20.253 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 20.253 * [taylor]: Taking taylor expansion of 1/2 in n 20.253 * [backup-simplify]: Simplify 1/2 into 1/2 20.253 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.253 * [taylor]: Taking taylor expansion of k in n 20.253 * [backup-simplify]: Simplify k into k 20.253 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.253 * [taylor]: Taking taylor expansion of 1/2 in n 20.253 * [backup-simplify]: Simplify 1/2 into 1/2 20.253 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 20.253 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 20.253 * [taylor]: Taking taylor expansion of -2 in n 20.253 * [backup-simplify]: Simplify -2 into -2 20.253 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.253 * [taylor]: Taking taylor expansion of PI in n 20.253 * [backup-simplify]: Simplify PI into PI 20.253 * [taylor]: Taking taylor expansion of n in n 20.253 * [backup-simplify]: Simplify 0 into 0 20.253 * [backup-simplify]: Simplify 1 into 1 20.253 * [backup-simplify]: Simplify (/ PI 1) into PI 20.254 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 20.255 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 20.255 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 20.255 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 20.256 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 20.257 * [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))) 20.258 * [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)))) 20.258 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 20.258 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 20.258 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 20.259 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 20.259 * [taylor]: Taking taylor expansion of 1/2 in k 20.259 * [backup-simplify]: Simplify 1/2 into 1/2 20.259 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.259 * [taylor]: Taking taylor expansion of k in k 20.259 * [backup-simplify]: Simplify 0 into 0 20.259 * [backup-simplify]: Simplify 1 into 1 20.259 * [backup-simplify]: Simplify (/ 1 1) into 1 20.259 * [taylor]: Taking taylor expansion of 1/2 in k 20.259 * [backup-simplify]: Simplify 1/2 into 1/2 20.259 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 20.259 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 20.259 * [taylor]: Taking taylor expansion of (* -2 PI) in k 20.259 * [taylor]: Taking taylor expansion of -2 in k 20.259 * [backup-simplify]: Simplify -2 into -2 20.259 * [taylor]: Taking taylor expansion of PI in k 20.259 * [backup-simplify]: Simplify PI into PI 20.260 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 20.261 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 20.261 * [taylor]: Taking taylor expansion of (log n) in k 20.261 * [taylor]: Taking taylor expansion of n in k 20.261 * [backup-simplify]: Simplify n into n 20.261 * [backup-simplify]: Simplify (log n) into (log n) 20.262 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 20.262 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 20.262 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 20.263 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 20.265 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 20.266 * [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)))) 20.267 * [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)))) 20.268 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 20.269 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 20.271 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 20.271 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 20.272 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 20.272 * [backup-simplify]: Simplify (+ 0 0) into 0 20.273 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 20.275 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 20.277 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 20.277 * [taylor]: Taking taylor expansion of 0 in k 20.277 * [backup-simplify]: Simplify 0 into 0 20.277 * [backup-simplify]: Simplify 0 into 0 20.277 * [backup-simplify]: Simplify 0 into 0 20.278 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.280 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 20.283 * [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 20.284 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.285 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 20.285 * [backup-simplify]: Simplify (+ 0 0) into 0 20.287 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 20.288 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 20.294 * [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 20.294 * [taylor]: Taking taylor expansion of 0 in k 20.294 * [backup-simplify]: Simplify 0 into 0 20.294 * [backup-simplify]: Simplify 0 into 0 20.294 * [backup-simplify]: Simplify 0 into 0 20.294 * [backup-simplify]: Simplify 0 into 0 20.296 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.297 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 20.303 * [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 20.304 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.305 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 20.305 * [backup-simplify]: Simplify (+ 0 0) into 0 20.306 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 20.307 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 20.310 * [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 20.310 * [taylor]: Taking taylor expansion of 0 in k 20.310 * [backup-simplify]: Simplify 0 into 0 20.310 * [backup-simplify]: Simplify 0 into 0 20.312 * [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))))) 20.312 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1) 20.312 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) 20.312 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 20.313 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 20.313 * [taylor]: Taking taylor expansion of 2 in n 20.313 * [backup-simplify]: Simplify 2 into 2 20.313 * [taylor]: Taking taylor expansion of (* n PI) in n 20.313 * [taylor]: Taking taylor expansion of n in n 20.313 * [backup-simplify]: Simplify 0 into 0 20.313 * [backup-simplify]: Simplify 1 into 1 20.313 * [taylor]: Taking taylor expansion of PI in n 20.313 * [backup-simplify]: Simplify PI into PI 20.313 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 20.313 * [taylor]: Taking taylor expansion of 2 in n 20.313 * [backup-simplify]: Simplify 2 into 2 20.313 * [taylor]: Taking taylor expansion of (* n PI) in n 20.313 * [taylor]: Taking taylor expansion of n in n 20.313 * [backup-simplify]: Simplify 0 into 0 20.313 * [backup-simplify]: Simplify 1 into 1 20.313 * [taylor]: Taking taylor expansion of PI in n 20.313 * [backup-simplify]: Simplify PI into PI 20.314 * [backup-simplify]: Simplify (* 0 PI) into 0 20.314 * [backup-simplify]: Simplify (* 2 0) into 0 20.314 * [backup-simplify]: Simplify 0 into 0 20.316 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 20.317 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 20.318 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 20.319 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 20.320 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 20.320 * [backup-simplify]: Simplify 0 into 0 20.321 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 20.322 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 20.322 * [backup-simplify]: Simplify 0 into 0 20.323 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 20.323 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 20.323 * [backup-simplify]: Simplify 0 into 0 20.324 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 20.325 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 20.325 * [backup-simplify]: Simplify 0 into 0 20.326 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 20.327 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 20.327 * [backup-simplify]: Simplify 0 into 0 20.328 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 20.329 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 20.329 * [backup-simplify]: Simplify 0 into 0 20.330 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 20.330 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) 20.330 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 20.330 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 20.330 * [taylor]: Taking taylor expansion of 2 in n 20.330 * [backup-simplify]: Simplify 2 into 2 20.330 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.330 * [taylor]: Taking taylor expansion of PI in n 20.330 * [backup-simplify]: Simplify PI into PI 20.330 * [taylor]: Taking taylor expansion of n in n 20.330 * [backup-simplify]: Simplify 0 into 0 20.330 * [backup-simplify]: Simplify 1 into 1 20.331 * [backup-simplify]: Simplify (/ PI 1) into PI 20.331 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 20.331 * [taylor]: Taking taylor expansion of 2 in n 20.331 * [backup-simplify]: Simplify 2 into 2 20.331 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.331 * [taylor]: Taking taylor expansion of PI in n 20.331 * [backup-simplify]: Simplify PI into PI 20.331 * [taylor]: Taking taylor expansion of n in n 20.331 * [backup-simplify]: Simplify 0 into 0 20.331 * [backup-simplify]: Simplify 1 into 1 20.331 * [backup-simplify]: Simplify (/ PI 1) into PI 20.331 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 20.332 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 20.332 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 20.333 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 20.333 * [backup-simplify]: Simplify 0 into 0 20.333 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.334 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 20.334 * [backup-simplify]: Simplify 0 into 0 20.335 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.335 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 20.335 * [backup-simplify]: Simplify 0 into 0 20.336 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.337 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 20.337 * [backup-simplify]: Simplify 0 into 0 20.337 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.338 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 20.338 * [backup-simplify]: Simplify 0 into 0 20.339 * [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 20.340 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 20.340 * [backup-simplify]: Simplify 0 into 0 20.340 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 20.341 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n)) 20.341 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 20.341 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 20.341 * [taylor]: Taking taylor expansion of -2 in n 20.341 * [backup-simplify]: Simplify -2 into -2 20.341 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.341 * [taylor]: Taking taylor expansion of PI in n 20.341 * [backup-simplify]: Simplify PI into PI 20.341 * [taylor]: Taking taylor expansion of n in n 20.341 * [backup-simplify]: Simplify 0 into 0 20.341 * [backup-simplify]: Simplify 1 into 1 20.342 * [backup-simplify]: Simplify (/ PI 1) into PI 20.342 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 20.342 * [taylor]: Taking taylor expansion of -2 in n 20.342 * [backup-simplify]: Simplify -2 into -2 20.342 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.342 * [taylor]: Taking taylor expansion of PI in n 20.342 * [backup-simplify]: Simplify PI into PI 20.342 * [taylor]: Taking taylor expansion of n in n 20.342 * [backup-simplify]: Simplify 0 into 0 20.342 * [backup-simplify]: Simplify 1 into 1 20.342 * [backup-simplify]: Simplify (/ PI 1) into PI 20.343 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 20.343 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 20.344 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 20.345 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 20.345 * [backup-simplify]: Simplify 0 into 0 20.346 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.347 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 20.348 * [backup-simplify]: Simplify 0 into 0 20.349 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.350 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 20.350 * [backup-simplify]: Simplify 0 into 0 20.351 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.353 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 20.353 * [backup-simplify]: Simplify 0 into 0 20.354 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.356 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 20.356 * [backup-simplify]: Simplify 0 into 0 20.357 * [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 20.359 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 20.359 * [backup-simplify]: Simplify 0 into 0 20.360 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 20.360 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 20.361 * [backup-simplify]: Simplify (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) into (* (pow (/ 1 k) 1/4) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 20.361 * [approximate]: Taking taylor expansion of (* (pow (/ 1 k) 1/4) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 20.361 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/4) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 20.361 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 20.361 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 20.361 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 20.361 * [taylor]: Taking taylor expansion of 1/4 in k 20.361 * [backup-simplify]: Simplify 1/4 into 1/4 20.361 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 20.361 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.361 * [taylor]: Taking taylor expansion of k in k 20.361 * [backup-simplify]: Simplify 0 into 0 20.361 * [backup-simplify]: Simplify 1 into 1 20.361 * [backup-simplify]: Simplify (/ 1 1) into 1 20.362 * [backup-simplify]: Simplify (log 1) into 0 20.362 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 20.362 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 20.362 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 20.363 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 20.363 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 20.363 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 20.363 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 20.363 * [taylor]: Taking taylor expansion of 1/2 in k 20.363 * [backup-simplify]: Simplify 1/2 into 1/2 20.363 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 20.363 * [taylor]: Taking taylor expansion of 1/2 in k 20.363 * [backup-simplify]: Simplify 1/2 into 1/2 20.363 * [taylor]: Taking taylor expansion of k in k 20.363 * [backup-simplify]: Simplify 0 into 0 20.363 * [backup-simplify]: Simplify 1 into 1 20.363 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 20.363 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 20.363 * [taylor]: Taking taylor expansion of 2 in k 20.363 * [backup-simplify]: Simplify 2 into 2 20.363 * [taylor]: Taking taylor expansion of (* n PI) in k 20.363 * [taylor]: Taking taylor expansion of n in k 20.363 * [backup-simplify]: Simplify n into n 20.363 * [taylor]: Taking taylor expansion of PI in k 20.363 * [backup-simplify]: Simplify PI into PI 20.363 * [backup-simplify]: Simplify (* n PI) into (* n PI) 20.363 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 20.363 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 20.364 * [backup-simplify]: Simplify (* 1/2 0) into 0 20.364 * [backup-simplify]: Simplify (- 0) into 0 20.364 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 20.365 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 20.365 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 20.365 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/4) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 20.365 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in n 20.365 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in n 20.365 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in n 20.365 * [taylor]: Taking taylor expansion of 1/4 in n 20.365 * [backup-simplify]: Simplify 1/4 into 1/4 20.365 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in n 20.365 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.365 * [taylor]: Taking taylor expansion of k in n 20.365 * [backup-simplify]: Simplify k into k 20.365 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.365 * [backup-simplify]: Simplify (log (/ 1 k)) into (log (/ 1 k)) 20.365 * [backup-simplify]: Simplify (* 1/4 (log (/ 1 k))) into (* 1/4 (log (/ 1 k))) 20.365 * [backup-simplify]: Simplify (exp (* 1/4 (log (/ 1 k)))) into (pow (/ 1 k) 1/4) 20.365 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 20.365 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 20.365 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 20.365 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 20.365 * [taylor]: Taking taylor expansion of 1/2 in n 20.365 * [backup-simplify]: Simplify 1/2 into 1/2 20.365 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 20.365 * [taylor]: Taking taylor expansion of 1/2 in n 20.365 * [backup-simplify]: Simplify 1/2 into 1/2 20.365 * [taylor]: Taking taylor expansion of k in n 20.365 * [backup-simplify]: Simplify k into k 20.365 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 20.365 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 20.365 * [taylor]: Taking taylor expansion of 2 in n 20.365 * [backup-simplify]: Simplify 2 into 2 20.365 * [taylor]: Taking taylor expansion of (* n PI) in n 20.365 * [taylor]: Taking taylor expansion of n in n 20.365 * [backup-simplify]: Simplify 0 into 0 20.365 * [backup-simplify]: Simplify 1 into 1 20.365 * [taylor]: Taking taylor expansion of PI in n 20.365 * [backup-simplify]: Simplify PI into PI 20.366 * [backup-simplify]: Simplify (* 0 PI) into 0 20.366 * [backup-simplify]: Simplify (* 2 0) into 0 20.367 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 20.368 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 20.369 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 20.369 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 20.369 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 20.369 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 20.370 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 20.372 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 20.372 * [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))))) 20.372 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/4) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 20.372 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in n 20.372 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in n 20.372 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in n 20.372 * [taylor]: Taking taylor expansion of 1/4 in n 20.372 * [backup-simplify]: Simplify 1/4 into 1/4 20.372 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in n 20.372 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.372 * [taylor]: Taking taylor expansion of k in n 20.372 * [backup-simplify]: Simplify k into k 20.373 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.373 * [backup-simplify]: Simplify (log (/ 1 k)) into (log (/ 1 k)) 20.373 * [backup-simplify]: Simplify (* 1/4 (log (/ 1 k))) into (* 1/4 (log (/ 1 k))) 20.373 * [backup-simplify]: Simplify (exp (* 1/4 (log (/ 1 k)))) into (pow (/ 1 k) 1/4) 20.373 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 20.373 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 20.373 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 20.373 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 20.373 * [taylor]: Taking taylor expansion of 1/2 in n 20.373 * [backup-simplify]: Simplify 1/2 into 1/2 20.373 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 20.373 * [taylor]: Taking taylor expansion of 1/2 in n 20.373 * [backup-simplify]: Simplify 1/2 into 1/2 20.373 * [taylor]: Taking taylor expansion of k in n 20.373 * [backup-simplify]: Simplify k into k 20.373 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 20.373 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 20.373 * [taylor]: Taking taylor expansion of 2 in n 20.373 * [backup-simplify]: Simplify 2 into 2 20.373 * [taylor]: Taking taylor expansion of (* n PI) in n 20.373 * [taylor]: Taking taylor expansion of n in n 20.373 * [backup-simplify]: Simplify 0 into 0 20.373 * [backup-simplify]: Simplify 1 into 1 20.373 * [taylor]: Taking taylor expansion of PI in n 20.373 * [backup-simplify]: Simplify PI into PI 20.373 * [backup-simplify]: Simplify (* 0 PI) into 0 20.374 * [backup-simplify]: Simplify (* 2 0) into 0 20.374 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 20.375 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 20.376 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 20.376 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 20.376 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 20.376 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 20.377 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 20.378 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 20.379 * [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))))) 20.379 * [backup-simplify]: Simplify (* (pow (/ 1 k) 1/4) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) 20.379 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) in k 20.379 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 20.379 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 20.379 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 20.380 * [taylor]: Taking taylor expansion of 1/2 in k 20.380 * [backup-simplify]: Simplify 1/2 into 1/2 20.380 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 20.380 * [taylor]: Taking taylor expansion of 1/2 in k 20.380 * [backup-simplify]: Simplify 1/2 into 1/2 20.380 * [taylor]: Taking taylor expansion of k in k 20.380 * [backup-simplify]: Simplify 0 into 0 20.380 * [backup-simplify]: Simplify 1 into 1 20.380 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 20.380 * [taylor]: Taking taylor expansion of (log n) in k 20.380 * [taylor]: Taking taylor expansion of n in k 20.380 * [backup-simplify]: Simplify n into n 20.380 * [backup-simplify]: Simplify (log n) into (log n) 20.380 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 20.380 * [taylor]: Taking taylor expansion of (* 2 PI) in k 20.380 * [taylor]: Taking taylor expansion of 2 in k 20.380 * [backup-simplify]: Simplify 2 into 2 20.380 * [taylor]: Taking taylor expansion of PI in k 20.380 * [backup-simplify]: Simplify PI into PI 20.380 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 20.381 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 20.381 * [backup-simplify]: Simplify (* 1/2 0) into 0 20.381 * [backup-simplify]: Simplify (- 0) into 0 20.382 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 20.382 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 20.383 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 20.384 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 20.384 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 20.384 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 20.384 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 20.384 * [taylor]: Taking taylor expansion of 1/4 in k 20.384 * [backup-simplify]: Simplify 1/4 into 1/4 20.384 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 20.384 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.384 * [taylor]: Taking taylor expansion of k in k 20.384 * [backup-simplify]: Simplify 0 into 0 20.384 * [backup-simplify]: Simplify 1 into 1 20.384 * [backup-simplify]: Simplify (/ 1 1) into 1 20.384 * [backup-simplify]: Simplify (log 1) into 0 20.384 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 20.385 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 20.385 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 20.385 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k -1/4)) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) 20.386 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) 20.387 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 20.387 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 20.388 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 20.389 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 20.389 * [backup-simplify]: Simplify (- 0) into 0 20.389 * [backup-simplify]: Simplify (+ 0 0) into 0 20.390 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 20.391 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 20.392 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 20.392 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 20.393 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (/ 1 k) 1)))) 1) into 0 20.393 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log (/ 1 k)))) into 0 20.394 * [backup-simplify]: Simplify (* (exp (* 1/4 (log (/ 1 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 20.395 * [backup-simplify]: Simplify (+ (* (pow (/ 1 k) 1/4) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 20.395 * [taylor]: Taking taylor expansion of 0 in k 20.395 * [backup-simplify]: Simplify 0 into 0 20.395 * [backup-simplify]: Simplify 0 into 0 20.395 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 20.396 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 20.396 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 20.397 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0 20.397 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 20.397 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 20.398 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 20.399 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 20.399 * [backup-simplify]: Simplify (+ 0 0) into 0 20.400 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 20.400 * [backup-simplify]: Simplify (- 1/2) into -1/2 20.400 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 20.401 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 20.403 * [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))))))) 20.409 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (pow k -1/4))) into (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (/ 1 k) 1/4))))) 20.411 * [backup-simplify]: Simplify (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (/ 1 k) 1/4))))) into (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (/ 1 k) 1/4))))) 20.412 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 20.413 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 20.416 * [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 20.417 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 20.417 * [backup-simplify]: Simplify (- 0) into 0 20.418 * [backup-simplify]: Simplify (+ 0 0) into 0 20.419 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 20.421 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 20.424 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 20.424 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.426 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (/ 1 k) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (/ 1 k) 1)))) 2) into 0 20.426 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log (/ 1 k))))) into 0 20.428 * [backup-simplify]: Simplify (* (exp (* 1/4 (log (/ 1 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 20.430 * [backup-simplify]: Simplify (+ (* (pow (/ 1 k) 1/4) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 20.430 * [taylor]: Taking taylor expansion of 0 in k 20.430 * [backup-simplify]: Simplify 0 into 0 20.430 * [backup-simplify]: Simplify 0 into 0 20.430 * [backup-simplify]: Simplify 0 into 0 20.431 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.434 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 20.434 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 20.435 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 20.436 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 20.438 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 20.439 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 20.442 * [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 20.443 * [backup-simplify]: Simplify (+ 0 0) into 0 20.444 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 20.444 * [backup-simplify]: Simplify (- 0) into 0 20.445 * [backup-simplify]: Simplify (+ 0 0) into 0 20.447 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 20.450 * [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))))) 20.456 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 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))))) (pow k -1/4)))) into (+ (* 1/8 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/8 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (* 1/4 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))))) 20.460 * [backup-simplify]: Simplify (+ (* 1/8 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/8 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (* 1/4 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))))) into (+ (* 1/8 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/8 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (* 1/4 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))))) 20.468 * [backup-simplify]: Simplify (+ (* (+ (* 1/8 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/8 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (* 1/4 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))))) (pow (* k 1) 2)) (+ (* (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (/ 1 k) 1/4))))) (* k 1)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)))) into (- (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)) (pow (pow k 7) 1/4))) (+ (* 1/4 (* (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (pow (pow k 7) 1/4))) (* 1/8 (* (* (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (pow k 7) 1/4)))))) (+ (* 1/2 (* (* (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (pow k 3) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)) (pow (pow k 3) 1/4))))) 20.469 * [backup-simplify]: Simplify (/ (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (sqrt (/ 1 k)))) into (* (pow k 1/4) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 20.469 * [approximate]: Taking taylor expansion of (* (pow k 1/4) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 20.469 * [taylor]: Taking taylor expansion of (* (pow k 1/4) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 20.469 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 20.469 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 20.469 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 20.469 * [taylor]: Taking taylor expansion of 1/4 in k 20.469 * [backup-simplify]: Simplify 1/4 into 1/4 20.469 * [taylor]: Taking taylor expansion of (log k) in k 20.469 * [taylor]: Taking taylor expansion of k in k 20.469 * [backup-simplify]: Simplify 0 into 0 20.469 * [backup-simplify]: Simplify 1 into 1 20.469 * [backup-simplify]: Simplify (log 1) into 0 20.469 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 20.469 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 20.469 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 20.470 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 20.470 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 20.470 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 20.470 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 20.470 * [taylor]: Taking taylor expansion of 1/2 in k 20.470 * [backup-simplify]: Simplify 1/2 into 1/2 20.470 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 20.470 * [taylor]: Taking taylor expansion of 1/2 in k 20.470 * [backup-simplify]: Simplify 1/2 into 1/2 20.470 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.470 * [taylor]: Taking taylor expansion of k in k 20.470 * [backup-simplify]: Simplify 0 into 0 20.470 * [backup-simplify]: Simplify 1 into 1 20.470 * [backup-simplify]: Simplify (/ 1 1) into 1 20.470 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 20.470 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 20.470 * [taylor]: Taking taylor expansion of 2 in k 20.470 * [backup-simplify]: Simplify 2 into 2 20.470 * [taylor]: Taking taylor expansion of (/ PI n) in k 20.470 * [taylor]: Taking taylor expansion of PI in k 20.470 * [backup-simplify]: Simplify PI into PI 20.470 * [taylor]: Taking taylor expansion of n in k 20.470 * [backup-simplify]: Simplify n into n 20.470 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 20.470 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 20.470 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 20.471 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 20.471 * [backup-simplify]: Simplify (- 1/2) into -1/2 20.471 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 20.471 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 20.471 * [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)))) 20.471 * [taylor]: Taking taylor expansion of (* (pow k 1/4) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 20.471 * [taylor]: Taking taylor expansion of (pow k 1/4) in n 20.471 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in n 20.471 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in n 20.471 * [taylor]: Taking taylor expansion of 1/4 in n 20.471 * [backup-simplify]: Simplify 1/4 into 1/4 20.471 * [taylor]: Taking taylor expansion of (log k) in n 20.471 * [taylor]: Taking taylor expansion of k in n 20.471 * [backup-simplify]: Simplify k into k 20.471 * [backup-simplify]: Simplify (log k) into (log k) 20.471 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 20.471 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 20.471 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 20.472 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 20.472 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 20.472 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 20.472 * [taylor]: Taking taylor expansion of 1/2 in n 20.472 * [backup-simplify]: Simplify 1/2 into 1/2 20.472 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 20.472 * [taylor]: Taking taylor expansion of 1/2 in n 20.472 * [backup-simplify]: Simplify 1/2 into 1/2 20.472 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.472 * [taylor]: Taking taylor expansion of k in n 20.472 * [backup-simplify]: Simplify k into k 20.472 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.472 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 20.472 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 20.472 * [taylor]: Taking taylor expansion of 2 in n 20.472 * [backup-simplify]: Simplify 2 into 2 20.472 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.472 * [taylor]: Taking taylor expansion of PI in n 20.472 * [backup-simplify]: Simplify PI into PI 20.472 * [taylor]: Taking taylor expansion of n in n 20.472 * [backup-simplify]: Simplify 0 into 0 20.472 * [backup-simplify]: Simplify 1 into 1 20.472 * [backup-simplify]: Simplify (/ PI 1) into PI 20.472 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 20.473 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 20.473 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 20.473 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 20.473 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 20.474 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 20.475 * [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))) 20.476 * [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)))) 20.476 * [taylor]: Taking taylor expansion of (* (pow k 1/4) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 20.476 * [taylor]: Taking taylor expansion of (pow k 1/4) in n 20.476 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in n 20.476 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in n 20.476 * [taylor]: Taking taylor expansion of 1/4 in n 20.476 * [backup-simplify]: Simplify 1/4 into 1/4 20.476 * [taylor]: Taking taylor expansion of (log k) in n 20.476 * [taylor]: Taking taylor expansion of k in n 20.476 * [backup-simplify]: Simplify k into k 20.476 * [backup-simplify]: Simplify (log k) into (log k) 20.476 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 20.476 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 20.476 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 20.476 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 20.476 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 20.476 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 20.476 * [taylor]: Taking taylor expansion of 1/2 in n 20.476 * [backup-simplify]: Simplify 1/2 into 1/2 20.476 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 20.476 * [taylor]: Taking taylor expansion of 1/2 in n 20.476 * [backup-simplify]: Simplify 1/2 into 1/2 20.476 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.476 * [taylor]: Taking taylor expansion of k in n 20.476 * [backup-simplify]: Simplify k into k 20.476 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.476 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 20.476 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 20.476 * [taylor]: Taking taylor expansion of 2 in n 20.476 * [backup-simplify]: Simplify 2 into 2 20.476 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.476 * [taylor]: Taking taylor expansion of PI in n 20.476 * [backup-simplify]: Simplify PI into PI 20.476 * [taylor]: Taking taylor expansion of n in n 20.476 * [backup-simplify]: Simplify 0 into 0 20.476 * [backup-simplify]: Simplify 1 into 1 20.477 * [backup-simplify]: Simplify (/ PI 1) into PI 20.477 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 20.477 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 20.478 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 20.478 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 20.478 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 20.479 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 20.479 * [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))) 20.480 * [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)))) 20.481 * [backup-simplify]: Simplify (* (pow k 1/4) (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)))) (pow k 1/4)) 20.481 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (pow k 1/4)) in k 20.481 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 20.481 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 20.481 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 20.481 * [taylor]: Taking taylor expansion of 1/2 in k 20.481 * [backup-simplify]: Simplify 1/2 into 1/2 20.481 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 20.481 * [taylor]: Taking taylor expansion of 1/2 in k 20.481 * [backup-simplify]: Simplify 1/2 into 1/2 20.481 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.481 * [taylor]: Taking taylor expansion of k in k 20.481 * [backup-simplify]: Simplify 0 into 0 20.481 * [backup-simplify]: Simplify 1 into 1 20.481 * [backup-simplify]: Simplify (/ 1 1) into 1 20.481 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 20.481 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 20.481 * [taylor]: Taking taylor expansion of (* 2 PI) in k 20.481 * [taylor]: Taking taylor expansion of 2 in k 20.481 * [backup-simplify]: Simplify 2 into 2 20.481 * [taylor]: Taking taylor expansion of PI in k 20.481 * [backup-simplify]: Simplify PI into PI 20.482 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 20.483 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 20.483 * [taylor]: Taking taylor expansion of (log n) in k 20.483 * [taylor]: Taking taylor expansion of n in k 20.483 * [backup-simplify]: Simplify n into n 20.483 * [backup-simplify]: Simplify (log n) into (log n) 20.483 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 20.483 * [backup-simplify]: Simplify (- 1/2) into -1/2 20.483 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 20.483 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 20.484 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 20.485 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 20.485 * [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)))) 20.486 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 20.486 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 20.486 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 20.486 * [taylor]: Taking taylor expansion of 1/4 in k 20.486 * [backup-simplify]: Simplify 1/4 into 1/4 20.486 * [taylor]: Taking taylor expansion of (log k) in k 20.486 * [taylor]: Taking taylor expansion of k in k 20.486 * [backup-simplify]: Simplify 0 into 0 20.486 * [backup-simplify]: Simplify 1 into 1 20.486 * [backup-simplify]: Simplify (log 1) into 0 20.486 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 20.486 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 20.486 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 20.487 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (pow k 1/4)) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (pow k 1/4)) 20.488 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (pow k 1/4)) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (pow k 1/4)) 20.488 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 20.489 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 20.490 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 20.490 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 20.490 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 20.490 * [backup-simplify]: Simplify (- 0) into 0 20.491 * [backup-simplify]: Simplify (+ 0 0) into 0 20.492 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 20.492 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 20.493 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 20.494 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow k 1)))) 1) into 0 20.494 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 20.495 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 20.495 * [backup-simplify]: Simplify (+ (* (pow k 1/4) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 20.496 * [taylor]: Taking taylor expansion of 0 in k 20.496 * [backup-simplify]: Simplify 0 into 0 20.496 * [backup-simplify]: Simplify 0 into 0 20.496 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 20.497 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 20.497 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 20.497 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 20.498 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) (* 0 (pow k 1/4))) into 0 20.498 * [backup-simplify]: Simplify 0 into 0 20.499 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.500 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 20.502 * [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 20.502 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.503 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 20.503 * [backup-simplify]: Simplify (- 0) into 0 20.504 * [backup-simplify]: Simplify (+ 0 0) into 0 20.505 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 20.510 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 20.513 * [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 20.515 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow k 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow k 1)))) 2) into 0 20.516 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 20.517 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 20.519 * [backup-simplify]: Simplify (+ (* (pow k 1/4) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 20.519 * [taylor]: Taking taylor expansion of 0 in k 20.519 * [backup-simplify]: Simplify 0 into 0 20.519 * [backup-simplify]: Simplify 0 into 0 20.519 * [backup-simplify]: Simplify 0 into 0 20.522 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 20.523 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 20.524 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 20.525 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 20.527 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) (+ (* 0 0) (* 0 (pow k 1/4)))) into 0 20.527 * [backup-simplify]: Simplify 0 into 0 20.528 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.530 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 20.537 * [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 20.537 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.538 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 20.539 * [backup-simplify]: Simplify (- 0) into 0 20.539 * [backup-simplify]: Simplify (+ 0 0) into 0 20.541 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 20.543 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 20.546 * [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 20.549 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow k 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow k 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow k 1)))) 6) into 0 20.550 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0 20.552 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 20.554 * [backup-simplify]: Simplify (+ (* (pow k 1/4) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 20.554 * [taylor]: Taking taylor expansion of 0 in k 20.554 * [backup-simplify]: Simplify 0 into 0 20.554 * [backup-simplify]: Simplify 0 into 0 20.556 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) (pow (/ 1 k) 1/4)) into (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow (/ 1 k) 1/4)) 20.556 * [backup-simplify]: Simplify (/ (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (sqrt (/ 1 (- k))))) into (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 20.557 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0 20.557 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 20.557 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 20.557 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 20.557 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 20.557 * [taylor]: Taking taylor expansion of (/ -1 k) in k 20.557 * [taylor]: Taking taylor expansion of -1 in k 20.557 * [backup-simplify]: Simplify -1 into -1 20.557 * [taylor]: Taking taylor expansion of k in k 20.557 * [backup-simplify]: Simplify 0 into 0 20.557 * [backup-simplify]: Simplify 1 into 1 20.557 * [backup-simplify]: Simplify (/ -1 1) into -1 20.558 * [backup-simplify]: Simplify (sqrt 0) into 0 20.559 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 20.560 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 20.560 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 20.561 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 20.564 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 20.566 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 20.568 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 20.568 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 20.568 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 20.568 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 20.568 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 20.568 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 20.568 * [taylor]: Taking taylor expansion of 1/2 in k 20.568 * [backup-simplify]: Simplify 1/2 into 1/2 20.568 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.568 * [taylor]: Taking taylor expansion of k in k 20.568 * [backup-simplify]: Simplify 0 into 0 20.569 * [backup-simplify]: Simplify 1 into 1 20.569 * [backup-simplify]: Simplify (/ 1 1) into 1 20.569 * [taylor]: Taking taylor expansion of 1/2 in k 20.569 * [backup-simplify]: Simplify 1/2 into 1/2 20.569 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 20.569 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 20.569 * [taylor]: Taking taylor expansion of -2 in k 20.569 * [backup-simplify]: Simplify -2 into -2 20.569 * [taylor]: Taking taylor expansion of (/ PI n) in k 20.569 * [taylor]: Taking taylor expansion of PI in k 20.569 * [backup-simplify]: Simplify PI into PI 20.569 * [taylor]: Taking taylor expansion of n in k 20.569 * [backup-simplify]: Simplify n into n 20.569 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 20.569 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 20.569 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 20.570 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 20.570 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 20.570 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 20.571 * [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))) 20.571 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 20.571 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in n 20.571 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in n 20.571 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 20.571 * [taylor]: Taking taylor expansion of (/ -1 k) in n 20.571 * [taylor]: Taking taylor expansion of -1 in n 20.571 * [backup-simplify]: Simplify -1 into -1 20.571 * [taylor]: Taking taylor expansion of k in n 20.571 * [backup-simplify]: Simplify k into k 20.571 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 20.571 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 20.571 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 20.571 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 20.571 * [backup-simplify]: Simplify (/ 1 (sqrt (/ -1 k))) into (/ 1 (sqrt (/ -1 k))) 20.572 * [backup-simplify]: Simplify (sqrt (/ 1 (sqrt (/ -1 k)))) into (sqrt (/ 1 (sqrt (/ -1 k)))) 20.572 * [backup-simplify]: Simplify (- (+ (* (/ 1 (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 20.572 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 (sqrt (/ -1 k)))))) into 0 20.572 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 20.572 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 20.572 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 20.572 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 20.572 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 20.572 * [taylor]: Taking taylor expansion of 1/2 in n 20.572 * [backup-simplify]: Simplify 1/2 into 1/2 20.572 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.572 * [taylor]: Taking taylor expansion of k in n 20.572 * [backup-simplify]: Simplify k into k 20.572 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.572 * [taylor]: Taking taylor expansion of 1/2 in n 20.572 * [backup-simplify]: Simplify 1/2 into 1/2 20.572 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 20.572 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 20.572 * [taylor]: Taking taylor expansion of -2 in n 20.572 * [backup-simplify]: Simplify -2 into -2 20.572 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.573 * [taylor]: Taking taylor expansion of PI in n 20.573 * [backup-simplify]: Simplify PI into PI 20.573 * [taylor]: Taking taylor expansion of n in n 20.573 * [backup-simplify]: Simplify 0 into 0 20.573 * [backup-simplify]: Simplify 1 into 1 20.573 * [backup-simplify]: Simplify (/ PI 1) into PI 20.574 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 20.575 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 20.575 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 20.575 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 20.577 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 20.578 * [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))) 20.579 * [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)))) 20.579 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 20.579 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in n 20.579 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in n 20.579 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 20.579 * [taylor]: Taking taylor expansion of (/ -1 k) in n 20.579 * [taylor]: Taking taylor expansion of -1 in n 20.579 * [backup-simplify]: Simplify -1 into -1 20.579 * [taylor]: Taking taylor expansion of k in n 20.579 * [backup-simplify]: Simplify k into k 20.579 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 20.579 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 20.580 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 20.580 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 20.580 * [backup-simplify]: Simplify (/ 1 (sqrt (/ -1 k))) into (/ 1 (sqrt (/ -1 k))) 20.580 * [backup-simplify]: Simplify (sqrt (/ 1 (sqrt (/ -1 k)))) into (sqrt (/ 1 (sqrt (/ -1 k)))) 20.580 * [backup-simplify]: Simplify (- (+ (* (/ 1 (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 20.580 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 (sqrt (/ -1 k)))))) into 0 20.580 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 20.580 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 20.580 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 20.580 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 20.580 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 20.580 * [taylor]: Taking taylor expansion of 1/2 in n 20.580 * [backup-simplify]: Simplify 1/2 into 1/2 20.581 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.581 * [taylor]: Taking taylor expansion of k in n 20.581 * [backup-simplify]: Simplify k into k 20.581 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.581 * [taylor]: Taking taylor expansion of 1/2 in n 20.581 * [backup-simplify]: Simplify 1/2 into 1/2 20.581 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 20.581 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 20.581 * [taylor]: Taking taylor expansion of -2 in n 20.581 * [backup-simplify]: Simplify -2 into -2 20.581 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.581 * [taylor]: Taking taylor expansion of PI in n 20.581 * [backup-simplify]: Simplify PI into PI 20.581 * [taylor]: Taking taylor expansion of n in n 20.581 * [backup-simplify]: Simplify 0 into 0 20.581 * [backup-simplify]: Simplify 1 into 1 20.582 * [backup-simplify]: Simplify (/ PI 1) into PI 20.582 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 20.583 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 20.583 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 20.583 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 20.585 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 20.586 * [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))) 20.587 * [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)))) 20.589 * [backup-simplify]: Simplify (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 20.589 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k 20.589 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 20.589 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 20.589 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 20.589 * [taylor]: Taking taylor expansion of (/ -1 k) in k 20.589 * [taylor]: Taking taylor expansion of -1 in k 20.589 * [backup-simplify]: Simplify -1 into -1 20.589 * [taylor]: Taking taylor expansion of k in k 20.589 * [backup-simplify]: Simplify 0 into 0 20.589 * [backup-simplify]: Simplify 1 into 1 20.590 * [backup-simplify]: Simplify (/ -1 1) into -1 20.590 * [backup-simplify]: Simplify (sqrt 0) into 0 20.591 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 20.592 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 20.593 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 20.593 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 20.597 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 20.599 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 20.601 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 20.601 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 20.601 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 20.601 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 20.601 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 20.601 * [taylor]: Taking taylor expansion of 1/2 in k 20.601 * [backup-simplify]: Simplify 1/2 into 1/2 20.601 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.601 * [taylor]: Taking taylor expansion of k in k 20.601 * [backup-simplify]: Simplify 0 into 0 20.601 * [backup-simplify]: Simplify 1 into 1 20.601 * [backup-simplify]: Simplify (/ 1 1) into 1 20.601 * [taylor]: Taking taylor expansion of 1/2 in k 20.602 * [backup-simplify]: Simplify 1/2 into 1/2 20.602 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 20.602 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 20.602 * [taylor]: Taking taylor expansion of (* -2 PI) in k 20.602 * [taylor]: Taking taylor expansion of -2 in k 20.602 * [backup-simplify]: Simplify -2 into -2 20.602 * [taylor]: Taking taylor expansion of PI in k 20.602 * [backup-simplify]: Simplify PI into PI 20.602 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 20.603 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 20.603 * [taylor]: Taking taylor expansion of (log n) in k 20.603 * [taylor]: Taking taylor expansion of n in k 20.603 * [backup-simplify]: Simplify n into n 20.603 * [backup-simplify]: Simplify (log n) into (log n) 20.604 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 20.604 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 20.604 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 20.606 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 20.607 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 20.608 * [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)))) 20.609 * [backup-simplify]: Simplify (* (sqrt +nan.0) (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)))) (sqrt +nan.0)) 20.611 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)) 20.612 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 20.613 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 20.615 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 20.615 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 20.615 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 20.616 * [backup-simplify]: Simplify (+ 0 0) into 0 20.617 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 20.618 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 20.620 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 20.621 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (sqrt (/ -1 k)))) 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into 0 20.621 * [taylor]: Taking taylor expansion of 0 in k 20.622 * [backup-simplify]: Simplify 0 into 0 20.622 * [backup-simplify]: Simplify 0 into 0 20.624 * [backup-simplify]: Simplify (+ (* (sqrt +nan.0) 0) (* (/ +nan.0 (sqrt +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)))) (sqrt +nan.0)))) 20.626 * [backup-simplify]: Simplify (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)))) into (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)))) 20.627 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.628 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 20.632 * [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 20.632 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.633 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 20.633 * [backup-simplify]: Simplify (+ 0 0) into 0 20.635 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 20.636 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 20.639 * [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 20.639 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.640 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 20.640 * [backup-simplify]: Simplify (- (+ (* (/ 1 (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 20.641 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 (sqrt (/ -1 k)))))) into 0 20.642 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (sqrt (/ -1 k)))) 0) (+ (* 0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into 0 20.643 * [taylor]: Taking taylor expansion of 0 in k 20.643 * [backup-simplify]: Simplify 0 into 0 20.643 * [backup-simplify]: Simplify 0 into 0 20.643 * [backup-simplify]: Simplify 0 into 0 20.644 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.648 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 20.652 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 20.661 * [backup-simplify]: Simplify (/ (- (- +nan.0) (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) 20.671 * [backup-simplify]: Simplify (+ (* (sqrt +nan.0) 0) (+ (* (/ +nan.0 (sqrt +nan.0)) 0) (* (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +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)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)))))) 20.675 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)))))) into (- (+ (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)))))) 20.683 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) (sqrt +nan.0)))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) (sqrt +nan.0)))) (* (/ 1 (- k)) 1)) (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) (sqrt +nan.0)))) into (- (* (sqrt +nan.0) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (sqrt +nan.0) (pow k 2))))))))) 20.683 * * * * [progress]: [ 4 / 4 ] generating series at (2) 20.684 * [backup-simplify]: Simplify (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))) into (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) 20.684 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in (n k) around 0 20.684 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in k 20.684 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 20.684 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 20.684 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 20.684 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 20.684 * [taylor]: Taking taylor expansion of 1/2 in k 20.684 * [backup-simplify]: Simplify 1/2 into 1/2 20.684 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 20.684 * [taylor]: Taking taylor expansion of 1/2 in k 20.684 * [backup-simplify]: Simplify 1/2 into 1/2 20.684 * [taylor]: Taking taylor expansion of k in k 20.684 * [backup-simplify]: Simplify 0 into 0 20.684 * [backup-simplify]: Simplify 1 into 1 20.684 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 20.684 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 20.684 * [taylor]: Taking taylor expansion of 2 in k 20.684 * [backup-simplify]: Simplify 2 into 2 20.684 * [taylor]: Taking taylor expansion of (* n PI) in k 20.685 * [taylor]: Taking taylor expansion of n in k 20.685 * [backup-simplify]: Simplify n into n 20.685 * [taylor]: Taking taylor expansion of PI in k 20.685 * [backup-simplify]: Simplify PI into PI 20.685 * [backup-simplify]: Simplify (* n PI) into (* n PI) 20.685 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 20.685 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 20.685 * [backup-simplify]: Simplify (* 1/2 0) into 0 20.686 * [backup-simplify]: Simplify (- 0) into 0 20.686 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 20.686 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 20.686 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 20.686 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 20.686 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.686 * [taylor]: Taking taylor expansion of k in k 20.686 * [backup-simplify]: Simplify 0 into 0 20.686 * [backup-simplify]: Simplify 1 into 1 20.687 * [backup-simplify]: Simplify (/ 1 1) into 1 20.687 * [backup-simplify]: Simplify (sqrt 0) into 0 20.689 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 20.689 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n 20.689 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 20.689 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 20.689 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 20.689 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 20.689 * [taylor]: Taking taylor expansion of 1/2 in n 20.689 * [backup-simplify]: Simplify 1/2 into 1/2 20.689 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 20.689 * [taylor]: Taking taylor expansion of 1/2 in n 20.689 * [backup-simplify]: Simplify 1/2 into 1/2 20.689 * [taylor]: Taking taylor expansion of k in n 20.689 * [backup-simplify]: Simplify k into k 20.689 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 20.689 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 20.689 * [taylor]: Taking taylor expansion of 2 in n 20.689 * [backup-simplify]: Simplify 2 into 2 20.689 * [taylor]: Taking taylor expansion of (* n PI) in n 20.689 * [taylor]: Taking taylor expansion of n in n 20.689 * [backup-simplify]: Simplify 0 into 0 20.689 * [backup-simplify]: Simplify 1 into 1 20.689 * [taylor]: Taking taylor expansion of PI in n 20.689 * [backup-simplify]: Simplify PI into PI 20.690 * [backup-simplify]: Simplify (* 0 PI) into 0 20.690 * [backup-simplify]: Simplify (* 2 0) into 0 20.692 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 20.694 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 20.695 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 20.695 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 20.695 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 20.695 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 20.697 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 20.698 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 20.699 * [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))))) 20.699 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 20.699 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.699 * [taylor]: Taking taylor expansion of k in n 20.699 * [backup-simplify]: Simplify k into k 20.699 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.699 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 20.699 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 20.699 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 20.699 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n 20.700 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 20.700 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 20.700 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 20.700 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 20.700 * [taylor]: Taking taylor expansion of 1/2 in n 20.700 * [backup-simplify]: Simplify 1/2 into 1/2 20.700 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 20.700 * [taylor]: Taking taylor expansion of 1/2 in n 20.700 * [backup-simplify]: Simplify 1/2 into 1/2 20.700 * [taylor]: Taking taylor expansion of k in n 20.700 * [backup-simplify]: Simplify k into k 20.700 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 20.700 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 20.700 * [taylor]: Taking taylor expansion of 2 in n 20.700 * [backup-simplify]: Simplify 2 into 2 20.700 * [taylor]: Taking taylor expansion of (* n PI) in n 20.700 * [taylor]: Taking taylor expansion of n in n 20.700 * [backup-simplify]: Simplify 0 into 0 20.700 * [backup-simplify]: Simplify 1 into 1 20.700 * [taylor]: Taking taylor expansion of PI in n 20.700 * [backup-simplify]: Simplify PI into PI 20.701 * [backup-simplify]: Simplify (* 0 PI) into 0 20.701 * [backup-simplify]: Simplify (* 2 0) into 0 20.703 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 20.704 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 20.706 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 20.706 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 20.706 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 20.706 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 20.708 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 20.709 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 20.710 * [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))))) 20.710 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 20.710 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.710 * [taylor]: Taking taylor expansion of k in n 20.711 * [backup-simplify]: Simplify k into k 20.711 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.711 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 20.711 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 20.711 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 20.712 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) into (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 20.712 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k 20.712 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 20.712 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.712 * [taylor]: Taking taylor expansion of k in k 20.712 * [backup-simplify]: Simplify 0 into 0 20.712 * [backup-simplify]: Simplify 1 into 1 20.713 * [backup-simplify]: Simplify (/ 1 1) into 1 20.713 * [backup-simplify]: Simplify (sqrt 0) into 0 20.715 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 20.715 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 20.715 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 20.715 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 20.715 * [taylor]: Taking taylor expansion of 1/2 in k 20.715 * [backup-simplify]: Simplify 1/2 into 1/2 20.715 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 20.715 * [taylor]: Taking taylor expansion of 1/2 in k 20.715 * [backup-simplify]: Simplify 1/2 into 1/2 20.715 * [taylor]: Taking taylor expansion of k in k 20.715 * [backup-simplify]: Simplify 0 into 0 20.715 * [backup-simplify]: Simplify 1 into 1 20.715 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 20.715 * [taylor]: Taking taylor expansion of (log n) in k 20.715 * [taylor]: Taking taylor expansion of n in k 20.715 * [backup-simplify]: Simplify n into n 20.715 * [backup-simplify]: Simplify (log n) into (log n) 20.715 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 20.715 * [taylor]: Taking taylor expansion of (* 2 PI) in k 20.715 * [taylor]: Taking taylor expansion of 2 in k 20.715 * [backup-simplify]: Simplify 2 into 2 20.715 * [taylor]: Taking taylor expansion of PI in k 20.716 * [backup-simplify]: Simplify PI into PI 20.716 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 20.717 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 20.717 * [backup-simplify]: Simplify (* 1/2 0) into 0 20.718 * [backup-simplify]: Simplify (- 0) into 0 20.718 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 20.719 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 20.721 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 20.722 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 20.723 * [backup-simplify]: Simplify (* 0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) into 0 20.723 * [backup-simplify]: Simplify 0 into 0 20.724 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 20.725 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 20.727 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 20.728 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 20.728 * [backup-simplify]: Simplify (- 0) into 0 20.728 * [backup-simplify]: Simplify (+ 0 0) into 0 20.730 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 20.731 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 20.733 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 20.734 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 0) (* 0 (sqrt (/ 1 k)))) into 0 20.734 * [taylor]: Taking taylor expansion of 0 in k 20.734 * [backup-simplify]: Simplify 0 into 0 20.735 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 20.736 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 20.738 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 20.738 * [backup-simplify]: Simplify (+ 0 0) into 0 20.739 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 20.739 * [backup-simplify]: Simplify (- 1/2) into -1/2 20.740 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 20.742 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 20.745 * [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))))))) 20.750 * [backup-simplify]: Simplify (+ (* 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))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 20.751 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 20.751 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.752 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 20.753 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 20.755 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 20.758 * [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 20.759 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 20.760 * [backup-simplify]: Simplify (- 0) into 0 20.760 * [backup-simplify]: Simplify (+ 0 0) into 0 20.762 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 20.764 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 20.766 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 20.768 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 20.768 * [taylor]: Taking taylor expansion of 0 in k 20.768 * [backup-simplify]: Simplify 0 into 0 20.768 * [backup-simplify]: Simplify 0 into 0 20.770 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 20.771 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 20.775 * [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 20.775 * [backup-simplify]: Simplify (+ 0 0) into 0 20.776 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 20.777 * [backup-simplify]: Simplify (- 0) into 0 20.777 * [backup-simplify]: Simplify (+ 0 0) into 0 20.779 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 20.783 * [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))))) 20.784 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 20.787 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 20.798 * [backup-simplify]: Simplify (+ (* 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 (* (+ (* 1/2 (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)))))))) into (- (+ (* +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))) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))))) 20.802 * [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))))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))))) 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)))))))) 20.802 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.805 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 20.807 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 20.808 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 20.811 * [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 20.812 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 20.812 * [backup-simplify]: Simplify (- 0) into 0 20.812 * [backup-simplify]: Simplify (+ 0 0) into 0 20.813 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 20.814 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 20.816 * [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 20.817 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0 20.817 * [taylor]: Taking taylor expansion of 0 in k 20.817 * [backup-simplify]: Simplify 0 into 0 20.817 * [backup-simplify]: Simplify 0 into 0 20.817 * [backup-simplify]: Simplify 0 into 0 20.820 * [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 20.821 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 20.827 * [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 20.827 * [backup-simplify]: Simplify (+ 0 0) into 0 20.828 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 20.829 * [backup-simplify]: Simplify (- 0) into 0 20.829 * [backup-simplify]: Simplify (+ 0 0) into 0 20.832 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 20.836 * [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))))))) 20.837 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.839 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 20.850 * [backup-simplify]: Simplify (+ (* 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)))))))) (+ (* +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 (* (+ (* 1/2 (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))))))))) into (- (+ (* +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))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))))))))))))) 20.857 * [backup-simplify]: Simplify (- (+ (* +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))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))))))))))))) into (- (+ (* +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))))) (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)))))) (- (+ (* +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))))) (log n)))))))))))))) 20.875 * [backup-simplify]: Simplify (+ (* (- (+ (* +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))))) (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)))))) (- (+ (* +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))))) (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)))))))))))))))))))))) 20.876 * [backup-simplify]: Simplify (/ (/ (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (sqrt (/ 1 k)))) (sqrt (sqrt (/ 1 k)))) into (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) 20.876 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in (n k) around 0 20.876 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 20.876 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 20.876 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 20.876 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 20.876 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 20.876 * [taylor]: Taking taylor expansion of 1/2 in k 20.876 * [backup-simplify]: Simplify 1/2 into 1/2 20.876 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 20.876 * [taylor]: Taking taylor expansion of 1/2 in k 20.876 * [backup-simplify]: Simplify 1/2 into 1/2 20.876 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.876 * [taylor]: Taking taylor expansion of k in k 20.876 * [backup-simplify]: Simplify 0 into 0 20.876 * [backup-simplify]: Simplify 1 into 1 20.877 * [backup-simplify]: Simplify (/ 1 1) into 1 20.877 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 20.877 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 20.877 * [taylor]: Taking taylor expansion of 2 in k 20.877 * [backup-simplify]: Simplify 2 into 2 20.877 * [taylor]: Taking taylor expansion of (/ PI n) in k 20.877 * [taylor]: Taking taylor expansion of PI in k 20.877 * [backup-simplify]: Simplify PI into PI 20.877 * [taylor]: Taking taylor expansion of n in k 20.877 * [backup-simplify]: Simplify n into n 20.877 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 20.877 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 20.877 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 20.877 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 20.878 * [backup-simplify]: Simplify (- 1/2) into -1/2 20.878 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 20.878 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 20.878 * [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)))) 20.878 * [taylor]: Taking taylor expansion of (sqrt k) in k 20.878 * [taylor]: Taking taylor expansion of k in k 20.878 * [backup-simplify]: Simplify 0 into 0 20.878 * [backup-simplify]: Simplify 1 into 1 20.878 * [backup-simplify]: Simplify (sqrt 0) into 0 20.879 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 20.879 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n 20.879 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 20.879 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 20.879 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 20.879 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 20.880 * [taylor]: Taking taylor expansion of 1/2 in n 20.880 * [backup-simplify]: Simplify 1/2 into 1/2 20.880 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 20.880 * [taylor]: Taking taylor expansion of 1/2 in n 20.880 * [backup-simplify]: Simplify 1/2 into 1/2 20.880 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.880 * [taylor]: Taking taylor expansion of k in n 20.880 * [backup-simplify]: Simplify k into k 20.880 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.880 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 20.880 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 20.880 * [taylor]: Taking taylor expansion of 2 in n 20.880 * [backup-simplify]: Simplify 2 into 2 20.880 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.880 * [taylor]: Taking taylor expansion of PI in n 20.880 * [backup-simplify]: Simplify PI into PI 20.880 * [taylor]: Taking taylor expansion of n in n 20.880 * [backup-simplify]: Simplify 0 into 0 20.880 * [backup-simplify]: Simplify 1 into 1 20.880 * [backup-simplify]: Simplify (/ PI 1) into PI 20.880 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 20.881 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 20.881 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 20.881 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 20.881 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 20.882 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 20.883 * [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))) 20.884 * [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)))) 20.884 * [taylor]: Taking taylor expansion of (sqrt k) in n 20.884 * [taylor]: Taking taylor expansion of k in n 20.884 * [backup-simplify]: Simplify k into k 20.884 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 20.884 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 20.884 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n 20.884 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 20.884 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 20.884 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 20.884 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 20.884 * [taylor]: Taking taylor expansion of 1/2 in n 20.884 * [backup-simplify]: Simplify 1/2 into 1/2 20.884 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 20.884 * [taylor]: Taking taylor expansion of 1/2 in n 20.884 * [backup-simplify]: Simplify 1/2 into 1/2 20.884 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.884 * [taylor]: Taking taylor expansion of k in n 20.884 * [backup-simplify]: Simplify k into k 20.884 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.884 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 20.884 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 20.884 * [taylor]: Taking taylor expansion of 2 in n 20.884 * [backup-simplify]: Simplify 2 into 2 20.884 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.884 * [taylor]: Taking taylor expansion of PI in n 20.884 * [backup-simplify]: Simplify PI into PI 20.884 * [taylor]: Taking taylor expansion of n in n 20.884 * [backup-simplify]: Simplify 0 into 0 20.884 * [backup-simplify]: Simplify 1 into 1 20.884 * [backup-simplify]: Simplify (/ PI 1) into PI 20.885 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 20.885 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 20.885 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 20.886 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 20.886 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 20.886 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 20.887 * [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))) 20.888 * [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)))) 20.888 * [taylor]: Taking taylor expansion of (sqrt k) in n 20.888 * [taylor]: Taking taylor expansion of k in n 20.888 * [backup-simplify]: Simplify k into k 20.888 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 20.888 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 20.889 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) 20.889 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 20.889 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 20.889 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 20.889 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 20.889 * [taylor]: Taking taylor expansion of 1/2 in k 20.889 * [backup-simplify]: Simplify 1/2 into 1/2 20.889 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 20.889 * [taylor]: Taking taylor expansion of 1/2 in k 20.889 * [backup-simplify]: Simplify 1/2 into 1/2 20.889 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.889 * [taylor]: Taking taylor expansion of k in k 20.889 * [backup-simplify]: Simplify 0 into 0 20.889 * [backup-simplify]: Simplify 1 into 1 20.889 * [backup-simplify]: Simplify (/ 1 1) into 1 20.889 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 20.889 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 20.889 * [taylor]: Taking taylor expansion of (* 2 PI) in k 20.889 * [taylor]: Taking taylor expansion of 2 in k 20.889 * [backup-simplify]: Simplify 2 into 2 20.889 * [taylor]: Taking taylor expansion of PI in k 20.889 * [backup-simplify]: Simplify PI into PI 20.890 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 20.890 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 20.890 * [taylor]: Taking taylor expansion of (log n) in k 20.890 * [taylor]: Taking taylor expansion of n in k 20.890 * [backup-simplify]: Simplify n into n 20.890 * [backup-simplify]: Simplify (log n) into (log n) 20.891 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 20.891 * [backup-simplify]: Simplify (- 1/2) into -1/2 20.891 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 20.891 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 20.892 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 20.893 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 20.894 * [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)))) 20.894 * [taylor]: Taking taylor expansion of (sqrt k) in k 20.894 * [taylor]: Taking taylor expansion of k in k 20.894 * [backup-simplify]: Simplify 0 into 0 20.894 * [backup-simplify]: Simplify 1 into 1 20.894 * [backup-simplify]: Simplify (sqrt 0) into 0 20.895 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 20.896 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 20.896 * [backup-simplify]: Simplify 0 into 0 20.896 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 20.897 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 20.898 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 20.898 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 20.898 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 20.899 * [backup-simplify]: Simplify (- 0) into 0 20.899 * [backup-simplify]: Simplify (+ 0 0) into 0 20.900 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 20.900 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 20.904 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 20.905 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) (* 0 (sqrt k))) into 0 20.905 * [taylor]: Taking taylor expansion of 0 in k 20.905 * [backup-simplify]: Simplify 0 into 0 20.905 * [backup-simplify]: Simplify 0 into 0 20.907 * [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)))))) 20.907 * [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)))))) 20.908 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 20.909 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.909 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 20.913 * [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 20.913 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.914 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 20.915 * [backup-simplify]: Simplify (- 0) into 0 20.915 * [backup-simplify]: Simplify (+ 0 0) into 0 20.917 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 20.918 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 20.921 * [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 20.922 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0 20.922 * [taylor]: Taking taylor expansion of 0 in k 20.922 * [backup-simplify]: Simplify 0 into 0 20.923 * [backup-simplify]: Simplify 0 into 0 20.923 * [backup-simplify]: Simplify 0 into 0 20.926 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 20.928 * [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)))))) 20.929 * [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)))))) 20.930 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 20.931 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.932 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 20.938 * [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 20.939 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.940 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 20.941 * [backup-simplify]: Simplify (- 0) into 0 20.941 * [backup-simplify]: Simplify (+ 0 0) into 0 20.943 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 20.945 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 20.948 * [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 20.951 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0 20.951 * [taylor]: Taking taylor expansion of 0 in k 20.951 * [backup-simplify]: Simplify 0 into 0 20.951 * [backup-simplify]: Simplify 0 into 0 20.951 * [backup-simplify]: Simplify 0 into 0 20.951 * [backup-simplify]: Simplify 0 into 0 20.955 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 20.957 * [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)))))) 20.959 * [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)))))) 20.963 * [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)))))))) 20.964 * [backup-simplify]: Simplify (/ (/ (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (sqrt (/ 1 (- k))))) (sqrt (sqrt (/ 1 (- k))))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 20.964 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 20.964 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 20.964 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 20.964 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 20.964 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 20.964 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 20.964 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 20.964 * [taylor]: Taking taylor expansion of 1/2 in k 20.964 * [backup-simplify]: Simplify 1/2 into 1/2 20.964 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.964 * [taylor]: Taking taylor expansion of k in k 20.964 * [backup-simplify]: Simplify 0 into 0 20.964 * [backup-simplify]: Simplify 1 into 1 20.965 * [backup-simplify]: Simplify (/ 1 1) into 1 20.965 * [taylor]: Taking taylor expansion of 1/2 in k 20.965 * [backup-simplify]: Simplify 1/2 into 1/2 20.965 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 20.965 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 20.965 * [taylor]: Taking taylor expansion of -2 in k 20.965 * [backup-simplify]: Simplify -2 into -2 20.965 * [taylor]: Taking taylor expansion of (/ PI n) in k 20.965 * [taylor]: Taking taylor expansion of PI in k 20.965 * [backup-simplify]: Simplify PI into PI 20.965 * [taylor]: Taking taylor expansion of n in k 20.965 * [backup-simplify]: Simplify n into n 20.965 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 20.965 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 20.965 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 20.966 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 20.966 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 20.966 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 20.966 * [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))) 20.967 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 20.967 * [taylor]: Taking taylor expansion of (/ -1 k) in k 20.967 * [taylor]: Taking taylor expansion of -1 in k 20.967 * [backup-simplify]: Simplify -1 into -1 20.967 * [taylor]: Taking taylor expansion of k in k 20.967 * [backup-simplify]: Simplify 0 into 0 20.967 * [backup-simplify]: Simplify 1 into 1 20.967 * [backup-simplify]: Simplify (/ -1 1) into -1 20.967 * [backup-simplify]: Simplify (sqrt 0) into 0 20.969 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 20.969 * [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)))) 20.969 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 20.969 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 20.969 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 20.969 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 20.969 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 20.969 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 20.969 * [taylor]: Taking taylor expansion of 1/2 in n 20.969 * [backup-simplify]: Simplify 1/2 into 1/2 20.969 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.969 * [taylor]: Taking taylor expansion of k in n 20.969 * [backup-simplify]: Simplify k into k 20.970 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.970 * [taylor]: Taking taylor expansion of 1/2 in n 20.970 * [backup-simplify]: Simplify 1/2 into 1/2 20.970 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 20.970 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 20.970 * [taylor]: Taking taylor expansion of -2 in n 20.970 * [backup-simplify]: Simplify -2 into -2 20.970 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.970 * [taylor]: Taking taylor expansion of PI in n 20.970 * [backup-simplify]: Simplify PI into PI 20.970 * [taylor]: Taking taylor expansion of n in n 20.970 * [backup-simplify]: Simplify 0 into 0 20.970 * [backup-simplify]: Simplify 1 into 1 20.970 * [backup-simplify]: Simplify (/ PI 1) into PI 20.971 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 20.972 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 20.972 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 20.972 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 20.974 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 20.975 * [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))) 20.976 * [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)))) 20.976 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 20.976 * [taylor]: Taking taylor expansion of (/ -1 k) in n 20.976 * [taylor]: Taking taylor expansion of -1 in n 20.976 * [backup-simplify]: Simplify -1 into -1 20.976 * [taylor]: Taking taylor expansion of k in n 20.976 * [backup-simplify]: Simplify k into k 20.976 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 20.976 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 20.977 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 20.977 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 20.978 * [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))) 20.978 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 20.978 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 20.978 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 20.978 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 20.978 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 20.978 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 20.978 * [taylor]: Taking taylor expansion of 1/2 in n 20.978 * [backup-simplify]: Simplify 1/2 into 1/2 20.978 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.978 * [taylor]: Taking taylor expansion of k in n 20.978 * [backup-simplify]: Simplify k into k 20.978 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.978 * [taylor]: Taking taylor expansion of 1/2 in n 20.978 * [backup-simplify]: Simplify 1/2 into 1/2 20.978 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 20.978 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 20.978 * [taylor]: Taking taylor expansion of -2 in n 20.979 * [backup-simplify]: Simplify -2 into -2 20.979 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.979 * [taylor]: Taking taylor expansion of PI in n 20.979 * [backup-simplify]: Simplify PI into PI 20.979 * [taylor]: Taking taylor expansion of n in n 20.979 * [backup-simplify]: Simplify 0 into 0 20.979 * [backup-simplify]: Simplify 1 into 1 20.979 * [backup-simplify]: Simplify (/ PI 1) into PI 20.980 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 20.981 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 20.981 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 20.981 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 20.982 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 20.983 * [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))) 20.983 * [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)))) 20.984 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 20.984 * [taylor]: Taking taylor expansion of (/ -1 k) in n 20.984 * [taylor]: Taking taylor expansion of -1 in n 20.984 * [backup-simplify]: Simplify -1 into -1 20.984 * [taylor]: Taking taylor expansion of k in n 20.984 * [backup-simplify]: Simplify k into k 20.984 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 20.984 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 20.984 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 20.984 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 20.985 * [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))) 20.985 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 20.985 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 20.985 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 20.985 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 20.985 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 20.985 * [taylor]: Taking taylor expansion of 1/2 in k 20.985 * [backup-simplify]: Simplify 1/2 into 1/2 20.985 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.985 * [taylor]: Taking taylor expansion of k in k 20.985 * [backup-simplify]: Simplify 0 into 0 20.985 * [backup-simplify]: Simplify 1 into 1 20.985 * [backup-simplify]: Simplify (/ 1 1) into 1 20.985 * [taylor]: Taking taylor expansion of 1/2 in k 20.985 * [backup-simplify]: Simplify 1/2 into 1/2 20.985 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 20.985 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 20.985 * [taylor]: Taking taylor expansion of (* -2 PI) in k 20.985 * [taylor]: Taking taylor expansion of -2 in k 20.985 * [backup-simplify]: Simplify -2 into -2 20.985 * [taylor]: Taking taylor expansion of PI in k 20.985 * [backup-simplify]: Simplify PI into PI 20.986 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 20.986 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 20.986 * [taylor]: Taking taylor expansion of (log n) in k 20.986 * [taylor]: Taking taylor expansion of n in k 20.986 * [backup-simplify]: Simplify n into n 20.986 * [backup-simplify]: Simplify (log n) into (log n) 20.987 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 20.987 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 20.987 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 20.988 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 20.988 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 20.989 * [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)))) 20.989 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 20.989 * [taylor]: Taking taylor expansion of (/ -1 k) in k 20.989 * [taylor]: Taking taylor expansion of -1 in k 20.989 * [backup-simplify]: Simplify -1 into -1 20.989 * [taylor]: Taking taylor expansion of k in k 20.989 * [backup-simplify]: Simplify 0 into 0 20.989 * [backup-simplify]: Simplify 1 into 1 20.990 * [backup-simplify]: Simplify (/ -1 1) into -1 20.990 * [backup-simplify]: Simplify (sqrt 0) into 0 20.991 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 20.991 * [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))))) 20.992 * [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))))) 20.993 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 20.993 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 20.995 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 20.995 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 20.996 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 20.996 * [backup-simplify]: Simplify (+ 0 0) into 0 20.997 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 20.998 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 20.999 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 21.000 * [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 21.000 * [taylor]: Taking taylor expansion of 0 in k 21.000 * [backup-simplify]: Simplify 0 into 0 21.000 * [backup-simplify]: Simplify 0 into 0 21.001 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 21.003 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 21.004 * [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)))))) 21.005 * [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)))))) 21.006 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 21.006 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 21.008 * [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 21.008 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 21.009 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 21.009 * [backup-simplify]: Simplify (+ 0 0) into 0 21.011 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 21.013 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 21.015 * [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 21.015 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 21.016 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 21.018 * [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 21.018 * [taylor]: Taking taylor expansion of 0 in k 21.018 * [backup-simplify]: Simplify 0 into 0 21.018 * [backup-simplify]: Simplify 0 into 0 21.018 * [backup-simplify]: Simplify 0 into 0 21.019 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 21.023 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 21.027 * [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)))))) 21.027 * [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)))))) 21.032 * [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))))))))))) 21.032 * * * [progress]: simplifying candidates 21.033 * * * * [progress]: [ 1 / 4800 ] simplifiying candidate # 21.033 * * * * [progress]: [ 2 / 4800 ] simplifiying candidate # 21.033 * * * * [progress]: [ 3 / 4800 ] simplifiying candidate # 21.033 * * * * [progress]: [ 4 / 4800 ] simplifiying candidate # 21.033 * * * * [progress]: [ 5 / 4800 ] simplifiying candidate # 21.033 * * * * [progress]: [ 6 / 4800 ] simplifiying candidate # 21.033 * * * * [progress]: [ 7 / 4800 ] simplifiying candidate # 21.033 * * * * [progress]: [ 8 / 4800 ] simplifiying candidate # 21.033 * * * * [progress]: [ 9 / 4800 ] simplifiying candidate # 21.033 * * * * [progress]: [ 10 / 4800 ] simplifiying candidate # 21.033 * * * * [progress]: [ 11 / 4800 ] simplifiying candidate # 21.033 * * * * [progress]: [ 12 / 4800 ] simplifiying candidate # 21.033 * * * * [progress]: [ 13 / 4800 ] simplifiying candidate # 21.033 * * * * [progress]: [ 14 / 4800 ] simplifiying candidate # 21.033 * * * * [progress]: [ 15 / 4800 ] simplifiying candidate # 21.033 * * * * [progress]: [ 16 / 4800 ] simplifiying candidate # 21.033 * * * * [progress]: [ 17 / 4800 ] simplifiying candidate # 21.034 * * * * [progress]: [ 18 / 4800 ] simplifiying candidate # 21.034 * * * * [progress]: [ 19 / 4800 ] simplifiying candidate # 21.034 * * * * [progress]: [ 20 / 4800 ] simplifiying candidate # 21.034 * * * * [progress]: [ 21 / 4800 ] simplifiying candidate # 21.034 * * * * [progress]: [ 22 / 4800 ] simplifiying candidate # 21.034 * * * * [progress]: [ 23 / 4800 ] simplifiying candidate # 21.034 * * * * [progress]: [ 24 / 4800 ] simplifiying candidate # 21.034 * * * * [progress]: [ 25 / 4800 ] simplifiying candidate # 21.034 * * * * [progress]: [ 26 / 4800 ] simplifiying candidate # 21.034 * * * * [progress]: [ 27 / 4800 ] simplifiying candidate # 21.034 * * * * [progress]: [ 28 / 4800 ] simplifiying candidate # 21.034 * * * * [progress]: [ 29 / 4800 ] simplifiying candidate # 21.034 * * * * [progress]: [ 30 / 4800 ] simplifiying candidate # 21.034 * * * * [progress]: [ 31 / 4800 ] simplifiying candidate # 21.034 * * * * [progress]: [ 32 / 4800 ] simplifiying candidate # 21.034 * * * * [progress]: [ 33 / 4800 ] simplifiying candidate # 21.034 * * * * [progress]: [ 34 / 4800 ] simplifiying candidate # 21.035 * * * * [progress]: [ 35 / 4800 ] simplifiying candidate # 21.035 * * * * [progress]: [ 36 / 4800 ] simplifiying candidate # 21.035 * * * * [progress]: [ 37 / 4800 ] simplifiying candidate # 21.035 * * * * [progress]: [ 38 / 4800 ] simplifiying candidate # 21.035 * * * * [progress]: [ 39 / 4800 ] simplifiying candidate # 21.035 * * * * [progress]: [ 40 / 4800 ] simplifiying candidate # 21.035 * * * * [progress]: [ 41 / 4800 ] simplifiying candidate # 21.035 * * * * [progress]: [ 42 / 4800 ] simplifiying candidate # 21.035 * * * * [progress]: [ 43 / 4800 ] simplifiying candidate # 21.035 * * * * [progress]: [ 44 / 4800 ] simplifiying candidate # 21.035 * * * * [progress]: [ 45 / 4800 ] simplifiying candidate # 21.035 * * * * [progress]: [ 46 / 4800 ] simplifiying candidate # 21.035 * * * * [progress]: [ 47 / 4800 ] simplifiying candidate # 21.035 * * * * [progress]: [ 48 / 4800 ] simplifiying candidate # 21.035 * * * * [progress]: [ 49 / 4800 ] simplifiying candidate # 21.035 * * * * [progress]: [ 50 / 4800 ] simplifiying candidate # 21.035 * * * * [progress]: [ 51 / 4800 ] simplifiying candidate # 21.036 * * * * [progress]: [ 52 / 4800 ] simplifiying candidate # 21.036 * * * * [progress]: [ 53 / 4800 ] simplifiying candidate # 21.036 * * * * [progress]: [ 54 / 4800 ] simplifiying candidate # 21.036 * * * * [progress]: [ 55 / 4800 ] simplifiying candidate # 21.036 * * * * [progress]: [ 56 / 4800 ] simplifiying candidate # 21.036 * * * * [progress]: [ 57 / 4800 ] simplifiying candidate # 21.036 * * * * [progress]: [ 58 / 4800 ] simplifiying candidate # 21.036 * * * * [progress]: [ 59 / 4800 ] simplifiying candidate # 21.036 * * * * [progress]: [ 60 / 4800 ] simplifiying candidate # 21.036 * * * * [progress]: [ 61 / 4800 ] simplifiying candidate # 21.036 * * * * [progress]: [ 62 / 4800 ] simplifiying candidate # 21.036 * * * * [progress]: [ 63 / 4800 ] simplifiying candidate # 21.036 * * * * [progress]: [ 64 / 4800 ] simplifiying candidate # 21.036 * * * * [progress]: [ 65 / 4800 ] simplifiying candidate # 21.036 * * * * [progress]: [ 66 / 4800 ] simplifiying candidate # 21.036 * * * * [progress]: [ 67 / 4800 ] simplifiying candidate #real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (sqrt (sqrt k))))> 21.036 * * * * [progress]: [ 68 / 4800 ] simplifiying candidate # 21.036 * * * * [progress]: [ 69 / 4800 ] simplifiying candidate # 21.036 * * * * [progress]: [ 70 / 4800 ] simplifiying candidate # 21.037 * * * * [progress]: [ 71 / 4800 ] simplifiying candidate # 21.037 * * * * [progress]: [ 72 / 4800 ] simplifiying candidate # 21.037 * * * * [progress]: [ 73 / 4800 ] simplifiying candidate # 21.037 * * * * [progress]: [ 74 / 4800 ] simplifiying candidate # 21.037 * * * * [progress]: [ 75 / 4800 ] simplifiying candidate # 21.037 * * * * [progress]: [ 76 / 4800 ] simplifiying candidate # 21.037 * * * * [progress]: [ 77 / 4800 ] simplifiying candidate # 21.037 * * * * [progress]: [ 78 / 4800 ] simplifiying candidate # 21.037 * * * * [progress]: [ 79 / 4800 ] simplifiying candidate # 21.037 * * * * [progress]: [ 80 / 4800 ] simplifiying candidate # 21.037 * * * * [progress]: [ 81 / 4800 ] simplifiying candidate # 21.037 * * * * [progress]: [ 82 / 4800 ] simplifiying candidate # 21.037 * * * * [progress]: [ 83 / 4800 ] simplifiying candidate # 21.037 * * * * [progress]: [ 84 / 4800 ] simplifiying candidate # 21.037 * * * * [progress]: [ 85 / 4800 ] simplifiying candidate # 21.037 * * * * [progress]: [ 86 / 4800 ] simplifiying candidate # 21.037 * * * * [progress]: [ 87 / 4800 ] simplifiying candidate #real (real->posit16 (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))> 21.037 * * * * [progress]: [ 88 / 4800 ] simplifiying candidate # 21.037 * * * * [progress]: [ 89 / 4800 ] simplifiying candidate # 21.037 * * * * [progress]: [ 90 / 4800 ] simplifiying candidate # 21.038 * * * * [progress]: [ 91 / 4800 ] simplifiying candidate # 21.038 * * * * [progress]: [ 92 / 4800 ] simplifiying candidate # 21.038 * * * * [progress]: [ 93 / 4800 ] simplifiying candidate # 21.038 * * * * [progress]: [ 94 / 4800 ] simplifiying candidate # 21.038 * * * * [progress]: [ 95 / 4800 ] simplifiying candidate # 21.038 * * * * [progress]: [ 96 / 4800 ] simplifiying candidate # 21.038 * * * * [progress]: [ 97 / 4800 ] simplifiying candidate # 21.038 * * * * [progress]: [ 98 / 4800 ] simplifiying candidate # 21.038 * * * * [progress]: [ 99 / 4800 ] simplifiying candidate # 21.038 * * * * [progress]: [ 100 / 4800 ] simplifiying candidate # 21.038 * * * * [progress]: [ 101 / 4800 ] simplifiying candidate # 21.038 * * * * [progress]: [ 102 / 4800 ] simplifiying candidate # 21.038 * * * * [progress]: [ 103 / 4800 ] simplifiying candidate # 21.038 * * * * [progress]: [ 104 / 4800 ] simplifiying candidate # 21.038 * * * * [progress]: [ 105 / 4800 ] simplifiying candidate # 21.038 * * * * [progress]: [ 106 / 4800 ] simplifiying candidate # 21.038 * * * * [progress]: [ 107 / 4800 ] simplifiying candidate # 21.038 * * * * [progress]: [ 108 / 4800 ] simplifiying candidate # 21.038 * * * * [progress]: [ 109 / 4800 ] simplifiying candidate # 21.039 * * * * [progress]: [ 110 / 4800 ] simplifiying candidate # 21.039 * * * * [progress]: [ 111 / 4800 ] simplifiying candidate # 21.039 * * * * [progress]: [ 112 / 4800 ] simplifiying candidate # 21.039 * * * * [progress]: [ 113 / 4800 ] simplifiying candidate # 21.039 * * * * [progress]: [ 114 / 4800 ] simplifiying candidate # 21.039 * * * * [progress]: [ 115 / 4800 ] simplifiying candidate # 21.039 * * * * [progress]: [ 116 / 4800 ] simplifiying candidate # 21.039 * * * * [progress]: [ 117 / 4800 ] simplifiying candidate # 21.039 * * * * [progress]: [ 118 / 4800 ] simplifiying candidate # 21.039 * * * * [progress]: [ 119 / 4800 ] simplifiying candidate # 21.039 * * * * [progress]: [ 120 / 4800 ] simplifiying candidate # 21.039 * * * * [progress]: [ 121 / 4800 ] simplifiying candidate # 21.039 * * * * [progress]: [ 122 / 4800 ] simplifiying candidate # 21.039 * * * * [progress]: [ 123 / 4800 ] simplifiying candidate # 21.039 * * * * [progress]: [ 124 / 4800 ] simplifiying candidate # 21.039 * * * * [progress]: [ 125 / 4800 ] simplifiying candidate # 21.040 * * * * [progress]: [ 126 / 4800 ] simplifiying candidate # 21.040 * * * * [progress]: [ 127 / 4800 ] simplifiying candidate # 21.040 * * * * [progress]: [ 128 / 4800 ] simplifiying candidate # 21.040 * * * * [progress]: [ 129 / 4800 ] simplifiying candidate # 21.040 * * * * [progress]: [ 130 / 4800 ] simplifiying candidate # 21.040 * * * * [progress]: [ 131 / 4800 ] simplifiying candidate # 21.040 * * * * [progress]: [ 132 / 4800 ] simplifiying candidate # 21.040 * * * * [progress]: [ 133 / 4800 ] simplifiying candidate # 21.040 * * * * [progress]: [ 134 / 4800 ] simplifiying candidate # 21.040 * * * * [progress]: [ 135 / 4800 ] simplifiying candidate # 21.040 * * * * [progress]: [ 136 / 4800 ] 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(* 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)) 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n))))))))))) 22.035 * * [simplify]: iteration 0: 3687 enodes 23.162 * * [simplify]: iteration complete: 3687 enodes 23.173 * * [simplify]: Extracting #0: cost 3382 inf + 0 23.189 * * [simplify]: Extracting #1: cost 3485 inf + 0 23.207 * * [simplify]: Extracting #2: cost 3563 inf + 239 23.225 * * [simplify]: Extracting #3: cost 3569 inf + 3071 23.250 * * [simplify]: Extracting #4: cost 3495 inf + 30010 23.297 * * [simplify]: Extracting #5: cost 3192 inf + 203430 23.420 * * [simplify]: Extracting #6: cost 2264 inf + 895739 23.642 * * [simplify]: Extracting #7: cost 1449 inf + 1560047 23.990 * * [simplify]: Extracting #8: cost 755 inf + 2171537 24.233 * * [simplify]: Extracting #9: cost 339 inf + 2563700 24.618 * * [simplify]: Extracting #10: cost 32 inf + 2875194 25.001 * * [simplify]: Extracting #11: cost 14 inf + 2895019 25.403 * * [simplify]: Extracting #12: cost 15 inf + 2896047 25.777 * * [simplify]: Extracting #13: cost 14 inf + 2897991 26.094 * * [simplify]: Extracting #14: cost 16 inf + 2897991 26.445 * * [simplify]: Extracting #15: cost 16 inf + 2898657 26.859 * * [simplify]: Extracting #16: cost 18 inf + 2898657 27.188 * * [simplify]: Extracting #17: cost 18 inf + 2899283 27.543 * * [simplify]: Extracting #18: cost 20 inf + 2899283 27.856 * * [simplify]: Extracting #19: cost 20 inf + 2899739 28.190 * * [simplify]: Extracting #20: cost 18 inf + 2900691 28.566 * * [simplify]: Extracting #21: cost 17 inf + 2901347 28.918 * * [simplify]: Extracting #22: cost 15 inf + 2903069 29.233 * * [simplify]: Extracting #23: cost 13 inf + 2905361 29.602 * * [simplify]: Extracting #24: cost 12 inf + 2906627 29.937 * * [simplify]: Extracting #25: cost 8 inf + 2913331 30.274 * * [simplify]: Extracting #26: cost 6 inf + 2917043 30.700 * * [simplify]: Extracting #27: cost 4 inf + 2921575 31.113 * * [simplify]: Extracting #28: cost 1 inf + 2928993 31.435 * * [simplify]: Extracting #29: cost 0 inf + 2931599 31.895 * [simplify]: Simplified to: (expm1 (pow (* n (* 2 PI)) (- 1/2 (/ 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PI)) (* 2 (* n PI)) (* 2 (* n PI)) (- (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)) (pow (pow k 7) 1/4))) (+ (* 1/4 (* (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (pow (pow k 7) 1/4))) (* 1/8 (* (* (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (pow k 7) 1/4)))))) (+ (* 1/2 (* (* (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (pow k 3) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)) (pow (pow k 3) 1/4))))) (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow (/ 1 k) 1/4)) (- (* (sqrt +nan.0) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (sqrt +nan.0) (pow k 2))))))))) (- (+ (* +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))))))))))) 33.541 * * * [progress]: adding candidates to table 132.719 * [progress]: [Phase 3 of 3] Extracting. 132.720 * * [regime]: Finding splitpoints for: (# # # # # # #) 132.721 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2 PI) n) n k) 132.721 * * * * [regimes]: Trying to branch on (* (* 2 PI) n) from (# # # # # # #) 132.795 * * * * [regimes]: Trying to branch on n from (# # # # # # #) 132.852 * * * * [regimes]: Trying to branch on k from (# # # # # # #) 132.907 * * * [regime]: Found split indices: #