56.413 * [progress]: [Phase 1 of 3] Setting up. 0.003 * * * [progress]: [1/2] Preparing points 0.239 * * * [progress]: [2/2] Setting up program. 0.243 * [progress]: [Phase 2 of 3] Improving. 0.243 * * * * [progress]: [ 1 / 1 ] simplifiying candidate # 0.243 * [simplify]: Simplifying: (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 0.243 * * [simplify]: iteration 0: 13 enodes 0.246 * * [simplify]: iteration 1: 31 enodes 0.254 * * [simplify]: iteration 2: 62 enodes 0.275 * * [simplify]: iteration 3: 124 enodes 0.323 * * [simplify]: iteration 4: 328 enodes 0.625 * * [simplify]: iteration 5: 970 enodes 1.009 * * [simplify]: iteration 6: 2026 enodes 1.414 * * [simplify]: iteration complete: 2026 enodes 1.414 * * [simplify]: Extracting #0: cost 1 inf + 0 1.414 * * [simplify]: Extracting #1: cost 86 inf + 0 1.416 * * [simplify]: Extracting #2: cost 311 inf + 1 1.419 * * [simplify]: Extracting #3: cost 435 inf + 46 1.423 * * [simplify]: Extracting #4: cost 405 inf + 4118 1.433 * * [simplify]: Extracting #5: cost 293 inf + 28237 1.471 * * [simplify]: Extracting #6: cost 140 inf + 129132 1.509 * * [simplify]: Extracting #7: cost 9 inf + 256512 1.557 * * [simplify]: Extracting #8: cost 0 inf + 265066 1.609 * * [simplify]: Extracting #9: cost 0 inf + 265063 1.670 * * [simplify]: Extracting #10: cost 0 inf + 264810 1.725 * [simplify]: Simplified to: (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) 1.732 * * [progress]: iteration 1 / 4 1.732 * * * [progress]: picking best candidate 1.743 * * * * [pick]: Picked # 1.743 * * * [progress]: localizing error 1.776 * * * [progress]: generating rewritten candidates 1.776 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1) 1.794 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1) 1.819 * * * * [progress]: [ 3 / 3 ] rewriting at (2) 1.858 * * * [progress]: generating series expansions 1.858 * * * * [progress]: [ 1 / 3 ] generating series at (2 1) 1.859 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1.859 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1.859 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1.859 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1.859 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1.859 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1.859 * [taylor]: Taking taylor expansion of 1/2 in k 1.859 * [backup-simplify]: Simplify 1/2 into 1/2 1.859 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 1.859 * [taylor]: Taking taylor expansion of 1/2 in k 1.859 * [backup-simplify]: Simplify 1/2 into 1/2 1.859 * [taylor]: Taking taylor expansion of k in k 1.859 * [backup-simplify]: Simplify 0 into 0 1.859 * [backup-simplify]: Simplify 1 into 1 1.859 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 1.859 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 1.859 * [taylor]: Taking taylor expansion of 2 in k 1.859 * [backup-simplify]: Simplify 2 into 2 1.859 * [taylor]: Taking taylor expansion of (* n PI) in k 1.859 * [taylor]: Taking taylor expansion of n in k 1.860 * [backup-simplify]: Simplify n into n 1.860 * [taylor]: Taking taylor expansion of PI in k 1.860 * [backup-simplify]: Simplify PI into PI 1.860 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.860 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1.860 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1.860 * [backup-simplify]: Simplify (* 1/2 0) into 0 1.861 * [backup-simplify]: Simplify (- 0) into 0 1.861 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 1.861 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1.861 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1.861 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1.861 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1.861 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1.861 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1.861 * [taylor]: Taking taylor expansion of 1/2 in n 1.861 * [backup-simplify]: Simplify 1/2 into 1/2 1.861 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 1.861 * [taylor]: Taking taylor expansion of 1/2 in n 1.861 * [backup-simplify]: Simplify 1/2 into 1/2 1.862 * [taylor]: Taking taylor expansion of k in n 1.862 * [backup-simplify]: Simplify k into k 1.862 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.862 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.862 * [taylor]: Taking taylor expansion of 2 in n 1.862 * [backup-simplify]: Simplify 2 into 2 1.862 * [taylor]: Taking taylor expansion of (* n PI) in n 1.862 * [taylor]: Taking taylor expansion of n in n 1.862 * [backup-simplify]: Simplify 0 into 0 1.862 * [backup-simplify]: Simplify 1 into 1 1.862 * [taylor]: Taking taylor expansion of PI in n 1.862 * [backup-simplify]: Simplify PI into PI 1.862 * [backup-simplify]: Simplify (* 0 PI) into 0 1.862 * [backup-simplify]: Simplify (* 2 0) into 0 1.863 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.864 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1.865 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.865 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 1.865 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1.865 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1.866 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.867 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1.868 * [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))))) 1.868 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1.868 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1.868 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1.868 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1.868 * [taylor]: Taking taylor expansion of 1/2 in n 1.868 * [backup-simplify]: Simplify 1/2 into 1/2 1.868 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 1.868 * [taylor]: Taking taylor expansion of 1/2 in n 1.868 * [backup-simplify]: Simplify 1/2 into 1/2 1.868 * [taylor]: Taking taylor expansion of k in n 1.868 * [backup-simplify]: Simplify k into k 1.868 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.868 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.868 * [taylor]: Taking taylor expansion of 2 in n 1.868 * [backup-simplify]: Simplify 2 into 2 1.868 * [taylor]: Taking taylor expansion of (* n PI) in n 1.868 * [taylor]: Taking taylor expansion of n in n 1.868 * [backup-simplify]: Simplify 0 into 0 1.868 * [backup-simplify]: Simplify 1 into 1 1.868 * [taylor]: Taking taylor expansion of PI in n 1.868 * [backup-simplify]: Simplify PI into PI 1.869 * [backup-simplify]: Simplify (* 0 PI) into 0 1.869 * [backup-simplify]: Simplify (* 2 0) into 0 1.870 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.871 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1.871 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.871 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 1.872 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1.872 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1.872 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.873 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1.874 * [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))))) 1.874 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1.874 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1.874 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1.874 * [taylor]: Taking taylor expansion of 1/2 in k 1.874 * [backup-simplify]: Simplify 1/2 into 1/2 1.874 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 1.874 * [taylor]: Taking taylor expansion of 1/2 in k 1.874 * [backup-simplify]: Simplify 1/2 into 1/2 1.874 * [taylor]: Taking taylor expansion of k in k 1.874 * [backup-simplify]: Simplify 0 into 0 1.874 * [backup-simplify]: Simplify 1 into 1 1.874 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1.874 * [taylor]: Taking taylor expansion of (log n) in k 1.874 * [taylor]: Taking taylor expansion of n in k 1.874 * [backup-simplify]: Simplify n into n 1.874 * [backup-simplify]: Simplify (log n) into (log n) 1.874 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 1.874 * [taylor]: Taking taylor expansion of (* 2 PI) in k 1.874 * [taylor]: Taking taylor expansion of 2 in k 1.874 * [backup-simplify]: Simplify 2 into 2 1.874 * [taylor]: Taking taylor expansion of PI in k 1.874 * [backup-simplify]: Simplify PI into PI 1.875 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 1.875 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.876 * [backup-simplify]: Simplify (* 1/2 0) into 0 1.876 * [backup-simplify]: Simplify (- 0) into 0 1.876 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 1.877 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.877 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1.878 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1.879 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1.880 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.880 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1.881 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1.881 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1.882 * [backup-simplify]: Simplify (- 0) into 0 1.882 * [backup-simplify]: Simplify (+ 0 0) into 0 1.883 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.884 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1.885 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.885 * [taylor]: Taking taylor expansion of 0 in k 1.885 * [backup-simplify]: Simplify 0 into 0 1.885 * [backup-simplify]: Simplify 0 into 0 1.886 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.886 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 1.887 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1.887 * [backup-simplify]: Simplify (+ 0 0) into 0 1.888 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1.888 * [backup-simplify]: Simplify (- 1/2) into -1/2 1.888 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 1.889 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1.892 * [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))))))) 1.895 * [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))))))) 1.897 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.898 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.901 * [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 1.911 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1.912 * [backup-simplify]: Simplify (- 0) into 0 1.912 * [backup-simplify]: Simplify (+ 0 0) into 0 1.913 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.915 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1.917 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.917 * [taylor]: Taking taylor expansion of 0 in k 1.917 * [backup-simplify]: Simplify 0 into 0 1.917 * [backup-simplify]: Simplify 0 into 0 1.918 * [backup-simplify]: Simplify 0 into 0 1.919 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.919 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1.921 * [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 1.921 * [backup-simplify]: Simplify (+ 0 0) into 0 1.922 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1.922 * [backup-simplify]: Simplify (- 0) into 0 1.922 * [backup-simplify]: Simplify (+ 0 0) into 0 1.924 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1.926 * [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))))) 1.929 * [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))))) 1.936 * [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))))) 1.936 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1.936 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1.936 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1.936 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1.936 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1.936 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1.936 * [taylor]: Taking taylor expansion of 1/2 in k 1.936 * [backup-simplify]: Simplify 1/2 into 1/2 1.936 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1.936 * [taylor]: Taking taylor expansion of 1/2 in k 1.936 * [backup-simplify]: Simplify 1/2 into 1/2 1.936 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.936 * [taylor]: Taking taylor expansion of k in k 1.937 * [backup-simplify]: Simplify 0 into 0 1.937 * [backup-simplify]: Simplify 1 into 1 1.937 * [backup-simplify]: Simplify (/ 1 1) into 1 1.937 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1.937 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 1.937 * [taylor]: Taking taylor expansion of 2 in k 1.937 * [backup-simplify]: Simplify 2 into 2 1.937 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.937 * [taylor]: Taking taylor expansion of PI in k 1.937 * [backup-simplify]: Simplify PI into PI 1.937 * [taylor]: Taking taylor expansion of n in k 1.937 * [backup-simplify]: Simplify n into n 1.937 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.937 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1.937 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1.938 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 1.938 * [backup-simplify]: Simplify (- 1/2) into -1/2 1.938 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 1.938 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1.939 * [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)))) 1.939 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1.939 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1.939 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1.939 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1.939 * [taylor]: Taking taylor expansion of 1/2 in n 1.939 * [backup-simplify]: Simplify 1/2 into 1/2 1.939 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1.939 * [taylor]: Taking taylor expansion of 1/2 in n 1.939 * [backup-simplify]: Simplify 1/2 into 1/2 1.939 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.939 * [taylor]: Taking taylor expansion of k in n 1.939 * [backup-simplify]: Simplify k into k 1.939 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.939 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1.939 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.939 * [taylor]: Taking taylor expansion of 2 in n 1.939 * [backup-simplify]: Simplify 2 into 2 1.939 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.939 * [taylor]: Taking taylor expansion of PI in n 1.939 * [backup-simplify]: Simplify PI into PI 1.939 * [taylor]: Taking taylor expansion of n in n 1.939 * [backup-simplify]: Simplify 0 into 0 1.939 * [backup-simplify]: Simplify 1 into 1 1.940 * [backup-simplify]: Simplify (/ PI 1) into PI 1.940 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 1.941 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.941 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1.942 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1.942 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1.943 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1.944 * [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))) 1.945 * [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)))) 1.945 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1.946 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1.946 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1.946 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1.946 * [taylor]: Taking taylor expansion of 1/2 in n 1.946 * [backup-simplify]: Simplify 1/2 into 1/2 1.946 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1.946 * [taylor]: Taking taylor expansion of 1/2 in n 1.946 * [backup-simplify]: Simplify 1/2 into 1/2 1.946 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.946 * [taylor]: Taking taylor expansion of k in n 1.946 * [backup-simplify]: Simplify k into k 1.946 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.946 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1.946 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.946 * [taylor]: Taking taylor expansion of 2 in n 1.946 * [backup-simplify]: Simplify 2 into 2 1.946 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.946 * [taylor]: Taking taylor expansion of PI in n 1.946 * [backup-simplify]: Simplify PI into PI 1.946 * [taylor]: Taking taylor expansion of n in n 1.946 * [backup-simplify]: Simplify 0 into 0 1.946 * [backup-simplify]: Simplify 1 into 1 1.947 * [backup-simplify]: Simplify (/ PI 1) into PI 1.947 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 1.948 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.948 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1.948 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1.949 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1.950 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1.951 * [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))) 1.952 * [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)))) 1.953 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1.953 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1.953 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1.953 * [taylor]: Taking taylor expansion of 1/2 in k 1.953 * [backup-simplify]: Simplify 1/2 into 1/2 1.953 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1.953 * [taylor]: Taking taylor expansion of 1/2 in k 1.953 * [backup-simplify]: Simplify 1/2 into 1/2 1.953 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.953 * [taylor]: Taking taylor expansion of k in k 1.953 * [backup-simplify]: Simplify 0 into 0 1.953 * [backup-simplify]: Simplify 1 into 1 1.953 * [backup-simplify]: Simplify (/ 1 1) into 1 1.953 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1.953 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 1.953 * [taylor]: Taking taylor expansion of (* 2 PI) in k 1.953 * [taylor]: Taking taylor expansion of 2 in k 1.953 * [backup-simplify]: Simplify 2 into 2 1.953 * [taylor]: Taking taylor expansion of PI in k 1.953 * [backup-simplify]: Simplify PI into PI 1.954 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 1.954 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.954 * [taylor]: Taking taylor expansion of (log n) in k 1.954 * [taylor]: Taking taylor expansion of n in k 1.954 * [backup-simplify]: Simplify n into n 1.954 * [backup-simplify]: Simplify (log n) into (log n) 1.955 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 1.955 * [backup-simplify]: Simplify (- 1/2) into -1/2 1.955 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 1.955 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.956 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1.957 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1.957 * [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)))) 1.958 * [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)))) 1.959 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.959 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 1.960 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1.960 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.961 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1.961 * [backup-simplify]: Simplify (- 0) into 0 1.961 * [backup-simplify]: Simplify (+ 0 0) into 0 1.962 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1.963 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1.964 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1.964 * [taylor]: Taking taylor expansion of 0 in k 1.964 * [backup-simplify]: Simplify 0 into 0 1.964 * [backup-simplify]: Simplify 0 into 0 1.964 * [backup-simplify]: Simplify 0 into 0 1.965 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.965 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1.967 * [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 1.967 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.968 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1.968 * [backup-simplify]: Simplify (- 0) into 0 1.969 * [backup-simplify]: Simplify (+ 0 0) into 0 1.969 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1.970 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1.972 * [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 1.972 * [taylor]: Taking taylor expansion of 0 in k 1.972 * [backup-simplify]: Simplify 0 into 0 1.972 * [backup-simplify]: Simplify 0 into 0 1.972 * [backup-simplify]: Simplify 0 into 0 1.972 * [backup-simplify]: Simplify 0 into 0 1.973 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.973 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.977 * [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 1.977 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.978 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1.978 * [backup-simplify]: Simplify (- 0) into 0 1.978 * [backup-simplify]: Simplify (+ 0 0) into 0 1.979 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1.980 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1.983 * [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 1.983 * [taylor]: Taking taylor expansion of 0 in k 1.983 * [backup-simplify]: Simplify 0 into 0 1.983 * [backup-simplify]: Simplify 0 into 0 1.985 * [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))))) 1.985 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 1.985 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1.985 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1.985 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1.985 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1.985 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1.985 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1.986 * [taylor]: Taking taylor expansion of 1/2 in k 1.986 * [backup-simplify]: Simplify 1/2 into 1/2 1.986 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.986 * [taylor]: Taking taylor expansion of k in k 1.986 * [backup-simplify]: Simplify 0 into 0 1.986 * [backup-simplify]: Simplify 1 into 1 1.986 * [backup-simplify]: Simplify (/ 1 1) into 1 1.986 * [taylor]: Taking taylor expansion of 1/2 in k 1.986 * [backup-simplify]: Simplify 1/2 into 1/2 1.986 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1.986 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 1.986 * [taylor]: Taking taylor expansion of -2 in k 1.986 * [backup-simplify]: Simplify -2 into -2 1.986 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.986 * [taylor]: Taking taylor expansion of PI in k 1.986 * [backup-simplify]: Simplify PI into PI 1.986 * [taylor]: Taking taylor expansion of n in k 1.986 * [backup-simplify]: Simplify n into n 1.986 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.986 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1.986 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1.987 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 1.987 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 1.987 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1.988 * [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))) 1.988 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1.988 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1.988 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1.988 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1.988 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1.988 * [taylor]: Taking taylor expansion of 1/2 in n 1.988 * [backup-simplify]: Simplify 1/2 into 1/2 1.988 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.988 * [taylor]: Taking taylor expansion of k in n 1.988 * [backup-simplify]: Simplify k into k 1.988 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.988 * [taylor]: Taking taylor expansion of 1/2 in n 1.988 * [backup-simplify]: Simplify 1/2 into 1/2 1.988 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1.988 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 1.988 * [taylor]: Taking taylor expansion of -2 in n 1.988 * [backup-simplify]: Simplify -2 into -2 1.988 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.988 * [taylor]: Taking taylor expansion of PI in n 1.988 * [backup-simplify]: Simplify PI into PI 1.988 * [taylor]: Taking taylor expansion of n in n 1.988 * [backup-simplify]: Simplify 0 into 0 1.988 * [backup-simplify]: Simplify 1 into 1 1.989 * [backup-simplify]: Simplify (/ PI 1) into PI 1.989 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 1.990 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1.990 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1.991 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 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 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1.994 * [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)))) 1.994 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1.995 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1.995 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1.995 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1.995 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1.995 * [taylor]: Taking taylor expansion of 1/2 in n 1.995 * [backup-simplify]: Simplify 1/2 into 1/2 1.995 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.995 * [taylor]: Taking taylor expansion of k in n 1.995 * [backup-simplify]: Simplify k into k 1.995 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.995 * [taylor]: Taking taylor expansion of 1/2 in n 1.995 * [backup-simplify]: Simplify 1/2 into 1/2 1.995 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1.995 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 1.995 * [taylor]: Taking taylor expansion of -2 in n 1.995 * [backup-simplify]: Simplify -2 into -2 1.995 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.995 * [taylor]: Taking taylor expansion of PI in n 1.995 * [backup-simplify]: Simplify PI into PI 1.995 * [taylor]: Taking taylor expansion of n in n 1.995 * [backup-simplify]: Simplify 0 into 0 1.995 * [backup-simplify]: Simplify 1 into 1 1.996 * [backup-simplify]: Simplify (/ PI 1) into PI 1.996 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 1.997 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1.997 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1.997 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1.998 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1.999 * [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))) 2.000 * [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)))) 2.000 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 2.000 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 2.000 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.000 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.000 * [taylor]: Taking taylor expansion of 1/2 in k 2.000 * [backup-simplify]: Simplify 1/2 into 1/2 2.000 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.000 * [taylor]: Taking taylor expansion of k in k 2.000 * [backup-simplify]: Simplify 0 into 0 2.000 * [backup-simplify]: Simplify 1 into 1 2.000 * [backup-simplify]: Simplify (/ 1 1) into 1 2.000 * [taylor]: Taking taylor expansion of 1/2 in k 2.000 * [backup-simplify]: Simplify 1/2 into 1/2 2.000 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 2.000 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 2.000 * [taylor]: Taking taylor expansion of (* -2 PI) in k 2.000 * [taylor]: Taking taylor expansion of -2 in k 2.000 * [backup-simplify]: Simplify -2 into -2 2.000 * [taylor]: Taking taylor expansion of PI in k 2.000 * [backup-simplify]: Simplify PI into PI 2.001 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.001 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.001 * [taylor]: Taking taylor expansion of (log n) in k 2.001 * [taylor]: Taking taylor expansion of n in k 2.001 * [backup-simplify]: Simplify n into n 2.001 * [backup-simplify]: Simplify (log n) into (log n) 2.002 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.002 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.002 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.003 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 2.003 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 2.004 * [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)))) 2.005 * [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)))) 2.006 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.006 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.007 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 2.007 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.008 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.008 * [backup-simplify]: Simplify (+ 0 0) into 0 2.009 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.010 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 2.011 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.011 * [taylor]: Taking taylor expansion of 0 in k 2.011 * [backup-simplify]: Simplify 0 into 0 2.011 * [backup-simplify]: Simplify 0 into 0 2.011 * [backup-simplify]: Simplify 0 into 0 2.012 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.012 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.016 * [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 2.016 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.017 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.017 * [backup-simplify]: Simplify (+ 0 0) into 0 2.018 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.019 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 2.021 * [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 2.021 * [taylor]: Taking taylor expansion of 0 in k 2.021 * [backup-simplify]: Simplify 0 into 0 2.021 * [backup-simplify]: Simplify 0 into 0 2.021 * [backup-simplify]: Simplify 0 into 0 2.021 * [backup-simplify]: Simplify 0 into 0 2.022 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.022 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.027 * [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 2.027 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.028 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 2.029 * [backup-simplify]: Simplify (+ 0 0) into 0 2.030 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.032 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 2.036 * [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 2.036 * [taylor]: Taking taylor expansion of 0 in k 2.036 * [backup-simplify]: Simplify 0 into 0 2.036 * [backup-simplify]: Simplify 0 into 0 2.037 * [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))))) 2.037 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1) 2.038 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) 2.038 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 2.038 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.038 * [taylor]: Taking taylor expansion of 2 in n 2.038 * [backup-simplify]: Simplify 2 into 2 2.038 * [taylor]: Taking taylor expansion of (* n PI) in n 2.038 * [taylor]: Taking taylor expansion of n in n 2.038 * [backup-simplify]: Simplify 0 into 0 2.038 * [backup-simplify]: Simplify 1 into 1 2.038 * [taylor]: Taking taylor expansion of PI in n 2.038 * [backup-simplify]: Simplify PI into PI 2.038 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.038 * [taylor]: Taking taylor expansion of 2 in n 2.038 * [backup-simplify]: Simplify 2 into 2 2.038 * [taylor]: Taking taylor expansion of (* n PI) in n 2.038 * [taylor]: Taking taylor expansion of n in n 2.038 * [backup-simplify]: Simplify 0 into 0 2.038 * [backup-simplify]: Simplify 1 into 1 2.038 * [taylor]: Taking taylor expansion of PI in n 2.038 * [backup-simplify]: Simplify PI into PI 2.039 * [backup-simplify]: Simplify (* 0 PI) into 0 2.039 * [backup-simplify]: Simplify (* 2 0) into 0 2.039 * [backup-simplify]: Simplify 0 into 0 2.041 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.042 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.042 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.043 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.044 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 2.044 * [backup-simplify]: Simplify 0 into 0 2.044 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.045 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.045 * [backup-simplify]: Simplify 0 into 0 2.046 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.047 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.047 * [backup-simplify]: Simplify 0 into 0 2.048 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.048 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 2.049 * [backup-simplify]: Simplify 0 into 0 2.050 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.051 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 2.051 * [backup-simplify]: Simplify 0 into 0 2.052 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.053 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.053 * [backup-simplify]: Simplify 0 into 0 2.053 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 2.054 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) 2.054 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 2.054 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.054 * [taylor]: Taking taylor expansion of 2 in n 2.054 * [backup-simplify]: Simplify 2 into 2 2.054 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.054 * [taylor]: Taking taylor expansion of PI in n 2.054 * [backup-simplify]: Simplify PI into PI 2.054 * [taylor]: Taking taylor expansion of n in n 2.054 * [backup-simplify]: Simplify 0 into 0 2.054 * [backup-simplify]: Simplify 1 into 1 2.054 * [backup-simplify]: Simplify (/ PI 1) into PI 2.054 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.054 * [taylor]: Taking taylor expansion of 2 in n 2.054 * [backup-simplify]: Simplify 2 into 2 2.054 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.054 * [taylor]: Taking taylor expansion of PI in n 2.054 * [backup-simplify]: Simplify PI into PI 2.054 * [taylor]: Taking taylor expansion of n in n 2.054 * [backup-simplify]: Simplify 0 into 0 2.054 * [backup-simplify]: Simplify 1 into 1 2.054 * [backup-simplify]: Simplify (/ PI 1) into PI 2.055 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.055 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.056 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.056 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.056 * [backup-simplify]: Simplify 0 into 0 2.057 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.057 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.058 * [backup-simplify]: Simplify 0 into 0 2.058 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.059 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.059 * [backup-simplify]: Simplify 0 into 0 2.060 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.060 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.060 * [backup-simplify]: Simplify 0 into 0 2.061 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.062 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.062 * [backup-simplify]: Simplify 0 into 0 2.063 * [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 2.064 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.064 * [backup-simplify]: Simplify 0 into 0 2.064 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 2.064 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n)) 2.064 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 2.064 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.064 * [taylor]: Taking taylor expansion of -2 in n 2.064 * [backup-simplify]: Simplify -2 into -2 2.065 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.065 * [taylor]: Taking taylor expansion of PI in n 2.065 * [backup-simplify]: Simplify PI into PI 2.065 * [taylor]: Taking taylor expansion of n in n 2.065 * [backup-simplify]: Simplify 0 into 0 2.065 * [backup-simplify]: Simplify 1 into 1 2.065 * [backup-simplify]: Simplify (/ PI 1) into PI 2.065 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.065 * [taylor]: Taking taylor expansion of -2 in n 2.065 * [backup-simplify]: Simplify -2 into -2 2.065 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.065 * [taylor]: Taking taylor expansion of PI in n 2.065 * [backup-simplify]: Simplify PI into PI 2.065 * [taylor]: Taking taylor expansion of n in n 2.065 * [backup-simplify]: Simplify 0 into 0 2.065 * [backup-simplify]: Simplify 1 into 1 2.065 * [backup-simplify]: Simplify (/ PI 1) into PI 2.066 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.066 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.067 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.067 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.067 * [backup-simplify]: Simplify 0 into 0 2.068 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.068 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.068 * [backup-simplify]: Simplify 0 into 0 2.069 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.070 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.070 * [backup-simplify]: Simplify 0 into 0 2.071 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.073 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.073 * [backup-simplify]: Simplify 0 into 0 2.074 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.076 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.076 * [backup-simplify]: Simplify 0 into 0 2.077 * [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 2.079 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.079 * [backup-simplify]: Simplify 0 into 0 2.079 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 2.079 * * * * [progress]: [ 3 / 3 ] generating series at (2) 2.080 * [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)))) 2.080 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 2.080 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 2.080 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.080 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.080 * [taylor]: Taking taylor expansion of k in k 2.080 * [backup-simplify]: Simplify 0 into 0 2.080 * [backup-simplify]: Simplify 1 into 1 2.081 * [backup-simplify]: Simplify (/ 1 1) into 1 2.081 * [backup-simplify]: Simplify (sqrt 0) into 0 2.083 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.083 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 2.083 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 2.083 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 2.083 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 2.083 * [taylor]: Taking taylor expansion of 1/2 in k 2.083 * [backup-simplify]: Simplify 1/2 into 1/2 2.083 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 2.083 * [taylor]: Taking taylor expansion of 1/2 in k 2.083 * [backup-simplify]: Simplify 1/2 into 1/2 2.083 * [taylor]: Taking taylor expansion of k in k 2.083 * [backup-simplify]: Simplify 0 into 0 2.083 * [backup-simplify]: Simplify 1 into 1 2.083 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 2.083 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 2.083 * [taylor]: Taking taylor expansion of 2 in k 2.083 * [backup-simplify]: Simplify 2 into 2 2.083 * [taylor]: Taking taylor expansion of (* n PI) in k 2.083 * [taylor]: Taking taylor expansion of n in k 2.083 * [backup-simplify]: Simplify n into n 2.083 * [taylor]: Taking taylor expansion of PI in k 2.083 * [backup-simplify]: Simplify PI into PI 2.083 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.083 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 2.083 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 2.084 * [backup-simplify]: Simplify (* 1/2 0) into 0 2.084 * [backup-simplify]: Simplify (- 0) into 0 2.085 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.085 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 2.085 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 2.085 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 2.085 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.085 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.085 * [taylor]: Taking taylor expansion of k in n 2.085 * [backup-simplify]: Simplify k into k 2.085 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.085 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 2.085 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.085 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 2.085 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 2.085 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 2.085 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 2.085 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 2.085 * [taylor]: Taking taylor expansion of 1/2 in n 2.086 * [backup-simplify]: Simplify 1/2 into 1/2 2.086 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 2.086 * [taylor]: Taking taylor expansion of 1/2 in n 2.086 * [backup-simplify]: Simplify 1/2 into 1/2 2.086 * [taylor]: Taking taylor expansion of k in n 2.086 * [backup-simplify]: Simplify k into k 2.086 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 2.086 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.086 * [taylor]: Taking taylor expansion of 2 in n 2.086 * [backup-simplify]: Simplify 2 into 2 2.086 * [taylor]: Taking taylor expansion of (* n PI) in n 2.086 * [taylor]: Taking taylor expansion of n in n 2.086 * [backup-simplify]: Simplify 0 into 0 2.086 * [backup-simplify]: Simplify 1 into 1 2.086 * [taylor]: Taking taylor expansion of PI in n 2.086 * [backup-simplify]: Simplify PI into PI 2.086 * [backup-simplify]: Simplify (* 0 PI) into 0 2.086 * [backup-simplify]: Simplify (* 2 0) into 0 2.087 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.088 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.089 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.089 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 2.089 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 2.089 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 2.090 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.091 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 2.091 * [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))))) 2.091 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 2.091 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.091 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.091 * [taylor]: Taking taylor expansion of k in n 2.091 * [backup-simplify]: Simplify k into k 2.092 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.092 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 2.092 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.092 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 2.092 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 2.092 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 2.092 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 2.092 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 2.092 * [taylor]: Taking taylor expansion of 1/2 in n 2.092 * [backup-simplify]: Simplify 1/2 into 1/2 2.092 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 2.092 * [taylor]: Taking taylor expansion of 1/2 in n 2.092 * [backup-simplify]: Simplify 1/2 into 1/2 2.092 * [taylor]: Taking taylor expansion of k in n 2.092 * [backup-simplify]: Simplify k into k 2.092 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 2.092 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.092 * [taylor]: Taking taylor expansion of 2 in n 2.092 * [backup-simplify]: Simplify 2 into 2 2.092 * [taylor]: Taking taylor expansion of (* n PI) in n 2.092 * [taylor]: Taking taylor expansion of n in n 2.092 * [backup-simplify]: Simplify 0 into 0 2.092 * [backup-simplify]: Simplify 1 into 1 2.092 * [taylor]: Taking taylor expansion of PI in n 2.092 * [backup-simplify]: Simplify PI into PI 2.092 * [backup-simplify]: Simplify (* 0 PI) into 0 2.093 * [backup-simplify]: Simplify (* 2 0) into 0 2.094 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.095 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.096 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.096 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 2.096 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 2.096 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 2.097 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.098 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 2.098 * [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))))) 2.099 * [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))) 2.099 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 2.099 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 2.099 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 2.099 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 2.099 * [taylor]: Taking taylor expansion of 1/2 in k 2.099 * [backup-simplify]: Simplify 1/2 into 1/2 2.099 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 2.099 * [taylor]: Taking taylor expansion of 1/2 in k 2.099 * [backup-simplify]: Simplify 1/2 into 1/2 2.099 * [taylor]: Taking taylor expansion of k in k 2.099 * [backup-simplify]: Simplify 0 into 0 2.099 * [backup-simplify]: Simplify 1 into 1 2.099 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 2.099 * [taylor]: Taking taylor expansion of (log n) in k 2.099 * [taylor]: Taking taylor expansion of n in k 2.099 * [backup-simplify]: Simplify n into n 2.099 * [backup-simplify]: Simplify (log n) into (log n) 2.099 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.099 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.099 * [taylor]: Taking taylor expansion of 2 in k 2.099 * [backup-simplify]: Simplify 2 into 2 2.099 * [taylor]: Taking taylor expansion of PI in k 2.099 * [backup-simplify]: Simplify PI into PI 2.100 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.100 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.101 * [backup-simplify]: Simplify (* 1/2 0) into 0 2.101 * [backup-simplify]: Simplify (- 0) into 0 2.101 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.102 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.103 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 2.103 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 2.103 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.103 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.103 * [taylor]: Taking taylor expansion of k in k 2.103 * [backup-simplify]: Simplify 0 into 0 2.103 * [backup-simplify]: Simplify 1 into 1 2.104 * [backup-simplify]: Simplify (/ 1 1) into 1 2.104 * [backup-simplify]: Simplify (sqrt 0) into 0 2.105 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.106 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 2.106 * [backup-simplify]: Simplify 0 into 0 2.106 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.107 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 2.108 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.108 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 2.108 * [backup-simplify]: Simplify (- 0) into 0 2.109 * [backup-simplify]: Simplify (+ 0 0) into 0 2.110 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.110 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 2.111 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.112 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 2.112 * [taylor]: Taking taylor expansion of 0 in k 2.112 * [backup-simplify]: Simplify 0 into 0 2.113 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.113 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.115 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.115 * [backup-simplify]: Simplify (+ 0 0) into 0 2.116 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 2.117 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.117 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.119 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2.122 * [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))))))) 2.130 * [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))))))) 2.131 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 2.132 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.134 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.137 * [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 2.138 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 2.138 * [backup-simplify]: Simplify (- 0) into 0 2.139 * [backup-simplify]: Simplify (+ 0 0) into 0 2.140 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.142 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.145 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.145 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.145 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 2.147 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 2.147 * [taylor]: Taking taylor expansion of 0 in k 2.147 * [backup-simplify]: Simplify 0 into 0 2.147 * [backup-simplify]: Simplify 0 into 0 2.148 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.151 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.153 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.154 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.157 * [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 2.158 * [backup-simplify]: Simplify (+ 0 0) into 0 2.159 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 2.159 * [backup-simplify]: Simplify (- 0) into 0 2.159 * [backup-simplify]: Simplify (+ 0 0) into 0 2.161 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.165 * [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))))) 2.172 * [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)))))))) 2.175 * [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)))))))) 2.176 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.177 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.180 * [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 2.181 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 2.181 * [backup-simplify]: Simplify (- 0) into 0 2.182 * [backup-simplify]: Simplify (+ 0 0) into 0 2.182 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.184 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 2.185 * [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 2.185 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.186 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 2.187 * [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 2.187 * [taylor]: Taking taylor expansion of 0 in k 2.187 * [backup-simplify]: Simplify 0 into 0 2.187 * [backup-simplify]: Simplify 0 into 0 2.187 * [backup-simplify]: Simplify 0 into 0 2.188 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.190 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.192 * [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 2.192 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.195 * [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 2.196 * [backup-simplify]: Simplify (+ 0 0) into 0 2.196 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 2.197 * [backup-simplify]: Simplify (- 0) into 0 2.197 * [backup-simplify]: Simplify (+ 0 0) into 0 2.198 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 2.202 * [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))))))) 2.213 * [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)))))))))))))) 2.220 * [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)))))))))))))) 2.243 * [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)))))))))))))))))))))) 2.244 * [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))))) 2.244 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 2.244 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 2.244 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.244 * [taylor]: Taking taylor expansion of k in k 2.244 * [backup-simplify]: Simplify 0 into 0 2.244 * [backup-simplify]: Simplify 1 into 1 2.244 * [backup-simplify]: Simplify (sqrt 0) into 0 2.246 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.246 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 2.246 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 2.246 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 2.246 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.246 * [taylor]: Taking taylor expansion of 1/2 in k 2.246 * [backup-simplify]: Simplify 1/2 into 1/2 2.246 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.246 * [taylor]: Taking taylor expansion of 1/2 in k 2.246 * [backup-simplify]: Simplify 1/2 into 1/2 2.246 * [taylor]: Taking taylor expansion of (/ 1 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 (/ 1 1) into 1 2.247 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 2.247 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 2.247 * [taylor]: Taking taylor expansion of 2 in k 2.247 * [backup-simplify]: Simplify 2 into 2 2.247 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.247 * [taylor]: Taking taylor expansion of PI in k 2.247 * [backup-simplify]: Simplify PI into PI 2.247 * [taylor]: Taking taylor expansion of n in k 2.247 * [backup-simplify]: Simplify n into n 2.247 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.247 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 2.247 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 2.248 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.248 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.248 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.249 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 2.249 * [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)))) 2.249 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 2.249 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.249 * [taylor]: Taking taylor expansion of k in n 2.249 * [backup-simplify]: Simplify k into k 2.249 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.249 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.249 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.249 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.249 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.249 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.249 * [taylor]: Taking taylor expansion of 1/2 in n 2.249 * [backup-simplify]: Simplify 1/2 into 1/2 2.249 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.249 * [taylor]: Taking taylor expansion of 1/2 in n 2.249 * [backup-simplify]: Simplify 1/2 into 1/2 2.249 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.249 * [taylor]: Taking taylor expansion of k in n 2.249 * [backup-simplify]: Simplify k into k 2.249 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.249 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.249 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.249 * [taylor]: Taking taylor expansion of 2 in n 2.249 * [backup-simplify]: Simplify 2 into 2 2.249 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.250 * [taylor]: Taking taylor expansion of PI in n 2.250 * [backup-simplify]: Simplify PI into PI 2.250 * [taylor]: Taking taylor expansion of n in n 2.250 * [backup-simplify]: Simplify 0 into 0 2.250 * [backup-simplify]: Simplify 1 into 1 2.250 * [backup-simplify]: Simplify (/ PI 1) into PI 2.251 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.252 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.252 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.252 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.252 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.253 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.255 * [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))) 2.256 * [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)))) 2.256 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 2.256 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.256 * [taylor]: Taking taylor expansion of k in n 2.256 * [backup-simplify]: Simplify k into k 2.256 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.257 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.257 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.257 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.257 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.257 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.257 * [taylor]: Taking taylor expansion of 1/2 in n 2.257 * [backup-simplify]: Simplify 1/2 into 1/2 2.257 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.257 * [taylor]: Taking taylor expansion of 1/2 in n 2.257 * [backup-simplify]: Simplify 1/2 into 1/2 2.257 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.257 * [taylor]: Taking taylor expansion of k in n 2.257 * [backup-simplify]: Simplify k into k 2.257 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.257 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.257 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.257 * [taylor]: Taking taylor expansion of 2 in n 2.257 * [backup-simplify]: Simplify 2 into 2 2.257 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.257 * [taylor]: Taking taylor expansion of PI in n 2.257 * [backup-simplify]: Simplify PI into PI 2.257 * [taylor]: Taking taylor expansion of n in n 2.257 * [backup-simplify]: Simplify 0 into 0 2.257 * [backup-simplify]: Simplify 1 into 1 2.258 * [backup-simplify]: Simplify (/ PI 1) into PI 2.258 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.259 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.259 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.259 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.259 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.260 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.260 * [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))) 2.261 * [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)))) 2.262 * [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)) 2.262 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 2.262 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 2.262 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 2.262 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.262 * [taylor]: Taking taylor expansion of 1/2 in k 2.262 * [backup-simplify]: Simplify 1/2 into 1/2 2.262 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.262 * [taylor]: Taking taylor expansion of 1/2 in k 2.262 * [backup-simplify]: Simplify 1/2 into 1/2 2.262 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.262 * [taylor]: Taking taylor expansion of k in k 2.262 * [backup-simplify]: Simplify 0 into 0 2.262 * [backup-simplify]: Simplify 1 into 1 2.262 * [backup-simplify]: Simplify (/ 1 1) into 1 2.262 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 2.262 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.262 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.262 * [taylor]: Taking taylor expansion of 2 in k 2.262 * [backup-simplify]: Simplify 2 into 2 2.262 * [taylor]: Taking taylor expansion of PI in k 2.262 * [backup-simplify]: Simplify PI into PI 2.263 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.263 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.263 * [taylor]: Taking taylor expansion of (log n) in k 2.263 * [taylor]: Taking taylor expansion of n in k 2.263 * [backup-simplify]: Simplify n into n 2.263 * [backup-simplify]: Simplify (log n) into (log n) 2.264 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.264 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.264 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.264 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.265 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 2.266 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (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)))) 2.266 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.266 * [taylor]: Taking taylor expansion of k in k 2.266 * [backup-simplify]: Simplify 0 into 0 2.266 * [backup-simplify]: Simplify 1 into 1 2.267 * [backup-simplify]: Simplify (sqrt 0) into 0 2.268 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.268 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 2.268 * [backup-simplify]: Simplify 0 into 0 2.269 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.269 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.270 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.271 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.271 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.271 * [backup-simplify]: Simplify (- 0) into 0 2.271 * [backup-simplify]: Simplify (+ 0 0) into 0 2.272 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.273 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 2.274 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.275 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 2.275 * [taylor]: Taking taylor expansion of 0 in k 2.275 * [backup-simplify]: Simplify 0 into 0 2.275 * [backup-simplify]: Simplify 0 into 0 2.276 * [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)))))) 2.277 * [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)))))) 2.277 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.278 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.280 * [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 2.280 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.281 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.281 * [backup-simplify]: Simplify (- 0) into 0 2.281 * [backup-simplify]: Simplify (+ 0 0) into 0 2.282 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.283 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 2.284 * [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 2.285 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 2.286 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 2.286 * [taylor]: Taking taylor expansion of 0 in k 2.286 * [backup-simplify]: Simplify 0 into 0 2.286 * [backup-simplify]: Simplify 0 into 0 2.286 * [backup-simplify]: Simplify 0 into 0 2.289 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.291 * [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)))))) 2.292 * [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)))))) 2.294 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.295 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.301 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 2.301 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.303 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 2.303 * [backup-simplify]: Simplify (- 0) into 0 2.304 * [backup-simplify]: Simplify (+ 0 0) into 0 2.305 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.307 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 2.310 * [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 2.311 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 2.313 * [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 2.313 * [taylor]: Taking taylor expansion of 0 in k 2.313 * [backup-simplify]: Simplify 0 into 0 2.313 * [backup-simplify]: Simplify 0 into 0 2.313 * [backup-simplify]: Simplify 0 into 0 2.313 * [backup-simplify]: Simplify 0 into 0 2.317 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.319 * [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)))))) 2.321 * [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)))))) 2.325 * [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)))))))) 2.326 * [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))) 2.326 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 2.326 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 2.326 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 2.326 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 2.326 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 2.326 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.326 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.326 * [taylor]: Taking taylor expansion of 1/2 in k 2.326 * [backup-simplify]: Simplify 1/2 into 1/2 2.326 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.326 * [taylor]: Taking taylor expansion of k in k 2.326 * [backup-simplify]: Simplify 0 into 0 2.326 * [backup-simplify]: Simplify 1 into 1 2.327 * [backup-simplify]: Simplify (/ 1 1) into 1 2.327 * [taylor]: Taking taylor expansion of 1/2 in k 2.327 * [backup-simplify]: Simplify 1/2 into 1/2 2.327 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 2.327 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 2.327 * [taylor]: Taking taylor expansion of -2 in k 2.327 * [backup-simplify]: Simplify -2 into -2 2.327 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.327 * [taylor]: Taking taylor expansion of PI in k 2.327 * [backup-simplify]: Simplify PI into PI 2.327 * [taylor]: Taking taylor expansion of n in k 2.327 * [backup-simplify]: Simplify n into n 2.327 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.327 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 2.327 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 2.328 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.328 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.328 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 2.328 * [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))) 2.328 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.328 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.329 * [taylor]: Taking taylor expansion of -1 in k 2.329 * [backup-simplify]: Simplify -1 into -1 2.329 * [taylor]: Taking taylor expansion of k in k 2.329 * [backup-simplify]: Simplify 0 into 0 2.329 * [backup-simplify]: Simplify 1 into 1 2.329 * [backup-simplify]: Simplify (/ -1 1) into -1 2.330 * [backup-simplify]: Simplify (sqrt 0) into 0 2.331 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.331 * [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)))) 2.331 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 2.332 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.332 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.332 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.332 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.332 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.332 * [taylor]: Taking taylor expansion of 1/2 in n 2.332 * [backup-simplify]: Simplify 1/2 into 1/2 2.332 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.332 * [taylor]: Taking taylor expansion of k in n 2.332 * [backup-simplify]: Simplify k into k 2.332 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.332 * [taylor]: Taking taylor expansion of 1/2 in n 2.332 * [backup-simplify]: Simplify 1/2 into 1/2 2.332 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.332 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.332 * [taylor]: Taking taylor expansion of -2 in n 2.332 * [backup-simplify]: Simplify -2 into -2 2.332 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.332 * [taylor]: Taking taylor expansion of PI in n 2.332 * [backup-simplify]: Simplify PI into PI 2.332 * [taylor]: Taking taylor expansion of n in n 2.332 * [backup-simplify]: Simplify 0 into 0 2.332 * [backup-simplify]: Simplify 1 into 1 2.333 * [backup-simplify]: Simplify (/ PI 1) into PI 2.333 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.335 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.335 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.335 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.337 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.338 * [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))) 2.339 * [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)))) 2.339 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.339 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.339 * [taylor]: Taking taylor expansion of -1 in n 2.339 * [backup-simplify]: Simplify -1 into -1 2.339 * [taylor]: Taking taylor expansion of k in n 2.339 * [backup-simplify]: Simplify k into k 2.340 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.340 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.340 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.340 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.341 * [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))) 2.341 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 2.341 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.341 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.341 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.341 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.341 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.341 * [taylor]: Taking taylor expansion of 1/2 in n 2.341 * [backup-simplify]: Simplify 1/2 into 1/2 2.342 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.342 * [taylor]: Taking taylor expansion of k in n 2.342 * [backup-simplify]: Simplify k into k 2.342 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.342 * [taylor]: Taking taylor expansion of 1/2 in n 2.342 * [backup-simplify]: Simplify 1/2 into 1/2 2.342 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.342 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.342 * [taylor]: Taking taylor expansion of -2 in n 2.342 * [backup-simplify]: Simplify -2 into -2 2.342 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.342 * [taylor]: Taking taylor expansion of PI in n 2.342 * [backup-simplify]: Simplify PI into PI 2.342 * [taylor]: Taking taylor expansion of n in n 2.342 * [backup-simplify]: Simplify 0 into 0 2.342 * [backup-simplify]: Simplify 1 into 1 2.342 * [backup-simplify]: Simplify (/ PI 1) into PI 2.343 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.344 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.344 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.344 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.346 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.347 * [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))) 2.348 * [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)))) 2.349 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.349 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.349 * [taylor]: Taking taylor expansion of -1 in n 2.349 * [backup-simplify]: Simplify -1 into -1 2.349 * [taylor]: Taking taylor expansion of k in n 2.349 * [backup-simplify]: Simplify k into k 2.349 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.349 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.349 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.349 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.350 * [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))) 2.350 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 2.350 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 2.351 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 2.351 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.351 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.351 * [taylor]: Taking taylor expansion of 1/2 in k 2.351 * [backup-simplify]: Simplify 1/2 into 1/2 2.351 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.351 * [taylor]: Taking taylor expansion of k in k 2.351 * [backup-simplify]: Simplify 0 into 0 2.351 * [backup-simplify]: Simplify 1 into 1 2.351 * [backup-simplify]: Simplify (/ 1 1) into 1 2.351 * [taylor]: Taking taylor expansion of 1/2 in k 2.351 * [backup-simplify]: Simplify 1/2 into 1/2 2.351 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 2.351 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 2.351 * [taylor]: Taking taylor expansion of (* -2 PI) in k 2.351 * [taylor]: Taking taylor expansion of -2 in k 2.351 * [backup-simplify]: Simplify -2 into -2 2.351 * [taylor]: Taking taylor expansion of PI in k 2.351 * [backup-simplify]: Simplify PI into PI 2.352 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.353 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.353 * [taylor]: Taking taylor expansion of (log n) in k 2.353 * [taylor]: Taking taylor expansion of n in k 2.353 * [backup-simplify]: Simplify n into n 2.353 * [backup-simplify]: Simplify (log n) into (log n) 2.353 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.354 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.354 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.355 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 2.360 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 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 k 2.361 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.361 * [taylor]: Taking taylor expansion of -1 in k 2.361 * [backup-simplify]: Simplify -1 into -1 2.362 * [taylor]: Taking taylor expansion of k in k 2.362 * [backup-simplify]: Simplify 0 into 0 2.362 * [backup-simplify]: Simplify 1 into 1 2.362 * [backup-simplify]: Simplify (/ -1 1) into -1 2.362 * [backup-simplify]: Simplify (sqrt 0) into 0 2.364 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.365 * [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))))) 2.367 * [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))))) 2.368 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.369 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.370 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 2.371 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.371 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.372 * [backup-simplify]: Simplify (+ 0 0) into 0 2.373 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.374 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 2.376 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.378 * [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 2.378 * [taylor]: Taking taylor expansion of 0 in k 2.378 * [backup-simplify]: Simplify 0 into 0 2.378 * [backup-simplify]: Simplify 0 into 0 2.379 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.382 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.384 * [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)))))) 2.385 * [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)))))) 2.387 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.388 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.391 * [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 2.393 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.393 * [backup-simplify]: Simplify (+ 0 0) into 0 2.395 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.396 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 2.399 * [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 2.399 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.400 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 2.401 * [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 2.401 * [taylor]: Taking taylor expansion of 0 in k 2.401 * [backup-simplify]: Simplify 0 into 0 2.401 * [backup-simplify]: Simplify 0 into 0 2.401 * [backup-simplify]: Simplify 0 into 0 2.403 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.407 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.410 * [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)))))) 2.412 * [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)))))) 2.416 * [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))))))))))) 2.416 * * * [progress]: simplifying candidates 2.416 * * * * [progress]: [ 1 / 445 ] simplifiying candidate # 2.416 * * * * [progress]: [ 2 / 445 ] simplifiying candidate # 2.416 * * * * [progress]: [ 3 / 445 ] simplifiying candidate # 2.416 * * * * [progress]: [ 4 / 445 ] simplifiying candidate # 2.416 * * * * [progress]: [ 5 / 445 ] simplifiying candidate # 2.416 * * * * [progress]: [ 6 / 445 ] simplifiying candidate # 2.417 * * * * [progress]: [ 7 / 445 ] simplifiying candidate # 2.417 * * * * [progress]: [ 8 / 445 ] simplifiying candidate # 2.417 * * * * [progress]: [ 9 / 445 ] simplifiying candidate # 2.417 * * * * 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2.420 * * * * [progress]: [ 57 / 445 ] simplifiying candidate # 2.420 * * * * [progress]: [ 58 / 445 ] simplifiying candidate # 2.421 * * * * [progress]: [ 59 / 445 ] simplifiying candidate # 2.421 * * * * [progress]: [ 60 / 445 ] simplifiying candidate # 2.421 * * * * [progress]: [ 61 / 445 ] simplifiying candidate # 2.421 * * * * [progress]: [ 62 / 445 ] simplifiying candidate # 2.421 * * * * [progress]: [ 63 / 445 ] simplifiying candidate # 2.421 * * * * [progress]: [ 64 / 445 ] simplifiying candidate # 2.421 * * * * [progress]: [ 65 / 445 ] simplifiying candidate # 2.421 * * * * [progress]: [ 66 / 445 ] simplifiying candidate # 2.421 * * * * [progress]: [ 67 / 445 ] simplifiying candidate #real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))> 2.421 * * * * [progress]: [ 68 / 445 ] simplifiying candidate # 2.421 * * * * [progress]: [ 69 / 445 ] simplifiying candidate # 2.421 * * * * [progress]: [ 70 / 445 ] simplifiying candidate # 2.421 * * * * [progress]: [ 71 / 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* * [progress]: [ 87 / 445 ] simplifiying candidate #real (real->posit16 (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))> 2.422 * * * * [progress]: [ 88 / 445 ] simplifiying candidate # 2.422 * * * * [progress]: [ 89 / 445 ] simplifiying candidate # 2.423 * * * * [progress]: [ 90 / 445 ] simplifiying candidate # 2.423 * * * * [progress]: [ 91 / 445 ] simplifiying candidate # 2.423 * * * * [progress]: [ 92 / 445 ] simplifiying candidate # 2.423 * * * * [progress]: [ 93 / 445 ] simplifiying candidate # 2.423 * * * * [progress]: [ 94 / 445 ] simplifiying candidate # 2.423 * * * * [progress]: [ 95 / 445 ] simplifiying candidate # 2.423 * * * * [progress]: [ 96 / 445 ] simplifiying candidate # 2.423 * * * * [progress]: [ 97 / 445 ] simplifiying candidate # 2.423 * * * * [progress]: [ 98 / 445 ] simplifiying candidate # 2.423 * * * * [progress]: [ 99 / 445 ] simplifiying candidate # 2.423 * * * * [progress]: [ 100 / 445 ] simplifiying candidate # 2.423 * * * * [progress]: [ 101 / 445 ] 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candidate # 2.451 * * * * [progress]: [ 438 / 445 ] simplifiying candidate # 2.451 * * * * [progress]: [ 439 / 445 ] simplifiying candidate # 2.451 * * * * [progress]: [ 440 / 445 ] simplifiying candidate # 2.451 * * * * [progress]: [ 441 / 445 ] simplifiying candidate # 2.451 * * * * [progress]: [ 442 / 445 ] simplifiying candidate # 2.451 * * * * [progress]: [ 443 / 445 ] simplifiying candidate # 2.452 * * * * [progress]: [ 444 / 445 ] simplifiying candidate # 2.452 * * * * [progress]: [ 445 / 445 ] simplifiying candidate # 2.466 * [simplify]: Simplifying: (expm1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (log1p (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (/ k 2)) (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) (/ 1 1))))) (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) 1)))) (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1 2) k)))) (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) 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(* 2 (* n PI)) (* 2 (* n PI)) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 2.486 * * [simplify]: iteration 0: 695 enodes 2.784 * * [simplify]: iteration 1: 1526 enodes 3.223 * * [simplify]: iteration 2: 2001 enodes 3.617 * * [simplify]: iteration complete: 2001 enodes 3.618 * * [simplify]: Extracting #0: cost 233 inf + 0 3.619 * * [simplify]: Extracting #1: cost 515 inf + 1 3.621 * * [simplify]: Extracting #2: cost 739 inf + 1881 3.625 * * [simplify]: Extracting #3: cost 804 inf + 11914 3.638 * * [simplify]: Extracting #4: cost 562 inf + 88070 3.658 * * [simplify]: Extracting #5: cost 346 inf + 180910 3.741 * * [simplify]: Extracting #6: cost 193 inf + 273665 3.820 * * [simplify]: Extracting #7: cost 60 inf + 356856 3.888 * * [simplify]: Extracting #8: cost 23 inf + 387667 3.971 * * [simplify]: Extracting #9: cost 23 inf + 390493 4.068 * * [simplify]: Extracting #10: cost 15 inf + 395110 4.137 * * [simplify]: Extracting #11: cost 10 inf + 400340 4.206 * * [simplify]: Extracting #12: cost 4 inf + 408621 4.289 * * [simplify]: Extracting #13: cost 0 inf + 415390 4.361 * * [simplify]: Extracting #14: cost 0 inf + 415265 4.440 * * [simplify]: Extracting #15: cost 0 inf + 415190 4.555 * [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))) 4.681 * * * [progress]: adding candidates to table 7.488 * * [progress]: iteration 2 / 4 7.488 * * * [progress]: picking best candidate 7.547 * * * * [pick]: Picked # 7.547 * * * [progress]: localizing error 7.600 * * * [progress]: generating rewritten candidates 7.600 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 7.632 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 7.661 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 7.672 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 7.743 * * * [progress]: generating series expansions 7.743 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 7.745 * [backup-simplify]: Simplify (pow (* (* 2 PI) n) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) 7.745 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0 7.745 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 7.745 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 7.745 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 7.745 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k 7.745 * [taylor]: Taking taylor expansion of 1/2 in k 7.745 * [backup-simplify]: Simplify 1/2 into 1/2 7.745 * [taylor]: Taking taylor expansion of (- 1 k) in k 7.745 * [taylor]: Taking taylor expansion of 1 in k 7.745 * [backup-simplify]: Simplify 1 into 1 7.745 * [taylor]: Taking taylor expansion of k in k 7.745 * [backup-simplify]: Simplify 0 into 0 7.745 * [backup-simplify]: Simplify 1 into 1 7.745 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 7.745 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 7.745 * [taylor]: Taking taylor expansion of 2 in k 7.745 * [backup-simplify]: Simplify 2 into 2 7.745 * [taylor]: Taking taylor expansion of (* n PI) in k 7.745 * [taylor]: Taking taylor expansion of n in k 7.745 * [backup-simplify]: Simplify n into n 7.745 * [taylor]: Taking taylor expansion of PI in k 7.745 * [backup-simplify]: Simplify PI into PI 7.745 * [backup-simplify]: Simplify (* n PI) into (* n PI) 7.745 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 7.745 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 7.746 * [backup-simplify]: Simplify (- 0) into 0 7.746 * [backup-simplify]: Simplify (+ 1 0) into 1 7.747 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 7.747 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 7.747 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 7.747 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 7.747 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 7.747 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 7.747 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n 7.747 * [taylor]: Taking taylor expansion of 1/2 in n 7.747 * [backup-simplify]: Simplify 1/2 into 1/2 7.747 * [taylor]: Taking taylor expansion of (- 1 k) in n 7.747 * [taylor]: Taking taylor expansion of 1 in n 7.747 * [backup-simplify]: Simplify 1 into 1 7.747 * [taylor]: Taking taylor expansion of k in n 7.747 * [backup-simplify]: Simplify k into k 7.747 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 7.747 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 7.747 * [taylor]: Taking taylor expansion of 2 in n 7.747 * [backup-simplify]: Simplify 2 into 2 7.747 * [taylor]: Taking taylor expansion of (* n PI) in n 7.747 * [taylor]: Taking taylor expansion of n in n 7.747 * [backup-simplify]: Simplify 0 into 0 7.747 * [backup-simplify]: Simplify 1 into 1 7.747 * [taylor]: Taking taylor expansion of PI in n 7.747 * [backup-simplify]: Simplify PI into PI 7.748 * [backup-simplify]: Simplify (* 0 PI) into 0 7.748 * [backup-simplify]: Simplify (* 2 0) into 0 7.750 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 7.752 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 7.753 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 7.753 * [backup-simplify]: Simplify (- k) into (- k) 7.753 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k) 7.753 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 7.755 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 7.756 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 7.757 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 7.757 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 7.757 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 7.757 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 7.757 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n 7.757 * [taylor]: Taking taylor expansion of 1/2 in n 7.757 * [backup-simplify]: Simplify 1/2 into 1/2 7.757 * [taylor]: Taking taylor expansion of (- 1 k) in n 7.757 * [taylor]: Taking taylor expansion of 1 in n 7.757 * [backup-simplify]: Simplify 1 into 1 7.757 * [taylor]: Taking taylor expansion of k in n 7.757 * [backup-simplify]: Simplify k into k 7.757 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 7.757 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 7.757 * [taylor]: Taking taylor expansion of 2 in n 7.758 * [backup-simplify]: Simplify 2 into 2 7.758 * [taylor]: Taking taylor expansion of (* n PI) in n 7.758 * [taylor]: Taking taylor expansion of n in n 7.758 * [backup-simplify]: Simplify 0 into 0 7.758 * [backup-simplify]: Simplify 1 into 1 7.758 * [taylor]: Taking taylor expansion of PI in n 7.758 * [backup-simplify]: Simplify PI into PI 7.758 * [backup-simplify]: Simplify (* 0 PI) into 0 7.759 * [backup-simplify]: Simplify (* 2 0) into 0 7.760 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 7.762 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 7.763 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 7.763 * [backup-simplify]: Simplify (- k) into (- k) 7.763 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k) 7.763 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 7.764 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 7.765 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 7.766 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 7.767 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k 7.767 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k 7.767 * [taylor]: Taking taylor expansion of 1/2 in k 7.767 * [backup-simplify]: Simplify 1/2 into 1/2 7.767 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k 7.767 * [taylor]: Taking taylor expansion of (- 1 k) in k 7.767 * [taylor]: Taking taylor expansion of 1 in k 7.767 * [backup-simplify]: Simplify 1 into 1 7.767 * [taylor]: Taking taylor expansion of k in k 7.767 * [backup-simplify]: Simplify 0 into 0 7.767 * [backup-simplify]: Simplify 1 into 1 7.767 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 7.767 * [taylor]: Taking taylor expansion of (log n) in k 7.767 * [taylor]: Taking taylor expansion of n in k 7.767 * [backup-simplify]: Simplify n into n 7.767 * [backup-simplify]: Simplify (log n) into (log n) 7.767 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 7.767 * [taylor]: Taking taylor expansion of (* 2 PI) in k 7.767 * [taylor]: Taking taylor expansion of 2 in k 7.767 * [backup-simplify]: Simplify 2 into 2 7.767 * [taylor]: Taking taylor expansion of PI in k 7.767 * [backup-simplify]: Simplify PI into PI 7.768 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 7.769 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 7.769 * [backup-simplify]: Simplify (- 0) into 0 7.769 * [backup-simplify]: Simplify (+ 1 0) into 1 7.771 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 7.772 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI))) 7.773 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 7.774 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 7.775 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 7.776 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 7.777 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 7.779 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 7.780 * [backup-simplify]: Simplify (- 0) into 0 7.780 * [backup-simplify]: Simplify (+ 0 0) into 0 7.780 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0 7.782 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 7.783 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 7.785 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0 7.785 * [taylor]: Taking taylor expansion of 0 in k 7.785 * [backup-simplify]: Simplify 0 into 0 7.785 * [backup-simplify]: Simplify 0 into 0 7.786 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 7.787 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 7.789 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 7.789 * [backup-simplify]: Simplify (+ 0 0) into 0 7.790 * [backup-simplify]: Simplify (- 1) into -1 7.790 * [backup-simplify]: Simplify (+ 0 -1) into -1 7.792 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n))) 7.794 * [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))))) 7.797 * [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))))))) 7.800 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 7.802 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 7.803 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 7.806 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 7.807 * [backup-simplify]: Simplify (- 0) into 0 7.807 * [backup-simplify]: Simplify (+ 0 0) into 0 7.808 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0 7.810 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 7.811 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 7.814 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 7.814 * [taylor]: Taking taylor expansion of 0 in k 7.814 * [backup-simplify]: Simplify 0 into 0 7.814 * [backup-simplify]: Simplify 0 into 0 7.814 * [backup-simplify]: Simplify 0 into 0 7.816 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 7.817 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 7.820 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 7.821 * [backup-simplify]: Simplify (+ 0 0) into 0 7.821 * [backup-simplify]: Simplify (- 0) into 0 7.821 * [backup-simplify]: Simplify (+ 0 0) into 0 7.823 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 7.826 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 7.836 * [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))))) 7.841 * [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))))) 7.847 * [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))))) 7.847 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) 7.847 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0 7.847 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 7.847 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 7.847 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 7.847 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 7.847 * [taylor]: Taking taylor expansion of 1/2 in k 7.847 * [backup-simplify]: Simplify 1/2 into 1/2 7.847 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 7.847 * [taylor]: Taking taylor expansion of 1 in k 7.847 * [backup-simplify]: Simplify 1 into 1 7.847 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.847 * [taylor]: Taking taylor expansion of k in k 7.847 * [backup-simplify]: Simplify 0 into 0 7.847 * [backup-simplify]: Simplify 1 into 1 7.848 * [backup-simplify]: Simplify (/ 1 1) into 1 7.848 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 7.848 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 7.848 * [taylor]: Taking taylor expansion of 2 in k 7.848 * [backup-simplify]: Simplify 2 into 2 7.848 * [taylor]: Taking taylor expansion of (/ PI n) in k 7.848 * [taylor]: Taking taylor expansion of PI in k 7.848 * [backup-simplify]: Simplify PI into PI 7.848 * [taylor]: Taking taylor expansion of n in k 7.848 * [backup-simplify]: Simplify n into n 7.848 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 7.848 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 7.848 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 7.848 * [backup-simplify]: Simplify (- 1) into -1 7.848 * [backup-simplify]: Simplify (+ 0 -1) into -1 7.849 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2 7.849 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 7.849 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 7.849 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 7.849 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 7.849 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 7.849 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 7.849 * [taylor]: Taking taylor expansion of 1/2 in n 7.849 * [backup-simplify]: Simplify 1/2 into 1/2 7.849 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 7.849 * [taylor]: Taking taylor expansion of 1 in n 7.849 * [backup-simplify]: Simplify 1 into 1 7.849 * [taylor]: Taking taylor expansion of (/ 1 k) in n 7.849 * [taylor]: Taking taylor expansion of k in n 7.849 * [backup-simplify]: Simplify k into k 7.849 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 7.849 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 7.849 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 7.849 * [taylor]: Taking taylor expansion of 2 in n 7.849 * [backup-simplify]: Simplify 2 into 2 7.849 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.849 * [taylor]: Taking taylor expansion of PI in n 7.849 * [backup-simplify]: Simplify PI into PI 7.849 * [taylor]: Taking taylor expansion of n in n 7.849 * [backup-simplify]: Simplify 0 into 0 7.849 * [backup-simplify]: Simplify 1 into 1 7.849 * [backup-simplify]: Simplify (/ PI 1) into PI 7.850 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 7.850 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 7.850 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 7.850 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 7.851 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 7.851 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 7.852 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 7.853 * [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))))) 7.853 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 7.853 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 7.853 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 7.853 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 7.853 * [taylor]: Taking taylor expansion of 1/2 in n 7.853 * [backup-simplify]: Simplify 1/2 into 1/2 7.853 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 7.853 * [taylor]: Taking taylor expansion of 1 in n 7.853 * [backup-simplify]: Simplify 1 into 1 7.853 * [taylor]: Taking taylor expansion of (/ 1 k) in n 7.853 * [taylor]: Taking taylor expansion of k in n 7.853 * [backup-simplify]: Simplify k into k 7.853 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 7.853 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 7.853 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 7.853 * [taylor]: Taking taylor expansion of 2 in n 7.853 * [backup-simplify]: Simplify 2 into 2 7.853 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.853 * [taylor]: Taking taylor expansion of PI in n 7.853 * [backup-simplify]: Simplify PI into PI 7.853 * [taylor]: Taking taylor expansion of n in n 7.853 * [backup-simplify]: Simplify 0 into 0 7.853 * [backup-simplify]: Simplify 1 into 1 7.854 * [backup-simplify]: Simplify (/ PI 1) into PI 7.854 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 7.855 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 7.855 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 7.855 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 7.855 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 7.856 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 7.856 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 7.857 * [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))))) 7.857 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k 7.857 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k 7.857 * [taylor]: Taking taylor expansion of 1/2 in k 7.857 * [backup-simplify]: Simplify 1/2 into 1/2 7.857 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k 7.857 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 7.857 * [taylor]: Taking taylor expansion of 1 in k 7.857 * [backup-simplify]: Simplify 1 into 1 7.857 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.857 * [taylor]: Taking taylor expansion of k in k 7.857 * [backup-simplify]: Simplify 0 into 0 7.857 * [backup-simplify]: Simplify 1 into 1 7.858 * [backup-simplify]: Simplify (/ 1 1) into 1 7.858 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 7.858 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 7.858 * [taylor]: Taking taylor expansion of (* 2 PI) in k 7.858 * [taylor]: Taking taylor expansion of 2 in k 7.858 * [backup-simplify]: Simplify 2 into 2 7.858 * [taylor]: Taking taylor expansion of PI in k 7.858 * [backup-simplify]: Simplify PI into PI 7.858 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 7.859 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 7.859 * [taylor]: Taking taylor expansion of (log n) in k 7.859 * [taylor]: Taking taylor expansion of n in k 7.859 * [backup-simplify]: Simplify n into n 7.859 * [backup-simplify]: Simplify (log n) into (log n) 7.859 * [backup-simplify]: Simplify (- 1) into -1 7.859 * [backup-simplify]: Simplify (+ 0 -1) into -1 7.859 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 7.860 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 7.861 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) 7.861 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) 7.862 * [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))))) 7.863 * [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))))) 7.863 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 7.864 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 7.865 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 7.865 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 7.865 * [backup-simplify]: Simplify (- 0) into 0 7.865 * [backup-simplify]: Simplify (+ 0 0) into 0 7.866 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0 7.867 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 7.867 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 7.868 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 7.869 * [taylor]: Taking taylor expansion of 0 in k 7.869 * [backup-simplify]: Simplify 0 into 0 7.869 * [backup-simplify]: Simplify 0 into 0 7.869 * [backup-simplify]: Simplify 0 into 0 7.869 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.870 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 7.872 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 7.872 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 7.872 * [backup-simplify]: Simplify (- 0) into 0 7.872 * [backup-simplify]: Simplify (+ 0 0) into 0 7.873 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0 7.874 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 7.875 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 7.876 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 7.876 * [taylor]: Taking taylor expansion of 0 in k 7.876 * [backup-simplify]: Simplify 0 into 0 7.876 * [backup-simplify]: Simplify 0 into 0 7.876 * [backup-simplify]: Simplify 0 into 0 7.877 * [backup-simplify]: Simplify 0 into 0 7.877 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.878 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 7.881 * [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 7.881 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 7.882 * [backup-simplify]: Simplify (- 0) into 0 7.882 * [backup-simplify]: Simplify (+ 0 0) into 0 7.883 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0 7.884 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 7.885 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 7.886 * [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 7.886 * [taylor]: Taking taylor expansion of 0 in k 7.886 * [backup-simplify]: Simplify 0 into 0 7.886 * [backup-simplify]: Simplify 0 into 0 7.887 * [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)))))) 7.888 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) 7.888 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0 7.888 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 7.888 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 7.888 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 7.888 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 7.888 * [taylor]: Taking taylor expansion of 1/2 in k 7.888 * [backup-simplify]: Simplify 1/2 into 1/2 7.888 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 7.888 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.888 * [taylor]: Taking taylor expansion of k in k 7.888 * [backup-simplify]: Simplify 0 into 0 7.888 * [backup-simplify]: Simplify 1 into 1 7.888 * [backup-simplify]: Simplify (/ 1 1) into 1 7.888 * [taylor]: Taking taylor expansion of 1 in k 7.888 * [backup-simplify]: Simplify 1 into 1 7.888 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 7.888 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 7.888 * [taylor]: Taking taylor expansion of -2 in k 7.888 * [backup-simplify]: Simplify -2 into -2 7.888 * [taylor]: Taking taylor expansion of (/ PI n) in k 7.888 * [taylor]: Taking taylor expansion of PI in k 7.888 * [backup-simplify]: Simplify PI into PI 7.888 * [taylor]: Taking taylor expansion of n in k 7.888 * [backup-simplify]: Simplify n into n 7.888 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 7.888 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 7.888 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 7.889 * [backup-simplify]: Simplify (+ 1 0) into 1 7.889 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 7.889 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 7.889 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 7.889 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 7.889 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 7.889 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 7.889 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 7.889 * [taylor]: Taking taylor expansion of 1/2 in n 7.889 * [backup-simplify]: Simplify 1/2 into 1/2 7.889 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 7.889 * [taylor]: Taking taylor expansion of (/ 1 k) in n 7.889 * [taylor]: Taking taylor expansion of k in n 7.889 * [backup-simplify]: Simplify k into k 7.889 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 7.889 * [taylor]: Taking taylor expansion of 1 in n 7.889 * [backup-simplify]: Simplify 1 into 1 7.889 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 7.889 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 7.889 * [taylor]: Taking taylor expansion of -2 in n 7.889 * [backup-simplify]: Simplify -2 into -2 7.889 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.889 * [taylor]: Taking taylor expansion of PI in n 7.889 * [backup-simplify]: Simplify PI into PI 7.889 * [taylor]: Taking taylor expansion of n in n 7.889 * [backup-simplify]: Simplify 0 into 0 7.889 * [backup-simplify]: Simplify 1 into 1 7.890 * [backup-simplify]: Simplify (/ PI 1) into PI 7.890 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 7.891 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 7.891 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 7.891 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 7.892 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 7.893 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 7.893 * [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))))) 7.894 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 7.894 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 7.894 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 7.894 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 7.894 * [taylor]: Taking taylor expansion of 1/2 in n 7.894 * [backup-simplify]: Simplify 1/2 into 1/2 7.894 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 7.894 * [taylor]: Taking taylor expansion of (/ 1 k) in n 7.894 * [taylor]: Taking taylor expansion of k in n 7.894 * [backup-simplify]: Simplify k into k 7.894 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 7.894 * [taylor]: Taking taylor expansion of 1 in n 7.894 * [backup-simplify]: Simplify 1 into 1 7.894 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 7.894 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 7.894 * [taylor]: Taking taylor expansion of -2 in n 7.894 * [backup-simplify]: Simplify -2 into -2 7.894 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.894 * [taylor]: Taking taylor expansion of PI in n 7.894 * [backup-simplify]: Simplify PI into PI 7.894 * [taylor]: Taking taylor expansion of n in n 7.894 * [backup-simplify]: Simplify 0 into 0 7.894 * [backup-simplify]: Simplify 1 into 1 7.894 * [backup-simplify]: Simplify (/ PI 1) into PI 7.895 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 7.896 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 7.896 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 7.896 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 7.897 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 7.897 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 7.898 * [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))))) 7.898 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k 7.898 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k 7.898 * [taylor]: Taking taylor expansion of 1/2 in k 7.898 * [backup-simplify]: Simplify 1/2 into 1/2 7.898 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k 7.898 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 7.898 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.898 * [taylor]: Taking taylor expansion of k in k 7.898 * [backup-simplify]: Simplify 0 into 0 7.898 * [backup-simplify]: Simplify 1 into 1 7.899 * [backup-simplify]: Simplify (/ 1 1) into 1 7.899 * [taylor]: Taking taylor expansion of 1 in k 7.899 * [backup-simplify]: Simplify 1 into 1 7.899 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 7.899 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 7.899 * [taylor]: Taking taylor expansion of (* -2 PI) in k 7.899 * [taylor]: Taking taylor expansion of -2 in k 7.899 * [backup-simplify]: Simplify -2 into -2 7.899 * [taylor]: Taking taylor expansion of PI in k 7.899 * [backup-simplify]: Simplify PI into PI 7.899 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 7.900 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 7.900 * [taylor]: Taking taylor expansion of (log n) in k 7.900 * [taylor]: Taking taylor expansion of n in k 7.900 * [backup-simplify]: Simplify n into n 7.900 * [backup-simplify]: Simplify (log n) into (log n) 7.900 * [backup-simplify]: Simplify (+ 1 0) into 1 7.900 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 7.901 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 7.902 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) 7.902 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 7.903 * [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))))) 7.904 * [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))))) 7.904 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 7.905 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 7.906 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 7.906 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 7.906 * [backup-simplify]: Simplify (+ 0 0) into 0 7.906 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0 7.907 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 7.908 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 7.909 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 7.909 * [taylor]: Taking taylor expansion of 0 in k 7.909 * [backup-simplify]: Simplify 0 into 0 7.909 * [backup-simplify]: Simplify 0 into 0 7.909 * [backup-simplify]: Simplify 0 into 0 7.910 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.911 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 7.915 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 7.915 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 7.915 * [backup-simplify]: Simplify (+ 0 0) into 0 7.916 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0 7.918 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 7.919 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 7.922 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 7.922 * [taylor]: Taking taylor expansion of 0 in k 7.922 * [backup-simplify]: Simplify 0 into 0 7.922 * [backup-simplify]: Simplify 0 into 0 7.922 * [backup-simplify]: Simplify 0 into 0 7.922 * [backup-simplify]: Simplify 0 into 0 7.923 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.924 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 7.936 * [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 7.936 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 7.937 * [backup-simplify]: Simplify (+ 0 0) into 0 7.938 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0 7.939 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 7.941 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 7.945 * [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 7.945 * [taylor]: Taking taylor expansion of 0 in k 7.945 * [backup-simplify]: Simplify 0 into 0 7.945 * [backup-simplify]: Simplify 0 into 0 7.946 * [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)))))) 7.946 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 7.947 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 7.947 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 7.947 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 7.947 * [taylor]: Taking taylor expansion of 2 in n 7.947 * [backup-simplify]: Simplify 2 into 2 7.947 * [taylor]: Taking taylor expansion of (* n PI) in n 7.947 * [taylor]: Taking taylor expansion of n in n 7.947 * [backup-simplify]: Simplify 0 into 0 7.947 * [backup-simplify]: Simplify 1 into 1 7.947 * [taylor]: Taking taylor expansion of PI in n 7.947 * [backup-simplify]: Simplify PI into PI 7.947 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 7.947 * [taylor]: Taking taylor expansion of 2 in n 7.947 * [backup-simplify]: Simplify 2 into 2 7.947 * [taylor]: Taking taylor expansion of (* n PI) in n 7.947 * [taylor]: Taking taylor expansion of n in n 7.947 * [backup-simplify]: Simplify 0 into 0 7.947 * [backup-simplify]: Simplify 1 into 1 7.947 * [taylor]: Taking taylor expansion of PI in n 7.947 * [backup-simplify]: Simplify PI into PI 7.948 * [backup-simplify]: Simplify (* 0 PI) into 0 7.948 * [backup-simplify]: Simplify (* 2 0) into 0 7.948 * [backup-simplify]: Simplify 0 into 0 7.950 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 7.951 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 7.952 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 7.953 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 7.954 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 7.954 * [backup-simplify]: Simplify 0 into 0 7.955 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 7.956 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 7.956 * [backup-simplify]: Simplify 0 into 0 7.958 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 7.958 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 7.958 * [backup-simplify]: Simplify 0 into 0 7.959 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 7.960 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 7.960 * [backup-simplify]: Simplify 0 into 0 7.961 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 7.962 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 7.962 * [backup-simplify]: Simplify 0 into 0 7.963 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 7.964 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 7.964 * [backup-simplify]: Simplify 0 into 0 7.965 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 7.965 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n)) 7.965 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 7.965 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 7.965 * [taylor]: Taking taylor expansion of 2 in n 7.965 * [backup-simplify]: Simplify 2 into 2 7.965 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.965 * [taylor]: Taking taylor expansion of PI in n 7.965 * [backup-simplify]: Simplify PI into PI 7.965 * [taylor]: Taking taylor expansion of n in n 7.965 * [backup-simplify]: Simplify 0 into 0 7.965 * [backup-simplify]: Simplify 1 into 1 7.966 * [backup-simplify]: Simplify (/ PI 1) into PI 7.966 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 7.966 * [taylor]: Taking taylor expansion of 2 in n 7.966 * [backup-simplify]: Simplify 2 into 2 7.966 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.966 * [taylor]: Taking taylor expansion of PI in n 7.966 * [backup-simplify]: Simplify PI into PI 7.966 * [taylor]: Taking taylor expansion of n in n 7.966 * [backup-simplify]: Simplify 0 into 0 7.966 * [backup-simplify]: Simplify 1 into 1 7.966 * [backup-simplify]: Simplify (/ PI 1) into PI 7.966 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 7.967 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 7.967 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 7.968 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 7.968 * [backup-simplify]: Simplify 0 into 0 7.968 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.969 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 7.969 * [backup-simplify]: Simplify 0 into 0 7.970 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.970 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 7.970 * [backup-simplify]: Simplify 0 into 0 7.971 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.972 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 7.972 * [backup-simplify]: Simplify 0 into 0 7.972 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.973 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 7.973 * [backup-simplify]: Simplify 0 into 0 7.974 * [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 7.975 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 7.975 * [backup-simplify]: Simplify 0 into 0 7.975 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 7.976 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (- n))) into (* -2 (/ PI n)) 7.976 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 7.976 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 7.976 * [taylor]: Taking taylor expansion of -2 in n 7.976 * [backup-simplify]: Simplify -2 into -2 7.976 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.976 * [taylor]: Taking taylor expansion of PI in n 7.976 * [backup-simplify]: Simplify PI into PI 7.976 * [taylor]: Taking taylor expansion of n in n 7.976 * [backup-simplify]: Simplify 0 into 0 7.976 * [backup-simplify]: Simplify 1 into 1 7.976 * [backup-simplify]: Simplify (/ PI 1) into PI 7.976 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 7.976 * [taylor]: Taking taylor expansion of -2 in n 7.976 * [backup-simplify]: Simplify -2 into -2 7.976 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.976 * [taylor]: Taking taylor expansion of PI in n 7.976 * [backup-simplify]: Simplify PI into PI 7.976 * [taylor]: Taking taylor expansion of n in n 7.976 * [backup-simplify]: Simplify 0 into 0 7.976 * [backup-simplify]: Simplify 1 into 1 7.977 * [backup-simplify]: Simplify (/ PI 1) into PI 7.977 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 7.977 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 7.978 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 7.978 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 7.978 * [backup-simplify]: Simplify 0 into 0 7.979 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.979 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 7.979 * [backup-simplify]: Simplify 0 into 0 7.980 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.981 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 7.981 * [backup-simplify]: Simplify 0 into 0 7.981 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.982 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 7.982 * [backup-simplify]: Simplify 0 into 0 7.983 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.984 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 7.984 * [backup-simplify]: Simplify 0 into 0 7.984 * [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 7.985 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 7.985 * [backup-simplify]: Simplify 0 into 0 7.986 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 7.986 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 7.986 * [backup-simplify]: Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k)) 7.986 * [approximate]: Taking taylor expansion of (sqrt (/ 1 k)) in (k) around 0 7.986 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 7.986 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.986 * [taylor]: Taking taylor expansion of k in k 7.986 * [backup-simplify]: Simplify 0 into 0 7.986 * [backup-simplify]: Simplify 1 into 1 7.986 * [backup-simplify]: Simplify (/ 1 1) into 1 7.987 * [backup-simplify]: Simplify (sqrt 0) into 0 7.987 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 7.987 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 7.987 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.987 * [taylor]: Taking taylor expansion of k in k 7.987 * [backup-simplify]: Simplify 0 into 0 7.988 * [backup-simplify]: Simplify 1 into 1 7.988 * [backup-simplify]: Simplify (/ 1 1) into 1 7.988 * [backup-simplify]: Simplify (sqrt 0) into 0 7.989 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 7.989 * [backup-simplify]: Simplify 0 into 0 7.989 * [backup-simplify]: Simplify +nan.0 into +nan.0 7.989 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 7.992 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 7.992 * [backup-simplify]: Simplify +nan.0 into +nan.0 7.993 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.997 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 7.997 * [backup-simplify]: Simplify +nan.0 into +nan.0 7.997 * [backup-simplify]: Simplify (+ (* +nan.0 (pow k 2)) (+ (* +nan.0 k) +nan.0)) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 7.997 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k) 7.997 * [approximate]: Taking taylor expansion of (sqrt k) in (k) around 0 7.997 * [taylor]: Taking taylor expansion of (sqrt k) in k 7.997 * [taylor]: Taking taylor expansion of k in k 7.997 * [backup-simplify]: Simplify 0 into 0 7.997 * [backup-simplify]: Simplify 1 into 1 7.998 * [backup-simplify]: Simplify (sqrt 0) into 0 7.999 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 7.999 * [taylor]: Taking taylor expansion of (sqrt k) in k 7.999 * [taylor]: Taking taylor expansion of k in k 7.999 * [backup-simplify]: Simplify 0 into 0 7.999 * [backup-simplify]: Simplify 1 into 1 7.999 * [backup-simplify]: Simplify (sqrt 0) into 0 8.001 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.001 * [backup-simplify]: Simplify 0 into 0 8.001 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.004 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.004 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.008 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.008 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.008 * [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)))))))) 8.009 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 (- k)))) into (/ 1 (sqrt (/ -1 k))) 8.009 * [approximate]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in (k) around 0 8.009 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 8.009 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.009 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.009 * [taylor]: Taking taylor expansion of -1 in k 8.009 * [backup-simplify]: Simplify -1 into -1 8.009 * [taylor]: Taking taylor expansion of k in k 8.009 * [backup-simplify]: Simplify 0 into 0 8.009 * [backup-simplify]: Simplify 1 into 1 8.009 * [backup-simplify]: Simplify (/ -1 1) into -1 8.010 * [backup-simplify]: Simplify (sqrt 0) into 0 8.011 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.011 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 8.011 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 8.011 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.011 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.011 * [taylor]: Taking taylor expansion of -1 in k 8.011 * [backup-simplify]: Simplify -1 into -1 8.011 * [taylor]: Taking taylor expansion of k in k 8.012 * [backup-simplify]: Simplify 0 into 0 8.012 * [backup-simplify]: Simplify 1 into 1 8.012 * [backup-simplify]: Simplify (/ -1 1) into -1 8.012 * [backup-simplify]: Simplify (sqrt 0) into 0 8.014 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.014 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 8.014 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.015 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 8.018 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.020 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 8.020 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.022 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.025 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.029 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 8.029 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.030 * [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))))) 8.031 * * * * [progress]: [ 4 / 4 ] generating series at (2) 8.031 * [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))) 8.031 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k n) around 0 8.031 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n 8.031 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 8.031 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 8.031 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 8.031 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n 8.031 * [taylor]: Taking taylor expansion of 1/2 in n 8.031 * [backup-simplify]: Simplify 1/2 into 1/2 8.031 * [taylor]: Taking taylor expansion of (- 1 k) in n 8.032 * [taylor]: Taking taylor expansion of 1 in n 8.032 * [backup-simplify]: Simplify 1 into 1 8.032 * [taylor]: Taking taylor expansion of k in n 8.032 * [backup-simplify]: Simplify k into k 8.032 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 8.032 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 8.032 * [taylor]: Taking taylor expansion of 2 in n 8.032 * [backup-simplify]: Simplify 2 into 2 8.032 * [taylor]: Taking taylor expansion of (* n PI) in n 8.032 * [taylor]: Taking taylor expansion of n in n 8.032 * [backup-simplify]: Simplify 0 into 0 8.032 * [backup-simplify]: Simplify 1 into 1 8.032 * [taylor]: Taking taylor expansion of PI in n 8.032 * [backup-simplify]: Simplify PI into PI 8.032 * [backup-simplify]: Simplify (* 0 PI) into 0 8.033 * [backup-simplify]: Simplify (* 2 0) into 0 8.034 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.036 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 8.037 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.037 * [backup-simplify]: Simplify (- k) into (- k) 8.037 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k) 8.037 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 8.038 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 8.040 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 8.041 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 8.041 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 8.041 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.041 * [taylor]: Taking taylor expansion of k in n 8.041 * [backup-simplify]: Simplify k into k 8.041 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.041 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 8.041 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.041 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 8.041 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k 8.041 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 8.041 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 8.041 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 8.041 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k 8.041 * [taylor]: Taking taylor expansion of 1/2 in k 8.041 * [backup-simplify]: Simplify 1/2 into 1/2 8.041 * [taylor]: Taking taylor expansion of (- 1 k) in k 8.041 * [taylor]: Taking taylor expansion of 1 in k 8.042 * [backup-simplify]: Simplify 1 into 1 8.042 * [taylor]: Taking taylor expansion of k in k 8.042 * [backup-simplify]: Simplify 0 into 0 8.042 * [backup-simplify]: Simplify 1 into 1 8.042 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 8.042 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 8.042 * [taylor]: Taking taylor expansion of 2 in k 8.042 * [backup-simplify]: Simplify 2 into 2 8.042 * [taylor]: Taking taylor expansion of (* n PI) in k 8.042 * [taylor]: Taking taylor expansion of n in k 8.042 * [backup-simplify]: Simplify n into n 8.042 * [taylor]: Taking taylor expansion of PI in k 8.042 * [backup-simplify]: Simplify PI into PI 8.042 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.042 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 8.042 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 8.042 * [backup-simplify]: Simplify (- 0) into 0 8.043 * [backup-simplify]: Simplify (+ 1 0) into 1 8.043 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 8.043 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 8.043 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 8.044 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.044 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.044 * [taylor]: Taking taylor expansion of k in k 8.044 * [backup-simplify]: Simplify 0 into 0 8.044 * [backup-simplify]: Simplify 1 into 1 8.044 * [backup-simplify]: Simplify (/ 1 1) into 1 8.044 * [backup-simplify]: Simplify (sqrt 0) into 0 8.046 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.046 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k 8.046 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 8.046 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 8.046 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 8.046 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k 8.046 * [taylor]: Taking taylor expansion of 1/2 in k 8.046 * [backup-simplify]: Simplify 1/2 into 1/2 8.046 * [taylor]: Taking taylor expansion of (- 1 k) in k 8.046 * [taylor]: Taking taylor expansion of 1 in k 8.046 * [backup-simplify]: Simplify 1 into 1 8.046 * [taylor]: Taking taylor expansion of k in k 8.046 * [backup-simplify]: Simplify 0 into 0 8.046 * [backup-simplify]: Simplify 1 into 1 8.046 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 8.046 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 8.046 * [taylor]: Taking taylor expansion of 2 in k 8.046 * [backup-simplify]: Simplify 2 into 2 8.046 * [taylor]: Taking taylor expansion of (* n PI) in k 8.046 * [taylor]: Taking taylor expansion of n in k 8.046 * [backup-simplify]: Simplify n into n 8.046 * [taylor]: Taking taylor expansion of PI in k 8.046 * [backup-simplify]: Simplify PI into PI 8.046 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.046 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 8.046 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 8.047 * [backup-simplify]: Simplify (- 0) into 0 8.047 * [backup-simplify]: Simplify (+ 1 0) into 1 8.048 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 8.048 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 8.048 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 8.048 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.048 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.048 * [taylor]: Taking taylor expansion of k in k 8.048 * [backup-simplify]: Simplify 0 into 0 8.048 * [backup-simplify]: Simplify 1 into 1 8.048 * [backup-simplify]: Simplify (/ 1 1) into 1 8.049 * [backup-simplify]: Simplify (sqrt 0) into 0 8.050 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.050 * [backup-simplify]: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0 8.050 * [taylor]: Taking taylor expansion of 0 in n 8.050 * [backup-simplify]: Simplify 0 into 0 8.050 * [backup-simplify]: Simplify 0 into 0 8.051 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 8.052 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 8.052 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 8.053 * [backup-simplify]: Simplify (- 1) into -1 8.059 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.060 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2 8.060 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 8.061 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 8.061 * [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))))) 8.061 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 8.061 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 8.061 * [taylor]: Taking taylor expansion of +nan.0 in n 8.061 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.061 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 8.061 * [taylor]: Taking taylor expansion of (sqrt 2) in n 8.061 * [taylor]: Taking taylor expansion of 2 in n 8.061 * [backup-simplify]: Simplify 2 into 2 8.062 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 8.062 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 8.062 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 8.062 * [taylor]: Taking taylor expansion of (* n PI) in n 8.062 * [taylor]: Taking taylor expansion of n in n 8.063 * [backup-simplify]: Simplify 0 into 0 8.063 * [backup-simplify]: Simplify 1 into 1 8.063 * [taylor]: Taking taylor expansion of PI in n 8.063 * [backup-simplify]: Simplify PI into PI 8.063 * [backup-simplify]: Simplify (* 0 PI) into 0 8.065 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.065 * [backup-simplify]: Simplify (sqrt 0) into 0 8.067 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 8.067 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 8.067 * [backup-simplify]: Simplify (* +nan.0 0) into 0 8.068 * [backup-simplify]: Simplify (- 0) into 0 8.068 * [backup-simplify]: Simplify 0 into 0 8.068 * [backup-simplify]: Simplify 0 into 0 8.069 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 8.072 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.072 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 8.073 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 8.075 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0 8.075 * [backup-simplify]: Simplify (- 0) into 0 8.076 * [backup-simplify]: Simplify (+ 0 0) into 0 8.077 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0 8.077 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 8.078 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 8.079 * [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))))))) 8.079 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 8.079 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 8.079 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 8.079 * [taylor]: Taking taylor expansion of +nan.0 in n 8.079 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.079 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 8.079 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 8.079 * [taylor]: Taking taylor expansion of (sqrt 2) in n 8.079 * [taylor]: Taking taylor expansion of 2 in n 8.079 * [backup-simplify]: Simplify 2 into 2 8.080 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 8.080 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 8.080 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 8.080 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 8.080 * [taylor]: Taking taylor expansion of 2 in n 8.081 * [backup-simplify]: Simplify 2 into 2 8.081 * [taylor]: Taking taylor expansion of (* n PI) in n 8.081 * [taylor]: Taking taylor expansion of n in n 8.081 * [backup-simplify]: Simplify 0 into 0 8.081 * [backup-simplify]: Simplify 1 into 1 8.081 * [taylor]: Taking taylor expansion of PI in n 8.081 * [backup-simplify]: Simplify PI into PI 8.081 * [backup-simplify]: Simplify (* 0 PI) into 0 8.082 * [backup-simplify]: Simplify (* 2 0) into 0 8.083 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.085 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 8.086 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.086 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 8.086 * [taylor]: Taking taylor expansion of (* n PI) in n 8.086 * [taylor]: Taking taylor expansion of n in n 8.086 * [backup-simplify]: Simplify 0 into 0 8.086 * [backup-simplify]: Simplify 1 into 1 8.086 * [taylor]: Taking taylor expansion of PI in n 8.086 * [backup-simplify]: Simplify PI into PI 8.086 * [backup-simplify]: Simplify (* 0 PI) into 0 8.088 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.088 * [backup-simplify]: Simplify (sqrt 0) into 0 8.089 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 8.089 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 8.089 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 8.090 * [taylor]: Taking taylor expansion of +nan.0 in n 8.090 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.090 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 8.090 * [taylor]: Taking taylor expansion of (sqrt 2) in n 8.090 * [taylor]: Taking taylor expansion of 2 in n 8.090 * [backup-simplify]: Simplify 2 into 2 8.090 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 8.091 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 8.091 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 8.091 * [taylor]: Taking taylor expansion of (* n PI) in n 8.091 * [taylor]: Taking taylor expansion of n in n 8.091 * [backup-simplify]: Simplify 0 into 0 8.091 * [backup-simplify]: Simplify 1 into 1 8.091 * [taylor]: Taking taylor expansion of PI in n 8.091 * [backup-simplify]: Simplify PI into PI 8.091 * [backup-simplify]: Simplify (* 0 PI) into 0 8.093 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.093 * [backup-simplify]: Simplify (sqrt 0) into 0 8.095 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 8.096 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 8.098 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 8.099 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 8.100 * [backup-simplify]: Simplify (* +nan.0 0) into 0 8.100 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 8.101 * [backup-simplify]: Simplify (* +nan.0 0) into 0 8.101 * [backup-simplify]: Simplify (- 0) into 0 8.102 * [backup-simplify]: Simplify (+ 0 0) into 0 8.102 * [backup-simplify]: Simplify (- 0) into 0 8.102 * [backup-simplify]: Simplify 0 into 0 8.105 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 8.111 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 8.114 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 8.116 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 8.116 * [backup-simplify]: Simplify 0 into 0 8.116 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.119 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.119 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.120 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 8.122 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 (* n PI)) 1)))) 6) into 0 8.122 * [backup-simplify]: Simplify (- 0) into 0 8.122 * [backup-simplify]: Simplify (+ 0 0) into 0 8.123 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0 8.124 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 8.125 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 8.125 * [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))))))))) 8.126 * [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 8.126 * [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 8.126 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 8.126 * [taylor]: Taking taylor expansion of +nan.0 in n 8.126 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.126 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 8.126 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 8.126 * [taylor]: Taking taylor expansion of (sqrt 2) in n 8.126 * [taylor]: Taking taylor expansion of 2 in n 8.126 * [backup-simplify]: Simplify 2 into 2 8.126 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 8.126 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 8.126 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 8.126 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 8.126 * [taylor]: Taking taylor expansion of 2 in n 8.126 * [backup-simplify]: Simplify 2 into 2 8.126 * [taylor]: Taking taylor expansion of (* n PI) in n 8.126 * [taylor]: Taking taylor expansion of n in n 8.126 * [backup-simplify]: Simplify 0 into 0 8.126 * [backup-simplify]: Simplify 1 into 1 8.126 * [taylor]: Taking taylor expansion of PI in n 8.126 * [backup-simplify]: Simplify PI into PI 8.127 * [backup-simplify]: Simplify (* 0 PI) into 0 8.127 * [backup-simplify]: Simplify (* 2 0) into 0 8.128 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.129 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 8.130 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.130 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 8.130 * [taylor]: Taking taylor expansion of (* n PI) in n 8.130 * [taylor]: Taking taylor expansion of n in n 8.130 * [backup-simplify]: Simplify 0 into 0 8.130 * [backup-simplify]: Simplify 1 into 1 8.130 * [taylor]: Taking taylor expansion of PI in n 8.130 * [backup-simplify]: Simplify PI into PI 8.130 * [backup-simplify]: Simplify (* 0 PI) into 0 8.131 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.131 * [backup-simplify]: Simplify (sqrt 0) into 0 8.132 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 8.132 * [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 8.132 * [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 8.132 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 8.132 * [taylor]: Taking taylor expansion of +nan.0 in n 8.132 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.132 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 8.132 * [taylor]: Taking taylor expansion of (sqrt 2) in n 8.132 * [taylor]: Taking taylor expansion of 2 in n 8.132 * [backup-simplify]: Simplify 2 into 2 8.133 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 8.133 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 8.133 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 8.133 * [taylor]: Taking taylor expansion of (* n PI) in n 8.133 * [taylor]: Taking taylor expansion of n in n 8.133 * [backup-simplify]: Simplify 0 into 0 8.133 * [backup-simplify]: Simplify 1 into 1 8.133 * [taylor]: Taking taylor expansion of PI in n 8.133 * [backup-simplify]: Simplify PI into PI 8.133 * [backup-simplify]: Simplify (* 0 PI) into 0 8.134 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.135 * [backup-simplify]: Simplify (sqrt 0) into 0 8.135 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 8.136 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n 8.136 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 8.136 * [taylor]: Taking taylor expansion of +nan.0 in n 8.136 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.136 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 8.136 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 8.136 * [taylor]: Taking taylor expansion of (sqrt 2) in n 8.136 * [taylor]: Taking taylor expansion of 2 in n 8.136 * [backup-simplify]: Simplify 2 into 2 8.136 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 8.136 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 8.136 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 8.136 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 8.136 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 8.136 * [taylor]: Taking taylor expansion of 2 in n 8.136 * [backup-simplify]: Simplify 2 into 2 8.136 * [taylor]: Taking taylor expansion of (* n PI) in n 8.136 * [taylor]: Taking taylor expansion of n in n 8.136 * [backup-simplify]: Simplify 0 into 0 8.136 * [backup-simplify]: Simplify 1 into 1 8.136 * [taylor]: Taking taylor expansion of PI in n 8.136 * [backup-simplify]: Simplify PI into PI 8.137 * [backup-simplify]: Simplify (* 0 PI) into 0 8.137 * [backup-simplify]: Simplify (* 2 0) into 0 8.138 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.139 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 8.140 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.140 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 8.140 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 8.140 * [taylor]: Taking taylor expansion of (* n PI) in n 8.141 * [taylor]: Taking taylor expansion of n in n 8.141 * [backup-simplify]: Simplify 0 into 0 8.141 * [backup-simplify]: Simplify 1 into 1 8.141 * [taylor]: Taking taylor expansion of PI in n 8.141 * [backup-simplify]: Simplify PI into PI 8.141 * [backup-simplify]: Simplify (* 0 PI) into 0 8.142 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.142 * [backup-simplify]: Simplify (sqrt 0) into 0 8.143 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 8.144 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 8.145 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 8.146 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 8.146 * [backup-simplify]: Simplify (* +nan.0 0) into 0 8.147 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 8.147 * [backup-simplify]: Simplify (* +nan.0 0) into 0 8.149 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 8.150 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 8.152 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 8.154 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 8.155 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 8.156 * [backup-simplify]: Simplify (* +nan.0 0) into 0 8.156 * [backup-simplify]: Simplify (- 0) into 0 8.156 * [backup-simplify]: Simplify (+ 0 0) into 0 8.157 * [backup-simplify]: Simplify (- 0) into 0 8.157 * [backup-simplify]: Simplify (+ 0 0) into 0 8.157 * [backup-simplify]: Simplify (- 0) into 0 8.157 * [backup-simplify]: Simplify 0 into 0 8.159 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.160 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 8.161 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 8.163 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 8.164 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 8.167 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 8.172 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 8.178 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 8.181 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 8.183 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 8.189 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))))) 8.193 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 8.198 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 8.199 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.201 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 8.202 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 8.205 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 8.214 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 8.219 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 8.223 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 8.236 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) 8.237 * [backup-simplify]: Simplify (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) 8.237 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k n) around 0 8.237 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n 8.237 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 8.237 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 8.237 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 8.237 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 8.237 * [taylor]: Taking taylor expansion of 1/2 in n 8.237 * [backup-simplify]: Simplify 1/2 into 1/2 8.237 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 8.237 * [taylor]: Taking taylor expansion of 1 in n 8.237 * [backup-simplify]: Simplify 1 into 1 8.237 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.237 * [taylor]: Taking taylor expansion of k in n 8.237 * [backup-simplify]: Simplify k into k 8.237 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.237 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 8.237 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 8.237 * [taylor]: Taking taylor expansion of 2 in n 8.237 * [backup-simplify]: Simplify 2 into 2 8.237 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.237 * [taylor]: Taking taylor expansion of PI in n 8.237 * [backup-simplify]: Simplify PI into PI 8.237 * [taylor]: Taking taylor expansion of n in n 8.237 * [backup-simplify]: Simplify 0 into 0 8.237 * [backup-simplify]: Simplify 1 into 1 8.237 * [backup-simplify]: Simplify (/ PI 1) into PI 8.238 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.238 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.238 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.238 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 8.238 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 8.239 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.240 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 8.241 * [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))))) 8.241 * [taylor]: Taking taylor expansion of (sqrt k) in n 8.241 * [taylor]: Taking taylor expansion of k in n 8.241 * [backup-simplify]: Simplify k into k 8.241 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 8.241 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 8.241 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k 8.241 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 8.241 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 8.241 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 8.241 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 8.241 * [taylor]: Taking taylor expansion of 1/2 in k 8.241 * [backup-simplify]: Simplify 1/2 into 1/2 8.241 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 8.241 * [taylor]: Taking taylor expansion of 1 in k 8.241 * [backup-simplify]: Simplify 1 into 1 8.241 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.241 * [taylor]: Taking taylor expansion of k in k 8.241 * [backup-simplify]: Simplify 0 into 0 8.241 * [backup-simplify]: Simplify 1 into 1 8.241 * [backup-simplify]: Simplify (/ 1 1) into 1 8.241 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 8.241 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 8.241 * [taylor]: Taking taylor expansion of 2 in k 8.241 * [backup-simplify]: Simplify 2 into 2 8.242 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.242 * [taylor]: Taking taylor expansion of PI in k 8.242 * [backup-simplify]: Simplify PI into PI 8.242 * [taylor]: Taking taylor expansion of n in k 8.242 * [backup-simplify]: Simplify n into n 8.242 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.242 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 8.242 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 8.242 * [backup-simplify]: Simplify (- 1) into -1 8.242 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.242 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2 8.243 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 8.243 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 8.243 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.243 * [taylor]: Taking taylor expansion of k in k 8.243 * [backup-simplify]: Simplify 0 into 0 8.243 * [backup-simplify]: Simplify 1 into 1 8.243 * [backup-simplify]: Simplify (sqrt 0) into 0 8.244 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.244 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k 8.244 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 8.244 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 8.244 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 8.244 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 8.244 * [taylor]: Taking taylor expansion of 1/2 in k 8.244 * [backup-simplify]: Simplify 1/2 into 1/2 8.244 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 8.244 * [taylor]: Taking taylor expansion of 1 in k 8.244 * [backup-simplify]: Simplify 1 into 1 8.244 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.244 * [taylor]: Taking taylor expansion of k in k 8.244 * [backup-simplify]: Simplify 0 into 0 8.244 * [backup-simplify]: Simplify 1 into 1 8.244 * [backup-simplify]: Simplify (/ 1 1) into 1 8.244 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 8.244 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 8.244 * [taylor]: Taking taylor expansion of 2 in k 8.244 * [backup-simplify]: Simplify 2 into 2 8.244 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.244 * [taylor]: Taking taylor expansion of PI in k 8.244 * [backup-simplify]: Simplify PI into PI 8.245 * [taylor]: Taking taylor expansion of n in k 8.245 * [backup-simplify]: Simplify n into n 8.245 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.245 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 8.245 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 8.245 * [backup-simplify]: Simplify (- 1) into -1 8.245 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.245 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2 8.246 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 8.246 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 8.246 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.246 * [taylor]: Taking taylor expansion of k in k 8.246 * [backup-simplify]: Simplify 0 into 0 8.246 * [backup-simplify]: Simplify 1 into 1 8.246 * [backup-simplify]: Simplify (sqrt 0) into 0 8.247 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.247 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 0) into 0 8.247 * [taylor]: Taking taylor expansion of 0 in n 8.247 * [backup-simplify]: Simplify 0 into 0 8.247 * [backup-simplify]: Simplify 0 into 0 8.247 * [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)))))))) 8.247 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 8.247 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 8.247 * [taylor]: Taking taylor expansion of +nan.0 in n 8.247 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.247 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 8.248 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 8.248 * [taylor]: Taking taylor expansion of 1/2 in n 8.248 * [backup-simplify]: Simplify 1/2 into 1/2 8.248 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 8.248 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 8.248 * [taylor]: Taking taylor expansion of 1 in n 8.248 * [backup-simplify]: Simplify 1 into 1 8.248 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.248 * [taylor]: Taking taylor expansion of k in n 8.248 * [backup-simplify]: Simplify k into k 8.248 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.248 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 8.248 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 8.248 * [taylor]: Taking taylor expansion of 2 in n 8.248 * [backup-simplify]: Simplify 2 into 2 8.248 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.248 * [taylor]: Taking taylor expansion of PI in n 8.248 * [backup-simplify]: Simplify PI into PI 8.248 * [taylor]: Taking taylor expansion of n in n 8.248 * [backup-simplify]: Simplify 0 into 0 8.248 * [backup-simplify]: Simplify 1 into 1 8.248 * [backup-simplify]: Simplify (/ PI 1) into PI 8.248 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.249 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.249 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.249 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 8.250 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.251 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 8.252 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 8.252 * [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))))) 8.253 * [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)))))) 8.254 * [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))))))) 8.255 * [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))))))) 8.255 * [backup-simplify]: Simplify 0 into 0 8.256 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.257 * [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)))))))) 8.257 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 8.257 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 8.257 * [taylor]: Taking taylor expansion of +nan.0 in n 8.257 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.257 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 8.257 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 8.257 * [taylor]: Taking taylor expansion of 1/2 in n 8.257 * [backup-simplify]: Simplify 1/2 into 1/2 8.257 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 8.257 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 8.257 * [taylor]: Taking taylor expansion of 1 in n 8.257 * [backup-simplify]: Simplify 1 into 1 8.257 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.257 * [taylor]: Taking taylor expansion of k in n 8.257 * [backup-simplify]: Simplify k into k 8.257 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.257 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 8.257 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 8.257 * [taylor]: Taking taylor expansion of 2 in n 8.257 * [backup-simplify]: Simplify 2 into 2 8.257 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.257 * [taylor]: Taking taylor expansion of PI in n 8.257 * [backup-simplify]: Simplify PI into PI 8.257 * [taylor]: Taking taylor expansion of n in n 8.257 * [backup-simplify]: Simplify 0 into 0 8.257 * [backup-simplify]: Simplify 1 into 1 8.258 * [backup-simplify]: Simplify (/ PI 1) into PI 8.258 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.259 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.259 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.259 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 8.260 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.260 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 8.261 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 8.262 * [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))))) 8.263 * [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)))))) 8.264 * [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))))))) 8.264 * [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))))))) 8.265 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.266 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 8.267 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 8.268 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.268 * [backup-simplify]: Simplify (- 0) into 0 8.268 * [backup-simplify]: Simplify (+ 0 0) into 0 8.270 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.271 * [backup-simplify]: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 8.272 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0 8.274 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.280 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0 8.280 * [backup-simplify]: Simplify (- 0) into 0 8.280 * [backup-simplify]: Simplify 0 into 0 8.280 * [backup-simplify]: Simplify 0 into 0 8.283 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.283 * [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)))))))) 8.284 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 8.284 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 8.284 * [taylor]: Taking taylor expansion of +nan.0 in n 8.284 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.284 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 8.284 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 8.284 * [taylor]: Taking taylor expansion of 1/2 in n 8.284 * [backup-simplify]: Simplify 1/2 into 1/2 8.284 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 8.284 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 8.284 * [taylor]: Taking taylor expansion of 1 in n 8.284 * [backup-simplify]: Simplify 1 into 1 8.284 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.284 * [taylor]: Taking taylor expansion of k in n 8.284 * [backup-simplify]: Simplify k into k 8.284 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.284 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 8.284 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 8.284 * [taylor]: Taking taylor expansion of 2 in n 8.284 * [backup-simplify]: Simplify 2 into 2 8.284 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.284 * [taylor]: Taking taylor expansion of PI in n 8.284 * [backup-simplify]: Simplify PI into PI 8.284 * [taylor]: Taking taylor expansion of n in n 8.284 * [backup-simplify]: Simplify 0 into 0 8.284 * [backup-simplify]: Simplify 1 into 1 8.284 * [backup-simplify]: Simplify (/ PI 1) into PI 8.285 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 8.285 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 8.285 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.285 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 8.286 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 8.287 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 8.288 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 8.288 * [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))))) 8.289 * [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)))))) 8.290 * [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))))))) 8.291 * [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))))))) 8.294 * [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)))))))) 8.294 * [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))) 8.294 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (k n) around 0 8.294 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n 8.295 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 8.295 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 8.295 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 8.295 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 8.295 * [taylor]: Taking taylor expansion of 1/2 in n 8.295 * [backup-simplify]: Simplify 1/2 into 1/2 8.295 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 8.295 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.295 * [taylor]: Taking taylor expansion of k in n 8.295 * [backup-simplify]: Simplify k into k 8.295 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.295 * [taylor]: Taking taylor expansion of 1 in n 8.295 * [backup-simplify]: Simplify 1 into 1 8.295 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 8.295 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 8.295 * [taylor]: Taking taylor expansion of -2 in n 8.295 * [backup-simplify]: Simplify -2 into -2 8.295 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.295 * [taylor]: Taking taylor expansion of PI in n 8.295 * [backup-simplify]: Simplify PI into PI 8.295 * [taylor]: Taking taylor expansion of n in n 8.295 * [backup-simplify]: Simplify 0 into 0 8.295 * [backup-simplify]: Simplify 1 into 1 8.296 * [backup-simplify]: Simplify (/ PI 1) into PI 8.296 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 8.297 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 8.297 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 8.297 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 8.299 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.300 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 8.301 * [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))))) 8.301 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 8.301 * [taylor]: Taking taylor expansion of (/ -1 k) in n 8.301 * [taylor]: Taking taylor expansion of -1 in n 8.301 * [backup-simplify]: Simplify -1 into -1 8.301 * [taylor]: Taking taylor expansion of k in n 8.301 * [backup-simplify]: Simplify k into k 8.302 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 8.302 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 8.302 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 8.302 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 8.303 * [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))) 8.303 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k 8.303 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 8.303 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 8.303 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 8.303 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 8.303 * [taylor]: Taking taylor expansion of 1/2 in k 8.303 * [backup-simplify]: Simplify 1/2 into 1/2 8.303 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 8.303 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.303 * [taylor]: Taking taylor expansion of k in k 8.303 * [backup-simplify]: Simplify 0 into 0 8.303 * [backup-simplify]: Simplify 1 into 1 8.304 * [backup-simplify]: Simplify (/ 1 1) into 1 8.304 * [taylor]: Taking taylor expansion of 1 in k 8.304 * [backup-simplify]: Simplify 1 into 1 8.304 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 8.304 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 8.304 * [taylor]: Taking taylor expansion of -2 in k 8.304 * [backup-simplify]: Simplify -2 into -2 8.304 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.304 * [taylor]: Taking taylor expansion of PI in k 8.304 * [backup-simplify]: Simplify PI into PI 8.304 * [taylor]: Taking taylor expansion of n in k 8.304 * [backup-simplify]: Simplify n into n 8.304 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.304 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 8.304 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 8.305 * [backup-simplify]: Simplify (+ 1 0) into 1 8.305 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 8.305 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 8.305 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 8.306 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.306 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.306 * [taylor]: Taking taylor expansion of -1 in k 8.306 * [backup-simplify]: Simplify -1 into -1 8.306 * [taylor]: Taking taylor expansion of k in k 8.306 * [backup-simplify]: Simplify 0 into 0 8.306 * [backup-simplify]: Simplify 1 into 1 8.306 * [backup-simplify]: Simplify (/ -1 1) into -1 8.307 * [backup-simplify]: Simplify (sqrt 0) into 0 8.308 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.308 * [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))))) 8.308 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k 8.308 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 8.308 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 8.308 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 8.308 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 8.308 * [taylor]: Taking taylor expansion of 1/2 in k 8.308 * [backup-simplify]: Simplify 1/2 into 1/2 8.308 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 8.308 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.308 * [taylor]: Taking taylor expansion of k in k 8.308 * [backup-simplify]: Simplify 0 into 0 8.308 * [backup-simplify]: Simplify 1 into 1 8.309 * [backup-simplify]: Simplify (/ 1 1) into 1 8.309 * [taylor]: Taking taylor expansion of 1 in k 8.309 * [backup-simplify]: Simplify 1 into 1 8.309 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 8.309 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 8.309 * [taylor]: Taking taylor expansion of -2 in k 8.309 * [backup-simplify]: Simplify -2 into -2 8.309 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.309 * [taylor]: Taking taylor expansion of PI in k 8.309 * [backup-simplify]: Simplify PI into PI 8.309 * [taylor]: Taking taylor expansion of n in k 8.309 * [backup-simplify]: Simplify n into n 8.309 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.309 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 8.309 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 8.310 * [backup-simplify]: Simplify (+ 1 0) into 1 8.310 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 8.310 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 8.311 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 8.311 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.311 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.311 * [taylor]: Taking taylor expansion of -1 in k 8.311 * [backup-simplify]: Simplify -1 into -1 8.311 * [taylor]: Taking taylor expansion of k in k 8.311 * [backup-simplify]: Simplify 0 into 0 8.311 * [backup-simplify]: Simplify 1 into 1 8.311 * [backup-simplify]: Simplify (/ -1 1) into -1 8.312 * [backup-simplify]: Simplify (sqrt 0) into 0 8.313 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.313 * [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))))) 8.313 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 8.313 * [taylor]: Taking taylor expansion of +nan.0 in n 8.313 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.314 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 8.314 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 8.314 * [taylor]: Taking taylor expansion of 1/2 in n 8.314 * [backup-simplify]: Simplify 1/2 into 1/2 8.314 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 8.314 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 8.314 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 8.314 * [taylor]: Taking taylor expansion of -2 in n 8.314 * [backup-simplify]: Simplify -2 into -2 8.314 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.314 * [taylor]: Taking taylor expansion of PI in n 8.314 * [backup-simplify]: Simplify PI into PI 8.314 * [taylor]: Taking taylor expansion of n in n 8.314 * [backup-simplify]: Simplify 0 into 0 8.314 * [backup-simplify]: Simplify 1 into 1 8.315 * [backup-simplify]: Simplify (/ PI 1) into PI 8.315 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 8.316 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 8.316 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 8.316 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.316 * [taylor]: Taking taylor expansion of k in n 8.317 * [backup-simplify]: Simplify k into k 8.317 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.317 * [taylor]: Taking taylor expansion of 1 in n 8.317 * [backup-simplify]: Simplify 1 into 1 8.318 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.318 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 8.319 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 8.321 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 8.322 * [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))))) 8.323 * [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)))))) 8.324 * [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)))))) 8.325 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 8.328 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.329 * [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)))))) 8.329 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 8.329 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 8.329 * [taylor]: Taking taylor expansion of +nan.0 in n 8.329 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.329 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 8.329 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 8.329 * [taylor]: Taking taylor expansion of 1/2 in n 8.329 * [backup-simplify]: Simplify 1/2 into 1/2 8.329 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 8.330 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 8.330 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 8.330 * [taylor]: Taking taylor expansion of -2 in n 8.330 * [backup-simplify]: Simplify -2 into -2 8.330 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.330 * [taylor]: Taking taylor expansion of PI in n 8.330 * [backup-simplify]: Simplify PI into PI 8.330 * [taylor]: Taking taylor expansion of n in n 8.330 * [backup-simplify]: Simplify 0 into 0 8.330 * [backup-simplify]: Simplify 1 into 1 8.330 * [backup-simplify]: Simplify (/ PI 1) into PI 8.331 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 8.332 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 8.332 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 8.332 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.332 * [taylor]: Taking taylor expansion of k in n 8.332 * [backup-simplify]: Simplify k into k 8.332 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.332 * [taylor]: Taking taylor expansion of 1 in n 8.332 * [backup-simplify]: Simplify 1 into 1 8.333 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.334 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 8.335 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 8.336 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 8.337 * [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))))) 8.339 * [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)))))) 8.340 * [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))))))) 8.341 * [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))))))) 8.343 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.343 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.343 * [backup-simplify]: Simplify (+ 0 0) into 0 8.344 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.345 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 8.347 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 8.348 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0 8.350 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0 8.352 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.354 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0 8.354 * [backup-simplify]: Simplify 0 into 0 8.354 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.357 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.358 * [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)))))) 8.358 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 8.358 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 8.358 * [taylor]: Taking taylor expansion of +nan.0 in n 8.358 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.358 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 8.358 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 8.358 * [taylor]: Taking taylor expansion of 1/2 in n 8.358 * [backup-simplify]: Simplify 1/2 into 1/2 8.358 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 8.358 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 8.358 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 8.358 * [taylor]: Taking taylor expansion of -2 in n 8.358 * [backup-simplify]: Simplify -2 into -2 8.358 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.358 * [taylor]: Taking taylor expansion of PI in n 8.358 * [backup-simplify]: Simplify PI into PI 8.358 * [taylor]: Taking taylor expansion of n in n 8.358 * [backup-simplify]: Simplify 0 into 0 8.358 * [backup-simplify]: Simplify 1 into 1 8.358 * [backup-simplify]: Simplify (/ PI 1) into PI 8.359 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 8.359 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 8.359 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 8.359 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.359 * [taylor]: Taking taylor expansion of k in n 8.359 * [backup-simplify]: Simplify k into k 8.360 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.360 * [taylor]: Taking taylor expansion of 1 in n 8.360 * [backup-simplify]: Simplify 1 into 1 8.360 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 8.360 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 8.361 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 8.362 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 8.363 * [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))))) 8.363 * [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)))))) 8.364 * [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))))))) 8.365 * [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))))))) 8.367 * [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)))))))))))) 8.368 * * * [progress]: simplifying candidates 8.368 * * * * [progress]: [ 1 / 196 ] simplifiying candidate # 8.368 * * * * [progress]: [ 2 / 196 ] simplifiying candidate # 8.368 * * * * [progress]: [ 3 / 196 ] simplifiying candidate # 8.368 * * * * [progress]: [ 4 / 196 ] simplifiying candidate # 8.368 * * * * [progress]: [ 5 / 196 ] simplifiying candidate # 8.368 * * * * [progress]: [ 6 / 196 ] simplifiying candidate # 8.368 * * * * [progress]: [ 7 / 196 ] simplifiying candidate # 8.368 * * * * [progress]: [ 8 / 196 ] simplifiying candidate # 8.368 * * * * [progress]: [ 9 / 196 ] simplifiying candidate # 8.368 * * * * [progress]: [ 10 / 196 ] simplifiying candidate # 8.368 * * * * [progress]: [ 11 / 196 ] simplifiying candidate # 8.368 * * * * [progress]: [ 12 / 196 ] simplifiying candidate # 8.368 * * * * [progress]: [ 13 / 196 ] simplifiying candidate # 8.368 * * * * [progress]: [ 14 / 196 ] simplifiying candidate # 8.368 * * * * [progress]: [ 15 / 196 ] simplifiying candidate # 8.368 * * * * [progress]: [ 16 / 196 ] simplifiying candidate # 8.368 * * * * [progress]: [ 17 / 196 ] simplifiying candidate # 8.368 * * * * [progress]: [ 18 / 196 ] simplifiying candidate # 8.368 * * * * [progress]: [ 19 / 196 ] simplifiying candidate # 8.368 * * * * [progress]: [ 20 / 196 ] simplifiying candidate # 8.368 * * * * [progress]: [ 21 / 196 ] simplifiying candidate # 8.368 * * * * [progress]: [ 22 / 196 ] simplifiying candidate # 8.369 * * * * [progress]: [ 23 / 196 ] simplifiying candidate # 8.369 * * * * [progress]: [ 24 / 196 ] simplifiying candidate # 8.369 * * * * [progress]: [ 25 / 196 ] simplifiying candidate # 8.369 * * * * [progress]: [ 26 / 196 ] simplifiying candidate # 8.369 * * * * [progress]: [ 27 / 196 ] simplifiying candidate # 8.369 * * * * [progress]: [ 28 / 196 ] simplifiying candidate # 8.369 * * * * [progress]: [ 29 / 196 ] simplifiying candidate # 8.369 * * * * [progress]: [ 30 / 196 ] simplifiying candidate # 8.369 * * * * [progress]: [ 31 / 196 ] simplifiying candidate # 8.369 * * * * [progress]: [ 32 / 196 ] simplifiying candidate # 8.369 * * * * [progress]: [ 33 / 196 ] simplifiying candidate # 8.369 * * * * [progress]: [ 34 / 196 ] simplifiying candidate # 8.369 * * * * [progress]: [ 35 / 196 ] simplifiying candidate # 8.369 * * * * [progress]: [ 36 / 196 ] simplifiying candidate # 8.369 * * * * [progress]: [ 37 / 196 ] simplifiying candidate # 8.369 * * * * [progress]: [ 38 / 196 ] simplifiying candidate # 8.369 * * * * [progress]: [ 39 / 196 ] simplifiying candidate # 8.369 * * * * [progress]: [ 40 / 196 ] simplifiying candidate # 8.369 * * * * [progress]: [ 41 / 196 ] simplifiying candidate # 8.369 * * * * [progress]: [ 42 / 196 ] simplifiying candidate #real (real->posit16 (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))> 8.369 * * * * [progress]: [ 43 / 196 ] simplifiying candidate # 8.369 * * * * [progress]: [ 44 / 196 ] simplifiying candidate # 8.369 * * * * [progress]: [ 45 / 196 ] simplifiying candidate # 8.369 * * * * [progress]: [ 46 / 196 ] simplifiying candidate # 8.369 * * * * [progress]: [ 47 / 196 ] simplifiying candidate # 8.370 * * * * [progress]: [ 48 / 196 ] simplifiying candidate # 8.370 * * * * [progress]: [ 49 / 196 ] simplifiying candidate # 8.370 * * * * [progress]: [ 50 / 196 ] simplifiying candidate # 8.370 * * * * [progress]: [ 51 / 196 ] simplifiying candidate # 8.370 * * * * [progress]: [ 52 / 196 ] simplifiying candidate # 8.370 * * * * [progress]: [ 53 / 196 ] simplifiying candidate # 8.370 * * * * [progress]: [ 54 / 196 ] simplifiying candidate # 8.370 * * * * [progress]: [ 55 / 196 ] simplifiying candidate # 8.370 * * * * [progress]: [ 56 / 196 ] simplifiying candidate # 8.370 * * * * [progress]: [ 57 / 196 ] simplifiying candidate # 8.370 * * * * [progress]: [ 58 / 196 ] simplifiying candidate # 8.370 * * * * [progress]: [ 59 / 196 ] simplifiying candidate # 8.370 * * * * [progress]: [ 60 / 196 ] simplifiying candidate # 8.370 * * * * [progress]: [ 61 / 196 ] simplifiying candidate # 8.370 * * * * [progress]: [ 62 / 196 ] simplifiying candidate #real (real->posit16 (* (* 2 PI) n))) (/ (- 1 k) 2))))> 8.370 * * * * [progress]: [ 63 / 196 ] simplifiying candidate # 8.370 * * * * [progress]: [ 64 / 196 ] simplifiying 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111 / 196 ] simplifiying candidate #real (real->posit16 (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> 8.372 * * * * [progress]: [ 112 / 196 ] simplifiying candidate # 8.372 * * * * [progress]: [ 113 / 196 ] simplifiying candidate # 8.372 * * * * [progress]: [ 114 / 196 ] simplifiying candidate # 8.372 * * * * [progress]: [ 115 / 196 ] simplifiying candidate # 8.372 * * * * [progress]: [ 116 / 196 ] simplifiying candidate # 8.372 * * * * [progress]: [ 117 / 196 ] simplifiying candidate # 8.372 * * * * [progress]: [ 118 / 196 ] simplifiying candidate # 8.372 * * * * [progress]: [ 119 / 196 ] simplifiying candidate # 8.372 * * * * [progress]: [ 120 / 196 ] simplifiying candidate # 8.372 * * * * [progress]: [ 121 / 196 ] simplifiying candidate # 8.372 * * * * [progress]: [ 122 / 196 ] simplifiying candidate # 8.372 * * * * [progress]: [ 123 / 196 ] simplifiying candidate # 8.372 * * * * [progress]: [ 124 / 196 ] simplifiying candidate # 8.372 * * * * [progress]: [ 125 / 196 ] 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candidate # 8.375 * * * * [progress]: [ 186 / 196 ] simplifiying candidate # 8.375 * * * * [progress]: [ 187 / 196 ] simplifiying candidate # 8.375 * * * * [progress]: [ 188 / 196 ] simplifiying candidate # 8.375 * * * * [progress]: [ 189 / 196 ] simplifiying candidate # 8.375 * * * * [progress]: [ 190 / 196 ] simplifiying candidate # 8.375 * * * * [progress]: [ 191 / 196 ] simplifiying candidate # 8.375 * * * * [progress]: [ 192 / 196 ] simplifiying candidate # 8.375 * * * * [progress]: [ 193 / 196 ] simplifiying candidate # 8.375 * * * * [progress]: [ 194 / 196 ] simplifiying candidate # 8.375 * * * * [progress]: [ 195 / 196 ] simplifiying candidate # 8.375 * * * * [progress]: [ 196 / 196 ] simplifiying candidate # 8.377 * [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) 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(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)))))))))))) 8.380 * * [simplify]: iteration 0: 353 enodes 8.525 * * [simplify]: iteration 1: 952 enodes 8.796 * * [simplify]: iteration 2: 2004 enodes 9.273 * * [simplify]: iteration complete: 2004 enodes 9.274 * * [simplify]: Extracting #0: cost 104 inf + 0 9.275 * * [simplify]: Extracting #1: cost 328 inf + 3 9.278 * * [simplify]: Extracting #2: cost 659 inf + 2719 9.290 * * [simplify]: Extracting #3: cost 597 inf + 35761 9.306 * * [simplify]: Extracting #4: cost 372 inf + 122281 9.339 * * [simplify]: Extracting #5: cost 114 inf + 227963 9.390 * * [simplify]: Extracting #6: cost 45 inf + 261486 9.445 * * [simplify]: Extracting #7: cost 27 inf + 266399 9.501 * * [simplify]: Extracting #8: cost 6 inf + 276969 9.561 * * [simplify]: Extracting #9: cost 0 inf + 281237 9.627 * [simplify]: Simplified to: (expm1 (pow (* (* PI 2) n) (/ (- 1 k) 2))) (log1p (pow (* (* PI 2) n) (/ (- 1 k) 2))) (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (/ (- 1 k) 2) (/ (- 1 k) 2) (/ (- 1 k) 2) (sqrt (* (* PI 2) n)) (pow (* (* PI 2) n) (/ k 2)) (pow (* (* PI 2) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (pow (* (* PI 2) n) (sqrt (/ (- 1 k) 2))) (pow (* (* PI 2) n) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2)))) (pow (* (* PI 2) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (pow (* (* PI 2) n) (* (cbrt (- 1 k)) (cbrt (- 1 k)))) (pow (* (* PI 2) n) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2))) (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) (sqrt 2))) (pow (* (* PI 2) n) (sqrt (- 1 k))) (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* PI 2) n) (/ 1 (sqrt 2))) (* (* PI 2) n) (pow (* (* PI 2) n) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (cbrt 2))) (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) (sqrt 2))) (pow (* (* PI 2) n) (+ (sqrt k) 1)) (pow (* (* PI 2) n) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (cbrt 2))) (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) (sqrt 2))) (pow (* (* PI 2) n) (+ (sqrt k) 1)) (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* PI 2) n) (/ 1 (sqrt 2))) (* (* PI 2) n) (* (* PI 2) n) (pow (* (* PI 2) n) (- 1 k)) (pow (* PI 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)) (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (exp (pow (* (* PI 2) n) (/ (- 1 k) 2))) (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (* (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (pow (* (* PI 2) n) (/ (- 1 k) 2))) (pow (* (* PI 2) n) (/ (- 1 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(expm1 (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (log1p (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (fma (/ (- 1 k) 2) (log (* (* PI 2) n)) (- (log (sqrt k)))) (fma (/ (- 1 k) 2) (log (* (* PI 2) n)) (- (log (sqrt k)))) (fma (/ (- 1 k) 2) (log (* (* PI 2) n)) (- (log (sqrt k)))) (fma (/ (- 1 k) 2) (log (* (* PI 2) n)) (- (log (sqrt k)))) (fma (/ (- 1 k) 2) (log (* (* PI 2) n)) (- (log (sqrt k)))) (fma (/ (- 1 k) 2) (log (* (* PI 2) n)) (- (log (sqrt k)))) (fma (/ (- 1 k) 2) (log (* (* PI 2) n)) (- (log (sqrt k)))) (fma (/ (- 1 k) 2) (log (* (* PI 2) n)) (- (log (sqrt k)))) (fma (/ (- 1 k) 2) (log (* (* PI 2) n)) (- (log (sqrt k)))) (fma (/ (- 1 k) 2) (log (* (* PI 2) n)) (- (log (sqrt k)))) (fma (/ (- 1 k) 2) (log (* (* PI 2) n)) (- (log (sqrt k)))) (fma (/ (- 1 k) 2) (log (* (* PI 2) n)) (- (log (sqrt k)))) (fma (/ (- 1 k) 2) (log (* (* PI 2) n)) (- (log (sqrt k)))) (fma (/ (- 1 k) 2) (log (* (* PI 2) n)) (- (log (sqrt k)))) (fma (/ (- 1 k) 2) (log (* (* PI 2) n)) (- (log (sqrt k)))) (fma (/ (- 1 k) 2) (log (* (* PI 2) n)) (- (log (sqrt k)))) (fma (/ (- 1 k) 2) (log (* (* PI 2) n)) (- (log (sqrt k)))) (fma (/ (- 1 k) 2) (log (* (* PI 2) n)) (- (log (sqrt k)))) (fma (/ (- 1 k) 2) (log (* (* PI 2) n)) (- (log (sqrt k)))) (fma (/ (- 1 k) 2) (log (* (* PI 2) n)) (- (log (sqrt k)))) (fma (/ (- 1 k) 2) (log (* (* PI 2) n)) (- (log (sqrt k)))) (exp (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (/ (* (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (pow (* (* PI 2) n) (/ (- 1 k) 2))) (pow (* (* PI 2) n) (/ (- 1 k) 2))) (* k (sqrt k))) (* (* (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (pow (* (* PI 2) n) (/ (- 1 k) 2))) (pow (* (* PI 2) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (/ (/ 1 (sqrt k)) (sqrt k)))) (* (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (* (* (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (* (* PI 2) n)) (* (pow (* (* PI 2) n) (/ k 2)) (sqrt k)) (* (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k)))) (* (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k)))) (* (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (/ 1 (sqrt k)))) (* (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (/ 1 (sqrt k)))) (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (/ (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (sqrt k)) (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k)) (/ 1 (sqrt k)) (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt k)) (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (cbrt (/ 1 (sqrt k)))) (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (cbrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (cbrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (cbrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (cbrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (cbrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (cbrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) (/ (sqrt (* (* PI 2) n)) (sqrt k)) (pow (* (* PI 2) n) (/ (- 1 k) 2)) (real->posit16 (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (fma 1/4 (* (* (log (* PI 2)) (exp (* 1/2 (log (* (* PI 2) n))))) (* (* k k) (log n))) (- (fma (* 1/8 (exp (* 1/2 (log (* (* PI 2) n))))) (* (* (* k k) (log n)) (log n)) (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 (* k (+ (* (exp (* 1/2 (log (* (* PI 2) n)))) (log n)) (* (log (* PI 2)) (exp (* 1/2 (log (* (* PI 2) n)))))))))) (exp (* 1/2 (* (log (* (* PI 2) n)) (- 1 k)))) (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n))))) (* (* PI 2) n) (* (* PI 2) n) (* (* PI 2) 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)) (+ (* (* +nan.0 (sqrt 2)) (- (* (* n PI) k))) (+ (- (* (* +nan.0 (sqrt 2)) (* n PI)) (* +nan.0 (* (* (* (* n PI) k) (sqrt 2)) (log (* PI 2))))) (* (* +nan.0 (sqrt 2)) (- (* (* n PI) (* (log n) k)) (* (* n PI) (* n PI)))))) (- (- (/ (* +nan.0 (exp (* 1/2 (* (log (* (* PI 2) n)) (- 1 k))))) k) (- (* +nan.0 (/ (exp (* 1/2 (* (log (* (* PI 2) n)) (- 1 k)))) (* k k))) (* (/ +nan.0 k) (/ (exp (* 1/2 (* (log (* (* PI 2) n)) (- 1 k)))) (* k k)))))) (- (- (* (/ (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n))))) k) +nan.0) (- (* +nan.0 (/ (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n))))) (* k k))) (* +nan.0 (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n))))))))) 9.641 * * * [progress]: adding candidates to table 10.456 * * [progress]: iteration 3 / 4 10.456 * * * [progress]: picking best candidate 10.498 * * * * [pick]: Picked # 10.498 * * * [progress]: localizing error 10.552 * * * [progress]: generating rewritten candidates 10.552 * * * * [progress]: [ 1 / 3 ] rewriting at (2 2) 10.569 * * * * [progress]: [ 2 / 3 ] rewriting at (2 2 1) 10.583 * * * * [progress]: [ 3 / 3 ] rewriting at (2) 10.630 * * * [progress]: generating series expansions 10.630 * * * * [progress]: [ 1 / 3 ] generating series at (2 2) 10.632 * [backup-simplify]: Simplify (pow (* (* 2 PI) n) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) 10.632 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0 10.632 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 10.632 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 10.632 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 10.632 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k 10.632 * [taylor]: Taking taylor expansion of 1/2 in k 10.632 * [backup-simplify]: Simplify 1/2 into 1/2 10.632 * [taylor]: Taking taylor expansion of (- 1 k) in k 10.632 * [taylor]: Taking taylor expansion of 1 in k 10.632 * [backup-simplify]: Simplify 1 into 1 10.632 * [taylor]: Taking taylor expansion of k in k 10.632 * [backup-simplify]: Simplify 0 into 0 10.632 * [backup-simplify]: Simplify 1 into 1 10.632 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 10.632 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 10.632 * [taylor]: Taking taylor expansion of 2 in k 10.632 * [backup-simplify]: Simplify 2 into 2 10.632 * [taylor]: Taking taylor expansion of (* n PI) in k 10.632 * [taylor]: Taking taylor expansion of n in k 10.632 * [backup-simplify]: Simplify n into n 10.632 * [taylor]: Taking taylor expansion of PI in k 10.632 * [backup-simplify]: Simplify PI into PI 10.632 * [backup-simplify]: Simplify (* n PI) into (* n PI) 10.632 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 10.632 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 10.633 * [backup-simplify]: Simplify (- 0) into 0 10.633 * [backup-simplify]: Simplify (+ 1 0) into 1 10.634 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 10.634 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 10.634 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 10.634 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 10.634 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 10.634 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 10.634 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n 10.634 * [taylor]: Taking taylor expansion of 1/2 in n 10.634 * [backup-simplify]: Simplify 1/2 into 1/2 10.634 * [taylor]: Taking taylor expansion of (- 1 k) in n 10.634 * [taylor]: Taking taylor expansion of 1 in n 10.634 * [backup-simplify]: Simplify 1 into 1 10.634 * [taylor]: Taking taylor expansion of k in n 10.634 * [backup-simplify]: Simplify k into k 10.634 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 10.634 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 10.634 * [taylor]: Taking taylor expansion of 2 in n 10.634 * [backup-simplify]: Simplify 2 into 2 10.635 * [taylor]: Taking taylor expansion of (* n PI) in n 10.635 * [taylor]: Taking taylor expansion of n in n 10.635 * [backup-simplify]: Simplify 0 into 0 10.635 * [backup-simplify]: Simplify 1 into 1 10.635 * [taylor]: Taking taylor expansion of PI in n 10.635 * [backup-simplify]: Simplify PI into PI 10.635 * [backup-simplify]: Simplify (* 0 PI) into 0 10.636 * [backup-simplify]: Simplify (* 2 0) into 0 10.637 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.639 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 10.640 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 10.640 * [backup-simplify]: Simplify (- k) into (- k) 10.641 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k) 10.641 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 10.642 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 10.643 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 10.644 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 10.645 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 10.645 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 10.645 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 10.645 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n 10.645 * [taylor]: Taking taylor expansion of 1/2 in n 10.645 * [backup-simplify]: Simplify 1/2 into 1/2 10.645 * [taylor]: Taking taylor expansion of (- 1 k) in n 10.645 * [taylor]: Taking taylor expansion of 1 in n 10.645 * [backup-simplify]: Simplify 1 into 1 10.645 * [taylor]: Taking taylor expansion of k in n 10.645 * [backup-simplify]: Simplify k into k 10.645 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 10.645 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 10.645 * [taylor]: Taking taylor expansion of 2 in n 10.645 * [backup-simplify]: Simplify 2 into 2 10.645 * [taylor]: Taking taylor expansion of (* n PI) in n 10.645 * [taylor]: Taking taylor expansion of n in n 10.645 * [backup-simplify]: Simplify 0 into 0 10.645 * [backup-simplify]: Simplify 1 into 1 10.645 * [taylor]: Taking taylor expansion of PI in n 10.645 * [backup-simplify]: Simplify PI into PI 10.646 * [backup-simplify]: Simplify (* 0 PI) into 0 10.646 * [backup-simplify]: Simplify (* 2 0) into 0 10.648 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.649 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 10.650 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 10.650 * [backup-simplify]: Simplify (- k) into (- k) 10.650 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k) 10.650 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 10.651 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 10.652 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 10.653 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 10.653 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k 10.653 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k 10.653 * [taylor]: Taking taylor expansion of 1/2 in k 10.653 * [backup-simplify]: Simplify 1/2 into 1/2 10.653 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k 10.653 * [taylor]: Taking taylor expansion of (- 1 k) in k 10.653 * [taylor]: Taking taylor expansion of 1 in k 10.653 * [backup-simplify]: Simplify 1 into 1 10.653 * [taylor]: Taking taylor expansion of k in k 10.653 * [backup-simplify]: Simplify 0 into 0 10.653 * [backup-simplify]: Simplify 1 into 1 10.653 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 10.653 * [taylor]: Taking taylor expansion of (log n) in k 10.653 * [taylor]: Taking taylor expansion of n in k 10.653 * [backup-simplify]: Simplify n into n 10.653 * [backup-simplify]: Simplify (log n) into (log n) 10.653 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 10.653 * [taylor]: Taking taylor expansion of (* 2 PI) in k 10.653 * [taylor]: Taking taylor expansion of 2 in k 10.653 * [backup-simplify]: Simplify 2 into 2 10.653 * [taylor]: Taking taylor expansion of PI in k 10.653 * [backup-simplify]: Simplify PI into PI 10.654 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 10.654 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 10.654 * [backup-simplify]: Simplify (- 0) into 0 10.655 * [backup-simplify]: Simplify (+ 1 0) into 1 10.655 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 10.656 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI))) 10.657 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 10.658 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 10.658 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 10.659 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 10.660 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 10.661 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 10.662 * [backup-simplify]: Simplify (- 0) into 0 10.662 * [backup-simplify]: Simplify (+ 0 0) into 0 10.662 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0 10.663 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 10.664 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 10.665 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0 10.665 * [taylor]: Taking taylor expansion of 0 in k 10.665 * [backup-simplify]: Simplify 0 into 0 10.665 * [backup-simplify]: Simplify 0 into 0 10.666 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 10.666 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 10.667 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 10.667 * [backup-simplify]: Simplify (+ 0 0) into 0 10.668 * [backup-simplify]: Simplify (- 1) into -1 10.668 * [backup-simplify]: Simplify (+ 0 -1) into -1 10.669 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n))) 10.670 * [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))))) 10.672 * [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))))))) 10.674 * [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))))))) 10.675 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 10.676 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 10.677 * [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 10.678 * [backup-simplify]: Simplify (- 0) into 0 10.678 * [backup-simplify]: Simplify (+ 0 0) into 0 10.678 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0 10.679 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 10.681 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 10.682 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 10.682 * [taylor]: Taking taylor expansion of 0 in k 10.682 * [backup-simplify]: Simplify 0 into 0 10.682 * [backup-simplify]: Simplify 0 into 0 10.682 * [backup-simplify]: Simplify 0 into 0 10.683 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 10.684 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 10.686 * [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 10.686 * [backup-simplify]: Simplify (+ 0 0) into 0 10.686 * [backup-simplify]: Simplify (- 0) into 0 10.686 * [backup-simplify]: Simplify (+ 0 0) into 0 10.687 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 10.689 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 10.691 * [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))))) 10.694 * [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))))) 10.701 * [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))))) 10.701 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) 10.701 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0 10.701 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 10.701 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 10.701 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 10.701 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 10.701 * [taylor]: Taking taylor expansion of 1/2 in k 10.701 * [backup-simplify]: Simplify 1/2 into 1/2 10.701 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 10.701 * [taylor]: Taking taylor expansion of 1 in k 10.701 * [backup-simplify]: Simplify 1 into 1 10.701 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.701 * [taylor]: Taking taylor expansion of k in k 10.701 * [backup-simplify]: Simplify 0 into 0 10.701 * [backup-simplify]: Simplify 1 into 1 10.702 * [backup-simplify]: Simplify (/ 1 1) into 1 10.702 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 10.702 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 10.702 * [taylor]: Taking taylor expansion of 2 in k 10.702 * [backup-simplify]: Simplify 2 into 2 10.702 * [taylor]: Taking taylor expansion of (/ PI n) in k 10.702 * [taylor]: Taking taylor expansion of PI in k 10.702 * [backup-simplify]: Simplify PI into PI 10.702 * [taylor]: Taking taylor expansion of n in k 10.702 * [backup-simplify]: Simplify n into n 10.702 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 10.702 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 10.702 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 10.702 * [backup-simplify]: Simplify (- 1) into -1 10.702 * [backup-simplify]: Simplify (+ 0 -1) into -1 10.703 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2 10.703 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 10.703 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 10.703 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 10.703 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 10.703 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 10.703 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 10.703 * [taylor]: Taking taylor expansion of 1/2 in n 10.703 * [backup-simplify]: Simplify 1/2 into 1/2 10.703 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 10.703 * [taylor]: Taking taylor expansion of 1 in n 10.703 * [backup-simplify]: Simplify 1 into 1 10.703 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.703 * [taylor]: Taking taylor expansion of k in n 10.703 * [backup-simplify]: Simplify k into k 10.703 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.703 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 10.703 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 10.703 * [taylor]: Taking taylor expansion of 2 in n 10.703 * [backup-simplify]: Simplify 2 into 2 10.703 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.703 * [taylor]: Taking taylor expansion of PI in n 10.703 * [backup-simplify]: Simplify PI into PI 10.703 * [taylor]: Taking taylor expansion of n in n 10.703 * [backup-simplify]: Simplify 0 into 0 10.703 * [backup-simplify]: Simplify 1 into 1 10.703 * [backup-simplify]: Simplify (/ PI 1) into PI 10.704 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 10.704 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 10.704 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 10.705 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 10.705 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 10.706 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 10.706 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 10.707 * [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))))) 10.707 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 10.707 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 10.707 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 10.707 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 10.707 * [taylor]: Taking taylor expansion of 1/2 in n 10.707 * [backup-simplify]: Simplify 1/2 into 1/2 10.707 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 10.707 * [taylor]: Taking taylor expansion of 1 in n 10.707 * [backup-simplify]: Simplify 1 into 1 10.707 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.707 * [taylor]: Taking taylor expansion of k in n 10.707 * [backup-simplify]: Simplify k into k 10.707 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.707 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 10.707 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 10.707 * [taylor]: Taking taylor expansion of 2 in n 10.707 * [backup-simplify]: Simplify 2 into 2 10.707 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.707 * [taylor]: Taking taylor expansion of PI in n 10.707 * [backup-simplify]: Simplify PI into PI 10.707 * [taylor]: Taking taylor expansion of n in n 10.707 * [backup-simplify]: Simplify 0 into 0 10.707 * [backup-simplify]: Simplify 1 into 1 10.708 * [backup-simplify]: Simplify (/ PI 1) into PI 10.708 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 10.709 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 10.709 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 10.709 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 10.709 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 10.710 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 10.710 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 10.711 * [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))))) 10.711 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k 10.711 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k 10.711 * [taylor]: Taking taylor expansion of 1/2 in k 10.711 * [backup-simplify]: Simplify 1/2 into 1/2 10.711 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k 10.711 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 10.711 * [taylor]: Taking taylor expansion of 1 in k 10.711 * [backup-simplify]: Simplify 1 into 1 10.711 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.711 * [taylor]: Taking taylor expansion of k in k 10.711 * [backup-simplify]: Simplify 0 into 0 10.711 * [backup-simplify]: Simplify 1 into 1 10.712 * [backup-simplify]: Simplify (/ 1 1) into 1 10.712 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 10.712 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 10.712 * [taylor]: Taking taylor expansion of (* 2 PI) in k 10.712 * [taylor]: Taking taylor expansion of 2 in k 10.712 * [backup-simplify]: Simplify 2 into 2 10.712 * [taylor]: Taking taylor expansion of PI in k 10.712 * [backup-simplify]: Simplify PI into PI 10.712 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 10.713 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 10.713 * [taylor]: Taking taylor expansion of (log n) in k 10.713 * [taylor]: Taking taylor expansion of n in k 10.713 * [backup-simplify]: Simplify n into n 10.713 * [backup-simplify]: Simplify (log n) into (log n) 10.713 * [backup-simplify]: Simplify (- 1) into -1 10.713 * [backup-simplify]: Simplify (+ 0 -1) into -1 10.714 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 10.714 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 10.715 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) 10.716 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) 10.716 * [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))))) 10.717 * [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))))) 10.718 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 10.718 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 10.719 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 10.719 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 10.724 * [backup-simplify]: Simplify (- 0) into 0 10.725 * [backup-simplify]: Simplify (+ 0 0) into 0 10.725 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0 10.726 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 10.727 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 10.728 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 10.728 * [taylor]: Taking taylor expansion of 0 in k 10.728 * [backup-simplify]: Simplify 0 into 0 10.728 * [backup-simplify]: Simplify 0 into 0 10.728 * [backup-simplify]: Simplify 0 into 0 10.729 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.730 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 10.732 * [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 10.732 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.732 * [backup-simplify]: Simplify (- 0) into 0 10.732 * [backup-simplify]: Simplify (+ 0 0) into 0 10.733 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0 10.734 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 10.735 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 10.736 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 10.736 * [taylor]: Taking taylor expansion of 0 in k 10.736 * [backup-simplify]: Simplify 0 into 0 10.736 * [backup-simplify]: Simplify 0 into 0 10.736 * [backup-simplify]: Simplify 0 into 0 10.736 * [backup-simplify]: Simplify 0 into 0 10.737 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.738 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 10.741 * [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 10.741 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.741 * [backup-simplify]: Simplify (- 0) into 0 10.741 * [backup-simplify]: Simplify (+ 0 0) into 0 10.742 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0 10.743 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 10.744 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 10.746 * [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 10.746 * [taylor]: Taking taylor expansion of 0 in k 10.746 * [backup-simplify]: Simplify 0 into 0 10.746 * [backup-simplify]: Simplify 0 into 0 10.747 * [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)))))) 10.747 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) 10.747 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0 10.747 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 10.747 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 10.747 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 10.747 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 10.747 * [taylor]: Taking taylor expansion of 1/2 in k 10.747 * [backup-simplify]: Simplify 1/2 into 1/2 10.747 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 10.747 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.747 * [taylor]: Taking taylor expansion of k in k 10.747 * [backup-simplify]: Simplify 0 into 0 10.747 * [backup-simplify]: Simplify 1 into 1 10.748 * [backup-simplify]: Simplify (/ 1 1) into 1 10.748 * [taylor]: Taking taylor expansion of 1 in k 10.748 * [backup-simplify]: Simplify 1 into 1 10.748 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 10.748 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 10.748 * [taylor]: Taking taylor expansion of -2 in k 10.748 * [backup-simplify]: Simplify -2 into -2 10.748 * [taylor]: Taking taylor expansion of (/ PI n) in k 10.748 * [taylor]: Taking taylor expansion of PI in k 10.748 * [backup-simplify]: Simplify PI into PI 10.748 * [taylor]: Taking taylor expansion of n in k 10.748 * [backup-simplify]: Simplify n into n 10.748 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 10.748 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 10.748 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 10.748 * [backup-simplify]: Simplify (+ 1 0) into 1 10.749 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 10.749 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 10.749 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 10.749 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 10.749 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 10.749 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 10.749 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 10.749 * [taylor]: Taking taylor expansion of 1/2 in n 10.749 * [backup-simplify]: Simplify 1/2 into 1/2 10.749 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 10.749 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.749 * [taylor]: Taking taylor expansion of k in n 10.749 * [backup-simplify]: Simplify k into k 10.749 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.749 * [taylor]: Taking taylor expansion of 1 in n 10.749 * [backup-simplify]: Simplify 1 into 1 10.749 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 10.749 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 10.749 * [taylor]: Taking taylor expansion of -2 in n 10.749 * [backup-simplify]: Simplify -2 into -2 10.749 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.749 * [taylor]: Taking taylor expansion of PI in n 10.749 * [backup-simplify]: Simplify PI into PI 10.749 * [taylor]: Taking taylor expansion of n in n 10.749 * [backup-simplify]: Simplify 0 into 0 10.749 * [backup-simplify]: Simplify 1 into 1 10.749 * [backup-simplify]: Simplify (/ PI 1) into PI 10.750 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 10.751 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 10.751 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 10.751 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 10.752 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 10.753 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 10.753 * [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))))) 10.753 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 10.754 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 10.754 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 10.754 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 10.754 * [taylor]: Taking taylor expansion of 1/2 in n 10.754 * [backup-simplify]: Simplify 1/2 into 1/2 10.754 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 10.754 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.754 * [taylor]: Taking taylor expansion of k in n 10.754 * [backup-simplify]: Simplify k into k 10.754 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.754 * [taylor]: Taking taylor expansion of 1 in n 10.754 * [backup-simplify]: Simplify 1 into 1 10.754 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 10.754 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 10.754 * [taylor]: Taking taylor expansion of -2 in n 10.754 * [backup-simplify]: Simplify -2 into -2 10.754 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.754 * [taylor]: Taking taylor expansion of PI in n 10.754 * [backup-simplify]: Simplify PI into PI 10.754 * [taylor]: Taking taylor expansion of n in n 10.754 * [backup-simplify]: Simplify 0 into 0 10.754 * [backup-simplify]: Simplify 1 into 1 10.754 * [backup-simplify]: Simplify (/ PI 1) into PI 10.755 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 10.755 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 10.755 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 10.756 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 10.756 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 10.757 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 10.758 * [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))))) 10.758 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k 10.758 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k 10.758 * [taylor]: Taking taylor expansion of 1/2 in k 10.758 * [backup-simplify]: Simplify 1/2 into 1/2 10.758 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k 10.758 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 10.758 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.758 * [taylor]: Taking taylor expansion of k in k 10.758 * [backup-simplify]: Simplify 0 into 0 10.758 * [backup-simplify]: Simplify 1 into 1 10.758 * [backup-simplify]: Simplify (/ 1 1) into 1 10.758 * [taylor]: Taking taylor expansion of 1 in k 10.758 * [backup-simplify]: Simplify 1 into 1 10.758 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 10.758 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 10.758 * [taylor]: Taking taylor expansion of (* -2 PI) in k 10.758 * [taylor]: Taking taylor expansion of -2 in k 10.758 * [backup-simplify]: Simplify -2 into -2 10.758 * [taylor]: Taking taylor expansion of PI in k 10.758 * [backup-simplify]: Simplify PI into PI 10.759 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 10.759 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 10.759 * [taylor]: Taking taylor expansion of (log n) in k 10.759 * [taylor]: Taking taylor expansion of n in k 10.760 * [backup-simplify]: Simplify n into n 10.760 * [backup-simplify]: Simplify (log n) into (log n) 10.760 * [backup-simplify]: Simplify (+ 1 0) into 1 10.760 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 10.761 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 10.761 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) 10.762 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 10.763 * [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))))) 10.765 * [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))))) 10.766 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 10.766 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 10.768 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 10.768 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 10.769 * [backup-simplify]: Simplify (+ 0 0) into 0 10.769 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0 10.771 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 10.772 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 10.774 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 10.774 * [taylor]: Taking taylor expansion of 0 in k 10.774 * [backup-simplify]: Simplify 0 into 0 10.774 * [backup-simplify]: Simplify 0 into 0 10.774 * [backup-simplify]: Simplify 0 into 0 10.776 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.777 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 10.779 * [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 10.779 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.779 * [backup-simplify]: Simplify (+ 0 0) into 0 10.780 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0 10.781 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 10.782 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 10.783 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 10.783 * [taylor]: Taking taylor expansion of 0 in k 10.783 * [backup-simplify]: Simplify 0 into 0 10.783 * [backup-simplify]: Simplify 0 into 0 10.783 * [backup-simplify]: Simplify 0 into 0 10.783 * [backup-simplify]: Simplify 0 into 0 10.784 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.785 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 10.788 * [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 10.788 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.788 * [backup-simplify]: Simplify (+ 0 0) into 0 10.789 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0 10.790 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 10.791 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 10.793 * [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 10.793 * [taylor]: Taking taylor expansion of 0 in k 10.793 * [backup-simplify]: Simplify 0 into 0 10.793 * [backup-simplify]: Simplify 0 into 0 10.794 * [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)))))) 10.794 * * * * [progress]: [ 2 / 3 ] generating series at (2 2 1) 10.794 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 10.794 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 10.794 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 10.794 * [taylor]: Taking taylor expansion of 2 in n 10.794 * [backup-simplify]: Simplify 2 into 2 10.794 * [taylor]: Taking taylor expansion of (* n PI) in n 10.794 * [taylor]: Taking taylor expansion of n in n 10.794 * [backup-simplify]: Simplify 0 into 0 10.794 * [backup-simplify]: Simplify 1 into 1 10.794 * [taylor]: Taking taylor expansion of PI in n 10.794 * [backup-simplify]: Simplify PI into PI 10.794 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 10.794 * [taylor]: Taking taylor expansion of 2 in n 10.794 * [backup-simplify]: Simplify 2 into 2 10.794 * [taylor]: Taking taylor expansion of (* n PI) in n 10.794 * [taylor]: Taking taylor expansion of n in n 10.794 * [backup-simplify]: Simplify 0 into 0 10.794 * [backup-simplify]: Simplify 1 into 1 10.794 * [taylor]: Taking taylor expansion of PI in n 10.794 * [backup-simplify]: Simplify PI into PI 10.795 * [backup-simplify]: Simplify (* 0 PI) into 0 10.795 * [backup-simplify]: Simplify (* 2 0) into 0 10.795 * [backup-simplify]: Simplify 0 into 0 10.796 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.797 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 10.797 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 10.798 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 10.799 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 10.799 * [backup-simplify]: Simplify 0 into 0 10.799 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 10.800 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 10.800 * [backup-simplify]: Simplify 0 into 0 10.801 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 10.802 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 10.802 * [backup-simplify]: Simplify 0 into 0 10.803 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 10.805 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 10.805 * [backup-simplify]: Simplify 0 into 0 10.806 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 10.807 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 10.807 * [backup-simplify]: Simplify 0 into 0 10.808 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 10.809 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 10.809 * [backup-simplify]: Simplify 0 into 0 10.810 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 10.811 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n)) 10.811 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 10.811 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 10.811 * [taylor]: Taking taylor expansion of 2 in n 10.811 * [backup-simplify]: Simplify 2 into 2 10.811 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.811 * [taylor]: Taking taylor expansion of PI in n 10.811 * [backup-simplify]: Simplify PI into PI 10.811 * [taylor]: Taking taylor expansion of n in n 10.811 * [backup-simplify]: Simplify 0 into 0 10.811 * [backup-simplify]: Simplify 1 into 1 10.812 * [backup-simplify]: Simplify (/ PI 1) into PI 10.812 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 10.812 * [taylor]: Taking taylor expansion of 2 in n 10.812 * [backup-simplify]: Simplify 2 into 2 10.812 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.812 * [taylor]: Taking taylor expansion of PI in n 10.812 * [backup-simplify]: Simplify PI into PI 10.812 * [taylor]: Taking taylor expansion of n in n 10.812 * [backup-simplify]: Simplify 0 into 0 10.812 * [backup-simplify]: Simplify 1 into 1 10.812 * [backup-simplify]: Simplify (/ PI 1) into PI 10.813 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 10.813 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 10.814 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 10.815 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 10.815 * [backup-simplify]: Simplify 0 into 0 10.816 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.818 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 10.818 * [backup-simplify]: Simplify 0 into 0 10.819 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.820 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 10.820 * [backup-simplify]: Simplify 0 into 0 10.821 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.823 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 10.823 * [backup-simplify]: Simplify 0 into 0 10.831 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.833 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 10.833 * [backup-simplify]: Simplify 0 into 0 10.834 * [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 10.836 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 10.836 * [backup-simplify]: Simplify 0 into 0 10.837 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 10.837 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (- n))) into (* -2 (/ PI n)) 10.837 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 10.837 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 10.837 * [taylor]: Taking taylor expansion of -2 in n 10.837 * [backup-simplify]: Simplify -2 into -2 10.837 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.837 * [taylor]: Taking taylor expansion of PI in n 10.837 * [backup-simplify]: Simplify PI into PI 10.837 * [taylor]: Taking taylor expansion of n in n 10.837 * [backup-simplify]: Simplify 0 into 0 10.837 * [backup-simplify]: Simplify 1 into 1 10.838 * [backup-simplify]: Simplify (/ PI 1) into PI 10.838 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 10.838 * [taylor]: Taking taylor expansion of -2 in n 10.838 * [backup-simplify]: Simplify -2 into -2 10.838 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.838 * [taylor]: Taking taylor expansion of PI in n 10.838 * [backup-simplify]: Simplify PI into PI 10.838 * [taylor]: Taking taylor expansion of n in n 10.838 * [backup-simplify]: Simplify 0 into 0 10.838 * [backup-simplify]: Simplify 1 into 1 10.839 * [backup-simplify]: Simplify (/ PI 1) into PI 10.839 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 10.840 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 10.841 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 10.841 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 10.842 * [backup-simplify]: Simplify 0 into 0 10.843 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.844 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 10.844 * [backup-simplify]: Simplify 0 into 0 10.845 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.846 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 10.846 * [backup-simplify]: Simplify 0 into 0 10.848 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.849 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 10.849 * [backup-simplify]: Simplify 0 into 0 10.850 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.852 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 10.852 * [backup-simplify]: Simplify 0 into 0 10.853 * [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 10.855 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 10.855 * [backup-simplify]: Simplify 0 into 0 10.856 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 10.856 * * * * [progress]: [ 3 / 3 ] generating series at (2) 10.856 * [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))) 10.856 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k n) around 0 10.857 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n 10.857 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 10.857 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 10.857 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 10.857 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n 10.857 * [taylor]: Taking taylor expansion of 1/2 in n 10.857 * [backup-simplify]: Simplify 1/2 into 1/2 10.857 * [taylor]: Taking taylor expansion of (- 1 k) in n 10.857 * [taylor]: Taking taylor expansion of 1 in n 10.857 * [backup-simplify]: Simplify 1 into 1 10.857 * [taylor]: Taking taylor expansion of k in n 10.857 * [backup-simplify]: Simplify k into k 10.857 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 10.857 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 10.857 * [taylor]: Taking taylor expansion of 2 in n 10.857 * [backup-simplify]: Simplify 2 into 2 10.857 * [taylor]: Taking taylor expansion of (* n PI) in n 10.857 * [taylor]: Taking taylor expansion of n in n 10.857 * [backup-simplify]: Simplify 0 into 0 10.857 * [backup-simplify]: Simplify 1 into 1 10.857 * [taylor]: Taking taylor expansion of PI in n 10.857 * [backup-simplify]: Simplify PI into PI 10.858 * [backup-simplify]: Simplify (* 0 PI) into 0 10.858 * [backup-simplify]: Simplify (* 2 0) into 0 10.860 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.861 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 10.862 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 10.862 * [backup-simplify]: Simplify (- k) into (- k) 10.862 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k) 10.862 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 10.864 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 10.865 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 10.866 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 10.866 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 10.866 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.866 * [taylor]: Taking taylor expansion of k in n 10.866 * [backup-simplify]: Simplify k into k 10.866 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.867 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 10.867 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 10.867 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 10.867 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k 10.867 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 10.867 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 10.867 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 10.867 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k 10.867 * [taylor]: Taking taylor expansion of 1/2 in k 10.867 * [backup-simplify]: Simplify 1/2 into 1/2 10.867 * [taylor]: Taking taylor expansion of (- 1 k) in k 10.867 * [taylor]: Taking taylor expansion of 1 in k 10.867 * [backup-simplify]: Simplify 1 into 1 10.867 * [taylor]: Taking taylor expansion of k in k 10.867 * [backup-simplify]: Simplify 0 into 0 10.867 * [backup-simplify]: Simplify 1 into 1 10.867 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 10.867 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 10.867 * [taylor]: Taking taylor expansion of 2 in k 10.867 * [backup-simplify]: Simplify 2 into 2 10.867 * [taylor]: Taking taylor expansion of (* n PI) in k 10.867 * [taylor]: Taking taylor expansion of n in k 10.867 * [backup-simplify]: Simplify n into n 10.867 * [taylor]: Taking taylor expansion of PI in k 10.867 * [backup-simplify]: Simplify PI into PI 10.867 * [backup-simplify]: Simplify (* n PI) into (* n PI) 10.867 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 10.868 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 10.868 * [backup-simplify]: Simplify (- 0) into 0 10.868 * [backup-simplify]: Simplify (+ 1 0) into 1 10.869 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 10.869 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 10.869 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 10.869 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 10.869 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.869 * [taylor]: Taking taylor expansion of k in k 10.869 * [backup-simplify]: Simplify 0 into 0 10.869 * [backup-simplify]: Simplify 1 into 1 10.870 * [backup-simplify]: Simplify (/ 1 1) into 1 10.870 * [backup-simplify]: Simplify (sqrt 0) into 0 10.872 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 10.872 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k 10.872 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 10.872 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 10.872 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 10.872 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k 10.872 * [taylor]: Taking taylor expansion of 1/2 in k 10.872 * [backup-simplify]: Simplify 1/2 into 1/2 10.872 * [taylor]: Taking taylor expansion of (- 1 k) in k 10.872 * [taylor]: Taking taylor expansion of 1 in k 10.872 * [backup-simplify]: Simplify 1 into 1 10.872 * [taylor]: Taking taylor expansion of k in k 10.872 * [backup-simplify]: Simplify 0 into 0 10.872 * [backup-simplify]: Simplify 1 into 1 10.872 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 10.872 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 10.872 * [taylor]: Taking taylor expansion of 2 in k 10.872 * [backup-simplify]: Simplify 2 into 2 10.872 * [taylor]: Taking taylor expansion of (* n PI) in k 10.872 * [taylor]: Taking taylor expansion of n in k 10.872 * [backup-simplify]: Simplify n into n 10.872 * [taylor]: Taking taylor expansion of PI in k 10.872 * [backup-simplify]: Simplify PI into PI 10.872 * [backup-simplify]: Simplify (* n PI) into (* n PI) 10.872 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 10.872 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 10.873 * [backup-simplify]: Simplify (- 0) into 0 10.873 * [backup-simplify]: Simplify (+ 1 0) into 1 10.874 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 10.874 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 10.874 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 10.874 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 10.874 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.874 * [taylor]: Taking taylor expansion of k in k 10.874 * [backup-simplify]: Simplify 0 into 0 10.874 * [backup-simplify]: Simplify 1 into 1 10.875 * [backup-simplify]: Simplify (/ 1 1) into 1 10.875 * [backup-simplify]: Simplify (sqrt 0) into 0 10.876 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 10.877 * [backup-simplify]: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0 10.877 * [taylor]: Taking taylor expansion of 0 in n 10.877 * [backup-simplify]: Simplify 0 into 0 10.877 * [backup-simplify]: Simplify 0 into 0 10.877 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 10.878 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 10.879 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 10.879 * [backup-simplify]: Simplify (- 1) into -1 10.879 * [backup-simplify]: Simplify (+ 0 -1) into -1 10.880 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2 10.881 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 10.881 * [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))))) 10.882 * [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))))) 10.882 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 10.882 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 10.882 * [taylor]: Taking taylor expansion of +nan.0 in n 10.882 * [backup-simplify]: Simplify +nan.0 into +nan.0 10.882 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 10.882 * [taylor]: Taking taylor expansion of (sqrt 2) in n 10.882 * [taylor]: Taking taylor expansion of 2 in n 10.882 * [backup-simplify]: Simplify 2 into 2 10.882 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 10.883 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 10.883 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 10.883 * [taylor]: Taking taylor expansion of (* n PI) in n 10.883 * [taylor]: Taking taylor expansion of n in n 10.883 * [backup-simplify]: Simplify 0 into 0 10.883 * [backup-simplify]: Simplify 1 into 1 10.883 * [taylor]: Taking taylor expansion of PI in n 10.883 * [backup-simplify]: Simplify PI into PI 10.884 * [backup-simplify]: Simplify (* 0 PI) into 0 10.885 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.886 * [backup-simplify]: Simplify (sqrt 0) into 0 10.887 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 10.887 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 10.888 * [backup-simplify]: Simplify (* +nan.0 0) into 0 10.888 * [backup-simplify]: Simplify (- 0) into 0 10.888 * [backup-simplify]: Simplify 0 into 0 10.888 * [backup-simplify]: Simplify 0 into 0 10.889 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 10.892 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 10.893 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 10.894 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 10.896 * [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 10.896 * [backup-simplify]: Simplify (- 0) into 0 10.897 * [backup-simplify]: Simplify (+ 0 0) into 0 10.898 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0 10.899 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 10.900 * [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))) 10.901 * [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))))))) 10.901 * [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 10.901 * [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 10.901 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 10.901 * [taylor]: Taking taylor expansion of +nan.0 in n 10.901 * [backup-simplify]: Simplify +nan.0 into +nan.0 10.901 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 10.901 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 10.901 * [taylor]: Taking taylor expansion of (sqrt 2) in n 10.901 * [taylor]: Taking taylor expansion of 2 in n 10.901 * [backup-simplify]: Simplify 2 into 2 10.901 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 10.902 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 10.902 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 10.902 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 10.902 * [taylor]: Taking taylor expansion of 2 in n 10.902 * [backup-simplify]: Simplify 2 into 2 10.902 * [taylor]: Taking taylor expansion of (* n PI) in n 10.902 * [taylor]: Taking taylor expansion of n in n 10.902 * [backup-simplify]: Simplify 0 into 0 10.902 * [backup-simplify]: Simplify 1 into 1 10.902 * [taylor]: Taking taylor expansion of PI in n 10.902 * [backup-simplify]: Simplify PI into PI 10.903 * [backup-simplify]: Simplify (* 0 PI) into 0 10.903 * [backup-simplify]: Simplify (* 2 0) into 0 10.905 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.906 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 10.907 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 10.907 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 10.907 * [taylor]: Taking taylor expansion of (* n PI) in n 10.907 * [taylor]: Taking taylor expansion of n in n 10.907 * [backup-simplify]: Simplify 0 into 0 10.907 * [backup-simplify]: Simplify 1 into 1 10.907 * [taylor]: Taking taylor expansion of PI in n 10.907 * [backup-simplify]: Simplify PI into PI 10.907 * [backup-simplify]: Simplify (* 0 PI) into 0 10.908 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.908 * [backup-simplify]: Simplify (sqrt 0) into 0 10.909 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 10.909 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 10.909 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 10.909 * [taylor]: Taking taylor expansion of +nan.0 in n 10.909 * [backup-simplify]: Simplify +nan.0 into +nan.0 10.909 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 10.909 * [taylor]: Taking taylor expansion of (sqrt 2) in n 10.909 * [taylor]: Taking taylor expansion of 2 in n 10.909 * [backup-simplify]: Simplify 2 into 2 10.910 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 10.910 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 10.910 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 10.910 * [taylor]: Taking taylor expansion of (* n PI) in n 10.910 * [taylor]: Taking taylor expansion of n in n 10.910 * [backup-simplify]: Simplify 0 into 0 10.910 * [backup-simplify]: Simplify 1 into 1 10.910 * [taylor]: Taking taylor expansion of PI in n 10.910 * [backup-simplify]: Simplify PI into PI 10.910 * [backup-simplify]: Simplify (* 0 PI) into 0 10.911 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.911 * [backup-simplify]: Simplify (sqrt 0) into 0 10.912 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 10.913 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 10.914 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 10.915 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 10.915 * [backup-simplify]: Simplify (* +nan.0 0) into 0 10.916 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 10.916 * [backup-simplify]: Simplify (* +nan.0 0) into 0 10.916 * [backup-simplify]: Simplify (- 0) into 0 10.916 * [backup-simplify]: Simplify (+ 0 0) into 0 10.917 * [backup-simplify]: Simplify (- 0) into 0 10.917 * [backup-simplify]: Simplify 0 into 0 10.919 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 10.922 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 10.924 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 10.925 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 10.925 * [backup-simplify]: Simplify 0 into 0 10.926 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.928 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 10.929 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 10.930 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 10.931 * [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 10.932 * [backup-simplify]: Simplify (- 0) into 0 10.932 * [backup-simplify]: Simplify (+ 0 0) into 0 10.933 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0 10.934 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 10.935 * [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))) 10.937 * [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))))))))) 10.937 * [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 10.937 * [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 10.937 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 10.937 * [taylor]: Taking taylor expansion of +nan.0 in n 10.937 * [backup-simplify]: Simplify +nan.0 into +nan.0 10.937 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 10.937 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 10.937 * [taylor]: Taking taylor expansion of (sqrt 2) in n 10.937 * [taylor]: Taking taylor expansion of 2 in n 10.937 * [backup-simplify]: Simplify 2 into 2 10.938 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 10.938 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 10.938 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 10.938 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 10.938 * [taylor]: Taking taylor expansion of 2 in n 10.938 * [backup-simplify]: Simplify 2 into 2 10.938 * [taylor]: Taking taylor expansion of (* n PI) in n 10.938 * [taylor]: Taking taylor expansion of n in n 10.938 * [backup-simplify]: Simplify 0 into 0 10.938 * [backup-simplify]: Simplify 1 into 1 10.938 * [taylor]: Taking taylor expansion of PI in n 10.938 * [backup-simplify]: Simplify PI into PI 10.939 * [backup-simplify]: Simplify (* 0 PI) into 0 10.939 * [backup-simplify]: Simplify (* 2 0) into 0 10.941 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.943 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 10.944 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 10.944 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 10.944 * [taylor]: Taking taylor expansion of (* n PI) in n 10.944 * [taylor]: Taking taylor expansion of n in n 10.944 * [backup-simplify]: Simplify 0 into 0 10.944 * [backup-simplify]: Simplify 1 into 1 10.944 * [taylor]: Taking taylor expansion of PI in n 10.944 * [backup-simplify]: Simplify PI into PI 10.944 * [backup-simplify]: Simplify (* 0 PI) into 0 10.946 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.946 * [backup-simplify]: Simplify (sqrt 0) into 0 10.948 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 10.948 * [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 10.948 * [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 10.948 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 10.948 * [taylor]: Taking taylor expansion of +nan.0 in n 10.948 * [backup-simplify]: Simplify +nan.0 into +nan.0 10.948 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 10.948 * [taylor]: Taking taylor expansion of (sqrt 2) in n 10.948 * [taylor]: Taking taylor expansion of 2 in n 10.948 * [backup-simplify]: Simplify 2 into 2 10.949 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 10.949 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 10.949 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 10.949 * [taylor]: Taking taylor expansion of (* n PI) in n 10.949 * [taylor]: Taking taylor expansion of n in n 10.949 * [backup-simplify]: Simplify 0 into 0 10.949 * [backup-simplify]: Simplify 1 into 1 10.949 * [taylor]: Taking taylor expansion of PI in n 10.949 * [backup-simplify]: Simplify PI into PI 10.950 * [backup-simplify]: Simplify (* 0 PI) into 0 10.952 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.952 * [backup-simplify]: Simplify (sqrt 0) into 0 10.953 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 10.953 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n 10.953 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 10.953 * [taylor]: Taking taylor expansion of +nan.0 in n 10.953 * [backup-simplify]: Simplify +nan.0 into +nan.0 10.953 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 10.953 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 10.954 * [taylor]: Taking taylor expansion of (sqrt 2) in n 10.954 * [taylor]: Taking taylor expansion of 2 in n 10.954 * [backup-simplify]: Simplify 2 into 2 10.954 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 10.955 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 10.955 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 10.955 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 10.955 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 10.955 * [taylor]: Taking taylor expansion of 2 in n 10.955 * [backup-simplify]: Simplify 2 into 2 10.955 * [taylor]: Taking taylor expansion of (* n PI) in n 10.955 * [taylor]: Taking taylor expansion of n in n 10.955 * [backup-simplify]: Simplify 0 into 0 10.955 * [backup-simplify]: Simplify 1 into 1 10.955 * [taylor]: Taking taylor expansion of PI in n 10.955 * [backup-simplify]: Simplify PI into PI 10.955 * [backup-simplify]: Simplify (* 0 PI) into 0 10.962 * [backup-simplify]: Simplify (* 2 0) into 0 10.965 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.966 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 10.968 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 10.969 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 10.969 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 10.969 * [taylor]: Taking taylor expansion of (* n PI) in n 10.969 * [taylor]: Taking taylor expansion of n in n 10.969 * [backup-simplify]: Simplify 0 into 0 10.969 * [backup-simplify]: Simplify 1 into 1 10.969 * [taylor]: Taking taylor expansion of PI in n 10.969 * [backup-simplify]: Simplify PI into PI 10.970 * [backup-simplify]: Simplify (* 0 PI) into 0 10.971 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.972 * [backup-simplify]: Simplify (sqrt 0) into 0 10.973 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 10.974 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 10.975 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 10.976 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 10.976 * [backup-simplify]: Simplify (* +nan.0 0) into 0 10.977 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 10.977 * [backup-simplify]: Simplify (* +nan.0 0) into 0 10.978 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 10.979 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 10.980 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 10.982 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 10.983 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 10.983 * [backup-simplify]: Simplify (* +nan.0 0) into 0 10.983 * [backup-simplify]: Simplify (- 0) into 0 10.984 * [backup-simplify]: Simplify (+ 0 0) into 0 10.984 * [backup-simplify]: Simplify (- 0) into 0 10.984 * [backup-simplify]: Simplify (+ 0 0) into 0 10.984 * [backup-simplify]: Simplify (- 0) into 0 10.984 * [backup-simplify]: Simplify 0 into 0 10.985 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 10.986 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 10.987 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 10.988 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 10.989 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 10.990 * [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)))))))) 10.995 * [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)))))))) 10.997 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 11.000 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 11.002 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 11.007 * [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)))))))))) 11.012 * [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))))))) 11.019 * [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))))))) 11.020 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.025 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 11.026 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 11.031 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 11.040 * [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)))) 11.045 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 11.049 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 11.063 * [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))))))))))))) 11.064 * [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)) 11.064 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k n) around 0 11.064 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n 11.064 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 11.064 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.064 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.064 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 11.064 * [taylor]: Taking taylor expansion of 1/2 in n 11.064 * [backup-simplify]: Simplify 1/2 into 1/2 11.064 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 11.064 * [taylor]: Taking taylor expansion of 1 in n 11.064 * [backup-simplify]: Simplify 1 into 1 11.064 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.064 * [taylor]: Taking taylor expansion of k in n 11.064 * [backup-simplify]: Simplify k into k 11.064 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.065 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.065 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.065 * [taylor]: Taking taylor expansion of 2 in n 11.065 * [backup-simplify]: Simplify 2 into 2 11.065 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.065 * [taylor]: Taking taylor expansion of PI in n 11.065 * [backup-simplify]: Simplify PI into PI 11.065 * [taylor]: Taking taylor expansion of n in n 11.065 * [backup-simplify]: Simplify 0 into 0 11.065 * [backup-simplify]: Simplify 1 into 1 11.065 * [backup-simplify]: Simplify (/ PI 1) into PI 11.066 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.066 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.067 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.067 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 11.067 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 11.068 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.069 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 11.069 * [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))))) 11.069 * [taylor]: Taking taylor expansion of (sqrt k) in n 11.069 * [taylor]: Taking taylor expansion of k in n 11.069 * [backup-simplify]: Simplify k into k 11.069 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 11.069 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 11.069 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k 11.069 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 11.069 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 11.069 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 11.069 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 11.070 * [taylor]: Taking taylor expansion of 1/2 in k 11.070 * [backup-simplify]: Simplify 1/2 into 1/2 11.070 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 11.070 * [taylor]: Taking taylor expansion of 1 in k 11.070 * [backup-simplify]: Simplify 1 into 1 11.070 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.070 * [taylor]: Taking taylor expansion of k in k 11.070 * [backup-simplify]: Simplify 0 into 0 11.070 * [backup-simplify]: Simplify 1 into 1 11.070 * [backup-simplify]: Simplify (/ 1 1) into 1 11.070 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 11.070 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 11.070 * [taylor]: Taking taylor expansion of 2 in k 11.070 * [backup-simplify]: Simplify 2 into 2 11.070 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.070 * [taylor]: Taking taylor expansion of PI in k 11.070 * [backup-simplify]: Simplify PI into PI 11.070 * [taylor]: Taking taylor expansion of n in k 11.070 * [backup-simplify]: Simplify n into n 11.070 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.070 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 11.070 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 11.070 * [backup-simplify]: Simplify (- 1) into -1 11.071 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.071 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2 11.071 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 11.071 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 11.071 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.071 * [taylor]: Taking taylor expansion of k in k 11.071 * [backup-simplify]: Simplify 0 into 0 11.071 * [backup-simplify]: Simplify 1 into 1 11.071 * [backup-simplify]: Simplify (sqrt 0) into 0 11.077 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.077 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k 11.077 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 11.077 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 11.077 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 11.077 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 11.077 * [taylor]: Taking taylor expansion of 1/2 in k 11.077 * [backup-simplify]: Simplify 1/2 into 1/2 11.077 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 11.077 * [taylor]: Taking taylor expansion of 1 in k 11.077 * [backup-simplify]: Simplify 1 into 1 11.077 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.077 * [taylor]: Taking taylor expansion of k in k 11.077 * [backup-simplify]: Simplify 0 into 0 11.077 * [backup-simplify]: Simplify 1 into 1 11.078 * [backup-simplify]: Simplify (/ 1 1) into 1 11.078 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 11.078 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 11.078 * [taylor]: Taking taylor expansion of 2 in k 11.078 * [backup-simplify]: Simplify 2 into 2 11.078 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.078 * [taylor]: Taking taylor expansion of PI in k 11.078 * [backup-simplify]: Simplify PI into PI 11.078 * [taylor]: Taking taylor expansion of n in k 11.078 * [backup-simplify]: Simplify n into n 11.078 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.078 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 11.078 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 11.078 * [backup-simplify]: Simplify (- 1) into -1 11.079 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.079 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2 11.079 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 11.079 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 11.079 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.079 * [taylor]: Taking taylor expansion of k in k 11.079 * [backup-simplify]: Simplify 0 into 0 11.079 * [backup-simplify]: Simplify 1 into 1 11.079 * [backup-simplify]: Simplify (sqrt 0) into 0 11.080 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.080 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 0) into 0 11.081 * [taylor]: Taking taylor expansion of 0 in n 11.081 * [backup-simplify]: Simplify 0 into 0 11.081 * [backup-simplify]: Simplify 0 into 0 11.081 * [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)))))))) 11.081 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 11.081 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 11.081 * [taylor]: Taking taylor expansion of +nan.0 in n 11.081 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.081 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 11.081 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 11.081 * [taylor]: Taking taylor expansion of 1/2 in n 11.081 * [backup-simplify]: Simplify 1/2 into 1/2 11.081 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 11.081 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 11.081 * [taylor]: Taking taylor expansion of 1 in n 11.081 * [backup-simplify]: Simplify 1 into 1 11.081 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.081 * [taylor]: Taking taylor expansion of k in n 11.081 * [backup-simplify]: Simplify k into k 11.081 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.081 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.081 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.081 * [taylor]: Taking taylor expansion of 2 in n 11.081 * [backup-simplify]: Simplify 2 into 2 11.081 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.081 * [taylor]: Taking taylor expansion of PI in n 11.081 * [backup-simplify]: Simplify PI into PI 11.081 * [taylor]: Taking taylor expansion of n in n 11.081 * [backup-simplify]: Simplify 0 into 0 11.081 * [backup-simplify]: Simplify 1 into 1 11.082 * [backup-simplify]: Simplify (/ PI 1) into PI 11.082 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.083 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.083 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.083 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 11.084 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.085 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 11.085 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 11.086 * [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))))) 11.087 * [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)))))) 11.088 * [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))))))) 11.088 * [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))))))) 11.088 * [backup-simplify]: Simplify 0 into 0 11.090 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.091 * [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)))))))) 11.091 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 11.091 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 11.091 * [taylor]: Taking taylor expansion of +nan.0 in n 11.091 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.091 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 11.091 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 11.091 * [taylor]: Taking taylor expansion of 1/2 in n 11.091 * [backup-simplify]: Simplify 1/2 into 1/2 11.091 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 11.091 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 11.091 * [taylor]: Taking taylor expansion of 1 in n 11.091 * [backup-simplify]: Simplify 1 into 1 11.091 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.091 * [taylor]: Taking taylor expansion of k in n 11.091 * [backup-simplify]: Simplify k into k 11.091 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.091 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.091 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.091 * [taylor]: Taking taylor expansion of 2 in n 11.091 * [backup-simplify]: Simplify 2 into 2 11.091 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.091 * [taylor]: Taking taylor expansion of PI in n 11.091 * [backup-simplify]: Simplify PI into PI 11.091 * [taylor]: Taking taylor expansion of n in n 11.091 * [backup-simplify]: Simplify 0 into 0 11.091 * [backup-simplify]: Simplify 1 into 1 11.092 * [backup-simplify]: Simplify (/ PI 1) into PI 11.092 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.093 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.093 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.093 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 11.094 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.094 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 11.095 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 11.096 * [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))))) 11.096 * [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)))))) 11.097 * [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))))))) 11.098 * [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))))))) 11.099 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.099 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 11.100 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.100 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.101 * [backup-simplify]: Simplify (- 0) into 0 11.101 * [backup-simplify]: Simplify (+ 0 0) into 0 11.102 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.102 * [backup-simplify]: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 11.103 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0 11.105 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.106 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0 11.106 * [backup-simplify]: Simplify (- 0) into 0 11.106 * [backup-simplify]: Simplify 0 into 0 11.106 * [backup-simplify]: Simplify 0 into 0 11.108 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.109 * [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)))))))) 11.109 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 11.109 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 11.109 * [taylor]: Taking taylor expansion of +nan.0 in n 11.109 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.109 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 11.109 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 11.109 * [taylor]: Taking taylor expansion of 1/2 in n 11.109 * [backup-simplify]: Simplify 1/2 into 1/2 11.109 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 11.109 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 11.109 * [taylor]: Taking taylor expansion of 1 in n 11.109 * [backup-simplify]: Simplify 1 into 1 11.109 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.109 * [taylor]: Taking taylor expansion of k in n 11.109 * [backup-simplify]: Simplify k into k 11.109 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.109 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.109 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.109 * [taylor]: Taking taylor expansion of 2 in n 11.109 * [backup-simplify]: Simplify 2 into 2 11.109 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.109 * [taylor]: Taking taylor expansion of PI in n 11.109 * [backup-simplify]: Simplify PI into PI 11.109 * [taylor]: Taking taylor expansion of n in n 11.109 * [backup-simplify]: Simplify 0 into 0 11.109 * [backup-simplify]: Simplify 1 into 1 11.110 * [backup-simplify]: Simplify (/ PI 1) into PI 11.110 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.111 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.111 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.111 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 11.112 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.112 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 11.113 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 11.114 * [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))))) 11.115 * [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)))))) 11.115 * [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))))))) 11.116 * [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))))))) 11.119 * [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)))))))) 11.119 * [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)))) 11.119 * [approximate]: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in (k n) around 0 11.119 * [taylor]: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in n 11.119 * [taylor]: Taking taylor expansion of (sqrt (/ k -1)) in n 11.119 * [taylor]: Taking taylor expansion of (/ k -1) in n 11.119 * [taylor]: Taking taylor expansion of k in n 11.119 * [backup-simplify]: Simplify k into k 11.119 * [taylor]: Taking taylor expansion of -1 in n 11.120 * [backup-simplify]: Simplify -1 into -1 11.120 * [backup-simplify]: Simplify (/ k -1) into (* -1 k) 11.120 * [backup-simplify]: Simplify (sqrt (* -1 k)) into (sqrt (* -1 k)) 11.120 * [backup-simplify]: Simplify (- (/ 0 -1) (+ (* (* -1 k) (/ 0 -1)))) into 0 11.120 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (* -1 k)))) into 0 11.120 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 11.120 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 11.120 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 11.120 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 11.120 * [taylor]: Taking taylor expansion of 1/2 in n 11.120 * [backup-simplify]: Simplify 1/2 into 1/2 11.120 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 11.120 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.120 * [taylor]: Taking taylor expansion of k in n 11.120 * [backup-simplify]: Simplify k into k 11.120 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.120 * [taylor]: Taking taylor expansion of 1 in n 11.120 * [backup-simplify]: Simplify 1 into 1 11.120 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.120 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.120 * [taylor]: Taking taylor expansion of -2 in n 11.120 * [backup-simplify]: Simplify -2 into -2 11.120 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.121 * [taylor]: Taking taylor expansion of PI in n 11.121 * [backup-simplify]: Simplify PI into PI 11.121 * [taylor]: Taking taylor expansion of n in n 11.121 * [backup-simplify]: Simplify 0 into 0 11.121 * [backup-simplify]: Simplify 1 into 1 11.121 * [backup-simplify]: Simplify (/ PI 1) into PI 11.121 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.122 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.122 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 11.122 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 11.123 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.124 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 11.125 * [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))))) 11.125 * [taylor]: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in k 11.125 * [taylor]: Taking taylor expansion of (sqrt (/ k -1)) in k 11.125 * [taylor]: Taking taylor expansion of (/ k -1) in k 11.125 * [taylor]: Taking taylor expansion of k in k 11.125 * [backup-simplify]: Simplify 0 into 0 11.125 * [backup-simplify]: Simplify 1 into 1 11.125 * [taylor]: Taking taylor expansion of -1 in k 11.125 * [backup-simplify]: Simplify -1 into -1 11.125 * [backup-simplify]: Simplify (/ 1 -1) into -1 11.125 * [backup-simplify]: Simplify (sqrt 0) into 0 11.126 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.126 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 11.126 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 11.126 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 11.126 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 11.126 * [taylor]: Taking taylor expansion of 1/2 in k 11.126 * [backup-simplify]: Simplify 1/2 into 1/2 11.126 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 11.126 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.126 * [taylor]: Taking taylor expansion of k in k 11.126 * [backup-simplify]: Simplify 0 into 0 11.126 * [backup-simplify]: Simplify 1 into 1 11.127 * [backup-simplify]: Simplify (/ 1 1) into 1 11.127 * [taylor]: Taking taylor expansion of 1 in k 11.127 * [backup-simplify]: Simplify 1 into 1 11.127 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 11.127 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 11.127 * [taylor]: Taking taylor expansion of -2 in k 11.127 * [backup-simplify]: Simplify -2 into -2 11.127 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.127 * [taylor]: Taking taylor expansion of PI in k 11.127 * [backup-simplify]: Simplify PI into PI 11.127 * [taylor]: Taking taylor expansion of n in k 11.127 * [backup-simplify]: Simplify n into n 11.127 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.127 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 11.127 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 11.127 * [backup-simplify]: Simplify (+ 1 0) into 1 11.128 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.128 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 11.128 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 11.128 * [taylor]: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in k 11.128 * [taylor]: Taking taylor expansion of (sqrt (/ k -1)) in k 11.128 * [taylor]: Taking taylor expansion of (/ k -1) in k 11.128 * [taylor]: Taking taylor expansion of k in k 11.128 * [backup-simplify]: Simplify 0 into 0 11.128 * [backup-simplify]: Simplify 1 into 1 11.128 * [taylor]: Taking taylor expansion of -1 in k 11.128 * [backup-simplify]: Simplify -1 into -1 11.128 * [backup-simplify]: Simplify (/ 1 -1) into -1 11.128 * [backup-simplify]: Simplify (sqrt 0) into 0 11.129 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.129 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 11.129 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 11.129 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 11.129 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 11.129 * [taylor]: Taking taylor expansion of 1/2 in k 11.129 * [backup-simplify]: Simplify 1/2 into 1/2 11.129 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 11.129 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.129 * [taylor]: Taking taylor expansion of k in k 11.130 * [backup-simplify]: Simplify 0 into 0 11.130 * [backup-simplify]: Simplify 1 into 1 11.130 * [backup-simplify]: Simplify (/ 1 1) into 1 11.130 * [taylor]: Taking taylor expansion of 1 in k 11.130 * [backup-simplify]: Simplify 1 into 1 11.130 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 11.130 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 11.130 * [taylor]: Taking taylor expansion of -2 in k 11.130 * [backup-simplify]: Simplify -2 into -2 11.130 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.130 * [taylor]: Taking taylor expansion of PI in k 11.130 * [backup-simplify]: Simplify PI into PI 11.130 * [taylor]: Taking taylor expansion of n in k 11.130 * [backup-simplify]: Simplify n into n 11.130 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.130 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 11.130 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 11.130 * [backup-simplify]: Simplify (+ 1 0) into 1 11.131 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.131 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 11.131 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 11.131 * [backup-simplify]: Simplify (* 0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) into 0 11.131 * [taylor]: Taking taylor expansion of 0 in n 11.131 * [backup-simplify]: Simplify 0 into 0 11.131 * [backup-simplify]: Simplify 0 into 0 11.131 * [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)))))) 11.132 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 11.132 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 11.132 * [taylor]: Taking taylor expansion of +nan.0 in n 11.132 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.132 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 11.132 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 11.132 * [taylor]: Taking taylor expansion of 1/2 in n 11.132 * [backup-simplify]: Simplify 1/2 into 1/2 11.132 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 11.132 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.132 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.132 * [taylor]: Taking taylor expansion of -2 in n 11.132 * [backup-simplify]: Simplify -2 into -2 11.132 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.132 * [taylor]: Taking taylor expansion of PI in n 11.132 * [backup-simplify]: Simplify PI into PI 11.132 * [taylor]: Taking taylor expansion of n in n 11.132 * [backup-simplify]: Simplify 0 into 0 11.132 * [backup-simplify]: Simplify 1 into 1 11.132 * [backup-simplify]: Simplify (/ PI 1) into PI 11.133 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.133 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.133 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 11.133 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.133 * [taylor]: Taking taylor expansion of k in n 11.133 * [backup-simplify]: Simplify k into k 11.133 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.134 * [taylor]: Taking taylor expansion of 1 in n 11.134 * [backup-simplify]: Simplify 1 into 1 11.135 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.135 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 11.135 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 11.136 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 11.137 * [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))))) 11.138 * [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)))))) 11.139 * [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))))))) 11.140 * [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))))))) 11.140 * [backup-simplify]: Simplify 0 into 0 11.140 * [backup-simplify]: Simplify (- (/ 0 -1) (+ (* -1 (/ 0 -1)))) into 0 11.142 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.143 * [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)))))) 11.143 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 11.143 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 11.143 * [taylor]: Taking taylor expansion of +nan.0 in n 11.143 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.143 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 11.143 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 11.143 * [taylor]: Taking taylor expansion of 1/2 in n 11.143 * [backup-simplify]: Simplify 1/2 into 1/2 11.143 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 11.143 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.143 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.143 * [taylor]: Taking taylor expansion of -2 in n 11.143 * [backup-simplify]: Simplify -2 into -2 11.143 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.143 * [taylor]: Taking taylor expansion of PI in n 11.143 * [backup-simplify]: Simplify PI into PI 11.143 * [taylor]: Taking taylor expansion of n in n 11.143 * [backup-simplify]: Simplify 0 into 0 11.143 * [backup-simplify]: Simplify 1 into 1 11.144 * [backup-simplify]: Simplify (/ PI 1) into PI 11.144 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.145 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.145 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 11.145 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.145 * [taylor]: Taking taylor expansion of k in n 11.145 * [backup-simplify]: Simplify k into k 11.145 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.145 * [taylor]: Taking taylor expansion of 1 in n 11.145 * [backup-simplify]: Simplify 1 into 1 11.146 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.146 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 11.147 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 11.147 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 11.148 * [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))))) 11.149 * [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)))))) 11.150 * [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))))))) 11.150 * [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))))))) 11.151 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.151 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.152 * [backup-simplify]: Simplify (+ 0 0) into 0 11.152 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.153 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 11.154 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 11.156 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0 11.157 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0 11.159 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.161 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0 11.162 * [backup-simplify]: Simplify (- 0) into 0 11.162 * [backup-simplify]: Simplify 0 into 0 11.162 * [backup-simplify]: Simplify 0 into 0 11.163 * [backup-simplify]: Simplify (- (/ 0 -1) (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 11.167 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.168 * [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)))))) 11.169 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 11.169 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 11.169 * [taylor]: Taking taylor expansion of +nan.0 in n 11.169 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.169 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 11.169 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 11.169 * [taylor]: Taking taylor expansion of 1/2 in n 11.169 * [backup-simplify]: Simplify 1/2 into 1/2 11.169 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 11.169 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.169 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.169 * [taylor]: Taking taylor expansion of -2 in n 11.169 * [backup-simplify]: Simplify -2 into -2 11.169 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.169 * [taylor]: Taking taylor expansion of PI in n 11.169 * [backup-simplify]: Simplify PI into PI 11.169 * [taylor]: Taking taylor expansion of n in n 11.169 * [backup-simplify]: Simplify 0 into 0 11.169 * [backup-simplify]: Simplify 1 into 1 11.170 * [backup-simplify]: Simplify (/ PI 1) into PI 11.170 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.171 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.171 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 11.171 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.171 * [taylor]: Taking taylor expansion of k in n 11.171 * [backup-simplify]: Simplify k into k 11.171 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.171 * [taylor]: Taking taylor expansion of 1 in n 11.171 * [backup-simplify]: Simplify 1 into 1 11.173 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.173 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 11.174 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 11.175 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 11.183 * [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))))) 11.185 * [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)))))) 11.186 * [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))))))) 11.187 * [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))))))) 11.192 * [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))))))) 11.192 * * * [progress]: simplifying candidates 11.192 * * * * [progress]: [ 1 / 118 ] simplifiying candidate # 11.192 * * * * [progress]: [ 2 / 118 ] simplifiying candidate # 11.192 * * * * [progress]: [ 3 / 118 ] simplifiying candidate # 11.192 * * * * [progress]: [ 4 / 118 ] simplifiying candidate # 11.192 * * * * [progress]: [ 5 / 118 ] simplifiying candidate # 11.192 * * * * [progress]: [ 6 / 118 ] simplifiying candidate # 11.192 * * * * [progress]: [ 7 / 118 ] simplifiying candidate # 11.192 * * * * [progress]: [ 8 / 118 ] simplifiying candidate # 11.192 * * * * [progress]: [ 9 / 118 ] simplifiying candidate # 11.193 * * * * [progress]: [ 10 / 118 ] simplifiying candidate # 11.193 * * * * [progress]: [ 11 / 118 ] simplifiying candidate # 11.193 * * * * [progress]: [ 12 / 118 ] simplifiying candidate # 11.193 * * * * [progress]: [ 13 / 118 ] simplifiying candidate # 11.193 * * * * [progress]: [ 14 / 118 ] simplifiying candidate # 11.193 * * * * [progress]: [ 15 / 118 ] simplifiying candidate # 11.193 * * * * [progress]: [ 16 / 118 ] simplifiying candidate # 11.193 * * * * [progress]: [ 17 / 118 ] simplifiying candidate # 11.193 * * * * [progress]: [ 18 / 118 ] simplifiying candidate # 11.193 * * * * [progress]: [ 19 / 118 ] simplifiying candidate # 11.193 * * * * [progress]: [ 20 / 118 ] simplifiying candidate # 11.193 * * * * [progress]: [ 21 / 118 ] simplifiying candidate # 11.193 * * * * [progress]: [ 22 / 118 ] simplifiying candidate # 11.193 * * * * [progress]: [ 23 / 118 ] simplifiying candidate # 11.194 * * * * [progress]: [ 24 / 118 ] simplifiying candidate # 11.194 * * * * [progress]: [ 25 / 118 ] simplifiying candidate # 11.194 * * * * [progress]: [ 26 / 118 ] simplifiying candidate # 11.194 * * * * [progress]: [ 27 / 118 ] simplifiying candidate # 11.194 * * * * [progress]: [ 28 / 118 ] simplifiying candidate # 11.194 * * * * [progress]: [ 29 / 118 ] simplifiying candidate # 11.194 * * * * [progress]: [ 30 / 118 ] simplifiying candidate # 11.194 * * * * [progress]: [ 31 / 118 ] simplifiying candidate # 11.194 * * * * [progress]: [ 32 / 118 ] simplifiying candidate # 11.194 * * * * [progress]: [ 33 / 118 ] simplifiying candidate # 11.194 * * * * [progress]: [ 34 / 118 ] simplifiying candidate # 11.194 * * * * [progress]: [ 35 / 118 ] simplifiying candidate # 11.194 * * * * [progress]: [ 36 / 118 ] simplifiying candidate # 11.194 * * * * [progress]: [ 37 / 118 ] simplifiying candidate # 11.194 * * * * [progress]: [ 38 / 118 ] simplifiying candidate # 11.195 * * * * [progress]: [ 39 / 118 ] simplifiying candidate # 11.195 * * * * [progress]: [ 40 / 118 ] simplifiying candidate # 11.195 * * * * [progress]: [ 41 / 118 ] simplifiying candidate # 11.195 * * * * [progress]: [ 42 / 118 ] simplifiying candidate #real (real->posit16 (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))> 11.195 * * * * [progress]: [ 43 / 118 ] simplifiying candidate # 11.195 * * * * [progress]: [ 44 / 118 ] simplifiying candidate # 11.195 * * * * [progress]: [ 45 / 118 ] simplifiying candidate # 11.195 * * * * [progress]: [ 46 / 118 ] simplifiying candidate # 11.195 * * * * [progress]: [ 47 / 118 ] simplifiying candidate # 11.195 * * * * [progress]: [ 48 / 118 ] simplifiying candidate # 11.195 * * * * [progress]: [ 49 / 118 ] simplifiying candidate # 11.195 * * * * [progress]: [ 50 / 118 ] simplifiying candidate # 11.195 * * * * [progress]: [ 51 / 118 ] simplifiying candidate # 11.195 * * * * [progress]: [ 52 / 118 ] simplifiying candidate # 11.195 * * * * [progress]: [ 53 / 118 ] simplifiying candidate # 11.195 * * * * [progress]: [ 54 / 118 ] simplifiying candidate # 11.196 * * * * [progress]: [ 55 / 118 ] simplifiying candidate # 11.196 * * * * [progress]: [ 56 / 118 ] simplifiying candidate # 11.196 * * * * [progress]: [ 57 / 118 ] simplifiying candidate # 11.196 * * * * [progress]: [ 58 / 118 ] simplifiying candidate # 11.196 * * * * [progress]: [ 59 / 118 ] simplifiying candidate # 11.196 * * * * [progress]: [ 60 / 118 ] simplifiying candidate # 11.196 * * * * [progress]: [ 61 / 118 ] simplifiying candidate # 11.196 * * * * [progress]: [ 62 / 118 ] simplifiying candidate #real (real->posit16 (* (* 2 PI) n))) (/ (- 1 k) 2))))> 11.196 * * * * [progress]: [ 63 / 118 ] simplifiying candidate # 11.196 * * * * [progress]: [ 64 / 118 ] simplifiying candidate # 11.196 * * * * [progress]: [ 65 / 118 ] simplifiying candidate # 11.196 * * * * [progress]: [ 66 / 118 ] simplifiying candidate # 11.196 * * * * [progress]: [ 67 / 118 ] simplifiying candidate # 11.196 * * * * [progress]: [ 68 / 118 ] simplifiying candidate # 11.196 * * * * [progress]: [ 69 / 118 ] simplifiying candidate # 11.196 * * * * [progress]: [ 70 / 118 ] simplifiying candidate # 11.197 * * * * [progress]: [ 71 / 118 ] simplifiying candidate # 11.197 * * * * [progress]: [ 72 / 118 ] simplifiying candidate # 11.197 * * * * [progress]: [ 73 / 118 ] simplifiying candidate # 11.197 * * * * [progress]: [ 74 / 118 ] simplifiying candidate # 11.197 * * * * [progress]: [ 75 / 118 ] simplifiying candidate # 11.197 * * * * [progress]: [ 76 / 118 ] simplifiying candidate # 11.197 * * * * [progress]: [ 77 / 118 ] simplifiying candidate # 11.197 * * * * [progress]: [ 78 / 118 ] simplifiying candidate # 11.197 * * * * [progress]: [ 79 / 118 ] simplifiying candidate # 11.197 * * * * [progress]: [ 80 / 118 ] simplifiying candidate # 11.197 * * * * [progress]: [ 81 / 118 ] simplifiying candidate # 11.197 * * * * [progress]: [ 82 / 118 ] simplifiying candidate # 11.197 * * * * [progress]: [ 83 / 118 ] simplifiying candidate # 11.197 * * * * [progress]: [ 84 / 118 ] simplifiying candidate # 11.197 * * * * [progress]: [ 85 / 118 ] simplifiying candidate # 11.198 * * * * [progress]: [ 86 / 118 ] simplifiying candidate # 11.198 * * * * [progress]: [ 87 / 118 ] simplifiying candidate # 11.198 * * * * [progress]: [ 88 / 118 ] simplifiying candidate # 11.198 * * * * [progress]: [ 89 / 118 ] simplifiying candidate # 11.198 * * * * [progress]: [ 90 / 118 ] simplifiying candidate # 11.198 * * * * [progress]: [ 91 / 118 ] simplifiying candidate # 11.198 * * * * [progress]: [ 92 / 118 ] simplifiying candidate # 11.198 * * * * [progress]: [ 93 / 118 ] simplifiying candidate # 11.198 * * * * [progress]: [ 94 / 118 ] simplifiying candidate # 11.198 * * * * [progress]: [ 95 / 118 ] simplifiying candidate # 11.198 * * * * [progress]: [ 96 / 118 ] simplifiying candidate # 11.198 * * * * [progress]: [ 97 / 118 ] simplifiying candidate # 11.198 * * * * [progress]: [ 98 / 118 ] simplifiying candidate # 11.198 * * * * [progress]: [ 99 / 118 ] simplifiying candidate # 11.198 * * * * [progress]: [ 100 / 118 ] simplifiying candidate # 11.199 * * * * [progress]: [ 101 / 118 ] simplifiying candidate # 11.199 * * * * [progress]: [ 102 / 118 ] simplifiying candidate # 11.199 * * * * [progress]: [ 103 / 118 ] simplifiying candidate # 11.199 * * * * [progress]: [ 104 / 118 ] simplifiying candidate # 11.199 * * * * [progress]: [ 105 / 118 ] simplifiying candidate # 11.199 * * * * [progress]: [ 106 / 118 ] simplifiying candidate # 11.199 * * * * [progress]: [ 107 / 118 ] simplifiying candidate # 11.199 * * * * [progress]: [ 108 / 118 ] simplifiying candidate #real (real->posit16 (* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))> 11.199 * * * * [progress]: [ 109 / 118 ] simplifiying candidate # 11.199 * * * * [progress]: [ 110 / 118 ] simplifiying candidate # 11.199 * * * * [progress]: [ 111 / 118 ] simplifiying candidate # 11.199 * * * * [progress]: [ 112 / 118 ] simplifiying candidate # 11.199 * * * * [progress]: [ 113 / 118 ] simplifiying candidate # 11.199 * * * * [progress]: [ 114 / 118 ] simplifiying candidate # 11.199 * * * * [progress]: [ 115 / 118 ] simplifiying candidate # 11.199 * * * * [progress]: [ 116 / 118 ] simplifiying candidate # 11.200 * * * * [progress]: [ 117 / 118 ] simplifiying candidate # 11.200 * * * * [progress]: [ 118 / 118 ] simplifiying candidate # 11.202 * [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))))))) 11.206 * * [simplify]: iteration 0: 264 enodes 11.312 * * [simplify]: iteration 1: 732 enodes 11.510 * * [simplify]: iteration 2: 2000 enodes 11.980 * * [simplify]: iteration complete: 2000 enodes 11.980 * * [simplify]: Extracting #0: cost 79 inf + 0 11.981 * * [simplify]: Extracting #1: cost 360 inf + 0 11.985 * * [simplify]: Extracting #2: cost 709 inf + 2790 11.996 * * [simplify]: Extracting #3: cost 631 inf + 45138 12.012 * * [simplify]: Extracting #4: cost 406 inf + 156428 12.062 * * [simplify]: Extracting #5: cost 157 inf + 250754 12.126 * * [simplify]: Extracting #6: cost 37 inf + 309619 12.175 * * [simplify]: Extracting #7: cost 11 inf + 323599 12.222 * * [simplify]: Extracting #8: cost 0 inf + 330536 12.294 * * [simplify]: Extracting #9: cost 0 inf + 329726 12.354 * [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)))) 12.361 * * * [progress]: adding candidates to table 12.919 * * [progress]: iteration 4 / 4 12.919 * * * [progress]: picking best candidate 12.944 * * * * [pick]: Picked # 12.945 * * * [progress]: localizing error 12.970 * * * [progress]: generating rewritten candidates 12.970 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 13.005 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1) 13.033 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2) 13.059 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 13.200 * * * [progress]: generating series expansions 13.200 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 13.201 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 13.202 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 13.202 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 13.202 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 13.202 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 13.202 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 13.202 * [taylor]: Taking taylor expansion of 1/2 in k 13.202 * [backup-simplify]: Simplify 1/2 into 1/2 13.202 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 13.202 * [taylor]: Taking taylor expansion of 1/2 in k 13.202 * [backup-simplify]: Simplify 1/2 into 1/2 13.202 * [taylor]: Taking taylor expansion of k in k 13.202 * [backup-simplify]: Simplify 0 into 0 13.202 * [backup-simplify]: Simplify 1 into 1 13.202 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 13.202 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 13.202 * [taylor]: Taking taylor expansion of 2 in k 13.202 * [backup-simplify]: Simplify 2 into 2 13.202 * [taylor]: Taking taylor expansion of (* n PI) in k 13.202 * [taylor]: Taking taylor expansion of n in k 13.202 * [backup-simplify]: Simplify n into n 13.202 * [taylor]: Taking taylor expansion of PI in k 13.202 * [backup-simplify]: Simplify PI into PI 13.202 * [backup-simplify]: Simplify (* n PI) into (* n PI) 13.202 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 13.202 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 13.203 * [backup-simplify]: Simplify (* 1/2 0) into 0 13.203 * [backup-simplify]: Simplify (- 0) into 0 13.204 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.204 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 13.204 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 13.204 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 13.204 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 13.204 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 13.204 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 13.204 * [taylor]: Taking taylor expansion of 1/2 in n 13.204 * [backup-simplify]: Simplify 1/2 into 1/2 13.204 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 13.204 * [taylor]: Taking taylor expansion of 1/2 in n 13.204 * [backup-simplify]: Simplify 1/2 into 1/2 13.204 * [taylor]: Taking taylor expansion of k in n 13.204 * [backup-simplify]: Simplify k into k 13.204 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 13.204 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 13.204 * [taylor]: Taking taylor expansion of 2 in n 13.204 * [backup-simplify]: Simplify 2 into 2 13.204 * [taylor]: Taking taylor expansion of (* n PI) in n 13.204 * [taylor]: Taking taylor expansion of n in n 13.204 * [backup-simplify]: Simplify 0 into 0 13.204 * [backup-simplify]: Simplify 1 into 1 13.204 * [taylor]: Taking taylor expansion of PI in n 13.204 * [backup-simplify]: Simplify PI into PI 13.205 * [backup-simplify]: Simplify (* 0 PI) into 0 13.205 * [backup-simplify]: Simplify (* 2 0) into 0 13.207 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.209 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 13.210 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.210 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 13.210 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 13.210 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 13.211 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.211 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 13.212 * [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))))) 13.212 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 13.212 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 13.212 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 13.212 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 13.212 * [taylor]: Taking taylor expansion of 1/2 in n 13.212 * [backup-simplify]: Simplify 1/2 into 1/2 13.212 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 13.212 * [taylor]: Taking taylor expansion of 1/2 in n 13.212 * [backup-simplify]: Simplify 1/2 into 1/2 13.212 * [taylor]: Taking taylor expansion of k in n 13.212 * [backup-simplify]: Simplify k into k 13.212 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 13.212 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 13.212 * [taylor]: Taking taylor expansion of 2 in n 13.212 * [backup-simplify]: Simplify 2 into 2 13.212 * [taylor]: Taking taylor expansion of (* n PI) in n 13.212 * [taylor]: Taking taylor expansion of n in n 13.212 * [backup-simplify]: Simplify 0 into 0 13.212 * [backup-simplify]: Simplify 1 into 1 13.212 * [taylor]: Taking taylor expansion of PI in n 13.212 * [backup-simplify]: Simplify PI into PI 13.213 * [backup-simplify]: Simplify (* 0 PI) into 0 13.213 * [backup-simplify]: Simplify (* 2 0) into 0 13.214 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.215 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 13.216 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.216 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 13.216 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 13.216 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 13.217 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.217 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 13.218 * [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))))) 13.218 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 13.218 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 13.218 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 13.218 * [taylor]: Taking taylor expansion of 1/2 in k 13.218 * [backup-simplify]: Simplify 1/2 into 1/2 13.218 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 13.218 * [taylor]: Taking taylor expansion of 1/2 in k 13.218 * [backup-simplify]: Simplify 1/2 into 1/2 13.218 * [taylor]: Taking taylor expansion of k in k 13.218 * [backup-simplify]: Simplify 0 into 0 13.218 * [backup-simplify]: Simplify 1 into 1 13.218 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 13.218 * [taylor]: Taking taylor expansion of (log n) in k 13.218 * [taylor]: Taking taylor expansion of n in k 13.218 * [backup-simplify]: Simplify n into n 13.218 * [backup-simplify]: Simplify (log n) into (log n) 13.218 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 13.218 * [taylor]: Taking taylor expansion of (* 2 PI) in k 13.218 * [taylor]: Taking taylor expansion of 2 in k 13.218 * [backup-simplify]: Simplify 2 into 2 13.218 * [taylor]: Taking taylor expansion of PI in k 13.218 * [backup-simplify]: Simplify PI into PI 13.219 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.219 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.220 * [backup-simplify]: Simplify (* 1/2 0) into 0 13.220 * [backup-simplify]: Simplify (- 0) into 0 13.220 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.221 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.221 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 13.222 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 13.223 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 13.224 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.224 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 13.225 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 13.226 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 13.226 * [backup-simplify]: Simplify (- 0) into 0 13.226 * [backup-simplify]: Simplify (+ 0 0) into 0 13.227 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.228 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 13.229 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.229 * [taylor]: Taking taylor expansion of 0 in k 13.229 * [backup-simplify]: Simplify 0 into 0 13.229 * [backup-simplify]: Simplify 0 into 0 13.230 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 13.230 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 13.231 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 13.232 * [backup-simplify]: Simplify (+ 0 0) into 0 13.232 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 13.232 * [backup-simplify]: Simplify (- 1/2) into -1/2 13.233 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 13.234 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 13.236 * [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))))))) 13.237 * [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))))))) 13.239 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 13.240 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 13.243 * [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 13.244 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 13.244 * [backup-simplify]: Simplify (- 0) into 0 13.245 * [backup-simplify]: Simplify (+ 0 0) into 0 13.246 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.248 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 13.250 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.250 * [taylor]: Taking taylor expansion of 0 in k 13.250 * [backup-simplify]: Simplify 0 into 0 13.250 * [backup-simplify]: Simplify 0 into 0 13.250 * [backup-simplify]: Simplify 0 into 0 13.252 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 13.266 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 13.269 * [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 13.269 * [backup-simplify]: Simplify (+ 0 0) into 0 13.270 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 13.270 * [backup-simplify]: Simplify (- 0) into 0 13.270 * [backup-simplify]: Simplify (+ 0 0) into 0 13.272 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 13.274 * [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))))) 13.280 * [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))))) 13.287 * [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))))) 13.288 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 13.288 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 13.288 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 13.288 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 13.288 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 13.288 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 13.288 * [taylor]: Taking taylor expansion of 1/2 in k 13.288 * [backup-simplify]: Simplify 1/2 into 1/2 13.288 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 13.288 * [taylor]: Taking taylor expansion of 1/2 in k 13.288 * [backup-simplify]: Simplify 1/2 into 1/2 13.288 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.288 * [taylor]: Taking taylor expansion of k in k 13.288 * [backup-simplify]: Simplify 0 into 0 13.288 * [backup-simplify]: Simplify 1 into 1 13.289 * [backup-simplify]: Simplify (/ 1 1) into 1 13.289 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 13.289 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 13.289 * [taylor]: Taking taylor expansion of 2 in k 13.289 * [backup-simplify]: Simplify 2 into 2 13.289 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.289 * [taylor]: Taking taylor expansion of PI in k 13.289 * [backup-simplify]: Simplify PI into PI 13.289 * [taylor]: Taking taylor expansion of n in k 13.289 * [backup-simplify]: Simplify n into n 13.289 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.289 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 13.289 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 13.290 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 13.290 * [backup-simplify]: Simplify (- 1/2) into -1/2 13.290 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 13.291 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 13.291 * [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)))) 13.291 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 13.291 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 13.291 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 13.291 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 13.291 * [taylor]: Taking taylor expansion of 1/2 in n 13.291 * [backup-simplify]: Simplify 1/2 into 1/2 13.291 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.291 * [taylor]: Taking taylor expansion of 1/2 in n 13.291 * [backup-simplify]: Simplify 1/2 into 1/2 13.291 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.291 * [taylor]: Taking taylor expansion of k in n 13.291 * [backup-simplify]: Simplify k into k 13.291 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.291 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 13.291 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 13.291 * [taylor]: Taking taylor expansion of 2 in n 13.291 * [backup-simplify]: Simplify 2 into 2 13.291 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.291 * [taylor]: Taking taylor expansion of PI in n 13.291 * [backup-simplify]: Simplify PI into PI 13.291 * [taylor]: Taking taylor expansion of n in n 13.291 * [backup-simplify]: Simplify 0 into 0 13.291 * [backup-simplify]: Simplify 1 into 1 13.292 * [backup-simplify]: Simplify (/ PI 1) into PI 13.292 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.293 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.294 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.294 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 13.294 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 13.295 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.296 * [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))) 13.298 * [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)))) 13.298 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 13.298 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 13.298 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 13.298 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 13.298 * [taylor]: Taking taylor expansion of 1/2 in n 13.298 * [backup-simplify]: Simplify 1/2 into 1/2 13.298 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.298 * [taylor]: Taking taylor expansion of 1/2 in n 13.298 * [backup-simplify]: Simplify 1/2 into 1/2 13.298 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.298 * [taylor]: Taking taylor expansion of k in n 13.298 * [backup-simplify]: Simplify k into k 13.298 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.298 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 13.298 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 13.298 * [taylor]: Taking taylor expansion of 2 in n 13.298 * [backup-simplify]: Simplify 2 into 2 13.298 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.298 * [taylor]: Taking taylor expansion of PI in n 13.298 * [backup-simplify]: Simplify PI into PI 13.298 * [taylor]: Taking taylor expansion of n in n 13.298 * [backup-simplify]: Simplify 0 into 0 13.298 * [backup-simplify]: Simplify 1 into 1 13.299 * [backup-simplify]: Simplify (/ PI 1) into PI 13.299 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.300 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.300 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.301 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 13.301 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 13.302 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.303 * [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))) 13.305 * [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)))) 13.305 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 13.305 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 13.305 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 13.305 * [taylor]: Taking taylor expansion of 1/2 in k 13.305 * [backup-simplify]: Simplify 1/2 into 1/2 13.305 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 13.305 * [taylor]: Taking taylor expansion of 1/2 in k 13.305 * [backup-simplify]: Simplify 1/2 into 1/2 13.305 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.305 * [taylor]: Taking taylor expansion of k in k 13.305 * [backup-simplify]: Simplify 0 into 0 13.305 * [backup-simplify]: Simplify 1 into 1 13.305 * [backup-simplify]: Simplify (/ 1 1) into 1 13.305 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 13.305 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 13.305 * [taylor]: Taking taylor expansion of (* 2 PI) in k 13.306 * [taylor]: Taking taylor expansion of 2 in k 13.306 * [backup-simplify]: Simplify 2 into 2 13.306 * [taylor]: Taking taylor expansion of PI in k 13.306 * [backup-simplify]: Simplify PI into PI 13.306 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.307 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.307 * [taylor]: Taking taylor expansion of (log n) in k 13.307 * [taylor]: Taking taylor expansion of n in k 13.307 * [backup-simplify]: Simplify n into n 13.307 * [backup-simplify]: Simplify (log n) into (log n) 13.308 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 13.308 * [backup-simplify]: Simplify (- 1/2) into -1/2 13.309 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 13.309 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.310 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 13.311 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 13.312 * [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)))) 13.313 * [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)))) 13.314 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.315 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 13.317 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 13.317 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.318 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 13.318 * [backup-simplify]: Simplify (- 0) into 0 13.318 * [backup-simplify]: Simplify (+ 0 0) into 0 13.320 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.321 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 13.323 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 13.323 * [taylor]: Taking taylor expansion of 0 in k 13.323 * [backup-simplify]: Simplify 0 into 0 13.323 * [backup-simplify]: Simplify 0 into 0 13.323 * [backup-simplify]: Simplify 0 into 0 13.325 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.326 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 13.329 * [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 13.330 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.331 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 13.331 * [backup-simplify]: Simplify (- 0) into 0 13.331 * [backup-simplify]: Simplify (+ 0 0) into 0 13.333 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.334 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 13.337 * [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 13.337 * [taylor]: Taking taylor expansion of 0 in k 13.337 * [backup-simplify]: Simplify 0 into 0 13.337 * [backup-simplify]: Simplify 0 into 0 13.337 * [backup-simplify]: Simplify 0 into 0 13.337 * [backup-simplify]: Simplify 0 into 0 13.338 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.340 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.346 * [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 13.346 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.347 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 13.348 * [backup-simplify]: Simplify (- 0) into 0 13.348 * [backup-simplify]: Simplify (+ 0 0) into 0 13.350 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.352 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 13.354 * [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 13.354 * [taylor]: Taking taylor expansion of 0 in k 13.355 * [backup-simplify]: Simplify 0 into 0 13.355 * [backup-simplify]: Simplify 0 into 0 13.356 * [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))))) 13.357 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 13.357 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 13.357 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 13.357 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 13.357 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 13.357 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 13.357 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 13.357 * [taylor]: Taking taylor expansion of 1/2 in k 13.357 * [backup-simplify]: Simplify 1/2 into 1/2 13.357 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.357 * [taylor]: Taking taylor expansion of k in k 13.357 * [backup-simplify]: Simplify 0 into 0 13.357 * [backup-simplify]: Simplify 1 into 1 13.357 * [backup-simplify]: Simplify (/ 1 1) into 1 13.357 * [taylor]: Taking taylor expansion of 1/2 in k 13.357 * [backup-simplify]: Simplify 1/2 into 1/2 13.357 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 13.357 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 13.357 * [taylor]: Taking taylor expansion of -2 in k 13.358 * [backup-simplify]: Simplify -2 into -2 13.358 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.358 * [taylor]: Taking taylor expansion of PI in k 13.358 * [backup-simplify]: Simplify PI into PI 13.358 * [taylor]: Taking taylor expansion of n in k 13.358 * [backup-simplify]: Simplify n into n 13.358 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.358 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 13.358 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 13.358 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 13.359 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.359 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 13.359 * [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))) 13.359 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 13.359 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 13.359 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 13.359 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 13.359 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.359 * [taylor]: Taking taylor expansion of 1/2 in n 13.359 * [backup-simplify]: Simplify 1/2 into 1/2 13.359 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.359 * [taylor]: Taking taylor expansion of k in n 13.359 * [backup-simplify]: Simplify k into k 13.360 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.360 * [taylor]: Taking taylor expansion of 1/2 in n 13.360 * [backup-simplify]: Simplify 1/2 into 1/2 13.360 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 13.360 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 13.360 * [taylor]: Taking taylor expansion of -2 in n 13.360 * [backup-simplify]: Simplify -2 into -2 13.360 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.360 * [taylor]: Taking taylor expansion of PI in n 13.360 * [backup-simplify]: Simplify PI into PI 13.360 * [taylor]: Taking taylor expansion of n in n 13.360 * [backup-simplify]: Simplify 0 into 0 13.360 * [backup-simplify]: Simplify 1 into 1 13.360 * [backup-simplify]: Simplify (/ PI 1) into PI 13.361 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 13.362 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 13.362 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.362 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 13.364 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.365 * [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))) 13.366 * [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)))) 13.366 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 13.366 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 13.366 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 13.367 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 13.367 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.367 * [taylor]: Taking taylor expansion of 1/2 in n 13.367 * [backup-simplify]: Simplify 1/2 into 1/2 13.367 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.367 * [taylor]: Taking taylor expansion of k in n 13.367 * [backup-simplify]: Simplify k into k 13.367 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.367 * [taylor]: Taking taylor expansion of 1/2 in n 13.367 * [backup-simplify]: Simplify 1/2 into 1/2 13.367 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 13.367 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 13.367 * [taylor]: Taking taylor expansion of -2 in n 13.367 * [backup-simplify]: Simplify -2 into -2 13.367 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.367 * [taylor]: Taking taylor expansion of PI in n 13.367 * [backup-simplify]: Simplify PI into PI 13.367 * [taylor]: Taking taylor expansion of n in n 13.367 * [backup-simplify]: Simplify 0 into 0 13.367 * [backup-simplify]: Simplify 1 into 1 13.368 * [backup-simplify]: Simplify (/ PI 1) into PI 13.368 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 13.369 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 13.370 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.370 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 13.372 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.373 * [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))) 13.374 * [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)))) 13.374 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 13.374 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 13.374 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 13.374 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 13.374 * [taylor]: Taking taylor expansion of 1/2 in k 13.374 * [backup-simplify]: Simplify 1/2 into 1/2 13.374 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.374 * [taylor]: Taking taylor expansion of k in k 13.374 * [backup-simplify]: Simplify 0 into 0 13.374 * [backup-simplify]: Simplify 1 into 1 13.375 * [backup-simplify]: Simplify (/ 1 1) into 1 13.375 * [taylor]: Taking taylor expansion of 1/2 in k 13.375 * [backup-simplify]: Simplify 1/2 into 1/2 13.375 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 13.375 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 13.375 * [taylor]: Taking taylor expansion of (* -2 PI) in k 13.375 * [taylor]: Taking taylor expansion of -2 in k 13.375 * [backup-simplify]: Simplify -2 into -2 13.375 * [taylor]: Taking taylor expansion of PI in k 13.375 * [backup-simplify]: Simplify PI into PI 13.375 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 13.376 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 13.376 * [taylor]: Taking taylor expansion of (log n) in k 13.377 * [taylor]: Taking taylor expansion of n in k 13.377 * [backup-simplify]: Simplify n into n 13.377 * [backup-simplify]: Simplify (log n) into (log n) 13.377 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 13.378 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.378 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.379 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 13.380 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 13.381 * [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)))) 13.382 * [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)))) 13.383 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.384 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 13.386 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 13.386 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.387 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 13.387 * [backup-simplify]: Simplify (+ 0 0) into 0 13.389 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.390 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 13.391 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 13.391 * [taylor]: Taking taylor expansion of 0 in k 13.391 * [backup-simplify]: Simplify 0 into 0 13.391 * [backup-simplify]: Simplify 0 into 0 13.391 * [backup-simplify]: Simplify 0 into 0 13.392 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.392 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 13.394 * [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 13.394 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.395 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 13.395 * [backup-simplify]: Simplify (+ 0 0) into 0 13.396 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.397 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 13.403 * [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 13.403 * [taylor]: Taking taylor expansion of 0 in k 13.403 * [backup-simplify]: Simplify 0 into 0 13.403 * [backup-simplify]: Simplify 0 into 0 13.403 * [backup-simplify]: Simplify 0 into 0 13.403 * [backup-simplify]: Simplify 0 into 0 13.404 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.405 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.408 * [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 13.408 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.409 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 13.409 * [backup-simplify]: Simplify (+ 0 0) into 0 13.410 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.412 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 13.413 * [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 13.413 * [taylor]: Taking taylor expansion of 0 in k 13.413 * [backup-simplify]: Simplify 0 into 0 13.413 * [backup-simplify]: Simplify 0 into 0 13.414 * [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))))) 13.414 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1) 13.415 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) 13.415 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 13.415 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 13.415 * [taylor]: Taking taylor expansion of 2 in n 13.415 * [backup-simplify]: Simplify 2 into 2 13.415 * [taylor]: Taking taylor expansion of (* n PI) in n 13.415 * [taylor]: Taking taylor expansion of n in n 13.415 * [backup-simplify]: Simplify 0 into 0 13.415 * [backup-simplify]: Simplify 1 into 1 13.415 * [taylor]: Taking taylor expansion of PI in n 13.415 * [backup-simplify]: Simplify PI into PI 13.415 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 13.415 * [taylor]: Taking taylor expansion of 2 in n 13.415 * [backup-simplify]: Simplify 2 into 2 13.415 * [taylor]: Taking taylor expansion of (* n PI) in n 13.415 * [taylor]: Taking taylor expansion of n in n 13.415 * [backup-simplify]: Simplify 0 into 0 13.415 * [backup-simplify]: Simplify 1 into 1 13.415 * [taylor]: Taking taylor expansion of PI in n 13.415 * [backup-simplify]: Simplify PI into PI 13.415 * [backup-simplify]: Simplify (* 0 PI) into 0 13.415 * [backup-simplify]: Simplify (* 2 0) into 0 13.415 * [backup-simplify]: Simplify 0 into 0 13.416 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.417 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 13.418 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.418 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.419 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 13.419 * [backup-simplify]: Simplify 0 into 0 13.420 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 13.420 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 13.420 * [backup-simplify]: Simplify 0 into 0 13.421 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.422 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 13.422 * [backup-simplify]: Simplify 0 into 0 13.423 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.424 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 13.424 * [backup-simplify]: Simplify 0 into 0 13.425 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.426 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 13.426 * [backup-simplify]: Simplify 0 into 0 13.427 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 13.428 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 13.428 * [backup-simplify]: Simplify 0 into 0 13.428 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 13.429 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) 13.429 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 13.429 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 13.429 * [taylor]: Taking taylor expansion of 2 in n 13.429 * [backup-simplify]: Simplify 2 into 2 13.429 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.429 * [taylor]: Taking taylor expansion of PI in n 13.429 * [backup-simplify]: Simplify PI into PI 13.429 * [taylor]: Taking taylor expansion of n in n 13.429 * [backup-simplify]: Simplify 0 into 0 13.429 * [backup-simplify]: Simplify 1 into 1 13.429 * [backup-simplify]: Simplify (/ PI 1) into PI 13.429 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 13.429 * [taylor]: Taking taylor expansion of 2 in n 13.429 * [backup-simplify]: Simplify 2 into 2 13.429 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.429 * [taylor]: Taking taylor expansion of PI in n 13.429 * [backup-simplify]: Simplify PI into PI 13.429 * [taylor]: Taking taylor expansion of n in n 13.429 * [backup-simplify]: Simplify 0 into 0 13.429 * [backup-simplify]: Simplify 1 into 1 13.430 * [backup-simplify]: Simplify (/ PI 1) into PI 13.430 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.430 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.431 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.431 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 13.431 * [backup-simplify]: Simplify 0 into 0 13.432 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.433 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 13.433 * [backup-simplify]: Simplify 0 into 0 13.433 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.434 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.434 * [backup-simplify]: Simplify 0 into 0 13.435 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.435 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.435 * [backup-simplify]: Simplify 0 into 0 13.436 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.437 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.437 * [backup-simplify]: Simplify 0 into 0 13.438 * [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 13.439 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.439 * [backup-simplify]: Simplify 0 into 0 13.439 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 13.440 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n)) 13.440 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 13.440 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 13.440 * [taylor]: Taking taylor expansion of -2 in n 13.440 * [backup-simplify]: Simplify -2 into -2 13.440 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.440 * [taylor]: Taking taylor expansion of PI in n 13.440 * [backup-simplify]: Simplify PI into PI 13.440 * [taylor]: Taking taylor expansion of n in n 13.440 * [backup-simplify]: Simplify 0 into 0 13.440 * [backup-simplify]: Simplify 1 into 1 13.440 * [backup-simplify]: Simplify (/ PI 1) into PI 13.440 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 13.440 * [taylor]: Taking taylor expansion of -2 in n 13.440 * [backup-simplify]: Simplify -2 into -2 13.440 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.440 * [taylor]: Taking taylor expansion of PI in n 13.440 * [backup-simplify]: Simplify PI into PI 13.440 * [taylor]: Taking taylor expansion of n in n 13.440 * [backup-simplify]: Simplify 0 into 0 13.440 * [backup-simplify]: Simplify 1 into 1 13.441 * [backup-simplify]: Simplify (/ PI 1) into PI 13.441 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 13.441 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 13.442 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.443 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 13.443 * [backup-simplify]: Simplify 0 into 0 13.444 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.445 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 13.445 * [backup-simplify]: Simplify 0 into 0 13.446 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.447 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.447 * [backup-simplify]: Simplify 0 into 0 13.449 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.450 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.450 * [backup-simplify]: Simplify 0 into 0 13.451 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.453 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.453 * [backup-simplify]: Simplify 0 into 0 13.454 * [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 13.456 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.456 * [backup-simplify]: Simplify 0 into 0 13.457 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 13.457 * * * * [progress]: [ 3 / 4 ] generating series at (2 2) 13.458 * [backup-simplify]: Simplify (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) into (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) 13.458 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in (k n) around 0 13.458 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in n 13.458 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 13.458 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 13.458 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 13.458 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 13.458 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 13.458 * [taylor]: Taking taylor expansion of 1/2 in n 13.458 * [backup-simplify]: Simplify 1/2 into 1/2 13.458 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 13.458 * [taylor]: Taking taylor expansion of 1/2 in n 13.458 * [backup-simplify]: Simplify 1/2 into 1/2 13.458 * [taylor]: Taking taylor expansion of k in n 13.458 * [backup-simplify]: Simplify k into k 13.458 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 13.458 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 13.458 * [taylor]: Taking taylor expansion of 2 in n 13.458 * [backup-simplify]: Simplify 2 into 2 13.458 * [taylor]: Taking taylor expansion of (* n PI) in n 13.458 * [taylor]: Taking taylor expansion of n in n 13.458 * [backup-simplify]: Simplify 0 into 0 13.458 * [backup-simplify]: Simplify 1 into 1 13.458 * [taylor]: Taking taylor expansion of PI in n 13.458 * [backup-simplify]: Simplify PI into PI 13.459 * [backup-simplify]: Simplify (* 0 PI) into 0 13.459 * [backup-simplify]: Simplify (* 2 0) into 0 13.460 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.462 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 13.463 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.463 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 13.463 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 13.463 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 13.464 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.465 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 13.466 * [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))))) 13.467 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 13.467 * [taylor]: Taking taylor expansion of (sqrt k) in n 13.467 * [taylor]: Taking taylor expansion of k in n 13.467 * [backup-simplify]: Simplify k into k 13.467 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 13.467 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 13.467 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 13.467 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 13.468 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 13.468 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 13.468 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 13.468 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 13.468 * [taylor]: Taking taylor expansion of 1/2 in k 13.468 * [backup-simplify]: Simplify 1/2 into 1/2 13.468 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 13.468 * [taylor]: Taking taylor expansion of 1/2 in k 13.468 * [backup-simplify]: Simplify 1/2 into 1/2 13.468 * [taylor]: Taking taylor expansion of k in k 13.468 * [backup-simplify]: Simplify 0 into 0 13.468 * [backup-simplify]: Simplify 1 into 1 13.468 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 13.468 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 13.468 * [taylor]: Taking taylor expansion of 2 in k 13.468 * [backup-simplify]: Simplify 2 into 2 13.468 * [taylor]: Taking taylor expansion of (* n PI) in k 13.468 * [taylor]: Taking taylor expansion of n in k 13.468 * [backup-simplify]: Simplify n into n 13.468 * [taylor]: Taking taylor expansion of PI in k 13.468 * [backup-simplify]: Simplify PI into PI 13.468 * [backup-simplify]: Simplify (* n PI) into (* n PI) 13.468 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 13.468 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 13.469 * [backup-simplify]: Simplify (* 1/2 0) into 0 13.469 * [backup-simplify]: Simplify (- 0) into 0 13.469 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.469 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 13.469 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 13.470 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 13.470 * [taylor]: Taking taylor expansion of (sqrt k) in k 13.470 * [taylor]: Taking taylor expansion of k in k 13.470 * [backup-simplify]: Simplify 0 into 0 13.470 * [backup-simplify]: Simplify 1 into 1 13.470 * [backup-simplify]: Simplify (sqrt 0) into 0 13.471 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.471 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 13.471 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 13.471 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 13.471 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 13.471 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 13.471 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 13.472 * [taylor]: Taking taylor expansion of 1/2 in k 13.472 * [backup-simplify]: Simplify 1/2 into 1/2 13.472 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 13.472 * [taylor]: Taking taylor expansion of 1/2 in k 13.472 * [backup-simplify]: Simplify 1/2 into 1/2 13.472 * [taylor]: Taking taylor expansion of k in k 13.472 * [backup-simplify]: Simplify 0 into 0 13.472 * [backup-simplify]: Simplify 1 into 1 13.472 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 13.472 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 13.472 * [taylor]: Taking taylor expansion of 2 in k 13.472 * [backup-simplify]: Simplify 2 into 2 13.472 * [taylor]: Taking taylor expansion of (* n PI) in k 13.472 * [taylor]: Taking taylor expansion of n in k 13.472 * [backup-simplify]: Simplify n into n 13.472 * [taylor]: Taking taylor expansion of PI in k 13.472 * [backup-simplify]: Simplify PI into PI 13.472 * [backup-simplify]: Simplify (* n PI) into (* n PI) 13.472 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 13.472 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 13.473 * [backup-simplify]: Simplify (* 1/2 0) into 0 13.473 * [backup-simplify]: Simplify (- 0) into 0 13.473 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.473 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 13.474 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 13.474 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 13.474 * [taylor]: Taking taylor expansion of (sqrt k) in k 13.474 * [taylor]: Taking taylor expansion of k in k 13.474 * [backup-simplify]: Simplify 0 into 0 13.474 * [backup-simplify]: Simplify 1 into 1 13.474 * [backup-simplify]: Simplify (sqrt 0) into 0 13.475 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.476 * [backup-simplify]: Simplify (* (sqrt (/ 1 (* PI (* n 2)))) 0) into 0 13.476 * [taylor]: Taking taylor expansion of 0 in n 13.476 * [backup-simplify]: Simplify 0 into 0 13.476 * [backup-simplify]: Simplify 0 into 0 13.476 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 13.477 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 13.477 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 13.478 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 13.478 * [backup-simplify]: Simplify (- 1/2) into -1/2 13.479 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 13.479 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 13.480 * [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))))) 13.480 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 13.482 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) 13.482 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 13.482 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 13.482 * [taylor]: Taking taylor expansion of +nan.0 in n 13.482 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.482 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 13.482 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 13.482 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 13.482 * [taylor]: Taking taylor expansion of (* n PI) in n 13.482 * [taylor]: Taking taylor expansion of n in n 13.482 * [backup-simplify]: Simplify 0 into 0 13.482 * [backup-simplify]: Simplify 1 into 1 13.482 * [taylor]: Taking taylor expansion of PI in n 13.482 * [backup-simplify]: Simplify PI into PI 13.482 * [backup-simplify]: Simplify (* 0 PI) into 0 13.484 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.484 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 13.484 * [backup-simplify]: Simplify (sqrt 0) into 0 13.487 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 13.487 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 13.487 * [taylor]: Taking taylor expansion of 1/2 in n 13.487 * [backup-simplify]: Simplify 1/2 into 1/2 13.487 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 13.488 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 13.491 * [backup-simplify]: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 13.492 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0 13.497 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 13.500 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 13.502 * [backup-simplify]: Simplify (- (* +nan.0 (/ (sqrt 1/2) PI))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 13.502 * [backup-simplify]: Simplify 0 into 0 13.505 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.506 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 13.507 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 13.508 * [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 13.509 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 13.509 * [backup-simplify]: Simplify (- 0) into 0 13.510 * [backup-simplify]: Simplify (+ 0 0) into 0 13.510 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 13.511 * [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))) 13.514 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) (pow (* 2 (* n PI)) 1/2))) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 13.526 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (+ (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) +nan.0) (* (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) 13.526 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) in n 13.526 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))) in n 13.526 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) in n 13.526 * [taylor]: Taking taylor expansion of +nan.0 in n 13.526 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.526 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))) in n 13.526 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) in n 13.526 * [taylor]: Taking taylor expansion of (sqrt 2) in n 13.526 * [taylor]: Taking taylor expansion of 2 in n 13.526 * [backup-simplify]: Simplify 2 into 2 13.526 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 13.527 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 13.527 * [taylor]: Taking taylor expansion of (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2)) in n 13.527 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 13.527 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 13.527 * [taylor]: Taking taylor expansion of 2 in n 13.527 * [backup-simplify]: Simplify 2 into 2 13.527 * [taylor]: Taking taylor expansion of (* n PI) in n 13.527 * [taylor]: Taking taylor expansion of n in n 13.527 * [backup-simplify]: Simplify 0 into 0 13.527 * [backup-simplify]: Simplify 1 into 1 13.527 * [taylor]: Taking taylor expansion of PI in n 13.527 * [backup-simplify]: Simplify PI into PI 13.528 * [backup-simplify]: Simplify (* 0 PI) into 0 13.528 * [backup-simplify]: Simplify (* 2 0) into 0 13.529 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.531 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 13.532 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.532 * [taylor]: Taking taylor expansion of (pow (sqrt 1/2) 2) in n 13.532 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 13.532 * [taylor]: Taking taylor expansion of 1/2 in n 13.532 * [backup-simplify]: Simplify 1/2 into 1/2 13.532 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 13.533 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 13.533 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 13.533 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 13.533 * [taylor]: Taking taylor expansion of (* n PI) in n 13.533 * [taylor]: Taking taylor expansion of n in n 13.533 * [backup-simplify]: Simplify 0 into 0 13.533 * [backup-simplify]: Simplify 1 into 1 13.533 * [taylor]: Taking taylor expansion of PI in n 13.533 * [backup-simplify]: Simplify PI into PI 13.533 * [backup-simplify]: Simplify (* 0 PI) into 0 13.535 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.535 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 13.536 * [backup-simplify]: Simplify (sqrt 0) into 0 13.539 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 13.539 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 13.539 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 13.539 * [taylor]: Taking taylor expansion of +nan.0 in n 13.539 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.539 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 13.539 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 13.539 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 13.539 * [taylor]: Taking taylor expansion of (* n PI) in n 13.539 * [taylor]: Taking taylor expansion of n in n 13.539 * [backup-simplify]: Simplify 0 into 0 13.539 * [backup-simplify]: Simplify 1 into 1 13.539 * [taylor]: Taking taylor expansion of PI in n 13.539 * [backup-simplify]: Simplify PI into PI 13.540 * [backup-simplify]: Simplify (* 0 PI) into 0 13.541 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.542 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 13.542 * [backup-simplify]: Simplify (sqrt 0) into 0 13.544 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 13.544 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 13.544 * [taylor]: Taking taylor expansion of 1/2 in n 13.544 * [backup-simplify]: Simplify 1/2 into 1/2 13.545 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 13.546 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 13.547 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.548 * [backup-simplify]: Simplify (* (sqrt 1/2) (sqrt 1/2)) into (pow (sqrt 1/2) 2) 13.550 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (pow (sqrt 1/2) 2)) into (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))) 13.552 * [backup-simplify]: Simplify (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) into (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 13.553 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.554 * [backup-simplify]: Simplify (+ (* (sqrt 1/2) 0) (* 0 (sqrt 1/2))) into 0 13.555 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.556 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 13.557 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 13.559 * [backup-simplify]: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (* 0 (pow (sqrt 1/2) 2))) into 0 13.561 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))))) into 0 13.564 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) (/ +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 13.566 * [backup-simplify]: Simplify (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 0) into 0 13.578 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 13.581 * [backup-simplify]: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 13.581 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0 13.585 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 13.588 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 13.596 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 13.608 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 13.619 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 13.619 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1/2))) into 0 13.620 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.621 * [backup-simplify]: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)))) into 0 13.623 * [backup-simplify]: Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2)) 13.632 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* (/ +nan.0 PI) 0) (* (/ +nan.0 (pow PI 2)) (sqrt 1/2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 13.638 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 13.641 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 13.643 * [backup-simplify]: Simplify (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 13.659 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) (* n k)) (+ (* (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (/ (sqrt 1/2) PI))) (* 1 k)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) 13.660 * [backup-simplify]: Simplify (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2)))) into (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) 13.660 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in (k n) around 0 13.660 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in n 13.660 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 13.660 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 13.660 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 13.660 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 13.660 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 13.660 * [taylor]: Taking taylor expansion of 1/2 in n 13.660 * [backup-simplify]: Simplify 1/2 into 1/2 13.660 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.660 * [taylor]: Taking taylor expansion of 1/2 in n 13.660 * [backup-simplify]: Simplify 1/2 into 1/2 13.660 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.660 * [taylor]: Taking taylor expansion of k in n 13.660 * [backup-simplify]: Simplify k into k 13.660 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.660 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 13.660 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 13.660 * [taylor]: Taking taylor expansion of 2 in n 13.660 * [backup-simplify]: Simplify 2 into 2 13.660 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.660 * [taylor]: Taking taylor expansion of PI in n 13.660 * [backup-simplify]: Simplify PI into PI 13.660 * [taylor]: Taking taylor expansion of n in n 13.660 * [backup-simplify]: Simplify 0 into 0 13.660 * [backup-simplify]: Simplify 1 into 1 13.661 * [backup-simplify]: Simplify (/ PI 1) into PI 13.661 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.662 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.662 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.662 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 13.662 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 13.663 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.664 * [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))) 13.665 * [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)))) 13.665 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 13.665 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 13.665 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.665 * [taylor]: Taking taylor expansion of k in n 13.665 * [backup-simplify]: Simplify k into k 13.666 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.666 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 13.666 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.666 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 13.666 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 13.666 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 13.666 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 13.666 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 13.666 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 13.666 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 13.666 * [taylor]: Taking taylor expansion of 1/2 in k 13.666 * [backup-simplify]: Simplify 1/2 into 1/2 13.666 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 13.666 * [taylor]: Taking taylor expansion of 1/2 in k 13.666 * [backup-simplify]: Simplify 1/2 into 1/2 13.666 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.666 * [taylor]: Taking taylor expansion of k in k 13.666 * [backup-simplify]: Simplify 0 into 0 13.666 * [backup-simplify]: Simplify 1 into 1 13.666 * [backup-simplify]: Simplify (/ 1 1) into 1 13.666 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 13.666 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 13.666 * [taylor]: Taking taylor expansion of 2 in k 13.666 * [backup-simplify]: Simplify 2 into 2 13.666 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.666 * [taylor]: Taking taylor expansion of PI in k 13.666 * [backup-simplify]: Simplify PI into PI 13.666 * [taylor]: Taking taylor expansion of n in k 13.666 * [backup-simplify]: Simplify n into n 13.666 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.666 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 13.667 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 13.667 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 13.667 * [backup-simplify]: Simplify (- 1/2) into -1/2 13.667 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 13.667 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 13.668 * [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)))) 13.668 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 13.668 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 13.668 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.668 * [taylor]: Taking taylor expansion of k in k 13.668 * [backup-simplify]: Simplify 0 into 0 13.668 * [backup-simplify]: Simplify 1 into 1 13.668 * [backup-simplify]: Simplify (/ 1 1) into 1 13.668 * [backup-simplify]: Simplify (sqrt 0) into 0 13.669 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.669 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 13.669 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 13.669 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 13.669 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 13.669 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 13.669 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 13.669 * [taylor]: Taking taylor expansion of 1/2 in k 13.669 * [backup-simplify]: Simplify 1/2 into 1/2 13.669 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 13.669 * [taylor]: Taking taylor expansion of 1/2 in k 13.669 * [backup-simplify]: Simplify 1/2 into 1/2 13.669 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.669 * [taylor]: Taking taylor expansion of k in k 13.669 * [backup-simplify]: Simplify 0 into 0 13.669 * [backup-simplify]: Simplify 1 into 1 13.670 * [backup-simplify]: Simplify (/ 1 1) into 1 13.670 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 13.670 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 13.670 * [taylor]: Taking taylor expansion of 2 in k 13.670 * [backup-simplify]: Simplify 2 into 2 13.670 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.670 * [taylor]: Taking taylor expansion of PI in k 13.670 * [backup-simplify]: Simplify PI into PI 13.670 * [taylor]: Taking taylor expansion of n in k 13.670 * [backup-simplify]: Simplify n into n 13.670 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.670 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 13.670 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 13.670 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 13.670 * [backup-simplify]: Simplify (- 1/2) into -1/2 13.671 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 13.671 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 13.671 * [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)))) 13.671 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 13.671 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 13.671 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.671 * [taylor]: Taking taylor expansion of k in k 13.671 * [backup-simplify]: Simplify 0 into 0 13.671 * [backup-simplify]: Simplify 1 into 1 13.671 * [backup-simplify]: Simplify (/ 1 1) into 1 13.671 * [backup-simplify]: Simplify (sqrt 0) into 0 13.672 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.672 * [backup-simplify]: Simplify (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 13.672 * [taylor]: Taking taylor expansion of 0 in n 13.672 * [backup-simplify]: Simplify 0 into 0 13.672 * [backup-simplify]: Simplify 0 into 0 13.673 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 13.673 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 13.673 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 13.673 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 13.673 * [taylor]: Taking taylor expansion of +nan.0 in n 13.673 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.673 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 13.673 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 13.673 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 13.673 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 13.673 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 13.673 * [taylor]: Taking taylor expansion of 1/2 in n 13.673 * [backup-simplify]: Simplify 1/2 into 1/2 13.673 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.673 * [taylor]: Taking taylor expansion of 1/2 in n 13.673 * [backup-simplify]: Simplify 1/2 into 1/2 13.673 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.673 * [taylor]: Taking taylor expansion of k in n 13.673 * [backup-simplify]: Simplify k into k 13.673 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.673 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 13.673 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 13.673 * [taylor]: Taking taylor expansion of 2 in n 13.673 * [backup-simplify]: Simplify 2 into 2 13.673 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.673 * [taylor]: Taking taylor expansion of PI in n 13.673 * [backup-simplify]: Simplify PI into PI 13.673 * [taylor]: Taking taylor expansion of n in n 13.673 * [backup-simplify]: Simplify 0 into 0 13.673 * [backup-simplify]: Simplify 1 into 1 13.674 * [backup-simplify]: Simplify (/ PI 1) into PI 13.674 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.675 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.675 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.675 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 13.675 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 13.676 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.677 * [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))) 13.677 * [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)))) 13.678 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 13.679 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 13.680 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 13.680 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 13.680 * [backup-simplify]: Simplify 0 into 0 13.681 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 13.683 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.683 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 13.683 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 13.684 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 13.684 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 13.684 * [taylor]: Taking taylor expansion of +nan.0 in n 13.684 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.684 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 13.684 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 13.684 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 13.684 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 13.684 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 13.684 * [taylor]: Taking taylor expansion of 1/2 in n 13.684 * [backup-simplify]: Simplify 1/2 into 1/2 13.684 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.684 * [taylor]: Taking taylor expansion of 1/2 in n 13.684 * [backup-simplify]: Simplify 1/2 into 1/2 13.684 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.684 * [taylor]: Taking taylor expansion of k in n 13.684 * [backup-simplify]: Simplify k into k 13.684 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.684 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 13.684 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 13.684 * [taylor]: Taking taylor expansion of 2 in n 13.684 * [backup-simplify]: Simplify 2 into 2 13.684 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.684 * [taylor]: Taking taylor expansion of PI in n 13.684 * [backup-simplify]: Simplify PI into PI 13.684 * [taylor]: Taking taylor expansion of n in n 13.684 * [backup-simplify]: Simplify 0 into 0 13.684 * [backup-simplify]: Simplify 1 into 1 13.684 * [backup-simplify]: Simplify (/ PI 1) into PI 13.685 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.685 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.685 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.685 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 13.685 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 13.686 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.687 * [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))) 13.688 * [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)))) 13.689 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 13.690 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 13.690 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 13.691 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 13.692 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.692 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 13.694 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 13.694 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.694 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 13.694 * [backup-simplify]: Simplify (- 0) into 0 13.695 * [backup-simplify]: Simplify (+ 0 0) into 0 13.696 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.696 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 13.698 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 13.701 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 13.703 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 13.703 * [backup-simplify]: Simplify (- 0) into 0 13.703 * [backup-simplify]: Simplify 0 into 0 13.703 * [backup-simplify]: Simplify 0 into 0 13.705 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.709 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.710 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 13.711 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 13.711 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 13.711 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 13.711 * [taylor]: Taking taylor expansion of +nan.0 in n 13.711 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.711 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 13.711 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 13.711 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 13.711 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 13.711 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 13.711 * [taylor]: Taking taylor expansion of 1/2 in n 13.711 * [backup-simplify]: Simplify 1/2 into 1/2 13.711 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.711 * [taylor]: Taking taylor expansion of 1/2 in n 13.711 * [backup-simplify]: Simplify 1/2 into 1/2 13.711 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.711 * [taylor]: Taking taylor expansion of k in n 13.712 * [backup-simplify]: Simplify k into k 13.712 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.712 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 13.712 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 13.712 * [taylor]: Taking taylor expansion of 2 in n 13.712 * [backup-simplify]: Simplify 2 into 2 13.712 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.712 * [taylor]: Taking taylor expansion of PI in n 13.712 * [backup-simplify]: Simplify PI into PI 13.712 * [taylor]: Taking taylor expansion of n in n 13.712 * [backup-simplify]: Simplify 0 into 0 13.712 * [backup-simplify]: Simplify 1 into 1 13.712 * [backup-simplify]: Simplify (/ PI 1) into PI 13.713 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.715 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.715 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.715 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 13.715 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 13.717 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.718 * [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))) 13.720 * [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)))) 13.722 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 13.723 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 13.724 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 13.726 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 13.730 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) 13.731 * [backup-simplify]: Simplify (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2)))) into (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 13.731 * [approximate]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (k n) around 0 13.731 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 13.731 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 13.731 * [taylor]: Taking taylor expansion of (/ -1 k) in n 13.731 * [taylor]: Taking taylor expansion of -1 in n 13.731 * [backup-simplify]: Simplify -1 into -1 13.731 * [taylor]: Taking taylor expansion of k in n 13.731 * [backup-simplify]: Simplify k into k 13.732 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 13.732 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 13.732 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 13.732 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 13.732 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 13.732 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 13.732 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 13.732 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 13.732 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.732 * [taylor]: Taking taylor expansion of 1/2 in n 13.732 * [backup-simplify]: Simplify 1/2 into 1/2 13.732 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.732 * [taylor]: Taking taylor expansion of k in n 13.732 * [backup-simplify]: Simplify k into k 13.732 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.732 * [taylor]: Taking taylor expansion of 1/2 in n 13.732 * [backup-simplify]: Simplify 1/2 into 1/2 13.732 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 13.732 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 13.732 * [taylor]: Taking taylor expansion of -2 in n 13.732 * [backup-simplify]: Simplify -2 into -2 13.732 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.733 * [taylor]: Taking taylor expansion of PI in n 13.733 * [backup-simplify]: Simplify PI into PI 13.733 * [taylor]: Taking taylor expansion of n in n 13.733 * [backup-simplify]: Simplify 0 into 0 13.733 * [backup-simplify]: Simplify 1 into 1 13.733 * [backup-simplify]: Simplify (/ PI 1) into PI 13.734 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 13.743 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 13.743 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.743 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 13.745 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.747 * [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))) 13.748 * [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)))) 13.749 * [backup-simplify]: Simplify (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 13.750 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 13.750 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 13.750 * [taylor]: Taking taylor expansion of (/ -1 k) in k 13.750 * [taylor]: Taking taylor expansion of -1 in k 13.750 * [backup-simplify]: Simplify -1 into -1 13.750 * [taylor]: Taking taylor expansion of k in k 13.750 * [backup-simplify]: Simplify 0 into 0 13.750 * [backup-simplify]: Simplify 1 into 1 13.750 * [backup-simplify]: Simplify (/ -1 1) into -1 13.751 * [backup-simplify]: Simplify (sqrt 0) into 0 13.752 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 13.752 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 13.752 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 13.752 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 13.752 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 13.752 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 13.752 * [taylor]: Taking taylor expansion of 1/2 in k 13.752 * [backup-simplify]: Simplify 1/2 into 1/2 13.752 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.752 * [taylor]: Taking taylor expansion of k in k 13.752 * [backup-simplify]: Simplify 0 into 0 13.752 * [backup-simplify]: Simplify 1 into 1 13.753 * [backup-simplify]: Simplify (/ 1 1) into 1 13.753 * [taylor]: Taking taylor expansion of 1/2 in k 13.753 * [backup-simplify]: Simplify 1/2 into 1/2 13.753 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 13.753 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 13.753 * [taylor]: Taking taylor expansion of -2 in k 13.753 * [backup-simplify]: Simplify -2 into -2 13.753 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.753 * [taylor]: Taking taylor expansion of PI in k 13.753 * [backup-simplify]: Simplify PI into PI 13.753 * [taylor]: Taking taylor expansion of n in k 13.753 * [backup-simplify]: Simplify n into n 13.753 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.753 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 13.753 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 13.754 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 13.755 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.755 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 13.755 * [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))) 13.755 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 13.755 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 13.755 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 13.755 * [taylor]: Taking taylor expansion of (/ -1 k) in k 13.755 * [taylor]: Taking taylor expansion of -1 in k 13.756 * [backup-simplify]: Simplify -1 into -1 13.756 * [taylor]: Taking taylor expansion of k in k 13.756 * [backup-simplify]: Simplify 0 into 0 13.756 * [backup-simplify]: Simplify 1 into 1 13.756 * [backup-simplify]: Simplify (/ -1 1) into -1 13.756 * [backup-simplify]: Simplify (sqrt 0) into 0 13.758 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 13.758 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 13.758 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 13.758 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 13.758 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 13.758 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 13.758 * [taylor]: Taking taylor expansion of 1/2 in k 13.758 * [backup-simplify]: Simplify 1/2 into 1/2 13.758 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.758 * [taylor]: Taking taylor expansion of k in k 13.758 * [backup-simplify]: Simplify 0 into 0 13.758 * [backup-simplify]: Simplify 1 into 1 13.758 * [backup-simplify]: Simplify (/ 1 1) into 1 13.758 * [taylor]: Taking taylor expansion of 1/2 in k 13.758 * [backup-simplify]: Simplify 1/2 into 1/2 13.758 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 13.758 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 13.758 * [taylor]: Taking taylor expansion of -2 in k 13.758 * [backup-simplify]: Simplify -2 into -2 13.758 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.758 * [taylor]: Taking taylor expansion of PI in k 13.758 * [backup-simplify]: Simplify PI into PI 13.758 * [taylor]: Taking taylor expansion of n in k 13.758 * [backup-simplify]: Simplify n into n 13.758 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.758 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 13.758 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 13.759 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 13.759 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.759 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 13.759 * [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))) 13.759 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 13.759 * [taylor]: Taking taylor expansion of (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 13.759 * [taylor]: Taking taylor expansion of +nan.0 in n 13.759 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.759 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 13.759 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 13.759 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 13.759 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 13.759 * [taylor]: Taking taylor expansion of -2 in n 13.759 * [backup-simplify]: Simplify -2 into -2 13.759 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.759 * [taylor]: Taking taylor expansion of PI in n 13.760 * [backup-simplify]: Simplify PI into PI 13.760 * [taylor]: Taking taylor expansion of n in n 13.760 * [backup-simplify]: Simplify 0 into 0 13.760 * [backup-simplify]: Simplify 1 into 1 13.760 * [backup-simplify]: Simplify (/ PI 1) into PI 13.760 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 13.761 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 13.761 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 13.761 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.761 * [taylor]: Taking taylor expansion of 1/2 in n 13.761 * [backup-simplify]: Simplify 1/2 into 1/2 13.761 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.761 * [taylor]: Taking taylor expansion of k in n 13.761 * [backup-simplify]: Simplify k into k 13.761 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.761 * [taylor]: Taking taylor expansion of 1/2 in n 13.761 * [backup-simplify]: Simplify 1/2 into 1/2 13.762 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.762 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.762 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 13.763 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 13.763 * [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)))) 13.764 * [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))))) 13.765 * [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))))) 13.766 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 13.767 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.768 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 13.768 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 13.768 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 13.768 * [taylor]: Taking taylor expansion of +nan.0 in n 13.768 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.768 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 13.768 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 13.768 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 13.768 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 13.768 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 13.768 * [taylor]: Taking taylor expansion of -2 in n 13.768 * [backup-simplify]: Simplify -2 into -2 13.768 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.768 * [taylor]: Taking taylor expansion of PI in n 13.768 * [backup-simplify]: Simplify PI into PI 13.768 * [taylor]: Taking taylor expansion of n in n 13.768 * [backup-simplify]: Simplify 0 into 0 13.768 * [backup-simplify]: Simplify 1 into 1 13.768 * [backup-simplify]: Simplify (/ PI 1) into PI 13.768 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 13.769 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 13.769 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 13.769 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.769 * [taylor]: Taking taylor expansion of 1/2 in n 13.769 * [backup-simplify]: Simplify 1/2 into 1/2 13.769 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.769 * [taylor]: Taking taylor expansion of k in n 13.769 * [backup-simplify]: Simplify k into k 13.769 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.769 * [taylor]: Taking taylor expansion of 1/2 in n 13.769 * [backup-simplify]: Simplify 1/2 into 1/2 13.770 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.770 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.770 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 13.771 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 13.772 * [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)))) 13.772 * [backup-simplify]: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 13.773 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 13.774 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 13.775 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 13.776 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.776 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.776 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 13.776 * [backup-simplify]: Simplify (+ 0 0) into 0 13.777 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.777 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 13.778 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 13.779 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 13.780 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 13.782 * [backup-simplify]: Simplify (- (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 13.783 * [backup-simplify]: Simplify 0 into 0 13.783 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.785 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.786 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (* (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 13.786 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 13.786 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 13.786 * [taylor]: Taking taylor expansion of +nan.0 in n 13.786 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.786 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 13.786 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 13.786 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 13.786 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 13.786 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 13.786 * [taylor]: Taking taylor expansion of -2 in n 13.786 * [backup-simplify]: Simplify -2 into -2 13.786 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.786 * [taylor]: Taking taylor expansion of PI in n 13.786 * [backup-simplify]: Simplify PI into PI 13.786 * [taylor]: Taking taylor expansion of n in n 13.786 * [backup-simplify]: Simplify 0 into 0 13.786 * [backup-simplify]: Simplify 1 into 1 13.787 * [backup-simplify]: Simplify (/ PI 1) into PI 13.787 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 13.788 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 13.788 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 13.788 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.788 * [taylor]: Taking taylor expansion of 1/2 in n 13.788 * [backup-simplify]: Simplify 1/2 into 1/2 13.788 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.788 * [taylor]: Taking taylor expansion of k in n 13.788 * [backup-simplify]: Simplify k into k 13.788 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.788 * [taylor]: Taking taylor expansion of 1/2 in n 13.788 * [backup-simplify]: Simplify 1/2 into 1/2 13.789 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.789 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.789 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 13.789 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 13.790 * [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)))) 13.791 * [backup-simplify]: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 13.792 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 13.792 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 13.793 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 13.798 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 13.798 * * * * [progress]: [ 4 / 4 ] generating series at (2) 13.799 * [backup-simplify]: Simplify (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 13.799 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (k n) around 0 13.799 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 13.799 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 13.799 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.799 * [taylor]: Taking taylor expansion of k in n 13.799 * [backup-simplify]: Simplify k into k 13.799 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.799 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 13.799 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.799 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 13.799 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 13.799 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 13.799 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 13.799 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 13.799 * [taylor]: Taking taylor expansion of 1/2 in n 13.799 * [backup-simplify]: Simplify 1/2 into 1/2 13.799 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 13.799 * [taylor]: Taking taylor expansion of 1/2 in n 13.799 * [backup-simplify]: Simplify 1/2 into 1/2 13.799 * [taylor]: Taking taylor expansion of k in n 13.800 * [backup-simplify]: Simplify k into k 13.800 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 13.800 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 13.800 * [taylor]: Taking taylor expansion of 2 in n 13.800 * [backup-simplify]: Simplify 2 into 2 13.800 * [taylor]: Taking taylor expansion of (* n PI) in n 13.800 * [taylor]: Taking taylor expansion of n in n 13.800 * [backup-simplify]: Simplify 0 into 0 13.800 * [backup-simplify]: Simplify 1 into 1 13.800 * [taylor]: Taking taylor expansion of PI in n 13.800 * [backup-simplify]: Simplify PI into PI 13.800 * [backup-simplify]: Simplify (* 0 PI) into 0 13.801 * [backup-simplify]: Simplify (* 2 0) into 0 13.803 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.804 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 13.805 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.805 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 13.805 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 13.805 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 13.807 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.808 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 13.809 * [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))))) 13.809 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 13.809 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 13.809 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.809 * [taylor]: Taking taylor expansion of k in k 13.810 * [backup-simplify]: Simplify 0 into 0 13.810 * [backup-simplify]: Simplify 1 into 1 13.810 * [backup-simplify]: Simplify (/ 1 1) into 1 13.810 * [backup-simplify]: Simplify (sqrt 0) into 0 13.812 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.812 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 13.812 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 13.812 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 13.812 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 13.812 * [taylor]: Taking taylor expansion of 1/2 in k 13.812 * [backup-simplify]: Simplify 1/2 into 1/2 13.812 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 13.812 * [taylor]: Taking taylor expansion of 1/2 in k 13.812 * [backup-simplify]: Simplify 1/2 into 1/2 13.812 * [taylor]: Taking taylor expansion of k in k 13.812 * [backup-simplify]: Simplify 0 into 0 13.812 * [backup-simplify]: Simplify 1 into 1 13.812 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 13.812 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 13.812 * [taylor]: Taking taylor expansion of 2 in k 13.812 * [backup-simplify]: Simplify 2 into 2 13.812 * [taylor]: Taking taylor expansion of (* n PI) in k 13.812 * [taylor]: Taking taylor expansion of n in k 13.812 * [backup-simplify]: Simplify n into n 13.812 * [taylor]: Taking taylor expansion of PI in k 13.812 * [backup-simplify]: Simplify PI into PI 13.812 * [backup-simplify]: Simplify (* n PI) into (* n PI) 13.812 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 13.813 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 13.813 * [backup-simplify]: Simplify (* 1/2 0) into 0 13.813 * [backup-simplify]: Simplify (- 0) into 0 13.814 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.814 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 13.814 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 13.814 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 13.814 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 13.814 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.814 * [taylor]: Taking taylor expansion of k in k 13.814 * [backup-simplify]: Simplify 0 into 0 13.814 * [backup-simplify]: Simplify 1 into 1 13.815 * [backup-simplify]: Simplify (/ 1 1) into 1 13.815 * [backup-simplify]: Simplify (sqrt 0) into 0 13.816 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.816 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 13.816 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 13.817 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 13.817 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 13.817 * [taylor]: Taking taylor expansion of 1/2 in k 13.817 * [backup-simplify]: Simplify 1/2 into 1/2 13.817 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 13.817 * [taylor]: Taking taylor expansion of 1/2 in k 13.817 * [backup-simplify]: Simplify 1/2 into 1/2 13.817 * [taylor]: Taking taylor expansion of k in k 13.817 * [backup-simplify]: Simplify 0 into 0 13.817 * [backup-simplify]: Simplify 1 into 1 13.817 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 13.817 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 13.817 * [taylor]: Taking taylor expansion of 2 in k 13.817 * [backup-simplify]: Simplify 2 into 2 13.817 * [taylor]: Taking taylor expansion of (* n PI) in k 13.817 * [taylor]: Taking taylor expansion of n in k 13.817 * [backup-simplify]: Simplify n into n 13.817 * [taylor]: Taking taylor expansion of PI in k 13.817 * [backup-simplify]: Simplify PI into PI 13.817 * [backup-simplify]: Simplify (* n PI) into (* n PI) 13.817 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 13.817 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 13.818 * [backup-simplify]: Simplify (* 1/2 0) into 0 13.818 * [backup-simplify]: Simplify (- 0) into 0 13.819 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.819 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 13.819 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 13.819 * [backup-simplify]: Simplify (* 0 (pow (* 2 (* n PI)) 1/2)) into 0 13.819 * [taylor]: Taking taylor expansion of 0 in n 13.819 * [backup-simplify]: Simplify 0 into 0 13.819 * [backup-simplify]: Simplify 0 into 0 13.820 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 13.820 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 13.821 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 13.822 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 13.822 * [backup-simplify]: Simplify (- 1/2) into -1/2 13.823 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 13.823 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 13.823 * [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))))) 13.824 * [backup-simplify]: Simplify (+ (* 0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 13.824 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 13.824 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 13.824 * [taylor]: Taking taylor expansion of +nan.0 in n 13.824 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.824 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 13.824 * [taylor]: Taking taylor expansion of (sqrt 2) in n 13.824 * [taylor]: Taking taylor expansion of 2 in n 13.824 * [backup-simplify]: Simplify 2 into 2 13.824 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 13.825 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 13.825 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 13.825 * [taylor]: Taking taylor expansion of (* n PI) in n 13.825 * [taylor]: Taking taylor expansion of n in n 13.825 * [backup-simplify]: Simplify 0 into 0 13.825 * [backup-simplify]: Simplify 1 into 1 13.825 * [taylor]: Taking taylor expansion of PI in n 13.825 * [backup-simplify]: Simplify PI into PI 13.826 * [backup-simplify]: Simplify (* 0 PI) into 0 13.827 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.828 * [backup-simplify]: Simplify (sqrt 0) into 0 13.829 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 13.829 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 13.830 * [backup-simplify]: Simplify (* +nan.0 0) into 0 13.830 * [backup-simplify]: Simplify (- 0) into 0 13.830 * [backup-simplify]: Simplify 0 into 0 13.830 * [backup-simplify]: Simplify 0 into 0 13.831 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 13.832 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 13.834 * [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 13.835 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 13.835 * [backup-simplify]: Simplify (- 0) into 0 13.835 * [backup-simplify]: Simplify (+ 0 0) into 0 13.836 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 13.837 * [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))) 13.838 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 13.841 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.842 * [backup-simplify]: Simplify (+ (* 0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) 13.842 * [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 13.842 * [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 13.842 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 13.842 * [taylor]: Taking taylor expansion of +nan.0 in n 13.842 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.842 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 13.842 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 13.842 * [taylor]: Taking taylor expansion of (sqrt 2) in n 13.842 * [taylor]: Taking taylor expansion of 2 in n 13.842 * [backup-simplify]: Simplify 2 into 2 13.842 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 13.843 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 13.843 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 13.843 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 13.843 * [taylor]: Taking taylor expansion of 2 in n 13.843 * [backup-simplify]: Simplify 2 into 2 13.843 * [taylor]: Taking taylor expansion of (* n PI) in n 13.843 * [taylor]: Taking taylor expansion of n in n 13.843 * [backup-simplify]: Simplify 0 into 0 13.843 * [backup-simplify]: Simplify 1 into 1 13.843 * [taylor]: Taking taylor expansion of PI in n 13.843 * [backup-simplify]: Simplify PI into PI 13.844 * [backup-simplify]: Simplify (* 0 PI) into 0 13.844 * [backup-simplify]: Simplify (* 2 0) into 0 13.846 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.847 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 13.848 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.848 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 13.848 * [taylor]: Taking taylor expansion of (* n PI) in n 13.848 * [taylor]: Taking taylor expansion of n in n 13.848 * [backup-simplify]: Simplify 0 into 0 13.848 * [backup-simplify]: Simplify 1 into 1 13.848 * [taylor]: Taking taylor expansion of PI in n 13.848 * [backup-simplify]: Simplify PI into PI 13.849 * [backup-simplify]: Simplify (* 0 PI) into 0 13.851 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.851 * [backup-simplify]: Simplify (sqrt 0) into 0 13.852 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 13.852 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 13.852 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 13.852 * [taylor]: Taking taylor expansion of +nan.0 in n 13.853 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.853 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 13.853 * [taylor]: Taking taylor expansion of (sqrt 2) in n 13.853 * [taylor]: Taking taylor expansion of 2 in n 13.853 * [backup-simplify]: Simplify 2 into 2 13.853 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 13.854 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 13.854 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 13.854 * [taylor]: Taking taylor expansion of (* n PI) in n 13.854 * [taylor]: Taking taylor expansion of n in n 13.854 * [backup-simplify]: Simplify 0 into 0 13.854 * [backup-simplify]: Simplify 1 into 1 13.854 * [taylor]: Taking taylor expansion of PI in n 13.854 * [backup-simplify]: Simplify PI into PI 13.854 * [backup-simplify]: Simplify (* 0 PI) into 0 13.856 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.856 * [backup-simplify]: Simplify (sqrt 0) into 0 13.858 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 13.859 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.861 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 13.869 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 13.870 * [backup-simplify]: Simplify (* +nan.0 0) into 0 13.871 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 13.872 * [backup-simplify]: Simplify (* +nan.0 0) into 0 13.872 * [backup-simplify]: Simplify (- 0) into 0 13.873 * [backup-simplify]: Simplify (+ 0 0) into 0 13.873 * [backup-simplify]: Simplify (- 0) into 0 13.873 * [backup-simplify]: Simplify 0 into 0 13.877 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 13.884 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 13.888 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 13.891 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 13.891 * [backup-simplify]: Simplify 0 into 0 13.892 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.893 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 13.896 * [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 13.898 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 13.898 * [backup-simplify]: Simplify (- 0) into 0 13.898 * [backup-simplify]: Simplify (+ 0 0) into 0 13.900 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 13.902 * [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))) 13.902 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.906 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.908 * [backup-simplify]: Simplify (+ (* 0 (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3)))) (+ (* +nan.0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) 13.908 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) in n 13.908 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))) in n 13.908 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 13.908 * [taylor]: Taking taylor expansion of +nan.0 in n 13.908 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.908 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 13.908 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 13.908 * [taylor]: Taking taylor expansion of (sqrt 2) in n 13.908 * [taylor]: Taking taylor expansion of 2 in n 13.908 * [backup-simplify]: Simplify 2 into 2 13.908 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 13.909 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 13.909 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 13.909 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 13.909 * [taylor]: Taking taylor expansion of 2 in n 13.909 * [backup-simplify]: Simplify 2 into 2 13.909 * [taylor]: Taking taylor expansion of (* n PI) in n 13.909 * [taylor]: Taking taylor expansion of n in n 13.909 * [backup-simplify]: Simplify 0 into 0 13.909 * [backup-simplify]: Simplify 1 into 1 13.909 * [taylor]: Taking taylor expansion of PI in n 13.909 * [backup-simplify]: Simplify PI into PI 13.910 * [backup-simplify]: Simplify (* 0 PI) into 0 13.910 * [backup-simplify]: Simplify (* 2 0) into 0 13.912 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.914 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 13.915 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.915 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 13.915 * [taylor]: Taking taylor expansion of (* n PI) in n 13.915 * [taylor]: Taking taylor expansion of n in n 13.915 * [backup-simplify]: Simplify 0 into 0 13.915 * [backup-simplify]: Simplify 1 into 1 13.915 * [taylor]: Taking taylor expansion of PI in n 13.915 * [backup-simplify]: Simplify PI into PI 13.916 * [backup-simplify]: Simplify (* 0 PI) into 0 13.917 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.918 * [backup-simplify]: Simplify (sqrt 0) into 0 13.919 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 13.919 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 13.919 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 13.919 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 13.919 * [taylor]: Taking taylor expansion of +nan.0 in n 13.919 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.919 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 13.919 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 13.919 * [taylor]: Taking taylor expansion of (sqrt 2) in n 13.919 * [taylor]: Taking taylor expansion of 2 in n 13.919 * [backup-simplify]: Simplify 2 into 2 13.920 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 13.920 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 13.920 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 13.920 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 13.920 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 13.920 * [taylor]: Taking taylor expansion of 2 in n 13.920 * [backup-simplify]: Simplify 2 into 2 13.920 * [taylor]: Taking taylor expansion of (* n PI) in n 13.920 * [taylor]: Taking taylor expansion of n in n 13.920 * [backup-simplify]: Simplify 0 into 0 13.921 * [backup-simplify]: Simplify 1 into 1 13.921 * [taylor]: Taking taylor expansion of PI in n 13.921 * [backup-simplify]: Simplify PI into PI 13.921 * [backup-simplify]: Simplify (* 0 PI) into 0 13.921 * [backup-simplify]: Simplify (* 2 0) into 0 13.923 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.925 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 13.927 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.928 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.928 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 13.928 * [taylor]: Taking taylor expansion of (* n PI) in n 13.928 * [taylor]: Taking taylor expansion of n in n 13.928 * [backup-simplify]: Simplify 0 into 0 13.928 * [backup-simplify]: Simplify 1 into 1 13.928 * [taylor]: Taking taylor expansion of PI in n 13.928 * [backup-simplify]: Simplify PI into PI 13.929 * [backup-simplify]: Simplify (* 0 PI) into 0 13.930 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.931 * [backup-simplify]: Simplify (sqrt 0) into 0 13.932 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 13.932 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 13.932 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 13.932 * [taylor]: Taking taylor expansion of +nan.0 in n 13.932 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.932 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 13.932 * [taylor]: Taking taylor expansion of (sqrt 2) in n 13.932 * [taylor]: Taking taylor expansion of 2 in n 13.932 * [backup-simplify]: Simplify 2 into 2 13.933 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 13.933 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 13.933 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 13.933 * [taylor]: Taking taylor expansion of (* n PI) in n 13.933 * [taylor]: Taking taylor expansion of n in n 13.933 * [backup-simplify]: Simplify 0 into 0 13.933 * [backup-simplify]: Simplify 1 into 1 13.933 * [taylor]: Taking taylor expansion of PI in n 13.933 * [backup-simplify]: Simplify PI into PI 13.934 * [backup-simplify]: Simplify (* 0 PI) into 0 13.935 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.936 * [backup-simplify]: Simplify (sqrt 0) into 0 13.937 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 13.939 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.940 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 13.942 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 13.942 * [backup-simplify]: Simplify (* +nan.0 0) into 0 13.943 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.945 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.947 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 13.948 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 13.950 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 13.951 * [backup-simplify]: Simplify (* +nan.0 0) into 0 13.951 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 13.952 * [backup-simplify]: Simplify (* +nan.0 0) into 0 13.952 * [backup-simplify]: Simplify (- 0) into 0 13.952 * [backup-simplify]: Simplify (+ 0 0) into 0 13.953 * [backup-simplify]: Simplify (- 0) into 0 13.953 * [backup-simplify]: Simplify (+ 0 0) into 0 13.953 * [backup-simplify]: Simplify (- 0) into 0 13.953 * [backup-simplify]: Simplify 0 into 0 13.954 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.956 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 13.957 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 13.959 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.960 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 13.963 * [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)))))))) 13.969 * [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)))))))) 13.972 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 13.978 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 13.981 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 13.990 * [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)))))))))) 13.998 * [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))))))) 14.004 * [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))))))) 14.005 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 14.013 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 14.013 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 14.017 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 14.023 * [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)))) 14.028 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 14.032 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 14.048 * [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))))))))))))) 14.050 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 14.050 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (k n) around 0 14.050 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 14.050 * [taylor]: Taking taylor expansion of (sqrt k) in n 14.050 * [taylor]: Taking taylor expansion of k in n 14.050 * [backup-simplify]: Simplify k into k 14.050 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 14.050 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 14.050 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 14.050 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 14.050 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 14.050 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 14.050 * [taylor]: Taking taylor expansion of 1/2 in n 14.050 * [backup-simplify]: Simplify 1/2 into 1/2 14.050 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 14.050 * [taylor]: Taking taylor expansion of 1/2 in n 14.050 * [backup-simplify]: Simplify 1/2 into 1/2 14.050 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.050 * [taylor]: Taking taylor expansion of k in n 14.050 * [backup-simplify]: Simplify k into k 14.050 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.050 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 14.050 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 14.050 * [taylor]: Taking taylor expansion of 2 in n 14.050 * [backup-simplify]: Simplify 2 into 2 14.050 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.050 * [taylor]: Taking taylor expansion of PI in n 14.051 * [backup-simplify]: Simplify PI into PI 14.051 * [taylor]: Taking taylor expansion of n in n 14.051 * [backup-simplify]: Simplify 0 into 0 14.051 * [backup-simplify]: Simplify 1 into 1 14.052 * [backup-simplify]: Simplify (/ PI 1) into PI 14.052 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 14.054 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 14.054 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 14.054 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 14.054 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 14.056 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 14.057 * [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))) 14.058 * [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)))) 14.058 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 14.059 * [taylor]: Taking taylor expansion of (sqrt k) in k 14.059 * [taylor]: Taking taylor expansion of k in k 14.059 * [backup-simplify]: Simplify 0 into 0 14.059 * [backup-simplify]: Simplify 1 into 1 14.059 * [backup-simplify]: Simplify (sqrt 0) into 0 14.061 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.061 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 14.062 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 14.062 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 14.062 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 14.062 * [taylor]: Taking taylor expansion of 1/2 in k 14.062 * [backup-simplify]: Simplify 1/2 into 1/2 14.062 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 14.062 * [taylor]: Taking taylor expansion of 1/2 in k 14.062 * [backup-simplify]: Simplify 1/2 into 1/2 14.062 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.062 * [taylor]: Taking taylor expansion of k in k 14.062 * [backup-simplify]: Simplify 0 into 0 14.062 * [backup-simplify]: Simplify 1 into 1 14.062 * [backup-simplify]: Simplify (/ 1 1) into 1 14.062 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 14.063 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 14.063 * [taylor]: Taking taylor expansion of 2 in k 14.063 * [backup-simplify]: Simplify 2 into 2 14.063 * [taylor]: Taking taylor expansion of (/ PI n) in k 14.063 * [taylor]: Taking taylor expansion of PI in k 14.063 * [backup-simplify]: Simplify PI into PI 14.063 * [taylor]: Taking taylor expansion of n in k 14.063 * [backup-simplify]: Simplify n into n 14.063 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 14.063 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 14.063 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 14.064 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 14.064 * [backup-simplify]: Simplify (- 1/2) into -1/2 14.065 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 14.065 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 14.065 * [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)))) 14.065 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 14.065 * [taylor]: Taking taylor expansion of (sqrt k) in k 14.065 * [taylor]: Taking taylor expansion of k in k 14.065 * [backup-simplify]: Simplify 0 into 0 14.065 * [backup-simplify]: Simplify 1 into 1 14.066 * [backup-simplify]: Simplify (sqrt 0) into 0 14.067 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.067 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 14.067 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 14.067 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 14.067 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 14.067 * [taylor]: Taking taylor expansion of 1/2 in k 14.067 * [backup-simplify]: Simplify 1/2 into 1/2 14.067 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 14.067 * [taylor]: Taking taylor expansion of 1/2 in k 14.068 * [backup-simplify]: Simplify 1/2 into 1/2 14.068 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.068 * [taylor]: Taking taylor expansion of k in k 14.068 * [backup-simplify]: Simplify 0 into 0 14.068 * [backup-simplify]: Simplify 1 into 1 14.068 * [backup-simplify]: Simplify (/ 1 1) into 1 14.068 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 14.068 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 14.068 * [taylor]: Taking taylor expansion of 2 in k 14.068 * [backup-simplify]: Simplify 2 into 2 14.068 * [taylor]: Taking taylor expansion of (/ PI n) in k 14.068 * [taylor]: Taking taylor expansion of PI in k 14.068 * [backup-simplify]: Simplify PI into PI 14.068 * [taylor]: Taking taylor expansion of n in k 14.068 * [backup-simplify]: Simplify n into n 14.068 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 14.068 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 14.068 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 14.069 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 14.069 * [backup-simplify]: Simplify (- 1/2) into -1/2 14.070 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 14.070 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 14.070 * [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)))) 14.070 * [backup-simplify]: Simplify (* 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into 0 14.070 * [taylor]: Taking taylor expansion of 0 in n 14.070 * [backup-simplify]: Simplify 0 into 0 14.070 * [backup-simplify]: Simplify 0 into 0 14.071 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 14.071 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 14.071 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 14.071 * [taylor]: Taking taylor expansion of +nan.0 in n 14.071 * [backup-simplify]: Simplify +nan.0 into +nan.0 14.071 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 14.071 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 14.071 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 14.071 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 14.071 * [taylor]: Taking taylor expansion of 1/2 in n 14.071 * [backup-simplify]: Simplify 1/2 into 1/2 14.071 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 14.071 * [taylor]: Taking taylor expansion of 1/2 in n 14.071 * [backup-simplify]: Simplify 1/2 into 1/2 14.071 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.071 * [taylor]: Taking taylor expansion of k in n 14.071 * [backup-simplify]: Simplify k into k 14.071 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.071 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 14.071 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 14.071 * [taylor]: Taking taylor expansion of 2 in n 14.071 * [backup-simplify]: Simplify 2 into 2 14.071 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.071 * [taylor]: Taking taylor expansion of PI in n 14.072 * [backup-simplify]: Simplify PI into PI 14.072 * [taylor]: Taking taylor expansion of n in n 14.072 * [backup-simplify]: Simplify 0 into 0 14.072 * [backup-simplify]: Simplify 1 into 1 14.072 * [backup-simplify]: Simplify (/ PI 1) into PI 14.073 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 14.074 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 14.074 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 14.074 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 14.074 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 14.075 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 14.076 * [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))) 14.078 * [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)))) 14.079 * [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))))) 14.080 * [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)))))) 14.081 * [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)))))) 14.081 * [backup-simplify]: Simplify 0 into 0 14.084 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 14.085 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 14.085 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 14.085 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 14.085 * [taylor]: Taking taylor expansion of +nan.0 in n 14.085 * [backup-simplify]: Simplify +nan.0 into +nan.0 14.085 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 14.085 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 14.085 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 14.085 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 14.086 * [taylor]: Taking taylor expansion of 1/2 in n 14.086 * [backup-simplify]: Simplify 1/2 into 1/2 14.086 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 14.086 * [taylor]: Taking taylor expansion of 1/2 in n 14.086 * [backup-simplify]: Simplify 1/2 into 1/2 14.086 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.086 * [taylor]: Taking taylor expansion of k in n 14.086 * [backup-simplify]: Simplify k into k 14.086 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.086 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 14.086 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 14.086 * [taylor]: Taking taylor expansion of 2 in n 14.086 * [backup-simplify]: Simplify 2 into 2 14.086 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.086 * [taylor]: Taking taylor expansion of PI in n 14.086 * [backup-simplify]: Simplify PI into PI 14.086 * [taylor]: Taking taylor expansion of n in n 14.086 * [backup-simplify]: Simplify 0 into 0 14.086 * [backup-simplify]: Simplify 1 into 1 14.086 * [backup-simplify]: Simplify (/ PI 1) into PI 14.086 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 14.087 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 14.087 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 14.087 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 14.087 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 14.088 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 14.089 * [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))) 14.090 * [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)))) 14.090 * [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))))) 14.091 * [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)))))) 14.092 * [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)))))) 14.092 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 14.093 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 14.094 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 14.094 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 14.094 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 14.094 * [backup-simplify]: Simplify (- 0) into 0 14.095 * [backup-simplify]: Simplify (+ 0 0) into 0 14.096 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 14.096 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 14.097 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 14.098 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 14.099 * [backup-simplify]: Simplify (- 0) into 0 14.099 * [backup-simplify]: Simplify 0 into 0 14.099 * [backup-simplify]: Simplify 0 into 0 14.101 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 14.102 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 14.102 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 14.102 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 14.102 * [taylor]: Taking taylor expansion of +nan.0 in n 14.102 * [backup-simplify]: Simplify +nan.0 into +nan.0 14.102 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 14.102 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 14.102 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 14.102 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 14.102 * [taylor]: Taking taylor expansion of 1/2 in n 14.102 * [backup-simplify]: Simplify 1/2 into 1/2 14.102 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 14.102 * [taylor]: Taking taylor expansion of 1/2 in n 14.102 * [backup-simplify]: Simplify 1/2 into 1/2 14.102 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.102 * [taylor]: Taking taylor expansion of k in n 14.102 * [backup-simplify]: Simplify k into k 14.102 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.102 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 14.102 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 14.102 * [taylor]: Taking taylor expansion of 2 in n 14.102 * [backup-simplify]: Simplify 2 into 2 14.102 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.102 * [taylor]: Taking taylor expansion of PI in n 14.102 * [backup-simplify]: Simplify PI into PI 14.102 * [taylor]: Taking taylor expansion of n in n 14.102 * [backup-simplify]: Simplify 0 into 0 14.102 * [backup-simplify]: Simplify 1 into 1 14.103 * [backup-simplify]: Simplify (/ PI 1) into PI 14.103 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 14.104 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 14.104 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 14.104 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 14.104 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 14.105 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 14.105 * [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))) 14.106 * [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)))) 14.107 * [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))))) 14.107 * [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)))))) 14.108 * [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)))))) 14.111 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 14.111 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 14.111 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (k n) around 0 14.111 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 14.111 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 14.112 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 14.112 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 14.112 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 14.112 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 14.112 * [taylor]: Taking taylor expansion of 1/2 in n 14.112 * [backup-simplify]: Simplify 1/2 into 1/2 14.112 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.112 * [taylor]: Taking taylor expansion of k in n 14.112 * [backup-simplify]: Simplify k into k 14.112 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.112 * [taylor]: Taking taylor expansion of 1/2 in n 14.112 * [backup-simplify]: Simplify 1/2 into 1/2 14.112 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 14.112 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 14.112 * [taylor]: Taking taylor expansion of -2 in n 14.112 * [backup-simplify]: Simplify -2 into -2 14.112 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.112 * [taylor]: Taking taylor expansion of PI in n 14.112 * [backup-simplify]: Simplify PI into PI 14.112 * [taylor]: Taking taylor expansion of n in n 14.112 * [backup-simplify]: Simplify 0 into 0 14.112 * [backup-simplify]: Simplify 1 into 1 14.112 * [backup-simplify]: Simplify (/ PI 1) into PI 14.112 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 14.113 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 14.113 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 14.113 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 14.115 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 14.116 * [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))) 14.117 * [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)))) 14.117 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 14.117 * [taylor]: Taking taylor expansion of (/ -1 k) in n 14.117 * [taylor]: Taking taylor expansion of -1 in n 14.117 * [backup-simplify]: Simplify -1 into -1 14.117 * [taylor]: Taking taylor expansion of k in n 14.117 * [backup-simplify]: Simplify k into k 14.117 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 14.117 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 14.117 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 14.117 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 14.119 * [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))) 14.119 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 14.119 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 14.119 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 14.119 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 14.119 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 14.119 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 14.119 * [taylor]: Taking taylor expansion of 1/2 in k 14.119 * [backup-simplify]: Simplify 1/2 into 1/2 14.119 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.119 * [taylor]: Taking taylor expansion of k in k 14.119 * [backup-simplify]: Simplify 0 into 0 14.119 * [backup-simplify]: Simplify 1 into 1 14.119 * [backup-simplify]: Simplify (/ 1 1) into 1 14.119 * [taylor]: Taking taylor expansion of 1/2 in k 14.119 * [backup-simplify]: Simplify 1/2 into 1/2 14.119 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 14.119 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 14.119 * [taylor]: Taking taylor expansion of -2 in k 14.119 * [backup-simplify]: Simplify -2 into -2 14.119 * [taylor]: Taking taylor expansion of (/ PI n) in k 14.119 * [taylor]: Taking taylor expansion of PI in k 14.119 * [backup-simplify]: Simplify PI into PI 14.120 * [taylor]: Taking taylor expansion of n in k 14.120 * [backup-simplify]: Simplify n into n 14.120 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 14.120 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 14.120 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 14.120 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 14.121 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 14.121 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 14.121 * [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))) 14.121 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 14.121 * [taylor]: Taking taylor expansion of (/ -1 k) in k 14.121 * [taylor]: Taking taylor expansion of -1 in k 14.121 * [backup-simplify]: Simplify -1 into -1 14.121 * [taylor]: Taking taylor expansion of k in k 14.121 * [backup-simplify]: Simplify 0 into 0 14.121 * [backup-simplify]: Simplify 1 into 1 14.121 * [backup-simplify]: Simplify (/ -1 1) into -1 14.122 * [backup-simplify]: Simplify (sqrt 0) into 0 14.123 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 14.123 * [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)))) 14.124 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 14.124 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 14.124 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 14.124 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 14.124 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 14.124 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 14.124 * [taylor]: Taking taylor expansion of 1/2 in k 14.124 * [backup-simplify]: Simplify 1/2 into 1/2 14.124 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.124 * [taylor]: Taking taylor expansion of k in k 14.124 * [backup-simplify]: Simplify 0 into 0 14.124 * [backup-simplify]: Simplify 1 into 1 14.124 * [backup-simplify]: Simplify (/ 1 1) into 1 14.124 * [taylor]: Taking taylor expansion of 1/2 in k 14.124 * [backup-simplify]: Simplify 1/2 into 1/2 14.124 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 14.124 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 14.124 * [taylor]: Taking taylor expansion of -2 in k 14.124 * [backup-simplify]: Simplify -2 into -2 14.124 * [taylor]: Taking taylor expansion of (/ PI n) in k 14.124 * [taylor]: Taking taylor expansion of PI in k 14.124 * [backup-simplify]: Simplify PI into PI 14.124 * [taylor]: Taking taylor expansion of n in k 14.124 * [backup-simplify]: Simplify n into n 14.125 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 14.125 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 14.125 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 14.125 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 14.126 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 14.126 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 14.126 * [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))) 14.126 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 14.126 * [taylor]: Taking taylor expansion of (/ -1 k) in k 14.126 * [taylor]: Taking taylor expansion of -1 in k 14.126 * [backup-simplify]: Simplify -1 into -1 14.126 * [taylor]: Taking taylor expansion of k in k 14.126 * [backup-simplify]: Simplify 0 into 0 14.126 * [backup-simplify]: Simplify 1 into 1 14.126 * [backup-simplify]: Simplify (/ -1 1) into -1 14.127 * [backup-simplify]: Simplify (sqrt 0) into 0 14.128 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 14.128 * [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)))) 14.128 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 14.128 * [taylor]: Taking taylor expansion of +nan.0 in n 14.128 * [backup-simplify]: Simplify +nan.0 into +nan.0 14.129 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 14.129 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 14.129 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 14.129 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 14.129 * [taylor]: Taking taylor expansion of -2 in n 14.129 * [backup-simplify]: Simplify -2 into -2 14.129 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.129 * [taylor]: Taking taylor expansion of PI in n 14.129 * [backup-simplify]: Simplify PI into PI 14.129 * [taylor]: Taking taylor expansion of n in n 14.129 * [backup-simplify]: Simplify 0 into 0 14.129 * [backup-simplify]: Simplify 1 into 1 14.129 * [backup-simplify]: Simplify (/ PI 1) into PI 14.130 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 14.131 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 14.131 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 14.131 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 14.131 * [taylor]: Taking taylor expansion of 1/2 in n 14.131 * [backup-simplify]: Simplify 1/2 into 1/2 14.131 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.131 * [taylor]: Taking taylor expansion of k in n 14.131 * [backup-simplify]: Simplify k into k 14.131 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.131 * [taylor]: Taking taylor expansion of 1/2 in n 14.131 * [backup-simplify]: Simplify 1/2 into 1/2 14.132 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 14.133 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 14.133 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 14.140 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 14.141 * [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)))) 14.142 * [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))))) 14.143 * [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))))) 14.144 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 14.147 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 14.148 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 14.148 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 14.148 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 14.148 * [taylor]: Taking taylor expansion of +nan.0 in n 14.148 * [backup-simplify]: Simplify +nan.0 into +nan.0 14.148 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 14.148 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 14.148 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 14.148 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 14.148 * [taylor]: Taking taylor expansion of -2 in n 14.148 * [backup-simplify]: Simplify -2 into -2 14.148 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.148 * [taylor]: Taking taylor expansion of PI in n 14.149 * [backup-simplify]: Simplify PI into PI 14.149 * [taylor]: Taking taylor expansion of n in n 14.149 * [backup-simplify]: Simplify 0 into 0 14.149 * [backup-simplify]: Simplify 1 into 1 14.149 * [backup-simplify]: Simplify (/ PI 1) into PI 14.150 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 14.151 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 14.151 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 14.151 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 14.151 * [taylor]: Taking taylor expansion of 1/2 in n 14.151 * [backup-simplify]: Simplify 1/2 into 1/2 14.151 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.151 * [taylor]: Taking taylor expansion of k in n 14.151 * [backup-simplify]: Simplify k into k 14.151 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.151 * [taylor]: Taking taylor expansion of 1/2 in n 14.151 * [backup-simplify]: Simplify 1/2 into 1/2 14.152 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 14.152 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 14.152 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 14.154 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 14.155 * [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)))) 14.156 * [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))))) 14.157 * [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)))))) 14.159 * [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)))))) 14.160 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 14.160 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 14.161 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 14.161 * [backup-simplify]: Simplify (+ 0 0) into 0 14.163 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 14.164 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 14.165 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 14.167 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 14.169 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 14.170 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into 0 14.171 * [backup-simplify]: Simplify 0 into 0 14.172 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.177 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 14.178 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 14.178 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 14.178 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 14.178 * [taylor]: Taking taylor expansion of +nan.0 in n 14.178 * [backup-simplify]: Simplify +nan.0 into +nan.0 14.178 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 14.178 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 14.179 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 14.179 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 14.179 * [taylor]: Taking taylor expansion of -2 in n 14.179 * [backup-simplify]: Simplify -2 into -2 14.179 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.179 * [taylor]: Taking taylor expansion of PI in n 14.179 * [backup-simplify]: Simplify PI into PI 14.179 * [taylor]: Taking taylor expansion of n in n 14.179 * [backup-simplify]: Simplify 0 into 0 14.179 * [backup-simplify]: Simplify 1 into 1 14.179 * [backup-simplify]: Simplify (/ PI 1) into PI 14.180 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 14.181 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 14.181 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 14.181 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 14.181 * [taylor]: Taking taylor expansion of 1/2 in n 14.181 * [backup-simplify]: Simplify 1/2 into 1/2 14.181 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.181 * [taylor]: Taking taylor expansion of k in n 14.181 * [backup-simplify]: Simplify k into k 14.181 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.181 * [taylor]: Taking taylor expansion of 1/2 in n 14.181 * [backup-simplify]: Simplify 1/2 into 1/2 14.182 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 14.183 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 14.183 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 14.184 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 14.185 * [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)))) 14.186 * [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))))) 14.187 * [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)))))) 14.189 * [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)))))) 14.191 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 14.192 * * * [progress]: simplifying candidates 14.192 * * * * [progress]: [ 1 / 1611 ] simplifiying candidate # 14.192 * * * * [progress]: [ 2 / 1611 ] simplifiying candidate # 14.192 * * * * [progress]: [ 3 / 1611 ] simplifiying candidate # 14.192 * * * * [progress]: [ 4 / 1611 ] simplifiying candidate # 14.192 * * * * [progress]: [ 5 / 1611 ] simplifiying candidate # 14.192 * * * * [progress]: [ 6 / 1611 ] simplifiying candidate # 14.192 * * * * [progress]: [ 7 / 1611 ] simplifiying candidate # 14.192 * * * * [progress]: [ 8 / 1611 ] simplifiying 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[progress]: [ 54 / 1611 ] simplifiying candidate # 14.194 * * * * [progress]: [ 55 / 1611 ] simplifiying candidate # 14.194 * * * * [progress]: [ 56 / 1611 ] simplifiying candidate # 14.194 * * * * [progress]: [ 57 / 1611 ] simplifiying candidate # 14.194 * * * * [progress]: [ 58 / 1611 ] simplifiying candidate # 14.194 * * * * [progress]: [ 59 / 1611 ] simplifiying candidate # 14.194 * * * * [progress]: [ 60 / 1611 ] simplifiying candidate # 14.195 * * * * [progress]: [ 61 / 1611 ] simplifiying candidate # 14.195 * * * * [progress]: [ 62 / 1611 ] simplifiying candidate # 14.195 * * * * [progress]: [ 63 / 1611 ] simplifiying candidate # 14.195 * * * * [progress]: [ 64 / 1611 ] simplifiying candidate # 14.195 * * * * [progress]: [ 65 / 1611 ] simplifiying candidate # 14.195 * * * * [progress]: [ 66 / 1611 ] simplifiying candidate # 14.195 * * * * [progress]: [ 67 / 1611 ] simplifiying candidate #real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))> 14.195 * * * * [progress]: [ 68 / 1611 ] simplifiying candidate # 14.195 * * * * [progress]: [ 69 / 1611 ] simplifiying candidate # 14.195 * * * * [progress]: [ 70 / 1611 ] simplifiying candidate # 14.195 * * * * [progress]: [ 71 / 1611 ] simplifiying candidate # 14.195 * * * * [progress]: [ 72 / 1611 ] simplifiying candidate # 14.195 * * * * [progress]: [ 73 / 1611 ] simplifiying candidate # 14.195 * * * * [progress]: [ 74 / 1611 ] simplifiying candidate # 14.195 * * * * [progress]: [ 75 / 1611 ] simplifiying candidate # 14.195 * * * * [progress]: [ 76 / 1611 ] simplifiying candidate # 14.195 * * * * [progress]: [ 77 / 1611 ] simplifiying candidate # 14.195 * * * * [progress]: [ 78 / 1611 ] simplifiying candidate # 14.195 * * * * [progress]: [ 79 / 1611 ] simplifiying candidate # 14.195 * * * * [progress]: [ 80 / 1611 ] simplifiying candidate # 14.195 * * * * [progress]: [ 81 / 1611 ] simplifiying candidate # 14.195 * * * * [progress]: [ 82 / 1611 ] simplifiying candidate # 14.195 * * * * [progress]: [ 83 / 1611 ] simplifiying candidate # 14.195 * * * * [progress]: [ 84 / 1611 ] simplifiying candidate # 14.195 * * * * [progress]: [ 85 / 1611 ] simplifiying candidate # 14.196 * * * * [progress]: [ 86 / 1611 ] simplifiying candidate # 14.196 * * * * [progress]: [ 87 / 1611 ] simplifiying candidate #real (real->posit16 (* n (* 2 PI)))) (- 1/2 (/ k 2))))))> 14.196 * * * * [progress]: [ 88 / 1611 ] simplifiying candidate # 14.196 * * * * [progress]: [ 89 / 1611 ] simplifiying candidate # 14.196 * * * * [progress]: [ 90 / 1611 ] simplifiying candidate # 14.196 * * * * [progress]: [ 91 / 1611 ] simplifiying candidate # 14.196 * * * * [progress]: [ 92 / 1611 ] simplifiying candidate # 14.196 * * * * [progress]: [ 93 / 1611 ] simplifiying candidate # 14.196 * * * * [progress]: [ 94 / 1611 ] simplifiying candidate # 14.196 * * * * [progress]: [ 95 / 1611 ] simplifiying candidate # 14.196 * * * * [progress]: [ 96 / 1611 ] simplifiying candidate # 14.196 * * * * [progress]: [ 97 / 1611 ] simplifiying 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14.296 * * * * [progress]: [ 1604 / 1611 ] simplifiying candidate # 14.296 * * * * [progress]: [ 1605 / 1611 ] simplifiying candidate # 14.296 * * * * [progress]: [ 1606 / 1611 ] simplifiying candidate # 14.296 * * * * [progress]: [ 1607 / 1611 ] simplifiying candidate # 14.296 * * * * [progress]: [ 1608 / 1611 ] simplifiying candidate # 14.296 * * * * [progress]: [ 1609 / 1611 ] simplifiying candidate # 14.296 * * * * [progress]: [ 1610 / 1611 ] simplifiying candidate # 14.297 * * * * [progress]: [ 1611 / 1611 ] simplifiying candidate # 14.356 * [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 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n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 14.449 * * [simplify]: iteration 0: 1728 enodes 15.316 * * [simplify]: iteration 1: 2002 enodes 15.717 * * [simplify]: iteration complete: 2002 enodes 15.719 * * [simplify]: Extracting #0: cost 1206 inf + 0 15.722 * * [simplify]: Extracting #1: cost 1366 inf + 42 15.733 * * [simplify]: Extracting #2: cost 1480 inf + 1030 15.737 * * [simplify]: Extracting #3: cost 1478 inf + 4950 15.744 * * [simplify]: Extracting #4: cost 1363 inf + 55431 15.785 * * [simplify]: Extracting #5: cost 1062 inf + 220654 15.838 * * [simplify]: Extracting #6: cost 798 inf + 382302 15.907 * * [simplify]: Extracting #7: cost 548 inf + 555326 15.992 * * [simplify]: Extracting #8: cost 311 inf + 744460 16.106 * * [simplify]: Extracting #9: cost 149 inf + 884289 16.244 * * [simplify]: Extracting #10: cost 72 inf + 952676 16.358 * * [simplify]: Extracting #11: cost 37 inf + 980879 16.514 * * [simplify]: Extracting #12: cost 21 inf + 989015 16.633 * * [simplify]: Extracting #13: cost 17 inf + 990253 16.747 * * [simplify]: Extracting #14: cost 11 inf + 994390 16.847 * * [simplify]: Extracting #15: cost 6 inf + 999751 16.940 * * [simplify]: Extracting #16: cost 4 inf + 1001443 17.047 * * [simplify]: Extracting #17: cost 1 inf + 1004851 17.174 * * [simplify]: Extracting #18: cost 0 inf + 1006257 17.341 * [simplify]: Simplified to: (expm1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (log1p (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* 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(pow (* n (* 2 PI)) (fma 1 1/2 (- (/ k 2)))))) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ 1 2) k)))))) (/ 1 (/ (sqrt (sqrt k)) (sqrt (* n (* 2 PI))))) (/ 1 (/ (sqrt (sqrt k)) (sqrt (* n (* 2 PI))))) (/ 1 (/ (sqrt (sqrt k)) (pow n (- 1/2 (/ k 2))))) (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))) (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ 1 (sqrt (sqrt k))) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (/ k 2)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (* (cbrt k) (cbrt k)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) 2) (sqrt k))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (/ k 2)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (/ k 2)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1 2) k)))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 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(sqrt 1/2) (- (/ k 2)))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ 1 2) k)))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (/ k 2)))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) (cbrt 2)) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (cbrt k) 2) (* (cbrt k) (cbrt k)))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ (sqrt k) 2) (sqrt k))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (/ k 2)))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (/ k 2)))) (pow (* n (* 2 PI)) (fma 1 1/2 (- (* (/ 1 2) k)))) (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI))) (pow n (- 1/2 (/ k 2))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1 (/ 1 (sqrt k)) (/ 1 (/ (sqrt k) (sqrt (* n (* 2 PI))))) (/ (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt 1)) (/ (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt 1)) (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ 1 (sqrt k)) (real->posit16 (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (- (fma 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (log (* n (* 2 PI))))) (* (log n) (* k k)))) (fma 1/8 (* (exp (* 1/2 (log (* n (* 2 PI))))) (* (* (log n) (log n)) (* k k))) (+ (exp (* 1/2 (log (* n (* 2 PI))))) (* 1/8 (* (* (log (* 2 PI)) (log (* 2 PI))) (* (exp (* 1/2 (log (* n (* 2 PI))))) (* k k))))))) (fma 1/2 (* (exp (* 1/2 (log (* n (* 2 PI))))) (* (log n) k)) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (log (* n (* 2 PI))))) k))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (- (fma +nan.0 (/ (* (sqrt 2) (* (* k k) (* (* (sqrt 1/2) (sqrt 1/2)) (log (* 2 PI))))) PI) (- (fma +nan.0 (/ (* (sqrt 1/2) (* k k)) PI) (- (fma +nan.0 (/ (* n (* (sqrt 1/2) k)) (* PI PI)) (- (fma +nan.0 (/ (* (log n) (* (sqrt 2) (* (* (sqrt 1/2) (sqrt 1/2)) (* k k)))) PI) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) (- (fma +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) k)) (- (fma +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) (* k k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n)))))))))))) (- (fma +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* k k))) (- (fma +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (* +nan.0 (exp (- (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) (- (fma +nan.0 (* (sqrt 2) (* n (* PI k))) (- (fma +nan.0 (* (sqrt 2) (* n PI)) (- (fma +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k)))) (- (fma +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k)))) (- (* +nan.0 (* (sqrt 2) (* (* n n) (* PI PI))))))))))))) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) (* k (* k k))) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) k) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) (* k k)))))))) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* k k)) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 17.928 * * * [progress]: adding candidates to table 29.556 * [progress]: [Phase 3 of 3] Extracting. 29.556 * * [regime]: Finding splitpoints for: (# # # # # # #) 29.557 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2 PI) n) n k) 29.557 * * * * [regimes]: Trying to branch on (* (* 2 PI) n) from (# # # # # # #) 29.617 * * * * [regimes]: Trying to branch on n from (# # # # # # #) 29.667 * * * * [regimes]: Trying to branch on k from (# # # # # # #) 29.727 * * * [regime]: Found split indices: #