53.798 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.182 * * * [progress]: [2/2] Setting up program. 0.185 * [progress]: [Phase 2 of 3] Improving. 0.185 * * * * [progress]: [ 1 / 1 ] simplifiying candidate # 0.186 * [simplify]: Simplifying: (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 0.186 * * [simplify]: iteration 1: (13 enodes) 0.189 * * [simplify]: iteration 2: (29 enodes) 0.195 * * [simplify]: iteration 3: (60 enodes) 0.214 * * [simplify]: iteration 4: (123 enodes) 0.299 * * [simplify]: iteration 5: (322 enodes) 0.562 * * [simplify]: iteration 6: (821 enodes) 1.530 * * [simplify]: Extracting #0: cost 1 inf + 0 1.530 * * [simplify]: Extracting #1: cost 58 inf + 0 1.531 * * [simplify]: Extracting #2: cost 184 inf + 1 1.532 * * [simplify]: Extracting #3: cost 251 inf + 46 1.536 * * [simplify]: Extracting #4: cost 228 inf + 1879 1.540 * * [simplify]: Extracting #5: cost 157 inf + 21169 1.574 * * [simplify]: Extracting #6: cost 45 inf + 113683 1.629 * * [simplify]: Extracting #7: cost 0 inf + 157567 1.687 * * [simplify]: Extracting #8: cost 0 inf + 157407 1.739 * [simplify]: Simplified to: (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1.748 * * [progress]: iteration 1 / 4 1.748 * * * [progress]: picking best candidate 1.757 * * * * [pick]: Picked # 1.757 * * * [progress]: localizing error 1.789 * * * [progress]: generating rewritten candidates 1.789 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1) 1.814 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1) 1.834 * * * * [progress]: [ 3 / 3 ] rewriting at (2) 1.881 * * * [progress]: generating series expansions 1.881 * * * * [progress]: [ 1 / 3 ] generating series at (2 1) 1.881 * [backup-simplify]: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1.881 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1.881 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1.881 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1.881 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1.881 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1.881 * [taylor]: Taking taylor expansion of 1/2 in k 1.881 * [backup-simplify]: Simplify 1/2 into 1/2 1.881 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 1.881 * [taylor]: Taking taylor expansion of 1/2 in k 1.881 * [backup-simplify]: Simplify 1/2 into 1/2 1.881 * [taylor]: Taking taylor expansion of k in k 1.881 * [backup-simplify]: Simplify 0 into 0 1.881 * [backup-simplify]: Simplify 1 into 1 1.881 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 1.881 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 1.881 * [taylor]: Taking taylor expansion of 2 in k 1.881 * [backup-simplify]: Simplify 2 into 2 1.881 * [taylor]: Taking taylor expansion of (* n PI) in k 1.881 * [taylor]: Taking taylor expansion of n in k 1.881 * [backup-simplify]: Simplify n into n 1.881 * [taylor]: Taking taylor expansion of PI in k 1.882 * [backup-simplify]: Simplify PI into PI 1.882 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.882 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1.882 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1.882 * [backup-simplify]: Simplify (* 1/2 0) into 0 1.883 * [backup-simplify]: Simplify (- 0) into 0 1.883 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 1.883 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1.883 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1.883 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1.883 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1.883 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1.883 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1.884 * [taylor]: Taking taylor expansion of 1/2 in n 1.884 * [backup-simplify]: Simplify 1/2 into 1/2 1.884 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 1.884 * [taylor]: Taking taylor expansion of 1/2 in n 1.884 * [backup-simplify]: Simplify 1/2 into 1/2 1.884 * [taylor]: Taking taylor expansion of k in n 1.884 * [backup-simplify]: Simplify k into k 1.884 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.884 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.884 * [taylor]: Taking taylor expansion of 2 in n 1.884 * [backup-simplify]: Simplify 2 into 2 1.884 * [taylor]: Taking taylor expansion of (* n PI) in n 1.884 * [taylor]: Taking taylor expansion of n in n 1.884 * [backup-simplify]: Simplify 0 into 0 1.884 * [backup-simplify]: Simplify 1 into 1 1.884 * [taylor]: Taking taylor expansion of PI in n 1.884 * [backup-simplify]: Simplify PI into PI 1.884 * [backup-simplify]: Simplify (* 0 PI) into 0 1.885 * [backup-simplify]: Simplify (* 2 0) into 0 1.886 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.888 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1.888 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.889 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 1.889 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1.889 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1.890 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.891 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1.892 * [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))))) 1.892 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1.892 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1.892 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1.892 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1.892 * [taylor]: Taking taylor expansion of 1/2 in n 1.892 * [backup-simplify]: Simplify 1/2 into 1/2 1.892 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 1.892 * [taylor]: Taking taylor expansion of 1/2 in n 1.892 * [backup-simplify]: Simplify 1/2 into 1/2 1.892 * [taylor]: Taking taylor expansion of k in n 1.892 * [backup-simplify]: Simplify k into k 1.892 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.892 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.892 * [taylor]: Taking taylor expansion of 2 in n 1.892 * [backup-simplify]: Simplify 2 into 2 1.892 * [taylor]: Taking taylor expansion of (* n PI) in n 1.892 * [taylor]: Taking taylor expansion of n in n 1.892 * [backup-simplify]: Simplify 0 into 0 1.892 * [backup-simplify]: Simplify 1 into 1 1.892 * [taylor]: Taking taylor expansion of PI in n 1.892 * [backup-simplify]: Simplify PI into PI 1.893 * [backup-simplify]: Simplify (* 0 PI) into 0 1.901 * [backup-simplify]: Simplify (* 2 0) into 0 1.903 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.904 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1.905 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.905 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 1.905 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1.905 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1.906 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.907 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1.908 * [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))))) 1.908 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1.908 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1.909 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1.909 * [taylor]: Taking taylor expansion of 1/2 in k 1.909 * [backup-simplify]: Simplify 1/2 into 1/2 1.909 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 1.909 * [taylor]: Taking taylor expansion of 1/2 in k 1.909 * [backup-simplify]: Simplify 1/2 into 1/2 1.909 * [taylor]: Taking taylor expansion of k in k 1.909 * [backup-simplify]: Simplify 0 into 0 1.909 * [backup-simplify]: Simplify 1 into 1 1.909 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1.909 * [taylor]: Taking taylor expansion of (log n) in k 1.909 * [taylor]: Taking taylor expansion of n in k 1.909 * [backup-simplify]: Simplify n into n 1.909 * [backup-simplify]: Simplify (log n) into (log n) 1.909 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 1.909 * [taylor]: Taking taylor expansion of (* 2 PI) in k 1.909 * [taylor]: Taking taylor expansion of 2 in k 1.909 * [backup-simplify]: Simplify 2 into 2 1.909 * [taylor]: Taking taylor expansion of PI in k 1.909 * [backup-simplify]: Simplify PI into PI 1.909 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 1.910 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.911 * [backup-simplify]: Simplify (* 1/2 0) into 0 1.911 * [backup-simplify]: Simplify (- 0) into 0 1.911 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 1.912 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.913 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1.914 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1.915 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1.916 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.917 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1.919 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1.919 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1.920 * [backup-simplify]: Simplify (- 0) into 0 1.920 * [backup-simplify]: Simplify (+ 0 0) into 0 1.921 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.922 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1.924 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.924 * [taylor]: Taking taylor expansion of 0 in k 1.924 * [backup-simplify]: Simplify 0 into 0 1.924 * [backup-simplify]: Simplify 0 into 0 1.925 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.925 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 1.927 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1.927 * [backup-simplify]: Simplify (+ 0 0) into 0 1.928 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1.928 * [backup-simplify]: Simplify (- 1/2) into -1/2 1.928 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 1.930 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1.933 * [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))))))) 1.935 * [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))))))) 1.936 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.937 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.940 * [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 1.940 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1.941 * [backup-simplify]: Simplify (- 0) into 0 1.941 * [backup-simplify]: Simplify (+ 0 0) into 0 1.942 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.944 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1.946 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.946 * [taylor]: Taking taylor expansion of 0 in k 1.946 * [backup-simplify]: Simplify 0 into 0 1.946 * [backup-simplify]: Simplify 0 into 0 1.946 * [backup-simplify]: Simplify 0 into 0 1.947 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.948 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1.951 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1.951 * [backup-simplify]: Simplify (+ 0 0) into 0 1.952 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1.952 * [backup-simplify]: Simplify (- 0) into 0 1.953 * [backup-simplify]: Simplify (+ 0 0) into 0 1.954 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1.958 * [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))))) 1.963 * [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))))) 1.972 * [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))))) 1.972 * [backup-simplify]: Simplify (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1.972 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1.972 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1.972 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1.973 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1.973 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1.973 * [taylor]: Taking taylor expansion of 1/2 in k 1.973 * [backup-simplify]: Simplify 1/2 into 1/2 1.973 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1.973 * [taylor]: Taking taylor expansion of 1/2 in k 1.973 * [backup-simplify]: Simplify 1/2 into 1/2 1.973 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.973 * [taylor]: Taking taylor expansion of k in k 1.973 * [backup-simplify]: Simplify 0 into 0 1.973 * [backup-simplify]: Simplify 1 into 1 1.973 * [backup-simplify]: Simplify (/ 1 1) into 1 1.973 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1.973 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 1.973 * [taylor]: Taking taylor expansion of 2 in k 1.973 * [backup-simplify]: Simplify 2 into 2 1.973 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.973 * [taylor]: Taking taylor expansion of PI in k 1.973 * [backup-simplify]: Simplify PI into PI 1.973 * [taylor]: Taking taylor expansion of n in k 1.973 * [backup-simplify]: Simplify n into n 1.973 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.973 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1.974 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1.974 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 1.974 * [backup-simplify]: Simplify (- 1/2) into -1/2 1.975 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 1.975 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1.975 * [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)))) 1.975 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1.975 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1.975 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1.975 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1.975 * [taylor]: Taking taylor expansion of 1/2 in n 1.975 * [backup-simplify]: Simplify 1/2 into 1/2 1.975 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1.975 * [taylor]: Taking taylor expansion of 1/2 in n 1.975 * [backup-simplify]: Simplify 1/2 into 1/2 1.975 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.975 * [taylor]: Taking taylor expansion of k in n 1.975 * [backup-simplify]: Simplify k into k 1.975 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.975 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1.975 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.975 * [taylor]: Taking taylor expansion of 2 in n 1.975 * [backup-simplify]: Simplify 2 into 2 1.976 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.976 * [taylor]: Taking taylor expansion of PI in n 1.976 * [backup-simplify]: Simplify PI into PI 1.976 * [taylor]: Taking taylor expansion of n in n 1.976 * [backup-simplify]: Simplify 0 into 0 1.976 * [backup-simplify]: Simplify 1 into 1 1.976 * [backup-simplify]: Simplify (/ PI 1) into PI 1.977 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 1.978 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.978 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1.978 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1.978 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 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))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1.981 * [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)))) 1.981 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1.981 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1.981 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1.982 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1.982 * [taylor]: Taking taylor expansion of 1/2 in n 1.982 * [backup-simplify]: Simplify 1/2 into 1/2 1.982 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1.982 * [taylor]: Taking taylor expansion of 1/2 in n 1.982 * [backup-simplify]: Simplify 1/2 into 1/2 1.982 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.982 * [taylor]: Taking taylor expansion of k in n 1.982 * [backup-simplify]: Simplify k into k 1.982 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.982 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1.982 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.982 * [taylor]: Taking taylor expansion of 2 in n 1.982 * [backup-simplify]: Simplify 2 into 2 1.982 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.982 * [taylor]: Taking taylor expansion of PI in n 1.982 * [backup-simplify]: Simplify PI into PI 1.982 * [taylor]: Taking taylor expansion of n in n 1.982 * [backup-simplify]: Simplify 0 into 0 1.982 * [backup-simplify]: Simplify 1 into 1 1.982 * [backup-simplify]: Simplify (/ PI 1) into PI 1.983 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 1.984 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.984 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1.984 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1.984 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1.986 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1.987 * [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))) 1.988 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1.988 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1.988 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1.988 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1.988 * [taylor]: Taking taylor expansion of 1/2 in k 1.988 * [backup-simplify]: Simplify 1/2 into 1/2 1.988 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1.988 * [taylor]: Taking taylor expansion of 1/2 in k 1.988 * [backup-simplify]: Simplify 1/2 into 1/2 1.988 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.988 * [taylor]: Taking taylor expansion of k in k 1.988 * [backup-simplify]: Simplify 0 into 0 1.988 * [backup-simplify]: Simplify 1 into 1 1.989 * [backup-simplify]: Simplify (/ 1 1) into 1 1.989 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1.989 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 1.989 * [taylor]: Taking taylor expansion of (* 2 PI) in k 1.989 * [taylor]: Taking taylor expansion of 2 in k 1.989 * [backup-simplify]: Simplify 2 into 2 1.989 * [taylor]: Taking taylor expansion of PI in k 1.989 * [backup-simplify]: Simplify PI 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 * [taylor]: Taking taylor expansion of (log n) in k 1.990 * [taylor]: Taking taylor expansion of n in k 1.990 * [backup-simplify]: Simplify n into n 1.990 * [backup-simplify]: Simplify (log n) into (log n) 1.991 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 1.991 * [backup-simplify]: Simplify (- 1/2) into -1/2 1.991 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 1.992 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.993 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1.994 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1.995 * [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)))) 1.996 * [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)))) 1.997 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.998 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 1.999 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1.999 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.000 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.000 * [backup-simplify]: Simplify (- 0) into 0 2.001 * [backup-simplify]: Simplify (+ 0 0) into 0 2.002 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.003 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 2.005 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.005 * [taylor]: Taking taylor expansion of 0 in k 2.005 * [backup-simplify]: Simplify 0 into 0 2.005 * [backup-simplify]: Simplify 0 into 0 2.005 * [backup-simplify]: Simplify 0 into 0 2.006 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.007 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.010 * [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 2.011 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.011 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.012 * [backup-simplify]: Simplify (- 0) into 0 2.012 * [backup-simplify]: Simplify (+ 0 0) into 0 2.014 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.015 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 2.017 * [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 2.018 * [taylor]: Taking taylor expansion of 0 in k 2.018 * [backup-simplify]: Simplify 0 into 0 2.018 * [backup-simplify]: Simplify 0 into 0 2.018 * [backup-simplify]: Simplify 0 into 0 2.018 * [backup-simplify]: Simplify 0 into 0 2.019 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.020 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.025 * [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 2.025 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.029 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 2.029 * [backup-simplify]: Simplify (- 0) into 0 2.029 * [backup-simplify]: Simplify (+ 0 0) into 0 2.031 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.032 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 2.035 * [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 2.035 * [taylor]: Taking taylor expansion of 0 in k 2.035 * [backup-simplify]: Simplify 0 into 0 2.035 * [backup-simplify]: Simplify 0 into 0 2.036 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 2.036 * [backup-simplify]: Simplify (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 2.036 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 2.036 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 2.036 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 2.036 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 2.036 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.036 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.036 * [taylor]: Taking taylor expansion of 1/2 in k 2.036 * [backup-simplify]: Simplify 1/2 into 1/2 2.036 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.036 * [taylor]: Taking taylor expansion of k in k 2.036 * [backup-simplify]: Simplify 0 into 0 2.037 * [backup-simplify]: Simplify 1 into 1 2.037 * [backup-simplify]: Simplify (/ 1 1) into 1 2.037 * [taylor]: Taking taylor expansion of 1/2 in k 2.037 * [backup-simplify]: Simplify 1/2 into 1/2 2.037 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 2.037 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 2.037 * [taylor]: Taking taylor expansion of -2 in k 2.037 * [backup-simplify]: Simplify -2 into -2 2.037 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.037 * [taylor]: Taking taylor expansion of PI in k 2.037 * [backup-simplify]: Simplify PI into PI 2.037 * [taylor]: Taking taylor expansion of n in k 2.037 * [backup-simplify]: Simplify n into n 2.037 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.037 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 2.037 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 2.037 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.038 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.038 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 2.038 * [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))) 2.038 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.038 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.038 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.038 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.038 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.038 * [taylor]: Taking taylor expansion of 1/2 in n 2.038 * [backup-simplify]: Simplify 1/2 into 1/2 2.038 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.038 * [taylor]: Taking taylor expansion of k in n 2.038 * [backup-simplify]: Simplify k into k 2.038 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.038 * [taylor]: Taking taylor expansion of 1/2 in n 2.038 * [backup-simplify]: Simplify 1/2 into 1/2 2.038 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.038 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) 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 (/ PI n) in n 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 n in n 2.038 * [backup-simplify]: Simplify 0 into 0 2.038 * [backup-simplify]: Simplify 1 into 1 2.039 * [backup-simplify]: Simplify (/ PI 1) into PI 2.039 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.039 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.039 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.040 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.040 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.041 * [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))) 2.042 * [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)))) 2.042 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.042 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.042 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.042 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.042 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.042 * [taylor]: Taking taylor expansion of 1/2 in n 2.042 * [backup-simplify]: Simplify 1/2 into 1/2 2.042 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.042 * [taylor]: Taking taylor expansion of k in n 2.042 * [backup-simplify]: Simplify k into k 2.042 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.042 * [taylor]: Taking taylor expansion of 1/2 in n 2.042 * [backup-simplify]: Simplify 1/2 into 1/2 2.042 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.042 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.042 * [taylor]: Taking taylor expansion of -2 in n 2.042 * [backup-simplify]: Simplify -2 into -2 2.042 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.042 * [taylor]: Taking taylor expansion of PI in n 2.042 * [backup-simplify]: Simplify PI into PI 2.042 * [taylor]: Taking taylor expansion of n in n 2.042 * [backup-simplify]: Simplify 0 into 0 2.042 * [backup-simplify]: Simplify 1 into 1 2.043 * [backup-simplify]: Simplify (/ PI 1) into PI 2.043 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.044 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.044 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.044 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.045 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.046 * [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))) 2.047 * [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)))) 2.047 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 2.047 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 2.047 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.047 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.047 * [taylor]: Taking taylor expansion of 1/2 in k 2.047 * [backup-simplify]: Simplify 1/2 into 1/2 2.047 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.047 * [taylor]: Taking taylor expansion of k in k 2.047 * [backup-simplify]: Simplify 0 into 0 2.048 * [backup-simplify]: Simplify 1 into 1 2.048 * [backup-simplify]: Simplify (/ 1 1) into 1 2.048 * [taylor]: Taking taylor expansion of 1/2 in k 2.048 * [backup-simplify]: Simplify 1/2 into 1/2 2.048 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 2.048 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 2.048 * [taylor]: Taking taylor expansion of (* -2 PI) in k 2.048 * [taylor]: Taking taylor expansion of -2 in k 2.048 * [backup-simplify]: Simplify -2 into -2 2.048 * [taylor]: Taking taylor expansion of PI in k 2.048 * [backup-simplify]: Simplify PI into PI 2.048 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.049 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.049 * [taylor]: Taking taylor expansion of (log n) in k 2.049 * [taylor]: Taking taylor expansion of n in k 2.049 * [backup-simplify]: Simplify n into n 2.050 * [backup-simplify]: Simplify (log n) into (log n) 2.050 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.050 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.050 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.051 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 2.052 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 2.053 * [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)))) 2.054 * [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)))) 2.055 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.056 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.058 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 2.058 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.058 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.059 * [backup-simplify]: Simplify (+ 0 0) into 0 2.060 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.061 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 2.063 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.063 * [taylor]: Taking taylor expansion of 0 in k 2.063 * [backup-simplify]: Simplify 0 into 0 2.063 * [backup-simplify]: Simplify 0 into 0 2.063 * [backup-simplify]: Simplify 0 into 0 2.064 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.065 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.068 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 2.068 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.069 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.069 * [backup-simplify]: Simplify (+ 0 0) into 0 2.070 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.072 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 2.074 * [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 2.074 * [taylor]: Taking taylor expansion of 0 in k 2.074 * [backup-simplify]: Simplify 0 into 0 2.074 * [backup-simplify]: Simplify 0 into 0 2.074 * [backup-simplify]: Simplify 0 into 0 2.074 * [backup-simplify]: Simplify 0 into 0 2.075 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.077 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.083 * [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 2.083 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.085 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 2.085 * [backup-simplify]: Simplify (+ 0 0) into 0 2.087 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.088 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 2.091 * [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 2.091 * [taylor]: Taking taylor expansion of 0 in k 2.091 * [backup-simplify]: Simplify 0 into 0 2.091 * [backup-simplify]: Simplify 0 into 0 2.093 * [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))))) 2.094 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1) 2.094 * [backup-simplify]: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 2.094 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 2.094 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.094 * [taylor]: Taking taylor expansion of 2 in n 2.094 * [backup-simplify]: Simplify 2 into 2 2.094 * [taylor]: Taking taylor expansion of (* n PI) in n 2.094 * [taylor]: Taking taylor expansion of n in n 2.094 * [backup-simplify]: Simplify 0 into 0 2.094 * [backup-simplify]: Simplify 1 into 1 2.094 * [taylor]: Taking taylor expansion of PI in n 2.094 * [backup-simplify]: Simplify PI into PI 2.094 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.094 * [taylor]: Taking taylor expansion of 2 in n 2.094 * [backup-simplify]: Simplify 2 into 2 2.094 * [taylor]: Taking taylor expansion of (* n PI) in n 2.094 * [taylor]: Taking taylor expansion of n in n 2.094 * [backup-simplify]: Simplify 0 into 0 2.094 * [backup-simplify]: Simplify 1 into 1 2.094 * [taylor]: Taking taylor expansion of PI in n 2.094 * [backup-simplify]: Simplify PI into PI 2.095 * [backup-simplify]: Simplify (* 0 PI) into 0 2.095 * [backup-simplify]: Simplify (* 2 0) into 0 2.096 * [backup-simplify]: Simplify 0 into 0 2.097 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.098 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.098 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.099 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.099 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 2.100 * [backup-simplify]: Simplify 0 into 0 2.100 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.101 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.101 * [backup-simplify]: Simplify 0 into 0 2.102 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.102 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.102 * [backup-simplify]: Simplify 0 into 0 2.103 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.104 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 2.104 * [backup-simplify]: Simplify 0 into 0 2.105 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.106 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 2.106 * [backup-simplify]: Simplify 0 into 0 2.107 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.108 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.108 * [backup-simplify]: Simplify 0 into 0 2.109 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 2.109 * [backup-simplify]: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 2.109 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 2.109 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.109 * [taylor]: Taking taylor expansion of 2 in n 2.109 * [backup-simplify]: Simplify 2 into 2 2.109 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.109 * [taylor]: Taking taylor expansion of PI in n 2.109 * [backup-simplify]: Simplify PI into PI 2.109 * [taylor]: Taking taylor expansion of n in n 2.109 * [backup-simplify]: Simplify 0 into 0 2.109 * [backup-simplify]: Simplify 1 into 1 2.109 * [backup-simplify]: Simplify (/ PI 1) into PI 2.109 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.109 * [taylor]: Taking taylor expansion of 2 in n 2.109 * [backup-simplify]: Simplify 2 into 2 2.109 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.109 * [taylor]: Taking taylor expansion of PI in n 2.109 * [backup-simplify]: Simplify PI into PI 2.109 * [taylor]: Taking taylor expansion of n in n 2.109 * [backup-simplify]: Simplify 0 into 0 2.109 * [backup-simplify]: Simplify 1 into 1 2.110 * [backup-simplify]: Simplify (/ PI 1) into PI 2.110 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.110 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.111 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.111 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.111 * [backup-simplify]: Simplify 0 into 0 2.112 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.113 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.113 * [backup-simplify]: Simplify 0 into 0 2.113 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.114 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.114 * [backup-simplify]: Simplify 0 into 0 2.115 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.115 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.115 * [backup-simplify]: Simplify 0 into 0 2.116 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.117 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.117 * [backup-simplify]: Simplify 0 into 0 2.118 * [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 2.119 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.119 * [backup-simplify]: Simplify 0 into 0 2.119 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 2.119 * [backup-simplify]: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 2.119 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 2.119 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.119 * [taylor]: Taking taylor expansion of -2 in n 2.119 * [backup-simplify]: Simplify -2 into -2 2.119 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.119 * [taylor]: Taking taylor expansion of PI in n 2.119 * [backup-simplify]: Simplify PI into PI 2.119 * [taylor]: Taking taylor expansion of n in n 2.119 * [backup-simplify]: Simplify 0 into 0 2.119 * [backup-simplify]: Simplify 1 into 1 2.119 * [backup-simplify]: Simplify (/ PI 1) into PI 2.119 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.120 * [taylor]: Taking taylor expansion of -2 in n 2.120 * [backup-simplify]: Simplify -2 into -2 2.120 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.120 * [taylor]: Taking taylor expansion of PI in n 2.120 * [backup-simplify]: Simplify PI into PI 2.120 * [taylor]: Taking taylor expansion of n in n 2.120 * [backup-simplify]: Simplify 0 into 0 2.120 * [backup-simplify]: Simplify 1 into 1 2.120 * [backup-simplify]: Simplify (/ PI 1) into PI 2.120 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.121 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.121 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.122 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.122 * [backup-simplify]: Simplify 0 into 0 2.122 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.123 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.123 * [backup-simplify]: Simplify 0 into 0 2.123 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.124 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.124 * [backup-simplify]: Simplify 0 into 0 2.125 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.126 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.126 * [backup-simplify]: Simplify 0 into 0 2.126 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.127 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.127 * [backup-simplify]: Simplify 0 into 0 2.128 * [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 2.129 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.129 * [backup-simplify]: Simplify 0 into 0 2.129 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 2.129 * * * * [progress]: [ 3 / 3 ] generating series at (2) 2.129 * [backup-simplify]: Simplify (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 2.129 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 2.129 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 2.129 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.129 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.129 * [taylor]: Taking taylor expansion of k in k 2.129 * [backup-simplify]: Simplify 0 into 0 2.129 * [backup-simplify]: Simplify 1 into 1 2.130 * [backup-simplify]: Simplify (/ 1 1) into 1 2.130 * [backup-simplify]: Simplify (sqrt 0) into 0 2.131 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.131 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 2.131 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 2.131 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 2.131 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 2.131 * [taylor]: Taking taylor expansion of 1/2 in k 2.131 * [backup-simplify]: Simplify 1/2 into 1/2 2.131 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 2.131 * [taylor]: Taking taylor expansion of 1/2 in k 2.131 * [backup-simplify]: Simplify 1/2 into 1/2 2.131 * [taylor]: Taking taylor expansion of k in k 2.131 * [backup-simplify]: Simplify 0 into 0 2.131 * [backup-simplify]: Simplify 1 into 1 2.131 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 2.131 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 2.131 * [taylor]: Taking taylor expansion of 2 in k 2.131 * [backup-simplify]: Simplify 2 into 2 2.131 * [taylor]: Taking taylor expansion of (* n PI) in k 2.131 * [taylor]: Taking taylor expansion of n in k 2.131 * [backup-simplify]: Simplify n into n 2.131 * [taylor]: Taking taylor expansion of PI in k 2.131 * [backup-simplify]: Simplify PI into PI 2.131 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.131 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 2.131 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 2.132 * [backup-simplify]: Simplify (* 1/2 0) into 0 2.132 * [backup-simplify]: Simplify (- 0) into 0 2.132 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.132 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 2.132 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 2.132 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 2.132 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.132 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.132 * [taylor]: Taking taylor expansion of k in n 2.132 * [backup-simplify]: Simplify k into k 2.132 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.132 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 2.133 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.133 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 2.133 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 2.133 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 2.133 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 2.133 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 2.133 * [taylor]: Taking taylor expansion of 1/2 in n 2.133 * [backup-simplify]: Simplify 1/2 into 1/2 2.133 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 2.133 * [taylor]: Taking taylor expansion of 1/2 in n 2.133 * [backup-simplify]: Simplify 1/2 into 1/2 2.133 * [taylor]: Taking taylor expansion of k in n 2.133 * [backup-simplify]: Simplify k into k 2.133 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 2.133 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.133 * [taylor]: Taking taylor expansion of 2 in n 2.133 * [backup-simplify]: Simplify 2 into 2 2.133 * [taylor]: Taking taylor expansion of (* n PI) in n 2.133 * [taylor]: Taking taylor expansion of n in n 2.133 * [backup-simplify]: Simplify 0 into 0 2.133 * [backup-simplify]: Simplify 1 into 1 2.133 * [taylor]: Taking taylor expansion of PI in n 2.133 * [backup-simplify]: Simplify PI into PI 2.133 * [backup-simplify]: Simplify (* 0 PI) into 0 2.133 * [backup-simplify]: Simplify (* 2 0) into 0 2.134 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.135 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.136 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.136 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 2.136 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 2.136 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 2.139 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.140 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 2.140 * [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))))) 2.140 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 2.140 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.140 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.140 * [taylor]: Taking taylor expansion of k in n 2.140 * [backup-simplify]: Simplify k into k 2.140 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.141 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 2.141 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.141 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 2.141 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 2.141 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 2.141 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 2.141 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 2.141 * [taylor]: Taking taylor expansion of 1/2 in n 2.141 * [backup-simplify]: Simplify 1/2 into 1/2 2.141 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 2.141 * [taylor]: Taking taylor expansion of 1/2 in n 2.141 * [backup-simplify]: Simplify 1/2 into 1/2 2.141 * [taylor]: Taking taylor expansion of k in n 2.141 * [backup-simplify]: Simplify k into k 2.141 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 2.141 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.141 * [taylor]: Taking taylor expansion of 2 in n 2.141 * [backup-simplify]: Simplify 2 into 2 2.141 * [taylor]: Taking taylor expansion of (* n PI) in n 2.141 * [taylor]: Taking taylor expansion of n in n 2.141 * [backup-simplify]: Simplify 0 into 0 2.141 * [backup-simplify]: Simplify 1 into 1 2.141 * [taylor]: Taking taylor expansion of PI in n 2.141 * [backup-simplify]: Simplify PI into PI 2.141 * [backup-simplify]: Simplify (* 0 PI) into 0 2.141 * [backup-simplify]: Simplify (* 2 0) into 0 2.142 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.143 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.144 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.144 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 2.144 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 2.144 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 2.145 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.146 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 2.146 * [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))))) 2.147 * [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))) 2.147 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 2.147 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 2.147 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 2.147 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 2.147 * [taylor]: Taking taylor expansion of 1/2 in k 2.147 * [backup-simplify]: Simplify 1/2 into 1/2 2.147 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 2.147 * [taylor]: Taking taylor expansion of 1/2 in k 2.147 * [backup-simplify]: Simplify 1/2 into 1/2 2.147 * [taylor]: Taking taylor expansion of k in k 2.147 * [backup-simplify]: Simplify 0 into 0 2.147 * [backup-simplify]: Simplify 1 into 1 2.147 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 2.147 * [taylor]: Taking taylor expansion of (log n) in k 2.147 * [taylor]: Taking taylor expansion of n in k 2.147 * [backup-simplify]: Simplify n into n 2.147 * [backup-simplify]: Simplify (log n) into (log n) 2.147 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.147 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.148 * [taylor]: Taking taylor expansion of 2 in k 2.148 * [backup-simplify]: Simplify 2 into 2 2.148 * [taylor]: Taking taylor expansion of PI in k 2.148 * [backup-simplify]: Simplify PI into PI 2.148 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.148 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.149 * [backup-simplify]: Simplify (* 1/2 0) into 0 2.149 * [backup-simplify]: Simplify (- 0) into 0 2.149 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.150 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.151 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 2.151 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 2.151 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.151 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.151 * [taylor]: Taking taylor expansion of k in k 2.151 * [backup-simplify]: Simplify 0 into 0 2.151 * [backup-simplify]: Simplify 1 into 1 2.152 * [backup-simplify]: Simplify (/ 1 1) into 1 2.152 * [backup-simplify]: Simplify (sqrt 0) into 0 2.153 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.153 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 2.153 * [backup-simplify]: Simplify 0 into 0 2.154 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.154 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 2.155 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.156 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 2.156 * [backup-simplify]: Simplify (- 0) into 0 2.156 * [backup-simplify]: Simplify (+ 0 0) into 0 2.157 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.158 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 2.159 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.160 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 2.160 * [taylor]: Taking taylor expansion of 0 in k 2.160 * [backup-simplify]: Simplify 0 into 0 2.160 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.161 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.163 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.163 * [backup-simplify]: Simplify (+ 0 0) into 0 2.164 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 2.164 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.165 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.166 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2.169 * [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))))))) 2.173 * [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))))))) 2.175 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 2.176 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.178 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.181 * [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 2.182 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 2.182 * [backup-simplify]: Simplify (- 0) into 0 2.183 * [backup-simplify]: Simplify (+ 0 0) into 0 2.184 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.186 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.189 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.189 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.189 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 2.190 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 2.190 * [taylor]: Taking taylor expansion of 0 in k 2.191 * [backup-simplify]: Simplify 0 into 0 2.191 * [backup-simplify]: Simplify 0 into 0 2.191 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.193 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.194 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.194 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.196 * [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 2.196 * [backup-simplify]: Simplify (+ 0 0) into 0 2.197 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 2.197 * [backup-simplify]: Simplify (- 0) into 0 2.198 * [backup-simplify]: Simplify (+ 0 0) into 0 2.199 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.201 * [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))))) 2.209 * [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)))))))) 2.214 * [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)))))))) 2.215 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.216 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.221 * [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 2.222 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 2.223 * [backup-simplify]: Simplify (- 0) into 0 2.223 * [backup-simplify]: Simplify (+ 0 0) into 0 2.224 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.226 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 2.229 * [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 2.229 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.230 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 2.232 * [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 2.232 * [taylor]: Taking taylor expansion of 0 in k 2.232 * [backup-simplify]: Simplify 0 into 0 2.232 * [backup-simplify]: Simplify 0 into 0 2.232 * [backup-simplify]: Simplify 0 into 0 2.233 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.236 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.239 * [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 2.240 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.245 * [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 2.245 * [backup-simplify]: Simplify (+ 0 0) into 0 2.246 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 2.246 * [backup-simplify]: Simplify (- 0) into 0 2.247 * [backup-simplify]: Simplify (+ 0 0) into 0 2.252 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 2.258 * [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))))))) 2.274 * [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)))))))))))))) 2.285 * [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)))))))))))))) 2.298 * [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)))))))))))))))))))))) 2.299 * [backup-simplify]: Simplify (/ (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 2.299 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 2.299 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 2.299 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.299 * [taylor]: Taking taylor expansion of k in k 2.299 * [backup-simplify]: Simplify 0 into 0 2.299 * [backup-simplify]: Simplify 1 into 1 2.299 * [backup-simplify]: Simplify (sqrt 0) into 0 2.300 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.300 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 2.300 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 2.300 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 2.300 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.300 * [taylor]: Taking taylor expansion of 1/2 in k 2.300 * [backup-simplify]: Simplify 1/2 into 1/2 2.300 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.300 * [taylor]: Taking taylor expansion of 1/2 in k 2.300 * [backup-simplify]: Simplify 1/2 into 1/2 2.300 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.300 * [taylor]: Taking taylor expansion of k in k 2.300 * [backup-simplify]: Simplify 0 into 0 2.300 * [backup-simplify]: Simplify 1 into 1 2.300 * [backup-simplify]: Simplify (/ 1 1) into 1 2.300 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 2.300 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 2.300 * [taylor]: Taking taylor expansion of 2 in k 2.300 * [backup-simplify]: Simplify 2 into 2 2.300 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.300 * [taylor]: Taking taylor expansion of PI in k 2.300 * [backup-simplify]: Simplify PI into PI 2.300 * [taylor]: Taking taylor expansion of n in k 2.300 * [backup-simplify]: Simplify n into n 2.301 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.301 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 2.301 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 2.301 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.301 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.301 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.301 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 2.302 * [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)))) 2.302 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 2.302 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.302 * [taylor]: Taking taylor expansion of k in n 2.302 * [backup-simplify]: Simplify k into k 2.302 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.302 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.302 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.302 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.302 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.302 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.302 * [taylor]: Taking taylor expansion of 1/2 in n 2.302 * [backup-simplify]: Simplify 1/2 into 1/2 2.302 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.302 * [taylor]: Taking taylor expansion of 1/2 in n 2.302 * [backup-simplify]: Simplify 1/2 into 1/2 2.302 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.302 * [taylor]: Taking taylor expansion of k in n 2.302 * [backup-simplify]: Simplify k into k 2.302 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.302 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.302 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.302 * [taylor]: Taking taylor expansion of 2 in n 2.302 * [backup-simplify]: Simplify 2 into 2 2.302 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.302 * [taylor]: Taking taylor expansion of PI in n 2.302 * [backup-simplify]: Simplify PI into PI 2.302 * [taylor]: Taking taylor expansion of n in n 2.302 * [backup-simplify]: Simplify 0 into 0 2.302 * [backup-simplify]: Simplify 1 into 1 2.302 * [backup-simplify]: Simplify (/ PI 1) into PI 2.303 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.303 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.303 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.303 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.304 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.305 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.306 * [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))) 2.307 * [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)))) 2.307 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 2.307 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.307 * [taylor]: Taking taylor expansion of k in n 2.307 * [backup-simplify]: Simplify k into k 2.307 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.307 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.307 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.307 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.307 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.307 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.307 * [taylor]: Taking taylor expansion of 1/2 in n 2.307 * [backup-simplify]: Simplify 1/2 into 1/2 2.307 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.307 * [taylor]: Taking taylor expansion of 1/2 in n 2.307 * [backup-simplify]: Simplify 1/2 into 1/2 2.307 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.307 * [taylor]: Taking taylor expansion of k in n 2.307 * [backup-simplify]: Simplify k into k 2.307 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.307 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.307 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.307 * [taylor]: Taking taylor expansion of 2 in n 2.307 * [backup-simplify]: Simplify 2 into 2 2.307 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.307 * [taylor]: Taking taylor expansion of PI in n 2.307 * [backup-simplify]: Simplify PI into PI 2.307 * [taylor]: Taking taylor expansion of n in n 2.307 * [backup-simplify]: Simplify 0 into 0 2.307 * [backup-simplify]: Simplify 1 into 1 2.308 * [backup-simplify]: Simplify (/ PI 1) into PI 2.308 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.309 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.309 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.309 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.309 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.310 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.310 * [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))) 2.311 * [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)))) 2.312 * [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)) 2.312 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 2.312 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 2.312 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 2.312 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.312 * [taylor]: Taking taylor expansion of 1/2 in k 2.312 * [backup-simplify]: Simplify 1/2 into 1/2 2.312 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.312 * [taylor]: Taking taylor expansion of 1/2 in k 2.312 * [backup-simplify]: Simplify 1/2 into 1/2 2.312 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.312 * [taylor]: Taking taylor expansion of k in k 2.312 * [backup-simplify]: Simplify 0 into 0 2.312 * [backup-simplify]: Simplify 1 into 1 2.312 * [backup-simplify]: Simplify (/ 1 1) into 1 2.312 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 2.312 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.312 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.312 * [taylor]: Taking taylor expansion of 2 in k 2.312 * [backup-simplify]: Simplify 2 into 2 2.312 * [taylor]: Taking taylor expansion of PI in k 2.313 * [backup-simplify]: Simplify PI into PI 2.313 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.313 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.313 * [taylor]: Taking taylor expansion of (log n) in k 2.313 * [taylor]: Taking taylor expansion of n in k 2.313 * [backup-simplify]: Simplify n into n 2.314 * [backup-simplify]: Simplify (log n) into (log n) 2.314 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.314 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.314 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.314 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.315 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 2.316 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 2.316 * [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)))) 2.316 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.316 * [taylor]: Taking taylor expansion of k in k 2.316 * [backup-simplify]: Simplify 0 into 0 2.316 * [backup-simplify]: Simplify 1 into 1 2.317 * [backup-simplify]: Simplify (sqrt 0) into 0 2.317 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.318 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 2.318 * [backup-simplify]: Simplify 0 into 0 2.319 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.319 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.320 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.320 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.321 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.321 * [backup-simplify]: Simplify (- 0) into 0 2.321 * [backup-simplify]: Simplify (+ 0 0) into 0 2.322 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.323 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 2.324 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.325 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 2.325 * [taylor]: Taking taylor expansion of 0 in k 2.325 * [backup-simplify]: Simplify 0 into 0 2.325 * [backup-simplify]: Simplify 0 into 0 2.326 * [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)))))) 2.326 * [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)))))) 2.327 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.328 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.330 * [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 2.330 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.330 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.331 * [backup-simplify]: Simplify (- 0) into 0 2.331 * [backup-simplify]: Simplify (+ 0 0) into 0 2.332 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.333 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 2.334 * [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 2.334 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 2.335 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 2.335 * [taylor]: Taking taylor expansion of 0 in k 2.335 * [backup-simplify]: Simplify 0 into 0 2.336 * [backup-simplify]: Simplify 0 into 0 2.336 * [backup-simplify]: Simplify 0 into 0 2.337 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.338 * [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)))))) 2.339 * [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)))))) 2.340 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.341 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.344 * [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 2.344 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.345 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 2.345 * [backup-simplify]: Simplify (- 0) into 0 2.345 * [backup-simplify]: Simplify (+ 0 0) into 0 2.348 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.349 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 2.351 * [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 2.351 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 2.353 * [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 2.353 * [taylor]: Taking taylor expansion of 0 in k 2.353 * [backup-simplify]: Simplify 0 into 0 2.353 * [backup-simplify]: Simplify 0 into 0 2.353 * [backup-simplify]: Simplify 0 into 0 2.353 * [backup-simplify]: Simplify 0 into 0 2.355 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.356 * [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)))))) 2.357 * [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)))))) 2.360 * [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)))))))) 2.360 * [backup-simplify]: Simplify (/ (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 2.360 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 2.360 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 2.360 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 2.360 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 2.360 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 2.360 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.360 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.360 * [taylor]: Taking taylor expansion of 1/2 in k 2.360 * [backup-simplify]: Simplify 1/2 into 1/2 2.360 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.360 * [taylor]: Taking taylor expansion of k in k 2.360 * [backup-simplify]: Simplify 0 into 0 2.360 * [backup-simplify]: Simplify 1 into 1 2.360 * [backup-simplify]: Simplify (/ 1 1) into 1 2.360 * [taylor]: Taking taylor expansion of 1/2 in k 2.360 * [backup-simplify]: Simplify 1/2 into 1/2 2.360 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 2.360 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 2.360 * [taylor]: Taking taylor expansion of -2 in k 2.360 * [backup-simplify]: Simplify -2 into -2 2.360 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.360 * [taylor]: Taking taylor expansion of PI in k 2.360 * [backup-simplify]: Simplify PI into PI 2.360 * [taylor]: Taking taylor expansion of n in k 2.360 * [backup-simplify]: Simplify n into n 2.360 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.360 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 2.361 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 2.361 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.361 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.361 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 2.361 * [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))) 2.361 * [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 2.361 * [taylor]: Taking taylor expansion of k in k 2.361 * [backup-simplify]: Simplify 0 into 0 2.361 * [backup-simplify]: Simplify 1 into 1 2.362 * [backup-simplify]: Simplify (/ -1 1) into -1 2.362 * [backup-simplify]: Simplify (sqrt 0) into 0 2.363 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.363 * [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)))) 2.363 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 2.363 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.363 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.363 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.363 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.363 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.363 * [taylor]: Taking taylor expansion of 1/2 in n 2.363 * [backup-simplify]: Simplify 1/2 into 1/2 2.363 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.363 * [taylor]: Taking taylor expansion of k in n 2.363 * [backup-simplify]: Simplify k into k 2.363 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.363 * [taylor]: Taking taylor expansion of 1/2 in n 2.363 * [backup-simplify]: Simplify 1/2 into 1/2 2.363 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.363 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.363 * [taylor]: Taking taylor expansion of -2 in n 2.363 * [backup-simplify]: Simplify -2 into -2 2.363 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.363 * [taylor]: Taking taylor expansion of PI in n 2.363 * [backup-simplify]: Simplify PI into PI 2.363 * [taylor]: Taking taylor expansion of n in n 2.363 * [backup-simplify]: Simplify 0 into 0 2.363 * [backup-simplify]: Simplify 1 into 1 2.363 * [backup-simplify]: Simplify (/ PI 1) into PI 2.364 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.364 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.364 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.365 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.365 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.366 * [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))) 2.367 * [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)))) 2.367 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.367 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.367 * [taylor]: Taking taylor expansion of -1 in n 2.367 * [backup-simplify]: Simplify -1 into -1 2.367 * [taylor]: Taking taylor expansion of k in n 2.367 * [backup-simplify]: Simplify k into k 2.367 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.367 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.367 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.367 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.368 * [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))) 2.368 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 2.368 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.368 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.368 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.368 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.368 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.368 * [taylor]: Taking taylor expansion of 1/2 in n 2.368 * [backup-simplify]: Simplify 1/2 into 1/2 2.368 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.368 * [taylor]: Taking taylor expansion of k in n 2.368 * [backup-simplify]: Simplify k into k 2.368 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.368 * [taylor]: Taking taylor expansion of 1/2 in n 2.368 * [backup-simplify]: Simplify 1/2 into 1/2 2.368 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.368 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.368 * [taylor]: Taking taylor expansion of -2 in n 2.368 * [backup-simplify]: Simplify -2 into -2 2.368 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.368 * [taylor]: Taking taylor expansion of PI in n 2.368 * [backup-simplify]: Simplify PI into PI 2.368 * [taylor]: Taking taylor expansion of n in n 2.368 * [backup-simplify]: Simplify 0 into 0 2.368 * [backup-simplify]: Simplify 1 into 1 2.369 * [backup-simplify]: Simplify (/ PI 1) into PI 2.369 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.370 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.370 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.370 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.371 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.371 * [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))) 2.372 * [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)))) 2.372 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.372 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.372 * [taylor]: Taking taylor expansion of -1 in n 2.372 * [backup-simplify]: Simplify -1 into -1 2.372 * [taylor]: Taking taylor expansion of k in n 2.372 * [backup-simplify]: Simplify k into k 2.372 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.372 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.372 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.373 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.374 * [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))) 2.374 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 2.374 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 2.374 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 2.374 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.374 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.374 * [taylor]: Taking taylor expansion of 1/2 in k 2.374 * [backup-simplify]: Simplify 1/2 into 1/2 2.374 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.374 * [taylor]: Taking taylor expansion of k in k 2.374 * [backup-simplify]: Simplify 0 into 0 2.374 * [backup-simplify]: Simplify 1 into 1 2.374 * [backup-simplify]: Simplify (/ 1 1) into 1 2.374 * [taylor]: Taking taylor expansion of 1/2 in k 2.374 * [backup-simplify]: Simplify 1/2 into 1/2 2.374 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 2.374 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 2.375 * [taylor]: Taking taylor expansion of (* -2 PI) in k 2.375 * [taylor]: Taking taylor expansion of -2 in k 2.375 * [backup-simplify]: Simplify -2 into -2 2.375 * [taylor]: Taking taylor expansion of PI in k 2.375 * [backup-simplify]: Simplify PI into PI 2.375 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.376 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.376 * [taylor]: Taking taylor expansion of (log n) in k 2.376 * [taylor]: Taking taylor expansion of n in k 2.376 * [backup-simplify]: Simplify n into n 2.376 * [backup-simplify]: Simplify (log n) into (log n) 2.377 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.377 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.377 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.378 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 2.379 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 2.379 * [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)))) 2.379 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.379 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.379 * [taylor]: Taking taylor expansion of -1 in k 2.379 * [backup-simplify]: Simplify -1 into -1 2.379 * [taylor]: Taking taylor expansion of k in k 2.379 * [backup-simplify]: Simplify 0 into 0 2.379 * [backup-simplify]: Simplify 1 into 1 2.380 * [backup-simplify]: Simplify (/ -1 1) into -1 2.380 * [backup-simplify]: Simplify (sqrt 0) into 0 2.381 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.382 * [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))))) 2.382 * [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))))) 2.383 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.383 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.384 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 2.384 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.385 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.385 * [backup-simplify]: Simplify (+ 0 0) into 0 2.386 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.387 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 2.388 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.389 * [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 2.389 * [taylor]: Taking taylor expansion of 0 in k 2.389 * [backup-simplify]: Simplify 0 into 0 2.389 * [backup-simplify]: Simplify 0 into 0 2.389 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.391 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.392 * [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)))))) 2.393 * [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)))))) 2.393 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.394 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.396 * [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 2.396 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.396 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.397 * [backup-simplify]: Simplify (+ 0 0) into 0 2.398 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.399 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 2.400 * [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 2.400 * [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 2.402 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.404 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.406 * [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)))))) 2.408 * [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)))))) 2.410 * [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))))))))))) 2.411 * * * [progress]: simplifying candidates 2.411 * * * * [progress]: [ 1 / 445 ] simplifiying candidate # 2.411 * * * * [progress]: [ 2 / 445 ] simplifiying candidate # 2.411 * * * * [progress]: [ 3 / 445 ] simplifiying candidate # 2.411 * * * * [progress]: [ 4 / 445 ] simplifiying candidate # 2.411 * * * * [progress]: [ 5 / 445 ] simplifiying candidate # 2.411 * * * * [progress]: [ 6 / 445 ] simplifiying candidate # 2.411 * * * * [progress]: [ 7 / 445 ] simplifiying candidate # 2.411 * * * * [progress]: [ 8 / 445 ] simplifiying candidate # 2.411 * * * * [progress]: [ 9 / 445 ] simplifiying candidate # 2.411 * * * * [progress]: [ 10 / 445 ] simplifiying candidate # 2.411 * * * * [progress]: [ 11 / 445 ] simplifiying candidate # 2.411 * * * * [progress]: [ 12 / 445 ] simplifiying candidate # 2.411 * * * * [progress]: [ 13 / 445 ] simplifiying candidate # 2.411 * * * * [progress]: [ 14 / 445 ] simplifiying candidate # 2.411 * * * * 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2.413 * * * * [progress]: [ 62 / 445 ] simplifiying candidate # 2.413 * * * * [progress]: [ 63 / 445 ] simplifiying candidate # 2.413 * * * * [progress]: [ 64 / 445 ] simplifiying candidate # 2.414 * * * * [progress]: [ 65 / 445 ] simplifiying candidate # 2.414 * * * * [progress]: [ 66 / 445 ] simplifiying candidate # 2.414 * * * * [progress]: [ 67 / 445 ] simplifiying candidate #real (real->posit16 (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k)))> 2.414 * * * * [progress]: [ 68 / 445 ] simplifiying candidate # 2.414 * * * * [progress]: [ 69 / 445 ] simplifiying candidate # 2.414 * * * * [progress]: [ 70 / 445 ] simplifiying candidate # 2.414 * * * * [progress]: [ 71 / 445 ] simplifiying candidate # 2.414 * * * * [progress]: [ 72 / 445 ] simplifiying candidate # 2.414 * * * * [progress]: [ 73 / 445 ] simplifiying candidate # 2.414 * * * * [progress]: [ 74 / 445 ] simplifiying candidate # 2.414 * * * * [progress]: [ 75 / 445 ] simplifiying candidate # 2.414 * * * * [progress]: [ 76 / 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candidate # 2.431 * * * * [progress]: [ 443 / 445 ] simplifiying candidate # 2.431 * * * * [progress]: [ 444 / 445 ] simplifiying candidate # 2.431 * * * * [progress]: [ 445 / 445 ] simplifiying candidate # 2.442 * [simplify]: Simplifying: (expm1 (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (log1p (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (+ (log PI) (+ (log n) (log 2))) (- 1/2 (/ k 2))) (* (+ (log PI) (log (* n 2))) (- 1/2 (/ k 2))) (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)) (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2)))) (pow (* PI (* n 2)) 1) (pow (* PI (* n 2)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* PI (* n 2)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (pow (* PI (* n 2)) 1) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* PI (* n 2)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (pow (* PI (* n 2)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (pow (* PI (* n 2)) (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 (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* PI (* n 2)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (pow (* PI (* n 2)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow (* PI (* n 2)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* PI (* n 2)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (pow (* PI (* n 2)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) 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(- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 2.465 * * [simplify]: iteration 1: (698 enodes) 2.759 * * [simplify]: iteration 2: (1515 enodes) 3.832 * * [simplify]: Extracting #0: cost 212 inf + 0 3.835 * * [simplify]: Extracting #1: cost 835 inf + 1 3.845 * * [simplify]: Extracting #2: cost 1371 inf + 2843 3.855 * * [simplify]: Extracting #3: cost 1490 inf + 50740 3.888 * * [simplify]: Extracting #4: cost 1165 inf + 173880 3.981 * * [simplify]: Extracting #5: cost 717 inf + 363097 4.084 * * [simplify]: Extracting #6: cost 398 inf + 548093 4.223 * * [simplify]: Extracting #7: cost 79 inf + 764685 4.357 * * [simplify]: Extracting #8: cost 2 inf + 822930 4.529 * * [simplify]: Extracting #9: cost 0 inf + 824546 4.657 * * [simplify]: Extracting #10: cost 0 inf + 824451 4.783 * * [simplify]: Extracting #11: cost 0 inf + 824426 4.975 * [simplify]: Simplified to: (expm1 (pow (* (* 2 n) PI) (- 1/2 (* 1/2 k)))) (log1p (pow (* (* 2 n) PI) (- 1/2 (* 1/2 k)))) (* (- 1/2 (* 1/2 k)) 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PI) (* (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))) (+ (- (/ (cbrt k) (cbrt 2))) (/ (cbrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (+ (- (/ (cbrt k) (sqrt 2))) (/ (cbrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (* (cbrt k) (cbrt k)) (+ (- (/ (cbrt k) 2)) (/ (cbrt k) 2))))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (+ (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (/ (sqrt k) (sqrt 2)) (+ (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma (/ k (cbrt 2)) (/ -1 (* (cbrt 2) (cbrt 2))) (/ (/ k (cbrt 2)) (* (cbrt 2) (cbrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma (/ k (sqrt 2)) (/ -1 (sqrt 2)) (/ (/ k (sqrt 2)) (sqrt 2))))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))) (+ (- (/ (cbrt k) (cbrt 2))) (/ (cbrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (+ (- (/ (cbrt k) (sqrt 2))) (/ (cbrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (* (cbrt k) (cbrt k)) (+ (- (/ (cbrt k) 2)) (/ (cbrt k) 2))))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (+ (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (/ (sqrt k) (sqrt 2)) (+ (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma (/ k (cbrt 2)) (/ -1 (* (cbrt 2) (cbrt 2))) (/ (/ k (cbrt 2)) (* (cbrt 2) (cbrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma (/ k (sqrt 2)) (/ -1 (sqrt 2)) (/ (/ k (sqrt 2)) (sqrt 2))))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))) (+ (- (/ (cbrt k) (cbrt 2))) (/ (cbrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (+ (- (/ (cbrt k) (sqrt 2))) (/ (cbrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (* (cbrt k) (cbrt k)) (+ (- (/ (cbrt k) 2)) (/ (cbrt k) 2))))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (+ (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (/ (sqrt k) (sqrt 2)) (+ (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma (/ k (cbrt 2)) (/ -1 (* (cbrt 2) (cbrt 2))) (/ (/ k (cbrt 2)) (* (cbrt 2) (cbrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma (/ k (sqrt 2)) (/ -1 (sqrt 2)) (/ (/ k (sqrt 2)) (sqrt 2))))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (* -1/2 k))) (/ (sqrt k) (pow (* (* 2 n) PI) (* -1/2 k))) (/ (sqrt k) (pow (* 2 n) (- 1/2 (* 1/2 k)))) (/ (sqrt k) (cbrt (pow (* (* 2 n) PI) (- 1/2 (* 1/2 k))))) (/ (sqrt k) (sqrt (pow (* (* 2 n) PI) (- 1/2 (* 1/2 k))))) (/ (sqrt k) (pow (* (* 2 n) PI) (- 1/2 (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (- 1/4 (/ k 4)))) (* (pow (* (* 2 n) PI) (* 1/2 k)) (sqrt k)) (real->posit16 (/ (pow (* (* 2 n) PI) (- 1/2 (* 1/2 k))) (sqrt k))) (fma (* 1/4 (log (* PI 2))) (* (* (exp (* (log (* (* 2 n) PI)) 1/2)) (log n)) (* k k)) (- (fma (* 1/8 (exp (* (log (* (* 2 n) PI)) 1/2))) (* (* (log n) k) (* (log n) k)) (fma 1/8 (* (exp (* (log (* (* 2 n) PI)) 1/2)) (* (* k k) (* (log (* PI 2)) (log (* PI 2))))) (exp (* (log (* (* 2 n) PI)) 1/2)))) (* (* k (+ (* (exp (* (log (* (* 2 n) PI)) 1/2)) (log n)) (* (log (* PI 2)) (exp (* (log (* (* 2 n) PI)) 1/2))))) 1/2))) (exp (* (- 1/2 (* 1/2 k)) (log (* (* 2 n) PI)))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n))))) (* (* 2 n) PI) (* (* 2 n) PI) (* (* 2 n) PI) (- (fma +nan.0 (* (* (* (exp (* (log (* (* 2 n) PI)) 1/2)) (log n)) (* k k)) (log (* PI 2))) (- (- (* (log (* PI 2)) (* (exp (* (log (* (* 2 n) PI)) 1/2)) (* (* k k) +nan.0))) (fma (* (exp (* (log (* (* 2 n) PI)) 1/2)) +nan.0) (* (* (log n) k) (* (log n) k)) (- (- (* (* (exp (* (log (* (* 2 n) PI)) 1/2)) +nan.0) k) (+ (- (* (exp (* (log (* (* 2 n) PI)) 1/2)) +nan.0) (* (* (log (* PI 2)) (log (* PI 2))) (* (exp (* (log (* (* 2 n) PI)) 1/2)) (* (* k k) +nan.0)))) (+ (- (* +nan.0 (* (* (exp (* (log (* (* 2 n) PI)) 1/2)) (log n)) (* k k))) (* (exp (* (log (* (* 2 n) PI)) 1/2)) (* (* k k) +nan.0))) (- (* +nan.0 (* (exp (* (log (* (* 2 n) PI)) 1/2)) (* k (log (* PI 2))))) (* (* (log n) k) (* (exp (* (log (* (* 2 n) PI)) 1/2)) +nan.0)))))))))))) (- (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (log (* (* 2 n) PI)))) (* k (* k k)))) (* +nan.0 (- (/ (exp (* (- 1/2 (* 1/2 k)) (log (* (* 2 n) PI)))) k) (/ (exp (* (- 1/2 (* 1/2 k)) (log (* (* 2 n) PI)))) (* k k)))))) (+ (* (- +nan.0) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n))))) k)) (* +nan.0 (- (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n))))) (* k k)) (exp (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n)))))))) 5.079 * * * [progress]: adding candidates to table 10.855 * * [progress]: iteration 2 / 4 10.855 * * * [progress]: picking best candidate 10.886 * * * * [pick]: Picked # 10.886 * * * [progress]: localizing error 10.916 * * * [progress]: generating rewritten candidates 10.916 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 10.942 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1) 10.955 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2) 10.967 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 11.102 * * * [progress]: generating series expansions 11.102 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 11.102 * [backup-simplify]: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 11.102 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 11.102 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 11.103 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 11.103 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 11.103 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.103 * [taylor]: Taking taylor expansion of 1/2 in k 11.103 * [backup-simplify]: Simplify 1/2 into 1/2 11.103 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.103 * [taylor]: Taking taylor expansion of 1/2 in k 11.103 * [backup-simplify]: Simplify 1/2 into 1/2 11.103 * [taylor]: Taking taylor expansion of k in k 11.103 * [backup-simplify]: Simplify 0 into 0 11.103 * [backup-simplify]: Simplify 1 into 1 11.103 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 11.103 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 11.103 * [taylor]: Taking taylor expansion of 2 in k 11.103 * [backup-simplify]: Simplify 2 into 2 11.103 * [taylor]: Taking taylor expansion of (* n PI) in k 11.103 * [taylor]: Taking taylor expansion of n in k 11.103 * [backup-simplify]: Simplify n into n 11.103 * [taylor]: Taking taylor expansion of PI in k 11.103 * [backup-simplify]: Simplify PI into PI 11.103 * [backup-simplify]: Simplify (* n PI) into (* n PI) 11.103 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 11.103 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 11.104 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.104 * [backup-simplify]: Simplify (- 0) into 0 11.104 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.104 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 11.104 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 11.104 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 11.104 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 11.104 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 11.104 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 11.104 * [taylor]: Taking taylor expansion of 1/2 in n 11.104 * [backup-simplify]: Simplify 1/2 into 1/2 11.104 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 11.104 * [taylor]: Taking taylor expansion of 1/2 in n 11.104 * [backup-simplify]: Simplify 1/2 into 1/2 11.104 * [taylor]: Taking taylor expansion of k in n 11.104 * [backup-simplify]: Simplify k into k 11.104 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.104 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.104 * [taylor]: Taking taylor expansion of 2 in n 11.104 * [backup-simplify]: Simplify 2 into 2 11.104 * [taylor]: Taking taylor expansion of (* n PI) in n 11.104 * [taylor]: Taking taylor expansion of n in n 11.104 * [backup-simplify]: Simplify 0 into 0 11.105 * [backup-simplify]: Simplify 1 into 1 11.105 * [taylor]: Taking taylor expansion of PI in n 11.105 * [backup-simplify]: Simplify PI into PI 11.105 * [backup-simplify]: Simplify (* 0 PI) into 0 11.105 * [backup-simplify]: Simplify (* 2 0) into 0 11.106 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.107 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.108 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.108 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 11.108 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 11.108 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 11.109 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.110 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 11.110 * [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))))) 11.110 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 11.110 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 11.110 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 11.110 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 11.110 * [taylor]: Taking taylor expansion of 1/2 in n 11.110 * [backup-simplify]: Simplify 1/2 into 1/2 11.110 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 11.110 * [taylor]: Taking taylor expansion of 1/2 in n 11.110 * [backup-simplify]: Simplify 1/2 into 1/2 11.110 * [taylor]: Taking taylor expansion of k in n 11.110 * [backup-simplify]: Simplify k into k 11.110 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.110 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.110 * [taylor]: Taking taylor expansion of 2 in n 11.110 * [backup-simplify]: Simplify 2 into 2 11.111 * [taylor]: Taking taylor expansion of (* n PI) in n 11.111 * [taylor]: Taking taylor expansion of n in n 11.111 * [backup-simplify]: Simplify 0 into 0 11.111 * [backup-simplify]: Simplify 1 into 1 11.111 * [taylor]: Taking taylor expansion of PI in n 11.111 * [backup-simplify]: Simplify PI into PI 11.111 * [backup-simplify]: Simplify (* 0 PI) into 0 11.111 * [backup-simplify]: Simplify (* 2 0) into 0 11.112 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.113 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.114 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.114 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 11.114 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 11.114 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 11.115 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.115 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 11.116 * [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))))) 11.116 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 11.116 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 11.116 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.116 * [taylor]: Taking taylor expansion of 1/2 in k 11.116 * [backup-simplify]: Simplify 1/2 into 1/2 11.116 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.116 * [taylor]: Taking taylor expansion of 1/2 in k 11.116 * [backup-simplify]: Simplify 1/2 into 1/2 11.116 * [taylor]: Taking taylor expansion of k in k 11.116 * [backup-simplify]: Simplify 0 into 0 11.116 * [backup-simplify]: Simplify 1 into 1 11.116 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 11.116 * [taylor]: Taking taylor expansion of (log n) in k 11.116 * [taylor]: Taking taylor expansion of n in k 11.116 * [backup-simplify]: Simplify n into n 11.116 * [backup-simplify]: Simplify (log n) into (log n) 11.116 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 11.116 * [taylor]: Taking taylor expansion of (* 2 PI) in k 11.116 * [taylor]: Taking taylor expansion of 2 in k 11.117 * [backup-simplify]: Simplify 2 into 2 11.117 * [taylor]: Taking taylor expansion of PI in k 11.117 * [backup-simplify]: Simplify PI into PI 11.117 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.117 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.118 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.118 * [backup-simplify]: Simplify (- 0) into 0 11.118 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.119 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.120 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 11.120 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 11.121 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 11.122 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.122 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 11.123 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.124 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 11.124 * [backup-simplify]: Simplify (- 0) into 0 11.124 * [backup-simplify]: Simplify (+ 0 0) into 0 11.125 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.126 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 11.127 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.127 * [taylor]: Taking taylor expansion of 0 in k 11.127 * [backup-simplify]: Simplify 0 into 0 11.127 * [backup-simplify]: Simplify 0 into 0 11.127 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 11.128 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 11.129 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.129 * [backup-simplify]: Simplify (+ 0 0) into 0 11.130 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 11.130 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.130 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.131 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 11.133 * [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))))))) 11.135 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 11.150 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 11.152 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 11.155 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 11.155 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 11.156 * [backup-simplify]: Simplify (- 0) into 0 11.156 * [backup-simplify]: Simplify (+ 0 0) into 0 11.157 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.159 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 11.161 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.161 * [taylor]: Taking taylor expansion of 0 in k 11.161 * [backup-simplify]: Simplify 0 into 0 11.161 * [backup-simplify]: Simplify 0 into 0 11.161 * [backup-simplify]: Simplify 0 into 0 11.162 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 11.163 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 11.166 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 11.167 * [backup-simplify]: Simplify (+ 0 0) into 0 11.167 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 11.168 * [backup-simplify]: Simplify (- 0) into 0 11.168 * [backup-simplify]: Simplify (+ 0 0) into 0 11.170 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 11.174 * [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))))) 11.179 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 11.189 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 11.190 * [backup-simplify]: Simplify (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 11.190 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 11.190 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 11.190 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 11.190 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 11.190 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 11.190 * [taylor]: Taking taylor expansion of 1/2 in k 11.190 * [backup-simplify]: Simplify 1/2 into 1/2 11.190 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.190 * [taylor]: Taking taylor expansion of 1/2 in k 11.190 * [backup-simplify]: Simplify 1/2 into 1/2 11.190 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.190 * [taylor]: Taking taylor expansion of k in k 11.190 * [backup-simplify]: Simplify 0 into 0 11.190 * [backup-simplify]: Simplify 1 into 1 11.190 * [backup-simplify]: Simplify (/ 1 1) into 1 11.190 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 11.190 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 11.190 * [taylor]: Taking taylor expansion of 2 in k 11.190 * [backup-simplify]: Simplify 2 into 2 11.191 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.191 * [taylor]: Taking taylor expansion of PI in k 11.191 * [backup-simplify]: Simplify PI into PI 11.191 * [taylor]: Taking taylor expansion of n in k 11.191 * [backup-simplify]: Simplify n into n 11.191 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.191 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 11.191 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 11.191 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.192 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.192 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.192 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 11.192 * [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)))) 11.192 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 11.192 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.193 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.193 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 11.193 * [taylor]: Taking taylor expansion of 1/2 in n 11.193 * [backup-simplify]: Simplify 1/2 into 1/2 11.193 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.193 * [taylor]: Taking taylor expansion of 1/2 in n 11.193 * [backup-simplify]: Simplify 1/2 into 1/2 11.193 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.193 * [taylor]: Taking taylor expansion of k in n 11.193 * [backup-simplify]: Simplify k into k 11.193 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.193 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.193 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.193 * [taylor]: Taking taylor expansion of 2 in n 11.193 * [backup-simplify]: Simplify 2 into 2 11.193 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.193 * [taylor]: Taking taylor expansion of PI in n 11.193 * [backup-simplify]: Simplify PI into PI 11.193 * [taylor]: Taking taylor expansion of n in n 11.193 * [backup-simplify]: Simplify 0 into 0 11.193 * [backup-simplify]: Simplify 1 into 1 11.194 * [backup-simplify]: Simplify (/ PI 1) into PI 11.194 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.195 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.195 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.195 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 11.196 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 11.197 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.198 * [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))) 11.199 * [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)))) 11.199 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 11.200 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.200 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.200 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 11.200 * [taylor]: Taking taylor expansion of 1/2 in n 11.200 * [backup-simplify]: Simplify 1/2 into 1/2 11.200 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.200 * [taylor]: Taking taylor expansion of 1/2 in n 11.200 * [backup-simplify]: Simplify 1/2 into 1/2 11.200 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.200 * [taylor]: Taking taylor expansion of k in n 11.200 * [backup-simplify]: Simplify k into k 11.200 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.200 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.200 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.200 * [taylor]: Taking taylor expansion of 2 in n 11.200 * [backup-simplify]: Simplify 2 into 2 11.200 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.200 * [taylor]: Taking taylor expansion of PI in n 11.200 * [backup-simplify]: Simplify PI into PI 11.200 * [taylor]: Taking taylor expansion of n in n 11.200 * [backup-simplify]: Simplify 0 into 0 11.200 * [backup-simplify]: Simplify 1 into 1 11.201 * [backup-simplify]: Simplify (/ PI 1) into PI 11.201 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.202 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.202 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.202 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 11.202 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 11.204 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.205 * [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))) 11.206 * [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)))) 11.206 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 11.206 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 11.206 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 11.206 * [taylor]: Taking taylor expansion of 1/2 in k 11.206 * [backup-simplify]: Simplify 1/2 into 1/2 11.206 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.206 * [taylor]: Taking taylor expansion of 1/2 in k 11.206 * [backup-simplify]: Simplify 1/2 into 1/2 11.207 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.207 * [taylor]: Taking taylor expansion of k in k 11.207 * [backup-simplify]: Simplify 0 into 0 11.207 * [backup-simplify]: Simplify 1 into 1 11.207 * [backup-simplify]: Simplify (/ 1 1) into 1 11.207 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 11.207 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 11.207 * [taylor]: Taking taylor expansion of (* 2 PI) in k 11.207 * [taylor]: Taking taylor expansion of 2 in k 11.207 * [backup-simplify]: Simplify 2 into 2 11.207 * [taylor]: Taking taylor expansion of PI in k 11.207 * [backup-simplify]: Simplify PI into PI 11.208 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.209 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.209 * [taylor]: Taking taylor expansion of (log n) in k 11.209 * [taylor]: Taking taylor expansion of n in k 11.209 * [backup-simplify]: Simplify n into n 11.209 * [backup-simplify]: Simplify (log n) into (log n) 11.209 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.210 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.210 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.210 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 11.211 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 11.212 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 11.214 * [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)))) 11.215 * [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)))) 11.216 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.216 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 11.218 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.218 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.219 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 11.219 * [backup-simplify]: Simplify (- 0) into 0 11.220 * [backup-simplify]: Simplify (+ 0 0) into 0 11.221 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.222 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 11.224 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 11.224 * [taylor]: Taking taylor expansion of 0 in k 11.224 * [backup-simplify]: Simplify 0 into 0 11.224 * [backup-simplify]: Simplify 0 into 0 11.224 * [backup-simplify]: Simplify 0 into 0 11.225 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.226 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 11.230 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 11.230 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.231 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 11.231 * [backup-simplify]: Simplify (- 0) into 0 11.232 * [backup-simplify]: Simplify (+ 0 0) into 0 11.233 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.235 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 11.237 * [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 11.237 * [taylor]: Taking taylor expansion of 0 in k 11.238 * [backup-simplify]: Simplify 0 into 0 11.238 * [backup-simplify]: Simplify 0 into 0 11.238 * [backup-simplify]: Simplify 0 into 0 11.238 * [backup-simplify]: Simplify 0 into 0 11.238 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.239 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.242 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 11.243 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.243 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 11.244 * [backup-simplify]: Simplify (- 0) into 0 11.244 * [backup-simplify]: Simplify (+ 0 0) into 0 11.245 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.247 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 11.250 * [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 11.250 * [taylor]: Taking taylor expansion of 0 in k 11.250 * [backup-simplify]: Simplify 0 into 0 11.250 * [backup-simplify]: Simplify 0 into 0 11.252 * [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))))) 11.252 * [backup-simplify]: Simplify (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 11.252 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 11.252 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 11.252 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 11.252 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 11.252 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 11.252 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.252 * [taylor]: Taking taylor expansion of 1/2 in k 11.252 * [backup-simplify]: Simplify 1/2 into 1/2 11.252 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.252 * [taylor]: Taking taylor expansion of k in k 11.252 * [backup-simplify]: Simplify 0 into 0 11.252 * [backup-simplify]: Simplify 1 into 1 11.253 * [backup-simplify]: Simplify (/ 1 1) into 1 11.253 * [taylor]: Taking taylor expansion of 1/2 in k 11.253 * [backup-simplify]: Simplify 1/2 into 1/2 11.253 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 11.253 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 11.253 * [taylor]: Taking taylor expansion of -2 in k 11.253 * [backup-simplify]: Simplify -2 into -2 11.253 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.253 * [taylor]: Taking taylor expansion of PI in k 11.253 * [backup-simplify]: Simplify PI into PI 11.253 * [taylor]: Taking taylor expansion of n in k 11.253 * [backup-simplify]: Simplify n into n 11.253 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.253 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 11.254 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 11.254 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.255 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.255 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 11.255 * [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))) 11.255 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 11.255 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 11.255 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 11.255 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 11.255 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.255 * [taylor]: Taking taylor expansion of 1/2 in n 11.255 * [backup-simplify]: Simplify 1/2 into 1/2 11.255 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.255 * [taylor]: Taking taylor expansion of k in n 11.255 * [backup-simplify]: Simplify k into k 11.255 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.255 * [taylor]: Taking taylor expansion of 1/2 in n 11.255 * [backup-simplify]: Simplify 1/2 into 1/2 11.255 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.255 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.255 * [taylor]: Taking taylor expansion of -2 in n 11.255 * [backup-simplify]: Simplify -2 into -2 11.256 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.256 * [taylor]: Taking taylor expansion of PI in n 11.256 * [backup-simplify]: Simplify PI into PI 11.256 * [taylor]: Taking taylor expansion of n in n 11.256 * [backup-simplify]: Simplify 0 into 0 11.256 * [backup-simplify]: Simplify 1 into 1 11.256 * [backup-simplify]: Simplify (/ PI 1) into PI 11.257 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.258 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.258 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.258 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 11.260 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.262 * [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))) 11.263 * [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)))) 11.263 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 11.263 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 11.263 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 11.263 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 11.263 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.263 * [taylor]: Taking taylor expansion of 1/2 in n 11.263 * [backup-simplify]: Simplify 1/2 into 1/2 11.263 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.263 * [taylor]: Taking taylor expansion of k in n 11.263 * [backup-simplify]: Simplify k into k 11.264 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.264 * [taylor]: Taking taylor expansion of 1/2 in n 11.264 * [backup-simplify]: Simplify 1/2 into 1/2 11.264 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.264 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.264 * [taylor]: Taking taylor expansion of -2 in n 11.264 * [backup-simplify]: Simplify -2 into -2 11.264 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.264 * [taylor]: Taking taylor expansion of PI in n 11.264 * [backup-simplify]: Simplify PI into PI 11.264 * [taylor]: Taking taylor expansion of n in n 11.264 * [backup-simplify]: Simplify 0 into 0 11.264 * [backup-simplify]: Simplify 1 into 1 11.265 * [backup-simplify]: Simplify (/ PI 1) into PI 11.265 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.266 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.266 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.266 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 11.268 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.269 * [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))) 11.271 * [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)))) 11.271 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 11.271 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 11.271 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 11.271 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.271 * [taylor]: Taking taylor expansion of 1/2 in k 11.271 * [backup-simplify]: Simplify 1/2 into 1/2 11.271 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.271 * [taylor]: Taking taylor expansion of k in k 11.271 * [backup-simplify]: Simplify 0 into 0 11.271 * [backup-simplify]: Simplify 1 into 1 11.272 * [backup-simplify]: Simplify (/ 1 1) into 1 11.272 * [taylor]: Taking taylor expansion of 1/2 in k 11.272 * [backup-simplify]: Simplify 1/2 into 1/2 11.272 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 11.272 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 11.272 * [taylor]: Taking taylor expansion of (* -2 PI) in k 11.272 * [taylor]: Taking taylor expansion of -2 in k 11.273 * [backup-simplify]: Simplify -2 into -2 11.273 * [taylor]: Taking taylor expansion of PI in k 11.273 * [backup-simplify]: Simplify PI into PI 11.273 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.275 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.275 * [taylor]: Taking taylor expansion of (log n) in k 11.275 * [taylor]: Taking taylor expansion of n in k 11.275 * [backup-simplify]: Simplify n into n 11.275 * [backup-simplify]: Simplify (log n) into (log n) 11.276 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.276 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.276 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 11.277 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 11.279 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 11.280 * [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)))) 11.281 * [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)))) 11.282 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.283 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 11.285 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 11.285 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.286 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 11.286 * [backup-simplify]: Simplify (+ 0 0) into 0 11.288 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.289 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 11.297 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 11.297 * [taylor]: Taking taylor expansion of 0 in k 11.297 * [backup-simplify]: Simplify 0 into 0 11.297 * [backup-simplify]: Simplify 0 into 0 11.297 * [backup-simplify]: Simplify 0 into 0 11.298 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.299 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 11.303 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 11.303 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.304 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 11.305 * [backup-simplify]: Simplify (+ 0 0) into 0 11.306 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.308 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 11.311 * [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 11.311 * [taylor]: Taking taylor expansion of 0 in k 11.311 * [backup-simplify]: Simplify 0 into 0 11.311 * [backup-simplify]: Simplify 0 into 0 11.311 * [backup-simplify]: Simplify 0 into 0 11.311 * [backup-simplify]: Simplify 0 into 0 11.313 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.314 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.321 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 11.321 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.322 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 11.322 * [backup-simplify]: Simplify (+ 0 0) into 0 11.323 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.324 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 11.326 * [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 11.326 * [taylor]: Taking taylor expansion of 0 in k 11.326 * [backup-simplify]: Simplify 0 into 0 11.326 * [backup-simplify]: Simplify 0 into 0 11.327 * [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))))) 11.327 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1) 11.327 * [backup-simplify]: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 11.327 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 11.327 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.327 * [taylor]: Taking taylor expansion of 2 in n 11.327 * [backup-simplify]: Simplify 2 into 2 11.327 * [taylor]: Taking taylor expansion of (* n PI) in n 11.327 * [taylor]: Taking taylor expansion of n in n 11.327 * [backup-simplify]: Simplify 0 into 0 11.327 * [backup-simplify]: Simplify 1 into 1 11.327 * [taylor]: Taking taylor expansion of PI in n 11.327 * [backup-simplify]: Simplify PI into PI 11.327 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.327 * [taylor]: Taking taylor expansion of 2 in n 11.327 * [backup-simplify]: Simplify 2 into 2 11.327 * [taylor]: Taking taylor expansion of (* n PI) in n 11.327 * [taylor]: Taking taylor expansion of n in n 11.327 * [backup-simplify]: Simplify 0 into 0 11.327 * [backup-simplify]: Simplify 1 into 1 11.327 * [taylor]: Taking taylor expansion of PI in n 11.327 * [backup-simplify]: Simplify PI into PI 11.328 * [backup-simplify]: Simplify (* 0 PI) into 0 11.328 * [backup-simplify]: Simplify (* 2 0) into 0 11.328 * [backup-simplify]: Simplify 0 into 0 11.329 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.330 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.330 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.331 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.332 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 11.332 * [backup-simplify]: Simplify 0 into 0 11.332 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 11.333 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 11.333 * [backup-simplify]: Simplify 0 into 0 11.334 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.335 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 11.335 * [backup-simplify]: Simplify 0 into 0 11.335 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.336 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 11.336 * [backup-simplify]: Simplify 0 into 0 11.338 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.339 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 11.339 * [backup-simplify]: Simplify 0 into 0 11.340 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 11.341 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 11.341 * [backup-simplify]: Simplify 0 into 0 11.341 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 11.341 * [backup-simplify]: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 11.341 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 11.341 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.341 * [taylor]: Taking taylor expansion of 2 in n 11.341 * [backup-simplify]: Simplify 2 into 2 11.342 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.342 * [taylor]: Taking taylor expansion of PI in n 11.342 * [backup-simplify]: Simplify PI into PI 11.342 * [taylor]: Taking taylor expansion of n in n 11.342 * [backup-simplify]: Simplify 0 into 0 11.342 * [backup-simplify]: Simplify 1 into 1 11.342 * [backup-simplify]: Simplify (/ PI 1) into PI 11.342 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.342 * [taylor]: Taking taylor expansion of 2 in n 11.342 * [backup-simplify]: Simplify 2 into 2 11.342 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.342 * [taylor]: Taking taylor expansion of PI in n 11.342 * [backup-simplify]: Simplify PI into PI 11.342 * [taylor]: Taking taylor expansion of n in n 11.342 * [backup-simplify]: Simplify 0 into 0 11.342 * [backup-simplify]: Simplify 1 into 1 11.342 * [backup-simplify]: Simplify (/ PI 1) into PI 11.343 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.343 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.344 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.344 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 11.344 * [backup-simplify]: Simplify 0 into 0 11.345 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.346 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 11.346 * [backup-simplify]: Simplify 0 into 0 11.347 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.347 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.347 * [backup-simplify]: Simplify 0 into 0 11.348 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.349 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.349 * [backup-simplify]: Simplify 0 into 0 11.350 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.350 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.350 * [backup-simplify]: Simplify 0 into 0 11.351 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.352 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.352 * [backup-simplify]: Simplify 0 into 0 11.352 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 11.353 * [backup-simplify]: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 11.353 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 11.353 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.353 * [taylor]: Taking taylor expansion of -2 in n 11.353 * [backup-simplify]: Simplify -2 into -2 11.353 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.353 * [taylor]: Taking taylor expansion of PI in n 11.353 * [backup-simplify]: Simplify PI into PI 11.353 * [taylor]: Taking taylor expansion of n in n 11.353 * [backup-simplify]: Simplify 0 into 0 11.353 * [backup-simplify]: Simplify 1 into 1 11.353 * [backup-simplify]: Simplify (/ PI 1) into PI 11.353 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.353 * [taylor]: Taking taylor expansion of -2 in n 11.353 * [backup-simplify]: Simplify -2 into -2 11.353 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.353 * [taylor]: Taking taylor expansion of PI in n 11.353 * [backup-simplify]: Simplify PI into PI 11.353 * [taylor]: Taking taylor expansion of n in n 11.353 * [backup-simplify]: Simplify 0 into 0 11.353 * [backup-simplify]: Simplify 1 into 1 11.354 * [backup-simplify]: Simplify (/ PI 1) into PI 11.354 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.354 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.355 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.355 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 11.355 * [backup-simplify]: Simplify 0 into 0 11.356 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.357 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 11.357 * [backup-simplify]: Simplify 0 into 0 11.357 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.358 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.358 * [backup-simplify]: Simplify 0 into 0 11.359 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.360 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.360 * [backup-simplify]: Simplify 0 into 0 11.360 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.361 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.361 * [backup-simplify]: Simplify 0 into 0 11.362 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.363 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.363 * [backup-simplify]: Simplify 0 into 0 11.363 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 11.363 * * * * [progress]: [ 3 / 4 ] generating series at (2 2) 11.364 * [backup-simplify]: Simplify (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) into (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) 11.364 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in (k n) around 0 11.364 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in n 11.364 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 11.364 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 11.364 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 11.364 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 11.364 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 11.364 * [taylor]: Taking taylor expansion of 1/2 in n 11.364 * [backup-simplify]: Simplify 1/2 into 1/2 11.364 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 11.364 * [taylor]: Taking taylor expansion of 1/2 in n 11.364 * [backup-simplify]: Simplify 1/2 into 1/2 11.364 * [taylor]: Taking taylor expansion of k in n 11.364 * [backup-simplify]: Simplify k into k 11.364 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.364 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.364 * [taylor]: Taking taylor expansion of 2 in n 11.364 * [backup-simplify]: Simplify 2 into 2 11.364 * [taylor]: Taking taylor expansion of (* n PI) in n 11.364 * [taylor]: Taking taylor expansion of n in n 11.364 * [backup-simplify]: Simplify 0 into 0 11.364 * [backup-simplify]: Simplify 1 into 1 11.364 * [taylor]: Taking taylor expansion of PI in n 11.364 * [backup-simplify]: Simplify PI into PI 11.364 * [backup-simplify]: Simplify (* 0 PI) into 0 11.364 * [backup-simplify]: Simplify (* 2 0) into 0 11.365 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.366 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.367 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.367 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 11.367 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 11.367 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 11.368 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.369 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 11.370 * [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))))) 11.370 * [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)))))) 11.370 * [taylor]: Taking taylor expansion of (sqrt k) in n 11.370 * [taylor]: Taking taylor expansion of k in n 11.370 * [backup-simplify]: Simplify k into k 11.370 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 11.370 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 11.370 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 11.370 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 11.370 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 11.370 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 11.371 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 11.371 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.371 * [taylor]: Taking taylor expansion of 1/2 in k 11.371 * [backup-simplify]: Simplify 1/2 into 1/2 11.371 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.371 * [taylor]: Taking taylor expansion of 1/2 in k 11.371 * [backup-simplify]: Simplify 1/2 into 1/2 11.371 * [taylor]: Taking taylor expansion of k in k 11.371 * [backup-simplify]: Simplify 0 into 0 11.371 * [backup-simplify]: Simplify 1 into 1 11.371 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 11.371 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 11.371 * [taylor]: Taking taylor expansion of 2 in k 11.371 * [backup-simplify]: Simplify 2 into 2 11.371 * [taylor]: Taking taylor expansion of (* n PI) in k 11.371 * [taylor]: Taking taylor expansion of n in k 11.371 * [backup-simplify]: Simplify n into n 11.371 * [taylor]: Taking taylor expansion of PI in k 11.371 * [backup-simplify]: Simplify PI into PI 11.371 * [backup-simplify]: Simplify (* n PI) into (* n PI) 11.371 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 11.371 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 11.371 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.371 * [backup-simplify]: Simplify (- 0) into 0 11.372 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.372 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 11.372 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 11.372 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 11.372 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.372 * [taylor]: Taking taylor expansion of k in k 11.372 * [backup-simplify]: Simplify 0 into 0 11.372 * [backup-simplify]: Simplify 1 into 1 11.372 * [backup-simplify]: Simplify (sqrt 0) into 0 11.373 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.373 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 11.373 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 11.373 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 11.373 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 11.374 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 11.374 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.374 * [taylor]: Taking taylor expansion of 1/2 in k 11.374 * [backup-simplify]: Simplify 1/2 into 1/2 11.374 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.374 * [taylor]: Taking taylor expansion of 1/2 in k 11.374 * [backup-simplify]: Simplify 1/2 into 1/2 11.374 * [taylor]: Taking taylor expansion of k in k 11.374 * [backup-simplify]: Simplify 0 into 0 11.374 * [backup-simplify]: Simplify 1 into 1 11.374 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 11.374 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 11.374 * [taylor]: Taking taylor expansion of 2 in k 11.374 * [backup-simplify]: Simplify 2 into 2 11.374 * [taylor]: Taking taylor expansion of (* n PI) in k 11.374 * [taylor]: Taking taylor expansion of n in k 11.374 * [backup-simplify]: Simplify n into n 11.374 * [taylor]: Taking taylor expansion of PI in k 11.374 * [backup-simplify]: Simplify PI into PI 11.374 * [backup-simplify]: Simplify (* n PI) into (* n PI) 11.374 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 11.374 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 11.375 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.375 * [backup-simplify]: Simplify (- 0) into 0 11.376 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.376 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 11.376 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 11.376 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 11.376 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.376 * [taylor]: Taking taylor expansion of k in k 11.376 * [backup-simplify]: Simplify 0 into 0 11.376 * [backup-simplify]: Simplify 1 into 1 11.376 * [backup-simplify]: Simplify (sqrt 0) into 0 11.378 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.378 * [backup-simplify]: Simplify (* (sqrt (/ 1 (* PI (* n 2)))) 0) into 0 11.378 * [taylor]: Taking taylor expansion of 0 in n 11.378 * [backup-simplify]: Simplify 0 into 0 11.378 * [backup-simplify]: Simplify 0 into 0 11.379 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 11.379 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 11.380 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 11.381 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 11.381 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.382 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.382 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 11.383 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 11.383 * [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))))) 11.385 * [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)))) 11.385 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 11.385 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 11.385 * [taylor]: Taking taylor expansion of +nan.0 in n 11.385 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.385 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 11.385 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 11.385 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 11.385 * [taylor]: Taking taylor expansion of (* n PI) in n 11.385 * [taylor]: Taking taylor expansion of n in n 11.386 * [backup-simplify]: Simplify 0 into 0 11.386 * [backup-simplify]: Simplify 1 into 1 11.386 * [taylor]: Taking taylor expansion of PI in n 11.386 * [backup-simplify]: Simplify PI into PI 11.386 * [backup-simplify]: Simplify (* 0 PI) into 0 11.388 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.388 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 11.389 * [backup-simplify]: Simplify (sqrt 0) into 0 11.391 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 11.391 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 11.391 * [taylor]: Taking taylor expansion of 1/2 in n 11.391 * [backup-simplify]: Simplify 1/2 into 1/2 11.391 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 11.392 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 11.395 * [backup-simplify]: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 11.396 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0 11.401 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 11.405 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 11.407 * [backup-simplify]: Simplify (- (* +nan.0 (/ (sqrt 1/2) PI))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 11.407 * [backup-simplify]: Simplify 0 into 0 11.413 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.414 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 11.415 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 11.416 * [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 11.417 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 11.417 * [backup-simplify]: Simplify (- 0) into 0 11.417 * [backup-simplify]: Simplify (+ 0 0) into 0 11.418 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 11.418 * [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))) 11.420 * [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)))))) 11.424 * [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)))))) 11.424 * [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 11.424 * [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 11.424 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) in n 11.424 * [taylor]: Taking taylor expansion of +nan.0 in n 11.424 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.424 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))) in n 11.424 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) in n 11.424 * [taylor]: Taking taylor expansion of (sqrt 2) in n 11.424 * [taylor]: Taking taylor expansion of 2 in n 11.424 * [backup-simplify]: Simplify 2 into 2 11.424 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 11.425 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 11.425 * [taylor]: Taking taylor expansion of (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2)) in n 11.425 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.425 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.425 * [taylor]: Taking taylor expansion of 2 in n 11.425 * [backup-simplify]: Simplify 2 into 2 11.425 * [taylor]: Taking taylor expansion of (* n PI) in n 11.425 * [taylor]: Taking taylor expansion of n in n 11.425 * [backup-simplify]: Simplify 0 into 0 11.425 * [backup-simplify]: Simplify 1 into 1 11.425 * [taylor]: Taking taylor expansion of PI in n 11.425 * [backup-simplify]: Simplify PI into PI 11.425 * [backup-simplify]: Simplify (* 0 PI) into 0 11.426 * [backup-simplify]: Simplify (* 2 0) into 0 11.427 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.427 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.428 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.428 * [taylor]: Taking taylor expansion of (pow (sqrt 1/2) 2) in n 11.428 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 11.428 * [taylor]: Taking taylor expansion of 1/2 in n 11.428 * [backup-simplify]: Simplify 1/2 into 1/2 11.428 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 11.429 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 11.429 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 11.429 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 11.429 * [taylor]: Taking taylor expansion of (* n PI) in n 11.429 * [taylor]: Taking taylor expansion of n in n 11.429 * [backup-simplify]: Simplify 0 into 0 11.429 * [backup-simplify]: Simplify 1 into 1 11.429 * [taylor]: Taking taylor expansion of PI in n 11.429 * [backup-simplify]: Simplify PI into PI 11.429 * [backup-simplify]: Simplify (* 0 PI) into 0 11.430 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.431 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 11.431 * [backup-simplify]: Simplify (sqrt 0) into 0 11.432 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 11.432 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 11.432 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 11.432 * [taylor]: Taking taylor expansion of +nan.0 in n 11.432 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.432 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 11.432 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 11.432 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 11.432 * [taylor]: Taking taylor expansion of (* n PI) in n 11.432 * [taylor]: Taking taylor expansion of n in n 11.432 * [backup-simplify]: Simplify 0 into 0 11.432 * [backup-simplify]: Simplify 1 into 1 11.432 * [taylor]: Taking taylor expansion of PI in n 11.432 * [backup-simplify]: Simplify PI into PI 11.433 * [backup-simplify]: Simplify (* 0 PI) into 0 11.434 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.434 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 11.434 * [backup-simplify]: Simplify (sqrt 0) into 0 11.435 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 11.436 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 11.436 * [taylor]: Taking taylor expansion of 1/2 in n 11.436 * [backup-simplify]: Simplify 1/2 into 1/2 11.436 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 11.436 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 11.437 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.439 * [backup-simplify]: Simplify (* (sqrt 1/2) (sqrt 1/2)) into (pow (sqrt 1/2) 2) 11.440 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (pow (sqrt 1/2) 2)) into (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))) 11.443 * [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))))) 11.444 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.445 * [backup-simplify]: Simplify (+ (* (sqrt 1/2) 0) (* 0 (sqrt 1/2))) into 0 11.447 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.448 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 11.449 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.451 * [backup-simplify]: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (* 0 (pow (sqrt 1/2) 2))) into 0 11.454 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))))) into 0 11.457 * [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))))) 11.460 * [backup-simplify]: Simplify (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 0) into 0 11.472 * [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))))) 11.474 * [backup-simplify]: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 11.475 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0 11.478 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 11.480 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 11.489 * [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))))))) 11.500 * [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))))))) 11.530 * [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))))))) 11.532 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1/2))) into 0 11.533 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.534 * [backup-simplify]: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)))) into 0 11.539 * [backup-simplify]: Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2)) 11.546 * [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)))) 11.555 * [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)))) 11.560 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 11.564 * [backup-simplify]: Simplify (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 11.590 * [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))))))))))) 11.590 * [backup-simplify]: Simplify (/ (sqrt (/ 1 k)) (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2)))) into (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) 11.590 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in (k n) around 0 11.590 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in n 11.590 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 11.590 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 11.590 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.590 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.590 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 11.591 * [taylor]: Taking taylor expansion of 1/2 in n 11.591 * [backup-simplify]: Simplify 1/2 into 1/2 11.591 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.591 * [taylor]: Taking taylor expansion of 1/2 in n 11.591 * [backup-simplify]: Simplify 1/2 into 1/2 11.591 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.591 * [taylor]: Taking taylor expansion of k in n 11.591 * [backup-simplify]: Simplify k into k 11.591 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.591 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.591 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.591 * [taylor]: Taking taylor expansion of 2 in n 11.591 * [backup-simplify]: Simplify 2 into 2 11.591 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.591 * [taylor]: Taking taylor expansion of PI in n 11.591 * [backup-simplify]: Simplify PI into PI 11.591 * [taylor]: Taking taylor expansion of n in n 11.591 * [backup-simplify]: Simplify 0 into 0 11.591 * [backup-simplify]: Simplify 1 into 1 11.591 * [backup-simplify]: Simplify (/ PI 1) into PI 11.592 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.592 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.592 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.592 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 11.592 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 11.593 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.594 * [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))) 11.595 * [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)))) 11.595 * [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))))) 11.596 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 11.596 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.596 * [taylor]: Taking taylor expansion of k in n 11.596 * [backup-simplify]: Simplify k into k 11.596 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.596 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 11.596 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.596 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 11.596 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 11.596 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 11.596 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 11.596 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 11.596 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 11.596 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 11.596 * [taylor]: Taking taylor expansion of 1/2 in k 11.596 * [backup-simplify]: Simplify 1/2 into 1/2 11.596 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.596 * [taylor]: Taking taylor expansion of 1/2 in k 11.596 * [backup-simplify]: Simplify 1/2 into 1/2 11.596 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.596 * [taylor]: Taking taylor expansion of k in k 11.596 * [backup-simplify]: Simplify 0 into 0 11.596 * [backup-simplify]: Simplify 1 into 1 11.596 * [backup-simplify]: Simplify (/ 1 1) into 1 11.596 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 11.596 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 11.596 * [taylor]: Taking taylor expansion of 2 in k 11.596 * [backup-simplify]: Simplify 2 into 2 11.596 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.596 * [taylor]: Taking taylor expansion of PI in k 11.596 * [backup-simplify]: Simplify PI into PI 11.596 * [taylor]: Taking taylor expansion of n in k 11.596 * [backup-simplify]: Simplify n into n 11.596 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.596 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 11.597 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 11.597 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.597 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.597 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.597 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 11.598 * [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)))) 11.598 * [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))))) 11.598 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.598 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.598 * [taylor]: Taking taylor expansion of k in k 11.598 * [backup-simplify]: Simplify 0 into 0 11.598 * [backup-simplify]: Simplify 1 into 1 11.598 * [backup-simplify]: Simplify (/ 1 1) into 1 11.598 * [backup-simplify]: Simplify (sqrt 0) into 0 11.599 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.599 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 11.599 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 11.599 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 11.599 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 11.599 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 11.599 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 11.599 * [taylor]: Taking taylor expansion of 1/2 in k 11.599 * [backup-simplify]: Simplify 1/2 into 1/2 11.599 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.599 * [taylor]: Taking taylor expansion of 1/2 in k 11.599 * [backup-simplify]: Simplify 1/2 into 1/2 11.599 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.599 * [taylor]: Taking taylor expansion of k in k 11.599 * [backup-simplify]: Simplify 0 into 0 11.599 * [backup-simplify]: Simplify 1 into 1 11.600 * [backup-simplify]: Simplify (/ 1 1) into 1 11.600 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 11.600 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 11.600 * [taylor]: Taking taylor expansion of 2 in k 11.600 * [backup-simplify]: Simplify 2 into 2 11.600 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.600 * [taylor]: Taking taylor expansion of PI in k 11.600 * [backup-simplify]: Simplify PI into PI 11.600 * [taylor]: Taking taylor expansion of n in k 11.600 * [backup-simplify]: Simplify n into n 11.600 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.600 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 11.600 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 11.600 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.601 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.601 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.601 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 11.601 * [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)))) 11.601 * [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))))) 11.601 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.601 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.601 * [taylor]: Taking taylor expansion of k in k 11.601 * [backup-simplify]: Simplify 0 into 0 11.601 * [backup-simplify]: Simplify 1 into 1 11.602 * [backup-simplify]: Simplify (/ 1 1) into 1 11.602 * [backup-simplify]: Simplify (sqrt 0) into 0 11.603 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.603 * [backup-simplify]: Simplify (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 11.603 * [taylor]: Taking taylor expansion of 0 in n 11.603 * [backup-simplify]: Simplify 0 into 0 11.603 * [backup-simplify]: Simplify 0 into 0 11.603 * [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 11.604 * [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))))))) 11.604 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 11.604 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 11.604 * [taylor]: Taking taylor expansion of +nan.0 in n 11.604 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.604 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 11.604 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 11.604 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.604 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.604 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 11.604 * [taylor]: Taking taylor expansion of 1/2 in n 11.604 * [backup-simplify]: Simplify 1/2 into 1/2 11.604 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.604 * [taylor]: Taking taylor expansion of 1/2 in n 11.604 * [backup-simplify]: Simplify 1/2 into 1/2 11.604 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.604 * [taylor]: Taking taylor expansion of k in n 11.604 * [backup-simplify]: Simplify k into k 11.604 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.604 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.604 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.604 * [taylor]: Taking taylor expansion of 2 in n 11.604 * [backup-simplify]: Simplify 2 into 2 11.604 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.604 * [taylor]: Taking taylor expansion of PI in n 11.604 * [backup-simplify]: Simplify PI into PI 11.604 * [taylor]: Taking taylor expansion of n in n 11.604 * [backup-simplify]: Simplify 0 into 0 11.604 * [backup-simplify]: Simplify 1 into 1 11.604 * [backup-simplify]: Simplify (/ PI 1) into PI 11.605 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.605 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.605 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.605 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 11.606 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 11.606 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.607 * [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))) 11.608 * [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)))) 11.609 * [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))))) 11.610 * [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))))) 11.610 * [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))))))) 11.611 * [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))))))) 11.611 * [backup-simplify]: Simplify 0 into 0 11.612 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 11.613 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.614 * [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 11.614 * [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))))))) 11.614 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 11.614 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 11.614 * [taylor]: Taking taylor expansion of +nan.0 in n 11.614 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.614 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 11.614 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 11.614 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.614 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.614 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 11.614 * [taylor]: Taking taylor expansion of 1/2 in n 11.614 * [backup-simplify]: Simplify 1/2 into 1/2 11.614 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.615 * [taylor]: Taking taylor expansion of 1/2 in n 11.615 * [backup-simplify]: Simplify 1/2 into 1/2 11.615 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.615 * [taylor]: Taking taylor expansion of k in n 11.615 * [backup-simplify]: Simplify k into k 11.615 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.615 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.615 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.615 * [taylor]: Taking taylor expansion of 2 in n 11.615 * [backup-simplify]: Simplify 2 into 2 11.615 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.615 * [taylor]: Taking taylor expansion of PI in n 11.615 * [backup-simplify]: Simplify PI into PI 11.615 * [taylor]: Taking taylor expansion of n in n 11.615 * [backup-simplify]: Simplify 0 into 0 11.615 * [backup-simplify]: Simplify 1 into 1 11.615 * [backup-simplify]: Simplify (/ PI 1) into PI 11.615 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.616 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.616 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.616 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 11.616 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 11.617 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.618 * [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))) 11.619 * [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)))) 11.619 * [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))))) 11.620 * [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))))) 11.621 * [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))))))) 11.622 * [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))))))) 11.622 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.623 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 11.624 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.624 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.624 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 11.625 * [backup-simplify]: Simplify (- 0) into 0 11.625 * [backup-simplify]: Simplify (+ 0 0) into 0 11.626 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.626 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 11.628 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 11.630 * [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 11.632 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 11.632 * [backup-simplify]: Simplify (- 0) into 0 11.632 * [backup-simplify]: Simplify 0 into 0 11.632 * [backup-simplify]: Simplify 0 into 0 11.634 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.639 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.640 * [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 11.641 * [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))))))) 11.641 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 11.642 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 11.642 * [taylor]: Taking taylor expansion of +nan.0 in n 11.642 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.642 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 11.642 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 11.642 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.642 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.642 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 11.642 * [taylor]: Taking taylor expansion of 1/2 in n 11.642 * [backup-simplify]: Simplify 1/2 into 1/2 11.642 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.642 * [taylor]: Taking taylor expansion of 1/2 in n 11.642 * [backup-simplify]: Simplify 1/2 into 1/2 11.642 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.642 * [taylor]: Taking taylor expansion of k in n 11.642 * [backup-simplify]: Simplify k into k 11.642 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.642 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.642 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.642 * [taylor]: Taking taylor expansion of 2 in n 11.642 * [backup-simplify]: Simplify 2 into 2 11.642 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.642 * [taylor]: Taking taylor expansion of PI in n 11.642 * [backup-simplify]: Simplify PI into PI 11.642 * [taylor]: Taking taylor expansion of n in n 11.642 * [backup-simplify]: Simplify 0 into 0 11.642 * [backup-simplify]: Simplify 1 into 1 11.644 * [backup-simplify]: Simplify (/ PI 1) into PI 11.644 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.646 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.646 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.646 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 11.646 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 11.648 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.649 * [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))) 11.650 * [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)))) 11.652 * [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))))) 11.659 * [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))))) 11.661 * [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))))))) 11.662 * [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))))))) 11.666 * [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)))))))))))) 11.667 * [backup-simplify]: Simplify (/ (sqrt (/ 1 (- k))) (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2)))) into (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 11.667 * [approximate]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (k n) around 0 11.667 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 11.667 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 11.667 * [taylor]: Taking taylor expansion of (/ -1 k) in n 11.667 * [taylor]: Taking taylor expansion of -1 in n 11.667 * [backup-simplify]: Simplify -1 into -1 11.667 * [taylor]: Taking taylor expansion of k in n 11.667 * [backup-simplify]: Simplify k into k 11.667 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 11.667 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 11.667 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 11.668 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 11.668 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 11.668 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 11.668 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 11.668 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 11.668 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.668 * [taylor]: Taking taylor expansion of 1/2 in n 11.668 * [backup-simplify]: Simplify 1/2 into 1/2 11.668 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.668 * [taylor]: Taking taylor expansion of k in n 11.668 * [backup-simplify]: Simplify k into k 11.668 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.668 * [taylor]: Taking taylor expansion of 1/2 in n 11.668 * [backup-simplify]: Simplify 1/2 into 1/2 11.668 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.668 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.668 * [taylor]: Taking taylor expansion of -2 in n 11.668 * [backup-simplify]: Simplify -2 into -2 11.668 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.668 * [taylor]: Taking taylor expansion of PI in n 11.668 * [backup-simplify]: Simplify PI into PI 11.668 * [taylor]: Taking taylor expansion of n in n 11.668 * [backup-simplify]: Simplify 0 into 0 11.668 * [backup-simplify]: Simplify 1 into 1 11.669 * [backup-simplify]: Simplify (/ PI 1) into PI 11.669 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.671 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.671 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.671 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 11.672 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.674 * [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))) 11.675 * [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)))) 11.676 * [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))))) 11.676 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 11.676 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.676 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.676 * [taylor]: Taking taylor expansion of -1 in k 11.676 * [backup-simplify]: Simplify -1 into -1 11.676 * [taylor]: Taking taylor expansion of k in k 11.676 * [backup-simplify]: Simplify 0 into 0 11.676 * [backup-simplify]: Simplify 1 into 1 11.677 * [backup-simplify]: Simplify (/ -1 1) into -1 11.677 * [backup-simplify]: Simplify (sqrt 0) into 0 11.679 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.679 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 11.679 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 11.679 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 11.679 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 11.679 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.679 * [taylor]: Taking taylor expansion of 1/2 in k 11.679 * [backup-simplify]: Simplify 1/2 into 1/2 11.679 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.679 * [taylor]: Taking taylor expansion of k in k 11.679 * [backup-simplify]: Simplify 0 into 0 11.679 * [backup-simplify]: Simplify 1 into 1 11.679 * [backup-simplify]: Simplify (/ 1 1) into 1 11.679 * [taylor]: Taking taylor expansion of 1/2 in k 11.679 * [backup-simplify]: Simplify 1/2 into 1/2 11.679 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 11.679 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 11.679 * [taylor]: Taking taylor expansion of -2 in k 11.679 * [backup-simplify]: Simplify -2 into -2 11.680 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.680 * [taylor]: Taking taylor expansion of PI in k 11.680 * [backup-simplify]: Simplify PI into PI 11.680 * [taylor]: Taking taylor expansion of n in k 11.680 * [backup-simplify]: Simplify n into n 11.680 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.680 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 11.680 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 11.680 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.681 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.681 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 11.681 * [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))) 11.681 * [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)))) 11.681 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 11.681 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.682 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.682 * [taylor]: Taking taylor expansion of -1 in k 11.682 * [backup-simplify]: Simplify -1 into -1 11.682 * [taylor]: Taking taylor expansion of k in k 11.682 * [backup-simplify]: Simplify 0 into 0 11.682 * [backup-simplify]: Simplify 1 into 1 11.682 * [backup-simplify]: Simplify (/ -1 1) into -1 11.683 * [backup-simplify]: Simplify (sqrt 0) into 0 11.684 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.684 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 11.684 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 11.684 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 11.684 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 11.684 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.684 * [taylor]: Taking taylor expansion of 1/2 in k 11.684 * [backup-simplify]: Simplify 1/2 into 1/2 11.684 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.684 * [taylor]: Taking taylor expansion of k in k 11.684 * [backup-simplify]: Simplify 0 into 0 11.684 * [backup-simplify]: Simplify 1 into 1 11.685 * [backup-simplify]: Simplify (/ 1 1) into 1 11.685 * [taylor]: Taking taylor expansion of 1/2 in k 11.685 * [backup-simplify]: Simplify 1/2 into 1/2 11.685 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 11.685 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 11.685 * [taylor]: Taking taylor expansion of -2 in k 11.685 * [backup-simplify]: Simplify -2 into -2 11.685 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.685 * [taylor]: Taking taylor expansion of PI in k 11.685 * [backup-simplify]: Simplify PI into PI 11.685 * [taylor]: Taking taylor expansion of n in k 11.685 * [backup-simplify]: Simplify n into n 11.685 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.685 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 11.685 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 11.686 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.686 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.686 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 11.686 * [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))) 11.687 * [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)))) 11.687 * [taylor]: Taking taylor expansion of (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 11.687 * [taylor]: Taking taylor expansion of +nan.0 in n 11.687 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.687 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 11.687 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 11.687 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.687 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.687 * [taylor]: Taking taylor expansion of -2 in n 11.687 * [backup-simplify]: Simplify -2 into -2 11.687 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.687 * [taylor]: Taking taylor expansion of PI in n 11.687 * [backup-simplify]: Simplify PI into PI 11.687 * [taylor]: Taking taylor expansion of n in n 11.687 * [backup-simplify]: Simplify 0 into 0 11.687 * [backup-simplify]: Simplify 1 into 1 11.688 * [backup-simplify]: Simplify (/ PI 1) into PI 11.688 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.689 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.689 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 11.689 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.689 * [taylor]: Taking taylor expansion of 1/2 in n 11.690 * [backup-simplify]: Simplify 1/2 into 1/2 11.690 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.690 * [taylor]: Taking taylor expansion of k in n 11.690 * [backup-simplify]: Simplify k into k 11.690 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.690 * [taylor]: Taking taylor expansion of 1/2 in n 11.690 * [backup-simplify]: Simplify 1/2 into 1/2 11.691 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.691 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.691 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 11.693 * [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))) 11.694 * [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)))) 11.695 * [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))))) 11.697 * [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))))) 11.698 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 11.701 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.702 * [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)))))) 11.702 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 11.702 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 11.702 * [taylor]: Taking taylor expansion of +nan.0 in n 11.702 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.702 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 11.702 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 11.702 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 11.702 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.702 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.702 * [taylor]: Taking taylor expansion of -2 in n 11.702 * [backup-simplify]: Simplify -2 into -2 11.702 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.702 * [taylor]: Taking taylor expansion of PI in n 11.702 * [backup-simplify]: Simplify PI into PI 11.702 * [taylor]: Taking taylor expansion of n in n 11.702 * [backup-simplify]: Simplify 0 into 0 11.702 * [backup-simplify]: Simplify 1 into 1 11.703 * [backup-simplify]: Simplify (/ PI 1) into PI 11.703 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.704 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.704 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 11.704 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.704 * [taylor]: Taking taylor expansion of 1/2 in n 11.704 * [backup-simplify]: Simplify 1/2 into 1/2 11.704 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.704 * [taylor]: Taking taylor expansion of k in n 11.704 * [backup-simplify]: Simplify k into k 11.704 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.704 * [taylor]: Taking taylor expansion of 1/2 in n 11.705 * [backup-simplify]: Simplify 1/2 into 1/2 11.706 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.706 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.706 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 11.707 * [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))) 11.709 * [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)))) 11.710 * [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))))) 11.711 * [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))))) 11.712 * [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))))))) 11.714 * [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))))))) 11.715 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.715 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.716 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 11.716 * [backup-simplify]: Simplify (+ 0 0) into 0 11.717 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.718 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 11.720 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 11.721 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 11.723 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 11.727 * [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 11.727 * [backup-simplify]: Simplify 0 into 0 11.728 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.731 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.731 * [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)))))) 11.731 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 11.731 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 11.731 * [taylor]: Taking taylor expansion of +nan.0 in n 11.731 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.731 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 11.731 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 11.731 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 11.731 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.731 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.731 * [taylor]: Taking taylor expansion of -2 in n 11.731 * [backup-simplify]: Simplify -2 into -2 11.731 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.731 * [taylor]: Taking taylor expansion of PI in n 11.731 * [backup-simplify]: Simplify PI into PI 11.731 * [taylor]: Taking taylor expansion of n in n 11.732 * [backup-simplify]: Simplify 0 into 0 11.732 * [backup-simplify]: Simplify 1 into 1 11.732 * [backup-simplify]: Simplify (/ PI 1) into PI 11.732 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.733 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.733 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 11.733 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.733 * [taylor]: Taking taylor expansion of 1/2 in n 11.733 * [backup-simplify]: Simplify 1/2 into 1/2 11.733 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.733 * [taylor]: Taking taylor expansion of k in n 11.733 * [backup-simplify]: Simplify k into k 11.733 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.733 * [taylor]: Taking taylor expansion of 1/2 in n 11.733 * [backup-simplify]: Simplify 1/2 into 1/2 11.734 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.734 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.734 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 11.735 * [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))) 11.735 * [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)))) 11.736 * [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))))) 11.737 * [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))))) 11.738 * [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))))))) 11.738 * [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))))))) 11.741 * [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)))))))))))) 11.741 * * * * [progress]: [ 4 / 4 ] generating series at (2) 11.741 * [backup-simplify]: Simplify (/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 11.741 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (k n) around 0 11.741 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 11.741 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 11.741 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.741 * [taylor]: Taking taylor expansion of k in n 11.741 * [backup-simplify]: Simplify k into k 11.741 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.741 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 11.741 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.741 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 11.742 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 11.742 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 11.742 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 11.742 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 11.742 * [taylor]: Taking taylor expansion of 1/2 in n 11.742 * [backup-simplify]: Simplify 1/2 into 1/2 11.742 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 11.742 * [taylor]: Taking taylor expansion of 1/2 in n 11.742 * [backup-simplify]: Simplify 1/2 into 1/2 11.742 * [taylor]: Taking taylor expansion of k in n 11.742 * [backup-simplify]: Simplify k into k 11.742 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.742 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.742 * [taylor]: Taking taylor expansion of 2 in n 11.742 * [backup-simplify]: Simplify 2 into 2 11.742 * [taylor]: Taking taylor expansion of (* n PI) in n 11.742 * [taylor]: Taking taylor expansion of n in n 11.742 * [backup-simplify]: Simplify 0 into 0 11.742 * [backup-simplify]: Simplify 1 into 1 11.742 * [taylor]: Taking taylor expansion of PI in n 11.742 * [backup-simplify]: Simplify PI into PI 11.742 * [backup-simplify]: Simplify (* 0 PI) into 0 11.742 * [backup-simplify]: Simplify (* 2 0) into 0 11.743 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.744 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.745 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.745 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 11.745 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 11.745 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 11.746 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.747 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 11.747 * [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))))) 11.747 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 11.747 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.747 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.747 * [taylor]: Taking taylor expansion of k in k 11.747 * [backup-simplify]: Simplify 0 into 0 11.747 * [backup-simplify]: Simplify 1 into 1 11.748 * [backup-simplify]: Simplify (/ 1 1) into 1 11.748 * [backup-simplify]: Simplify (sqrt 0) into 0 11.749 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.749 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 11.749 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 11.749 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 11.749 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.749 * [taylor]: Taking taylor expansion of 1/2 in k 11.749 * [backup-simplify]: Simplify 1/2 into 1/2 11.749 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.749 * [taylor]: Taking taylor expansion of 1/2 in k 11.749 * [backup-simplify]: Simplify 1/2 into 1/2 11.749 * [taylor]: Taking taylor expansion of k in k 11.749 * [backup-simplify]: Simplify 0 into 0 11.749 * [backup-simplify]: Simplify 1 into 1 11.749 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 11.749 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 11.749 * [taylor]: Taking taylor expansion of 2 in k 11.749 * [backup-simplify]: Simplify 2 into 2 11.749 * [taylor]: Taking taylor expansion of (* n PI) in k 11.749 * [taylor]: Taking taylor expansion of n in k 11.749 * [backup-simplify]: Simplify n into n 11.749 * [taylor]: Taking taylor expansion of PI in k 11.749 * [backup-simplify]: Simplify PI into PI 11.749 * [backup-simplify]: Simplify (* n PI) into (* n PI) 11.749 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 11.749 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 11.749 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.750 * [backup-simplify]: Simplify (- 0) into 0 11.750 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.750 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 11.750 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 11.750 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 11.750 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.750 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.750 * [taylor]: Taking taylor expansion of k in k 11.750 * [backup-simplify]: Simplify 0 into 0 11.750 * [backup-simplify]: Simplify 1 into 1 11.750 * [backup-simplify]: Simplify (/ 1 1) into 1 11.751 * [backup-simplify]: Simplify (sqrt 0) into 0 11.751 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.751 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 11.751 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 11.751 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 11.751 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.751 * [taylor]: Taking taylor expansion of 1/2 in k 11.751 * [backup-simplify]: Simplify 1/2 into 1/2 11.751 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.752 * [taylor]: Taking taylor expansion of 1/2 in k 11.752 * [backup-simplify]: Simplify 1/2 into 1/2 11.752 * [taylor]: Taking taylor expansion of k in k 11.752 * [backup-simplify]: Simplify 0 into 0 11.752 * [backup-simplify]: Simplify 1 into 1 11.752 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 11.752 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 11.752 * [taylor]: Taking taylor expansion of 2 in k 11.752 * [backup-simplify]: Simplify 2 into 2 11.752 * [taylor]: Taking taylor expansion of (* n PI) in k 11.752 * [taylor]: Taking taylor expansion of n in k 11.752 * [backup-simplify]: Simplify n into n 11.752 * [taylor]: Taking taylor expansion of PI in k 11.752 * [backup-simplify]: Simplify PI into PI 11.752 * [backup-simplify]: Simplify (* n PI) into (* n PI) 11.752 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 11.752 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 11.752 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.752 * [backup-simplify]: Simplify (- 0) into 0 11.753 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.753 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 11.753 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 11.753 * [backup-simplify]: Simplify (* 0 (pow (* 2 (* n PI)) 1/2)) into 0 11.753 * [taylor]: Taking taylor expansion of 0 in n 11.753 * [backup-simplify]: Simplify 0 into 0 11.753 * [backup-simplify]: Simplify 0 into 0 11.753 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 11.754 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 11.754 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 11.755 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 11.755 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.755 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.756 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 11.756 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 11.756 * [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))))) 11.756 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 11.756 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 11.756 * [taylor]: Taking taylor expansion of +nan.0 in n 11.756 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.756 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 11.756 * [taylor]: Taking taylor expansion of (sqrt 2) in n 11.756 * [taylor]: Taking taylor expansion of 2 in n 11.756 * [backup-simplify]: Simplify 2 into 2 11.756 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 11.757 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 11.757 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 11.757 * [taylor]: Taking taylor expansion of (* n PI) in n 11.757 * [taylor]: Taking taylor expansion of n in n 11.757 * [backup-simplify]: Simplify 0 into 0 11.757 * [backup-simplify]: Simplify 1 into 1 11.757 * [taylor]: Taking taylor expansion of PI in n 11.757 * [backup-simplify]: Simplify PI into PI 11.757 * [backup-simplify]: Simplify (* 0 PI) into 0 11.758 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.758 * [backup-simplify]: Simplify (sqrt 0) into 0 11.759 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 11.760 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 11.760 * [backup-simplify]: Simplify (* +nan.0 0) into 0 11.760 * [backup-simplify]: Simplify (- 0) into 0 11.760 * [backup-simplify]: Simplify 0 into 0 11.760 * [backup-simplify]: Simplify 0 into 0 11.761 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 11.761 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 11.762 * [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 11.763 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 11.763 * [backup-simplify]: Simplify (- 0) into 0 11.763 * [backup-simplify]: Simplify (+ 0 0) into 0 11.764 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 11.764 * [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))) 11.765 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 11.767 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.767 * [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))))))) 11.767 * [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 11.767 * [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 11.767 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 11.767 * [taylor]: Taking taylor expansion of +nan.0 in n 11.767 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.767 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 11.767 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 11.767 * [taylor]: Taking taylor expansion of (sqrt 2) in n 11.767 * [taylor]: Taking taylor expansion of 2 in n 11.767 * [backup-simplify]: Simplify 2 into 2 11.767 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 11.768 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 11.768 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.768 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.768 * [taylor]: Taking taylor expansion of 2 in n 11.768 * [backup-simplify]: Simplify 2 into 2 11.768 * [taylor]: Taking taylor expansion of (* n PI) in n 11.768 * [taylor]: Taking taylor expansion of n in n 11.768 * [backup-simplify]: Simplify 0 into 0 11.768 * [backup-simplify]: Simplify 1 into 1 11.768 * [taylor]: Taking taylor expansion of PI in n 11.768 * [backup-simplify]: Simplify PI into PI 11.768 * [backup-simplify]: Simplify (* 0 PI) into 0 11.768 * [backup-simplify]: Simplify (* 2 0) into 0 11.769 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.770 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.771 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.771 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 11.771 * [taylor]: Taking taylor expansion of (* n PI) in n 11.771 * [taylor]: Taking taylor expansion of n in n 11.771 * [backup-simplify]: Simplify 0 into 0 11.771 * [backup-simplify]: Simplify 1 into 1 11.771 * [taylor]: Taking taylor expansion of PI in n 11.771 * [backup-simplify]: Simplify PI into PI 11.771 * [backup-simplify]: Simplify (* 0 PI) into 0 11.772 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.773 * [backup-simplify]: Simplify (sqrt 0) into 0 11.778 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 11.778 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 11.778 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 11.778 * [taylor]: Taking taylor expansion of +nan.0 in n 11.778 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.778 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 11.778 * [taylor]: Taking taylor expansion of (sqrt 2) in n 11.778 * [taylor]: Taking taylor expansion of 2 in n 11.778 * [backup-simplify]: Simplify 2 into 2 11.778 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 11.778 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 11.778 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 11.779 * [taylor]: Taking taylor expansion of (* n PI) in n 11.779 * [taylor]: Taking taylor expansion of n in n 11.779 * [backup-simplify]: Simplify 0 into 0 11.779 * [backup-simplify]: Simplify 1 into 1 11.779 * [taylor]: Taking taylor expansion of PI in n 11.779 * [backup-simplify]: Simplify PI into PI 11.779 * [backup-simplify]: Simplify (* 0 PI) into 0 11.780 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.780 * [backup-simplify]: Simplify (sqrt 0) into 0 11.781 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 11.782 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.784 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 11.785 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 11.785 * [backup-simplify]: Simplify (* +nan.0 0) into 0 11.786 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 11.786 * [backup-simplify]: Simplify (* +nan.0 0) into 0 11.787 * [backup-simplify]: Simplify (- 0) into 0 11.787 * [backup-simplify]: Simplify (+ 0 0) into 0 11.787 * [backup-simplify]: Simplify (- 0) into 0 11.787 * [backup-simplify]: Simplify 0 into 0 11.790 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 11.796 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 11.799 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 11.802 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 11.802 * [backup-simplify]: Simplify 0 into 0 11.803 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.804 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 11.807 * [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 11.808 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 11.808 * [backup-simplify]: Simplify (- 0) into 0 11.809 * [backup-simplify]: Simplify (+ 0 0) into 0 11.810 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 11.812 * [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))) 11.812 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.816 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.817 * [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))))))))) 11.818 * [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 11.818 * [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 11.818 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 11.818 * [taylor]: Taking taylor expansion of +nan.0 in n 11.818 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.818 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 11.818 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 11.818 * [taylor]: Taking taylor expansion of (sqrt 2) in n 11.818 * [taylor]: Taking taylor expansion of 2 in n 11.818 * [backup-simplify]: Simplify 2 into 2 11.818 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 11.819 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 11.819 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.819 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.819 * [taylor]: Taking taylor expansion of 2 in n 11.819 * [backup-simplify]: Simplify 2 into 2 11.819 * [taylor]: Taking taylor expansion of (* n PI) in n 11.819 * [taylor]: Taking taylor expansion of n in n 11.819 * [backup-simplify]: Simplify 0 into 0 11.819 * [backup-simplify]: Simplify 1 into 1 11.819 * [taylor]: Taking taylor expansion of PI in n 11.819 * [backup-simplify]: Simplify PI into PI 11.820 * [backup-simplify]: Simplify (* 0 PI) into 0 11.820 * [backup-simplify]: Simplify (* 2 0) into 0 11.822 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.823 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.824 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.824 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 11.824 * [taylor]: Taking taylor expansion of (* n PI) in n 11.824 * [taylor]: Taking taylor expansion of n in n 11.824 * [backup-simplify]: Simplify 0 into 0 11.824 * [backup-simplify]: Simplify 1 into 1 11.824 * [taylor]: Taking taylor expansion of PI in n 11.824 * [backup-simplify]: Simplify PI into PI 11.825 * [backup-simplify]: Simplify (* 0 PI) into 0 11.827 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.827 * [backup-simplify]: Simplify (sqrt 0) into 0 11.828 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 11.829 * [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 11.829 * [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 11.829 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 11.829 * [taylor]: Taking taylor expansion of +nan.0 in n 11.829 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.829 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 11.829 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 11.829 * [taylor]: Taking taylor expansion of (sqrt 2) in n 11.829 * [taylor]: Taking taylor expansion of 2 in n 11.829 * [backup-simplify]: Simplify 2 into 2 11.829 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 11.830 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 11.830 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 11.830 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.830 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.830 * [taylor]: Taking taylor expansion of 2 in n 11.830 * [backup-simplify]: Simplify 2 into 2 11.830 * [taylor]: Taking taylor expansion of (* n PI) in n 11.830 * [taylor]: Taking taylor expansion of n in n 11.830 * [backup-simplify]: Simplify 0 into 0 11.830 * [backup-simplify]: Simplify 1 into 1 11.830 * [taylor]: Taking taylor expansion of PI in n 11.830 * [backup-simplify]: Simplify PI into PI 11.831 * [backup-simplify]: Simplify (* 0 PI) into 0 11.831 * [backup-simplify]: Simplify (* 2 0) into 0 11.833 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.834 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.835 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.837 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.837 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 11.837 * [taylor]: Taking taylor expansion of (* n PI) in n 11.837 * [taylor]: Taking taylor expansion of n in n 11.837 * [backup-simplify]: Simplify 0 into 0 11.837 * [backup-simplify]: Simplify 1 into 1 11.837 * [taylor]: Taking taylor expansion of PI in n 11.837 * [backup-simplify]: Simplify PI into PI 11.838 * [backup-simplify]: Simplify (* 0 PI) into 0 11.839 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.839 * [backup-simplify]: Simplify (sqrt 0) into 0 11.841 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 11.841 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 11.841 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 11.841 * [taylor]: Taking taylor expansion of +nan.0 in n 11.841 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.841 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 11.841 * [taylor]: Taking taylor expansion of (sqrt 2) in n 11.841 * [taylor]: Taking taylor expansion of 2 in n 11.841 * [backup-simplify]: Simplify 2 into 2 11.841 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 11.842 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 11.842 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 11.842 * [taylor]: Taking taylor expansion of (* n PI) in n 11.842 * [taylor]: Taking taylor expansion of n in n 11.842 * [backup-simplify]: Simplify 0 into 0 11.842 * [backup-simplify]: Simplify 1 into 1 11.842 * [taylor]: Taking taylor expansion of PI in n 11.842 * [backup-simplify]: Simplify PI into PI 11.843 * [backup-simplify]: Simplify (* 0 PI) into 0 11.845 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.845 * [backup-simplify]: Simplify (sqrt 0) into 0 11.847 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 11.848 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.850 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 11.851 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 11.851 * [backup-simplify]: Simplify (* +nan.0 0) into 0 11.853 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.854 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.856 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 11.858 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 11.859 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 11.860 * [backup-simplify]: Simplify (* +nan.0 0) into 0 11.860 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 11.861 * [backup-simplify]: Simplify (* +nan.0 0) into 0 11.861 * [backup-simplify]: Simplify (- 0) into 0 11.861 * [backup-simplify]: Simplify (+ 0 0) into 0 11.862 * [backup-simplify]: Simplify (- 0) into 0 11.862 * [backup-simplify]: Simplify (+ 0 0) into 0 11.863 * [backup-simplify]: Simplify (- 0) into 0 11.863 * [backup-simplify]: Simplify 0 into 0 11.864 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.865 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 11.866 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.868 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.869 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 11.872 * [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)))))))) 11.878 * [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)))))))) 11.881 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 11.886 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 11.890 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 11.898 * [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)))))))))) 11.903 * [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))))))) 11.912 * [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))))))) 11.913 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.915 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 11.916 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 11.918 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 11.923 * [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)))) 11.926 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 11.928 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 11.942 * [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))))))))))))) 11.942 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (/ 1 k)) (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 11.942 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (k n) around 0 11.942 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 11.943 * [taylor]: Taking taylor expansion of (sqrt k) in n 11.943 * [taylor]: Taking taylor expansion of k in n 11.943 * [backup-simplify]: Simplify k into k 11.943 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 11.943 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 11.943 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 11.943 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.943 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.943 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 11.943 * [taylor]: Taking taylor expansion of 1/2 in n 11.943 * [backup-simplify]: Simplify 1/2 into 1/2 11.943 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.943 * [taylor]: Taking taylor expansion of 1/2 in n 11.943 * [backup-simplify]: Simplify 1/2 into 1/2 11.943 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.943 * [taylor]: Taking taylor expansion of k in n 11.943 * [backup-simplify]: Simplify k into k 11.943 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.943 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.943 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.943 * [taylor]: Taking taylor expansion of 2 in n 11.943 * [backup-simplify]: Simplify 2 into 2 11.943 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.943 * [taylor]: Taking taylor expansion of PI in n 11.943 * [backup-simplify]: Simplify PI into PI 11.943 * [taylor]: Taking taylor expansion of n in n 11.943 * [backup-simplify]: Simplify 0 into 0 11.943 * [backup-simplify]: Simplify 1 into 1 11.944 * [backup-simplify]: Simplify (/ PI 1) into PI 11.944 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.945 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.945 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.945 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 11.946 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 11.947 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.948 * [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))) 11.949 * [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)))) 11.949 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 11.949 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.949 * [taylor]: Taking taylor expansion of k in k 11.949 * [backup-simplify]: Simplify 0 into 0 11.949 * [backup-simplify]: Simplify 1 into 1 11.950 * [backup-simplify]: Simplify (sqrt 0) into 0 11.951 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.951 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 11.951 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 11.951 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 11.951 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 11.951 * [taylor]: Taking taylor expansion of 1/2 in k 11.951 * [backup-simplify]: Simplify 1/2 into 1/2 11.951 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.951 * [taylor]: Taking taylor expansion of 1/2 in k 11.951 * [backup-simplify]: Simplify 1/2 into 1/2 11.951 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.951 * [taylor]: Taking taylor expansion of k in k 11.951 * [backup-simplify]: Simplify 0 into 0 11.951 * [backup-simplify]: Simplify 1 into 1 11.952 * [backup-simplify]: Simplify (/ 1 1) into 1 11.952 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 11.952 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 11.952 * [taylor]: Taking taylor expansion of 2 in k 11.952 * [backup-simplify]: Simplify 2 into 2 11.952 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.952 * [taylor]: Taking taylor expansion of PI in k 11.952 * [backup-simplify]: Simplify PI into PI 11.952 * [taylor]: Taking taylor expansion of n in k 11.952 * [backup-simplify]: Simplify n into n 11.952 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.952 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 11.952 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 11.953 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.953 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.953 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.954 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 11.954 * [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)))) 11.954 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 11.954 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.954 * [taylor]: Taking taylor expansion of k in k 11.954 * [backup-simplify]: Simplify 0 into 0 11.954 * [backup-simplify]: Simplify 1 into 1 11.954 * [backup-simplify]: Simplify (sqrt 0) into 0 11.955 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.955 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 11.956 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 11.956 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 11.956 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 11.956 * [taylor]: Taking taylor expansion of 1/2 in k 11.956 * [backup-simplify]: Simplify 1/2 into 1/2 11.956 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.956 * [taylor]: Taking taylor expansion of 1/2 in k 11.956 * [backup-simplify]: Simplify 1/2 into 1/2 11.956 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.956 * [taylor]: Taking taylor expansion of k in k 11.956 * [backup-simplify]: Simplify 0 into 0 11.956 * [backup-simplify]: Simplify 1 into 1 11.956 * [backup-simplify]: Simplify (/ 1 1) into 1 11.956 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 11.956 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 11.956 * [taylor]: Taking taylor expansion of 2 in k 11.956 * [backup-simplify]: Simplify 2 into 2 11.956 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.956 * [taylor]: Taking taylor expansion of PI in k 11.956 * [backup-simplify]: Simplify PI into PI 11.956 * [taylor]: Taking taylor expansion of n in k 11.956 * [backup-simplify]: Simplify n into n 11.956 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.956 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 11.957 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 11.957 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.957 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.958 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.958 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 11.958 * [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)))) 11.958 * [backup-simplify]: Simplify (* 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into 0 11.958 * [taylor]: Taking taylor expansion of 0 in n 11.958 * [backup-simplify]: Simplify 0 into 0 11.958 * [backup-simplify]: Simplify 0 into 0 11.959 * [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)))))) 11.959 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 11.959 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 11.959 * [taylor]: Taking taylor expansion of +nan.0 in n 11.959 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.959 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 11.959 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.959 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.959 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 11.959 * [taylor]: Taking taylor expansion of 1/2 in n 11.959 * [backup-simplify]: Simplify 1/2 into 1/2 11.959 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.959 * [taylor]: Taking taylor expansion of 1/2 in n 11.959 * [backup-simplify]: Simplify 1/2 into 1/2 11.959 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.959 * [taylor]: Taking taylor expansion of k in n 11.959 * [backup-simplify]: Simplify k into k 11.959 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.959 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.959 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.959 * [taylor]: Taking taylor expansion of 2 in n 11.960 * [backup-simplify]: Simplify 2 into 2 11.960 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.960 * [taylor]: Taking taylor expansion of PI in n 11.960 * [backup-simplify]: Simplify PI into PI 11.960 * [taylor]: Taking taylor expansion of n in n 11.960 * [backup-simplify]: Simplify 0 into 0 11.960 * [backup-simplify]: Simplify 1 into 1 11.960 * [backup-simplify]: Simplify (/ PI 1) into PI 11.961 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.962 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.962 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.962 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 11.962 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 11.963 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.964 * [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))) 11.965 * [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)))) 11.966 * [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))))) 11.967 * [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)))))) 11.968 * [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)))))) 11.968 * [backup-simplify]: Simplify 0 into 0 11.970 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.970 * [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)))))) 11.970 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 11.970 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 11.970 * [taylor]: Taking taylor expansion of +nan.0 in n 11.970 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.970 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 11.970 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.970 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.970 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 11.970 * [taylor]: Taking taylor expansion of 1/2 in n 11.970 * [backup-simplify]: Simplify 1/2 into 1/2 11.970 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.970 * [taylor]: Taking taylor expansion of 1/2 in n 11.970 * [backup-simplify]: Simplify 1/2 into 1/2 11.970 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.970 * [taylor]: Taking taylor expansion of k in n 11.970 * [backup-simplify]: Simplify k into k 11.970 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.970 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.970 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.970 * [taylor]: Taking taylor expansion of 2 in n 11.970 * [backup-simplify]: Simplify 2 into 2 11.970 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.971 * [taylor]: Taking taylor expansion of PI in n 11.971 * [backup-simplify]: Simplify PI into PI 11.971 * [taylor]: Taking taylor expansion of n in n 11.971 * [backup-simplify]: Simplify 0 into 0 11.971 * [backup-simplify]: Simplify 1 into 1 11.971 * [backup-simplify]: Simplify (/ PI 1) into PI 11.971 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.972 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.972 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.972 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 11.972 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 11.973 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.974 * [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))) 11.974 * [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)))) 11.975 * [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))))) 11.976 * [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)))))) 11.977 * [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)))))) 11.977 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.978 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 11.979 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.979 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.979 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 11.979 * [backup-simplify]: Simplify (- 0) into 0 11.980 * [backup-simplify]: Simplify (+ 0 0) into 0 11.980 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.981 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 11.982 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 11.983 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 11.983 * [backup-simplify]: Simplify (- 0) into 0 11.984 * [backup-simplify]: Simplify 0 into 0 11.984 * [backup-simplify]: Simplify 0 into 0 11.986 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.987 * [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)))))) 11.987 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 11.987 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 11.987 * [taylor]: Taking taylor expansion of +nan.0 in n 11.987 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.987 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 11.987 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.987 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.987 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 11.987 * [taylor]: Taking taylor expansion of 1/2 in n 11.987 * [backup-simplify]: Simplify 1/2 into 1/2 11.987 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.987 * [taylor]: Taking taylor expansion of 1/2 in n 11.987 * [backup-simplify]: Simplify 1/2 into 1/2 11.987 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.987 * [taylor]: Taking taylor expansion of k in n 11.987 * [backup-simplify]: Simplify k into k 11.987 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.987 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.987 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.987 * [taylor]: Taking taylor expansion of 2 in n 11.987 * [backup-simplify]: Simplify 2 into 2 11.987 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.987 * [taylor]: Taking taylor expansion of PI in n 11.987 * [backup-simplify]: Simplify PI into PI 11.987 * [taylor]: Taking taylor expansion of n in n 11.987 * [backup-simplify]: Simplify 0 into 0 11.987 * [backup-simplify]: Simplify 1 into 1 11.987 * [backup-simplify]: Simplify (/ PI 1) into PI 11.988 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.988 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.988 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.988 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 11.989 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 11.989 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.990 * [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))) 11.991 * [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)))) 11.992 * [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))))) 11.992 * [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)))))) 11.993 * [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)))))) 11.996 * [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)))))))) 11.996 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (/ 1 (- k))) (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 11.996 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (k n) around 0 11.996 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 11.996 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 11.996 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 11.996 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 11.996 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 11.996 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.996 * [taylor]: Taking taylor expansion of 1/2 in n 11.996 * [backup-simplify]: Simplify 1/2 into 1/2 11.996 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.996 * [taylor]: Taking taylor expansion of k in n 11.996 * [backup-simplify]: Simplify k into k 11.996 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.996 * [taylor]: Taking taylor expansion of 1/2 in n 11.996 * [backup-simplify]: Simplify 1/2 into 1/2 11.996 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.996 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.996 * [taylor]: Taking taylor expansion of -2 in n 11.996 * [backup-simplify]: Simplify -2 into -2 11.996 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.996 * [taylor]: Taking taylor expansion of PI in n 11.996 * [backup-simplify]: Simplify PI into PI 11.996 * [taylor]: Taking taylor expansion of n in n 11.996 * [backup-simplify]: Simplify 0 into 0 11.996 * [backup-simplify]: Simplify 1 into 1 11.997 * [backup-simplify]: Simplify (/ PI 1) into PI 11.997 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.998 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.998 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.998 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 11.999 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.999 * [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))) 12.000 * [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)))) 12.000 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 12.000 * [taylor]: Taking taylor expansion of (/ -1 k) in n 12.000 * [taylor]: Taking taylor expansion of -1 in n 12.000 * [backup-simplify]: Simplify -1 into -1 12.000 * [taylor]: Taking taylor expansion of k in n 12.000 * [backup-simplify]: Simplify k into k 12.000 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 12.000 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 12.000 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 12.000 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 12.001 * [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))) 12.001 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 12.001 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 12.001 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 12.001 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 12.001 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 12.001 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 12.001 * [taylor]: Taking taylor expansion of 1/2 in k 12.001 * [backup-simplify]: Simplify 1/2 into 1/2 12.001 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.001 * [taylor]: Taking taylor expansion of k in k 12.001 * [backup-simplify]: Simplify 0 into 0 12.001 * [backup-simplify]: Simplify 1 into 1 12.002 * [backup-simplify]: Simplify (/ 1 1) into 1 12.002 * [taylor]: Taking taylor expansion of 1/2 in k 12.002 * [backup-simplify]: Simplify 1/2 into 1/2 12.002 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 12.002 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 12.002 * [taylor]: Taking taylor expansion of -2 in k 12.002 * [backup-simplify]: Simplify -2 into -2 12.002 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.002 * [taylor]: Taking taylor expansion of PI in k 12.002 * [backup-simplify]: Simplify PI into PI 12.002 * [taylor]: Taking taylor expansion of n in k 12.002 * [backup-simplify]: Simplify n into n 12.002 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.002 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 12.002 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 12.002 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.002 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 12.002 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 12.003 * [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))) 12.003 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.003 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.003 * [taylor]: Taking taylor expansion of -1 in k 12.003 * [backup-simplify]: Simplify -1 into -1 12.003 * [taylor]: Taking taylor expansion of k in k 12.003 * [backup-simplify]: Simplify 0 into 0 12.003 * [backup-simplify]: Simplify 1 into 1 12.003 * [backup-simplify]: Simplify (/ -1 1) into -1 12.003 * [backup-simplify]: Simplify (sqrt 0) into 0 12.004 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.004 * [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)))) 12.004 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 12.004 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 12.004 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 12.004 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 12.004 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 12.004 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 12.004 * [taylor]: Taking taylor expansion of 1/2 in k 12.004 * [backup-simplify]: Simplify 1/2 into 1/2 12.004 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.004 * [taylor]: Taking taylor expansion of k in k 12.004 * [backup-simplify]: Simplify 0 into 0 12.004 * [backup-simplify]: Simplify 1 into 1 12.009 * [backup-simplify]: Simplify (/ 1 1) into 1 12.009 * [taylor]: Taking taylor expansion of 1/2 in k 12.009 * [backup-simplify]: Simplify 1/2 into 1/2 12.009 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 12.009 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 12.009 * [taylor]: Taking taylor expansion of -2 in k 12.009 * [backup-simplify]: Simplify -2 into -2 12.009 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.009 * [taylor]: Taking taylor expansion of PI in k 12.009 * [backup-simplify]: Simplify PI into PI 12.009 * [taylor]: Taking taylor expansion of n in k 12.009 * [backup-simplify]: Simplify n into n 12.009 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.009 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 12.009 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 12.010 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.010 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 12.010 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 12.010 * [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))) 12.010 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.010 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.010 * [taylor]: Taking taylor expansion of -1 in k 12.010 * [backup-simplify]: Simplify -1 into -1 12.010 * [taylor]: Taking taylor expansion of k in k 12.010 * [backup-simplify]: Simplify 0 into 0 12.010 * [backup-simplify]: Simplify 1 into 1 12.011 * [backup-simplify]: Simplify (/ -1 1) into -1 12.011 * [backup-simplify]: Simplify (sqrt 0) into 0 12.012 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.012 * [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)))) 12.012 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 12.012 * [taylor]: Taking taylor expansion of +nan.0 in n 12.012 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.012 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 12.012 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 12.012 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 12.012 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.012 * [taylor]: Taking taylor expansion of -2 in n 12.012 * [backup-simplify]: Simplify -2 into -2 12.012 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.012 * [taylor]: Taking taylor expansion of PI in n 12.012 * [backup-simplify]: Simplify PI into PI 12.012 * [taylor]: Taking taylor expansion of n in n 12.012 * [backup-simplify]: Simplify 0 into 0 12.012 * [backup-simplify]: Simplify 1 into 1 12.012 * [backup-simplify]: Simplify (/ PI 1) into PI 12.013 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.013 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.013 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 12.013 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.013 * [taylor]: Taking taylor expansion of 1/2 in n 12.013 * [backup-simplify]: Simplify 1/2 into 1/2 12.013 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.013 * [taylor]: Taking taylor expansion of k in n 12.013 * [backup-simplify]: Simplify k into k 12.013 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.013 * [taylor]: Taking taylor expansion of 1/2 in n 12.013 * [backup-simplify]: Simplify 1/2 into 1/2 12.014 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.014 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.014 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 12.015 * [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))) 12.016 * [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)))) 12.017 * [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))))) 12.018 * [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))))) 12.018 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 12.020 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.021 * [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))))) 12.021 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 12.021 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 12.021 * [taylor]: Taking taylor expansion of +nan.0 in n 12.021 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.021 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 12.021 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 12.021 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 12.021 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.021 * [taylor]: Taking taylor expansion of -2 in n 12.021 * [backup-simplify]: Simplify -2 into -2 12.021 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.021 * [taylor]: Taking taylor expansion of PI in n 12.021 * [backup-simplify]: Simplify PI into PI 12.021 * [taylor]: Taking taylor expansion of n in n 12.021 * [backup-simplify]: Simplify 0 into 0 12.021 * [backup-simplify]: Simplify 1 into 1 12.021 * [backup-simplify]: Simplify (/ PI 1) into PI 12.021 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.022 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.022 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 12.022 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.022 * [taylor]: Taking taylor expansion of 1/2 in n 12.022 * [backup-simplify]: Simplify 1/2 into 1/2 12.022 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.022 * [taylor]: Taking taylor expansion of k in n 12.022 * [backup-simplify]: Simplify k into k 12.022 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.022 * [taylor]: Taking taylor expansion of 1/2 in n 12.022 * [backup-simplify]: Simplify 1/2 into 1/2 12.023 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.023 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.023 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 12.024 * [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))) 12.025 * [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)))) 12.025 * [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))))) 12.026 * [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)))))) 12.027 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 12.028 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.028 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.028 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 12.028 * [backup-simplify]: Simplify (+ 0 0) into 0 12.029 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.029 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 12.030 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 12.031 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 12.032 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 12.033 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into 0 12.033 * [backup-simplify]: Simplify 0 into 0 12.034 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.036 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.037 * [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))))) 12.037 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 12.037 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 12.037 * [taylor]: Taking taylor expansion of +nan.0 in n 12.037 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.037 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 12.037 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 12.037 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 12.037 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.037 * [taylor]: Taking taylor expansion of -2 in n 12.037 * [backup-simplify]: Simplify -2 into -2 12.037 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.037 * [taylor]: Taking taylor expansion of PI in n 12.037 * [backup-simplify]: Simplify PI into PI 12.037 * [taylor]: Taking taylor expansion of n in n 12.037 * [backup-simplify]: Simplify 0 into 0 12.037 * [backup-simplify]: Simplify 1 into 1 12.038 * [backup-simplify]: Simplify (/ PI 1) into PI 12.038 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.039 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.039 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 12.039 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.039 * [taylor]: Taking taylor expansion of 1/2 in n 12.039 * [backup-simplify]: Simplify 1/2 into 1/2 12.039 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.039 * [taylor]: Taking taylor expansion of k in n 12.039 * [backup-simplify]: Simplify k into k 12.039 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.039 * [taylor]: Taking taylor expansion of 1/2 in n 12.039 * [backup-simplify]: Simplify 1/2 into 1/2 12.040 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.040 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.040 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 12.041 * [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))) 12.041 * [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)))) 12.042 * [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))))) 12.043 * [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)))))) 12.044 * [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)))))) 12.046 * [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))))))))))) 12.046 * * * [progress]: simplifying candidates 12.046 * * * * [progress]: [ 1 / 1611 ] simplifiying candidate # 12.046 * * * * [progress]: [ 2 / 1611 ] simplifiying candidate # 12.046 * * * * [progress]: [ 3 / 1611 ] simplifiying candidate # 12.046 * * * * [progress]: [ 4 / 1611 ] simplifiying candidate # 12.047 * * * * [progress]: [ 5 / 1611 ] simplifiying candidate # 12.047 * * * * [progress]: [ 6 / 1611 ] simplifiying candidate # 12.047 * * * * [progress]: [ 7 / 1611 ] simplifiying candidate # 12.047 * * * * [progress]: [ 8 / 1611 ] simplifiying candidate # 12.047 * * * * [progress]: [ 9 / 1611 ] simplifiying candidate # 12.047 * * * * [progress]: [ 10 / 1611 ] simplifiying candidate # 12.047 * * * * [progress]: [ 11 / 1611 ] simplifiying candidate # 12.047 * * * * [progress]: [ 12 / 1611 ] simplifiying candidate # 12.047 * * * * [progress]: [ 13 / 1611 ] simplifiying candidate # 12.047 * * * * [progress]: [ 14 / 1611 ] simplifiying candidate # 12.047 * * * * [progress]: [ 15 / 1611 ] simplifiying candidate # 12.047 * * * * [progress]: [ 16 / 1611 ] simplifiying candidate # 12.047 * * * * [progress]: [ 17 / 1611 ] simplifiying candidate # 12.047 * * * * [progress]: [ 18 / 1611 ] simplifiying candidate # 12.047 * * * * [progress]: [ 19 / 1611 ] simplifiying candidate # 12.047 * * * * [progress]: [ 20 / 1611 ] simplifiying candidate # 12.047 * * * * [progress]: [ 21 / 1611 ] simplifiying candidate # 12.047 * * * * [progress]: [ 22 / 1611 ] simplifiying candidate # 12.047 * * * * [progress]: [ 23 / 1611 ] simplifiying candidate # 12.047 * * * * [progress]: [ 24 / 1611 ] simplifiying candidate # 12.047 * * * * 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(- 1/2 (/ k 2)))) (pow (* PI (* n 2)) 1) (pow (* PI (* n 2)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* PI (* n 2)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (pow (* PI (* n 2)) 1) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* PI (* n 2)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (pow (* PI (* n 2)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (pow (* PI (* n 2)) (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 (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* PI (* n 2)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (pow (* PI (* n 2)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow (* PI (* n 2)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* PI (* n 2)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (pow (* PI (* n 2)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (pow (* PI (* n 2)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (pow (* PI (* n 2)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) (/ 1 1))))) (pow (* PI (* n 2)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) 1)))) (pow (* PI (* n 2)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1 2) k)))) (pow (* PI (* n 2)) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (pow (* PI (* n 2)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* PI (* n 2)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* PI (* n 2)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (pow (* PI (* n 2)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (pow (* PI (* n 2)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (pow (* PI (* n 2)) (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 (* PI (* n 2)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* PI (* n 2)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) 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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))))))))))) 12.302 * * [simplify]: iteration 1: (1731 enodes) 194.149 * * [simplify]: Extracting #0: cost 587 inf + 0 194.158 * * [simplify]: Extracting #1: cost 1621 inf + 43 194.170 * * [simplify]: Extracting #2: cost 1682 inf + 4606 194.183 * * [simplify]: Extracting #3: cost 1540 inf + 38528 194.214 * * [simplify]: Extracting #4: cost 1106 inf + 156846 194.292 * * [simplify]: Extracting #5: cost 745 inf + 324268 194.416 * * [simplify]: Extracting #6: cost 439 inf + 522409 194.586 * * [simplify]: Extracting #7: cost 164 inf + 722627 194.792 * * [simplify]: Extracting #8: cost 45 inf + 801756 194.967 * * [simplify]: Extracting #9: cost 17 inf + 817147 195.136 * * [simplify]: Extracting #10: cost 8 inf + 824150 195.304 * * [simplify]: Extracting #11: cost 2 inf + 829901 195.453 * * [simplify]: Extracting #12: cost 0 inf + 832303 195.607 * * [simplify]: Extracting #13: cost 0 inf + 832273 195.792 * [simplify]: Simplified to: (expm1 (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (log1p (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (- 1/2 (/ k 2)) (- 1/2 (/ k 2)) (- 1/2 (/ k 2)) (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)) (pow (* (* 2 n) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* (* 2 n) PI) (sqrt (- 1/2 (/ k 2)))) (* (* 2 n) PI) (pow (* (* 2 n) PI) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* (* 2 n) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (* (* 2 n) PI) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 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1/2)) (cbrt 1/2) (* (/ k (sqrt 2)) (- (/ 1 (sqrt 2))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (/ (- k) 2)))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (/ (- k) 2)))) (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (- 1/2) k))))) (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (/ (- k) 2)))) (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (cbrt k) (cbrt 2)) (- (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (cbrt k) (sqrt 2)) (- (/ (cbrt k) (/ (sqrt 2) (cbrt k)))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (cbrt k) 2) (- (* (cbrt k) (cbrt k))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (sqrt k) (cbrt 2)) (- (/ (/ (sqrt k) (cbrt 2)) (cbrt 2))))))) (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (sqrt k) (sqrt 2)) (- (/ (sqrt k) (sqrt 2)))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (sqrt k) 2) (- (sqrt k)))))) (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ k (cbrt 2)) (- (/ (/ 1 (cbrt 2)) (cbrt 2)))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ k (sqrt 2)) (- (/ 1 (sqrt 2))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (/ (- k) 2)))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (/ (- k) 2)))) (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (- 1/2) k))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (+ 1/2 (* (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (+ 1/2 (/ (- k) 2))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (cbrt k) (cbrt 2)) (- (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2)))))))) (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (cbrt k) (sqrt 2)) (- (/ (cbrt k) (/ (sqrt 2) (cbrt k))))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (cbrt k) 2) (- (* (cbrt k) (cbrt k))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (sqrt k) (cbrt 2)) (- (/ (/ (sqrt k) (cbrt 2)) (cbrt 2))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (sqrt k) (sqrt 2)) (- (/ (sqrt k) (sqrt 2))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (sqrt k) 2) (- (sqrt k)))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ k (cbrt 2)) (- (/ (/ 1 (cbrt 2)) (cbrt 2))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ k (sqrt 2)) (- (/ 1 (sqrt 2))))))) (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (+ 1/2 (/ (- k) 2))))) (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (+ 1/2 (/ (- k) 2))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (- 1/2 (* k 1/2)))) (* (/ 1 (sqrt (sqrt k))) (sqrt (* (* 2 n) PI))) (* (/ 1 (sqrt (sqrt k))) (sqrt (* (* 2 n) PI))) (/ 1 (/ (sqrt (sqrt k)) (pow PI (- 1/2 (/ k 2))))) (* (/ 1 (sqrt (sqrt k))) (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (/ 1 (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (- 1/4 (/ (/ k 2) 2)))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (/ (- k) 2))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (/ (cbrt k) (cbrt 2)) (- (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (/ (cbrt k) (sqrt 2)) (- (/ (cbrt k) (/ (sqrt 2) (cbrt k))))))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (/ (cbrt k) 2) (- (* (cbrt k) (cbrt k)))))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (/ (sqrt k) (cbrt 2)) (- (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)))))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (/ (sqrt k) (sqrt 2)) (- (/ (sqrt k) (sqrt 2)))))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (/ (sqrt k) 2) (- (sqrt k))))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (/ k (cbrt 2)) (- (/ (/ 1 (cbrt 2)) (cbrt 2)))))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (/ k (sqrt 2)) (- (/ 1 (sqrt 2)))))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (/ (- k) 2))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (/ (- k) 2))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (- 1/2) k))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (/ (- k) 2))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (cbrt k) (cbrt 2)) (- (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (cbrt k) (sqrt 2)) (- (/ (cbrt k) (/ (sqrt 2) (cbrt k))))))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (cbrt k) 2) (- (* (cbrt k) (cbrt k)))))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (sqrt k) (cbrt 2)) (- (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)))))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (sqrt k) (sqrt 2)) (- (/ (sqrt k) (sqrt 2)))))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (sqrt k) 2) (- (sqrt k))))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ k (cbrt 2)) (- (/ (/ 1 (cbrt 2)) (cbrt 2)))))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ k (sqrt 2)) (- (/ 1 (sqrt 2)))))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (/ (- k) 2))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (/ (- k) 2))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (- 1/2) k))) (pow (* (* 2 n) PI) (+ 1/2 (* (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* (* 2 n) PI) (+ 1/2 (/ (- k) 2))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (cbrt k) (cbrt 2)) (- (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (cbrt k) (sqrt 2)) (- (/ (cbrt k) (/ (sqrt 2) (cbrt k))))))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (cbrt k) 2) (- (* (cbrt k) (cbrt k)))))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (sqrt k) (cbrt 2)) (- (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)))))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (sqrt k) (sqrt 2)) (- (/ (sqrt k) (sqrt 2)))))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (sqrt k) 2) (- (sqrt k))))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ k (cbrt 2)) (- (/ (/ 1 (cbrt 2)) (cbrt 2)))))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ k (sqrt 2)) (- (/ 1 (sqrt 2)))))) (pow (* (* 2 n) PI) (+ 1/2 (/ (- k) 2))) (pow (* (* 2 n) PI) (+ 1/2 (/ (- k) 2))) (pow (* (* 2 n) PI) (- 1/2 (* k 1/2))) (sqrt (* (* 2 n) PI)) (sqrt (* (* 2 n) PI)) (pow PI (- 1/2 (/ k 2))) (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) 1 (pow (* (* 2 n) PI) (- 1/4 (/ (/ k 2) 2))) 1 (/ 1 (sqrt k)) (/ 1 (/ (sqrt k) (sqrt (* (* 2 n) PI)))) (/ (sqrt k) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ 1 (sqrt k)) (real->posit16 (/ 1 (/ (sqrt k) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) (- (fma 1/4 (* (* (log (* PI 2)) (exp (* 1/2 (+ (log n) (log (* PI 2)))))) (* (* k k) (log n))) (fma 1/8 (* (* (* k k) (* (log n) (log n))) (exp (* 1/2 (+ (log n) (log (* PI 2)))))) (+ (exp (* 1/2 (+ (log n) (log (* PI 2))))) (* (* (* (exp (* 1/2 (+ (log n) (log (* PI 2))))) (* k k)) (* (log (* PI 2)) (log (* PI 2)))) 1/8)))) (* 1/2 (+ (* (* (exp (* 1/2 (+ (log n) (log (* PI 2))))) (log n)) k) (* (log (* PI 2)) (* (exp (* 1/2 (+ (log n) (log (* PI 2))))) k))))) (exp (* (- (log (* PI 2)) (- (log n))) (- 1/2 (* k 1/2)))) (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2)))) (* (* 2 n) PI) (* (* 2 n) PI) (* (* 2 n) PI) (- (- (* +nan.0 (/ (* (* (sqrt 2) (* k k)) (* (log (* PI 2)) (* (sqrt 1/2) (sqrt 1/2)))) PI)) (- (* +nan.0 (/ (sqrt 1/2) (/ PI (* k k)))) (- (/ (* +nan.0 (* (* n (sqrt 1/2)) k)) (* PI PI)) (- (* (/ (log n) (/ PI (* (sqrt 2) (* (* k k) (* (sqrt 1/2) (sqrt 1/2)))))) +nan.0) (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))) (- (- (* (/ (exp (- (* (- (log (* PI 2)) (- (log n))) (- 1/2 (* k 1/2))))) k) +nan.0) (- (* (/ (exp (- (* (- (log (* PI 2)) (- (log n))) (- 1/2 (* k 1/2))))) (* k k)) +nan.0) (* (exp (- (* (- (log (* PI 2)) (- (log n))) (- 1/2 (* k 1/2))))) +nan.0)))) (- (- (* +nan.0 (/ (exp (- (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2))))) (* k k))) (- (* (/ (exp (- (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2))))) k) +nan.0) (* +nan.0 (exp (- (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2))))))))) (- (- (* (* +nan.0 (sqrt 2)) (* (* PI n) k)) (- (* +nan.0 (* (* PI n) (sqrt 2))) (- (* (* (log (* PI 2)) (* (* (* PI n) k) (sqrt 2))) +nan.0) (- (* (* (* (sqrt 2) n) (* PI (* (log n) k))) +nan.0) (* (* +nan.0 (sqrt 2)) (* (* n n) (* PI PI)))))))) (- (- (* (/ (exp (* (- (log (* PI 2)) (- (log n))) (- 1/2 (* k 1/2)))) (* k (* k k))) +nan.0) (- (* +nan.0 (/ (exp (* (- (log (* PI 2)) (- (log n))) (- 1/2 (* k 1/2)))) k)) (* +nan.0 (/ (exp (* (- (log (* PI 2)) (- (log n))) (- 1/2 (* k 1/2)))) (* k k)))))) (- (- (/ (* +nan.0 (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2))))) k) (- (* +nan.0 (/ (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2)))) (* k k))) (* +nan.0 (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2)))))))) 196.353 * * * [progress]: adding candidates to table 225.951 * * [progress]: iteration 3 / 4 225.952 * * * [progress]: picking best candidate 226.002 * * * * [pick]: Picked # 226.002 * * * [progress]: localizing error 226.046 * * * [progress]: generating rewritten candidates 226.046 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 2) 226.063 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1 2) 226.069 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2) 226.080 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2) 226.234 * * * [progress]: generating series expansions 226.234 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 2) 226.234 * [backup-simplify]: Simplify (pow (* n 2) (- 1/2 (/ k 2))) into (pow (* 2 n) (- 1/2 (* 1/2 k))) 226.234 * [approximate]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in (n k) around 0 226.234 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 226.234 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 226.235 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 226.235 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 226.235 * [taylor]: Taking taylor expansion of 1/2 in k 226.235 * [backup-simplify]: Simplify 1/2 into 1/2 226.235 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 226.235 * [taylor]: Taking taylor expansion of 1/2 in k 226.235 * [backup-simplify]: Simplify 1/2 into 1/2 226.235 * [taylor]: Taking taylor expansion of k in k 226.235 * [backup-simplify]: Simplify 0 into 0 226.235 * [backup-simplify]: Simplify 1 into 1 226.235 * [taylor]: Taking taylor expansion of (log (* 2 n)) in k 226.235 * [taylor]: Taking taylor expansion of (* 2 n) in k 226.235 * [taylor]: Taking taylor expansion of 2 in k 226.235 * [backup-simplify]: Simplify 2 into 2 226.235 * [taylor]: Taking taylor expansion of n in k 226.235 * [backup-simplify]: Simplify n into n 226.235 * [backup-simplify]: Simplify (* 2 n) into (* 2 n) 226.235 * [backup-simplify]: Simplify (log (* 2 n)) into (log (* 2 n)) 226.236 * [backup-simplify]: Simplify (* 1/2 0) into 0 226.237 * [backup-simplify]: Simplify (- 0) into 0 226.237 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 226.237 * [backup-simplify]: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 226.237 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 226.238 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 226.238 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 226.238 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 226.238 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 226.238 * [taylor]: Taking taylor expansion of 1/2 in n 226.238 * [backup-simplify]: Simplify 1/2 into 1/2 226.238 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 226.238 * [taylor]: Taking taylor expansion of 1/2 in n 226.238 * [backup-simplify]: Simplify 1/2 into 1/2 226.238 * [taylor]: Taking taylor expansion of k in n 226.238 * [backup-simplify]: Simplify k into k 226.238 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 226.238 * [taylor]: Taking taylor expansion of (* 2 n) in n 226.238 * [taylor]: Taking taylor expansion of 2 in n 226.238 * [backup-simplify]: Simplify 2 into 2 226.238 * [taylor]: Taking taylor expansion of n in n 226.238 * [backup-simplify]: Simplify 0 into 0 226.238 * [backup-simplify]: Simplify 1 into 1 226.239 * [backup-simplify]: Simplify (* 2 0) into 0 226.239 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 226.240 * [backup-simplify]: Simplify (log 2) into (log 2) 226.240 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 226.240 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 226.240 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 226.241 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 226.241 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 226.242 * [backup-simplify]: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 226.242 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 226.242 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 226.242 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 226.242 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 226.242 * [taylor]: Taking taylor expansion of 1/2 in n 226.242 * [backup-simplify]: Simplify 1/2 into 1/2 226.242 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 226.242 * [taylor]: Taking taylor expansion of 1/2 in n 226.242 * [backup-simplify]: Simplify 1/2 into 1/2 226.242 * [taylor]: Taking taylor expansion of k in n 226.242 * [backup-simplify]: Simplify k into k 226.242 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 226.242 * [taylor]: Taking taylor expansion of (* 2 n) in n 226.242 * [taylor]: Taking taylor expansion of 2 in n 226.242 * [backup-simplify]: Simplify 2 into 2 226.242 * [taylor]: Taking taylor expansion of n in n 226.242 * [backup-simplify]: Simplify 0 into 0 226.242 * [backup-simplify]: Simplify 1 into 1 226.242 * [backup-simplify]: Simplify (* 2 0) into 0 226.243 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 226.243 * [backup-simplify]: Simplify (log 2) into (log 2) 226.243 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 226.243 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 226.243 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 226.244 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 226.244 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 226.245 * [backup-simplify]: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 226.245 * [taylor]: Taking taylor expansion of (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) in k 226.245 * [taylor]: Taking taylor expansion of (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) in k 226.245 * [taylor]: Taking taylor expansion of (+ (log 2) (log n)) in k 226.245 * [taylor]: Taking taylor expansion of (log 2) in k 226.245 * [taylor]: Taking taylor expansion of 2 in k 226.245 * [backup-simplify]: Simplify 2 into 2 226.245 * [backup-simplify]: Simplify (log 2) into (log 2) 226.245 * [taylor]: Taking taylor expansion of (log n) in k 226.245 * [taylor]: Taking taylor expansion of n in k 226.245 * [backup-simplify]: Simplify n into n 226.245 * [backup-simplify]: Simplify (log n) into (log n) 226.245 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 226.245 * [taylor]: Taking taylor expansion of 1/2 in k 226.245 * [backup-simplify]: Simplify 1/2 into 1/2 226.245 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 226.245 * [taylor]: Taking taylor expansion of 1/2 in k 226.245 * [backup-simplify]: Simplify 1/2 into 1/2 226.246 * [taylor]: Taking taylor expansion of k in k 226.246 * [backup-simplify]: Simplify 0 into 0 226.246 * [backup-simplify]: Simplify 1 into 1 226.246 * [backup-simplify]: Simplify (+ (log 2) (log n)) into (+ (log 2) (log n)) 226.246 * [backup-simplify]: Simplify (* 1/2 0) into 0 226.246 * [backup-simplify]: Simplify (- 0) into 0 226.247 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 226.247 * [backup-simplify]: Simplify (* (+ (log 2) (log n)) 1/2) into (* 1/2 (+ (log 2) (log n))) 226.247 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 226.248 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 226.248 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0 226.249 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 226.250 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 226.250 * [backup-simplify]: Simplify (- 0) into 0 226.250 * [backup-simplify]: Simplify (+ 0 0) into 0 226.251 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 226.251 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log 2) (log n)))) into 0 226.252 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 226.252 * [taylor]: Taking taylor expansion of 0 in k 226.252 * [backup-simplify]: Simplify 0 into 0 226.252 * [backup-simplify]: Simplify 0 into 0 226.253 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 226.253 * [backup-simplify]: Simplify (- 1/2) into -1/2 226.253 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 226.254 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 226.255 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 226.255 * [backup-simplify]: Simplify (+ 0 0) into 0 226.255 * [backup-simplify]: Simplify (+ (* (+ (log 2) (log n)) -1/2) (* 0 1/2)) into (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 226.256 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 226.257 * [backup-simplify]: Simplify (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 226.258 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 226.260 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 226.261 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 226.261 * [backup-simplify]: Simplify (- 0) into 0 226.261 * [backup-simplify]: Simplify (+ 0 0) into 0 226.262 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 226.262 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0 226.263 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 226.263 * [taylor]: Taking taylor expansion of 0 in k 226.263 * [backup-simplify]: Simplify 0 into 0 226.263 * [backup-simplify]: Simplify 0 into 0 226.263 * [backup-simplify]: Simplify 0 into 0 226.264 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 226.264 * [backup-simplify]: Simplify (- 0) into 0 226.265 * [backup-simplify]: Simplify (+ 0 0) into 0 226.266 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 226.267 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 226.268 * [backup-simplify]: Simplify (+ 0 0) into 0 226.269 * [backup-simplify]: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 -1/2) (* 0 1/2))) into 0 226.270 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 226.272 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 226.275 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log 2) (log n)))))) into (- (+ (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (+ (* 1/4 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (* 1/8 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k))) (* 1/2 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k))))) 226.275 * [backup-simplify]: Simplify (pow (* (/ 1 n) 2) (- 1/2 (/ (/ 1 k) 2))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 226.275 * [approximate]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 226.275 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 226.275 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 226.275 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 226.275 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 226.276 * [taylor]: Taking taylor expansion of 1/2 in k 226.276 * [backup-simplify]: Simplify 1/2 into 1/2 226.276 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 226.276 * [taylor]: Taking taylor expansion of 1/2 in k 226.276 * [backup-simplify]: Simplify 1/2 into 1/2 226.276 * [taylor]: Taking taylor expansion of (/ 1 k) in k 226.276 * [taylor]: Taking taylor expansion of k in k 226.276 * [backup-simplify]: Simplify 0 into 0 226.276 * [backup-simplify]: Simplify 1 into 1 226.276 * [backup-simplify]: Simplify (/ 1 1) into 1 226.276 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in k 226.276 * [taylor]: Taking taylor expansion of (/ 2 n) in k 226.276 * [taylor]: Taking taylor expansion of 2 in k 226.276 * [backup-simplify]: Simplify 2 into 2 226.276 * [taylor]: Taking taylor expansion of n in k 226.276 * [backup-simplify]: Simplify n into n 226.276 * [backup-simplify]: Simplify (/ 2 n) into (/ 2 n) 226.276 * [backup-simplify]: Simplify (log (/ 2 n)) into (log (/ 2 n)) 226.276 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 226.277 * [backup-simplify]: Simplify (- 1/2) into -1/2 226.277 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 226.277 * [backup-simplify]: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 226.277 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 226.277 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 226.277 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 226.277 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 226.277 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 226.277 * [taylor]: Taking taylor expansion of 1/2 in n 226.277 * [backup-simplify]: Simplify 1/2 into 1/2 226.277 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 226.277 * [taylor]: Taking taylor expansion of 1/2 in n 226.277 * [backup-simplify]: Simplify 1/2 into 1/2 226.277 * [taylor]: Taking taylor expansion of (/ 1 k) in n 226.277 * [taylor]: Taking taylor expansion of k in n 226.277 * [backup-simplify]: Simplify k into k 226.277 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 226.277 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 226.277 * [taylor]: Taking taylor expansion of (/ 2 n) in n 226.277 * [taylor]: Taking taylor expansion of 2 in n 226.277 * [backup-simplify]: Simplify 2 into 2 226.277 * [taylor]: Taking taylor expansion of n in n 226.277 * [backup-simplify]: Simplify 0 into 0 226.277 * [backup-simplify]: Simplify 1 into 1 226.278 * [backup-simplify]: Simplify (/ 2 1) into 2 226.278 * [backup-simplify]: Simplify (log 2) into (log 2) 226.278 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 226.278 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 226.278 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 226.279 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 226.279 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 226.279 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 226.279 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 226.279 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 226.279 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 226.280 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 226.280 * [taylor]: Taking taylor expansion of 1/2 in n 226.280 * [backup-simplify]: Simplify 1/2 into 1/2 226.280 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 226.280 * [taylor]: Taking taylor expansion of 1/2 in n 226.280 * [backup-simplify]: Simplify 1/2 into 1/2 226.280 * [taylor]: Taking taylor expansion of (/ 1 k) in n 226.280 * [taylor]: Taking taylor expansion of k in n 226.280 * [backup-simplify]: Simplify k into k 226.280 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 226.280 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 226.280 * [taylor]: Taking taylor expansion of (/ 2 n) in n 226.280 * [taylor]: Taking taylor expansion of 2 in n 226.280 * [backup-simplify]: Simplify 2 into 2 226.280 * [taylor]: Taking taylor expansion of n in n 226.280 * [backup-simplify]: Simplify 0 into 0 226.280 * [backup-simplify]: Simplify 1 into 1 226.280 * [backup-simplify]: Simplify (/ 2 1) into 2 226.280 * [backup-simplify]: Simplify (log 2) into (log 2) 226.280 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 226.280 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 226.281 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 226.281 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 226.282 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 226.282 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 226.282 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) in k 226.282 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) in k 226.282 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 226.282 * [taylor]: Taking taylor expansion of 1/2 in k 226.282 * [backup-simplify]: Simplify 1/2 into 1/2 226.282 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 226.282 * [taylor]: Taking taylor expansion of 1/2 in k 226.282 * [backup-simplify]: Simplify 1/2 into 1/2 226.282 * [taylor]: Taking taylor expansion of (/ 1 k) in k 226.282 * [taylor]: Taking taylor expansion of k in k 226.282 * [backup-simplify]: Simplify 0 into 0 226.282 * [backup-simplify]: Simplify 1 into 1 226.283 * [backup-simplify]: Simplify (/ 1 1) into 1 226.283 * [taylor]: Taking taylor expansion of (- (log 2) (log n)) in k 226.283 * [taylor]: Taking taylor expansion of (log 2) in k 226.283 * [taylor]: Taking taylor expansion of 2 in k 226.283 * [backup-simplify]: Simplify 2 into 2 226.283 * [backup-simplify]: Simplify (log 2) into (log 2) 226.283 * [taylor]: Taking taylor expansion of (log n) in k 226.283 * [taylor]: Taking taylor expansion of n in k 226.283 * [backup-simplify]: Simplify n into n 226.283 * [backup-simplify]: Simplify (log n) into (log n) 226.283 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 226.283 * [backup-simplify]: Simplify (- 1/2) into -1/2 226.284 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 226.284 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 226.284 * [backup-simplify]: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) 226.284 * [backup-simplify]: Simplify (* -1/2 (- (log 2) (log n))) into (* -1/2 (- (log 2) (log n))) 226.285 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 226.285 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 226.286 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0 226.287 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 226.287 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 226.287 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 226.287 * [backup-simplify]: Simplify (- 0) into 0 226.288 * [backup-simplify]: Simplify (+ 0 0) into 0 226.288 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 226.288 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 226.289 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 226.290 * [taylor]: Taking taylor expansion of 0 in k 226.290 * [backup-simplify]: Simplify 0 into 0 226.290 * [backup-simplify]: Simplify 0 into 0 226.290 * [backup-simplify]: Simplify 0 into 0 226.291 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 226.294 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 226.294 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 226.295 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 226.295 * [backup-simplify]: Simplify (- 0) into 0 226.296 * [backup-simplify]: Simplify (+ 0 0) into 0 226.296 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 226.297 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 226.299 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 226.299 * [taylor]: Taking taylor expansion of 0 in k 226.299 * [backup-simplify]: Simplify 0 into 0 226.299 * [backup-simplify]: Simplify 0 into 0 226.299 * [backup-simplify]: Simplify 0 into 0 226.299 * [backup-simplify]: Simplify 0 into 0 226.301 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 226.306 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 226.307 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 226.308 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 226.308 * [backup-simplify]: Simplify (- 0) into 0 226.309 * [backup-simplify]: Simplify (+ 0 0) into 0 226.309 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 226.311 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 226.313 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 226.313 * [taylor]: Taking taylor expansion of 0 in k 226.313 * [backup-simplify]: Simplify 0 into 0 226.313 * [backup-simplify]: Simplify 0 into 0 226.314 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))) into (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) 226.314 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) 2) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 226.314 * [approximate]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 226.314 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 226.314 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 226.314 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 226.314 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 226.314 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 226.314 * [taylor]: Taking taylor expansion of 1/2 in k 226.314 * [backup-simplify]: Simplify 1/2 into 1/2 226.314 * [taylor]: Taking taylor expansion of (/ 1 k) in k 226.314 * [taylor]: Taking taylor expansion of k in k 226.314 * [backup-simplify]: Simplify 0 into 0 226.315 * [backup-simplify]: Simplify 1 into 1 226.315 * [backup-simplify]: Simplify (/ 1 1) into 1 226.315 * [taylor]: Taking taylor expansion of 1/2 in k 226.315 * [backup-simplify]: Simplify 1/2 into 1/2 226.315 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in k 226.315 * [taylor]: Taking taylor expansion of (/ -2 n) in k 226.315 * [taylor]: Taking taylor expansion of -2 in k 226.315 * [backup-simplify]: Simplify -2 into -2 226.315 * [taylor]: Taking taylor expansion of n in k 226.315 * [backup-simplify]: Simplify n into n 226.315 * [backup-simplify]: Simplify (/ -2 n) into (/ -2 n) 226.315 * [backup-simplify]: Simplify (log (/ -2 n)) into (log (/ -2 n)) 226.316 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 226.316 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 226.316 * [backup-simplify]: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 226.317 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 226.317 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 226.317 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 226.317 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 226.317 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 226.317 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 226.317 * [taylor]: Taking taylor expansion of 1/2 in n 226.317 * [backup-simplify]: Simplify 1/2 into 1/2 226.317 * [taylor]: Taking taylor expansion of (/ 1 k) in n 226.317 * [taylor]: Taking taylor expansion of k in n 226.317 * [backup-simplify]: Simplify k into k 226.317 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 226.317 * [taylor]: Taking taylor expansion of 1/2 in n 226.317 * [backup-simplify]: Simplify 1/2 into 1/2 226.317 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 226.317 * [taylor]: Taking taylor expansion of (/ -2 n) in n 226.317 * [taylor]: Taking taylor expansion of -2 in n 226.317 * [backup-simplify]: Simplify -2 into -2 226.317 * [taylor]: Taking taylor expansion of n in n 226.317 * [backup-simplify]: Simplify 0 into 0 226.317 * [backup-simplify]: Simplify 1 into 1 226.318 * [backup-simplify]: Simplify (/ -2 1) into -2 226.318 * [backup-simplify]: Simplify (log -2) into (log -2) 226.318 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 226.318 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 226.319 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 226.320 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 226.766 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 226.767 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 226.767 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 226.767 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 226.767 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 226.767 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 226.767 * [taylor]: Taking taylor expansion of 1/2 in n 226.767 * [backup-simplify]: Simplify 1/2 into 1/2 226.767 * [taylor]: Taking taylor expansion of (/ 1 k) in n 226.767 * [taylor]: Taking taylor expansion of k in n 226.767 * [backup-simplify]: Simplify k into k 226.767 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 226.767 * [taylor]: Taking taylor expansion of 1/2 in n 226.767 * [backup-simplify]: Simplify 1/2 into 1/2 226.767 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 226.767 * [taylor]: Taking taylor expansion of (/ -2 n) in n 226.767 * [taylor]: Taking taylor expansion of -2 in n 226.767 * [backup-simplify]: Simplify -2 into -2 226.767 * [taylor]: Taking taylor expansion of n in n 226.767 * [backup-simplify]: Simplify 0 into 0 226.767 * [backup-simplify]: Simplify 1 into 1 226.768 * [backup-simplify]: Simplify (/ -2 1) into -2 226.768 * [backup-simplify]: Simplify (log -2) into (log -2) 226.768 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 226.768 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 226.769 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 226.769 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 226.770 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 226.770 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) in k 226.770 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) in k 226.770 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 226.770 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 226.770 * [taylor]: Taking taylor expansion of 1/2 in k 226.770 * [backup-simplify]: Simplify 1/2 into 1/2 226.770 * [taylor]: Taking taylor expansion of (/ 1 k) in k 226.770 * [taylor]: Taking taylor expansion of k in k 226.770 * [backup-simplify]: Simplify 0 into 0 226.770 * [backup-simplify]: Simplify 1 into 1 226.770 * [backup-simplify]: Simplify (/ 1 1) into 1 226.770 * [taylor]: Taking taylor expansion of 1/2 in k 226.770 * [backup-simplify]: Simplify 1/2 into 1/2 226.770 * [taylor]: Taking taylor expansion of (- (log -2) (log n)) in k 226.770 * [taylor]: Taking taylor expansion of (log -2) in k 226.770 * [taylor]: Taking taylor expansion of -2 in k 226.770 * [backup-simplify]: Simplify -2 into -2 226.771 * [backup-simplify]: Simplify (log -2) into (log -2) 226.771 * [taylor]: Taking taylor expansion of (log n) in k 226.771 * [taylor]: Taking taylor expansion of n in k 226.771 * [backup-simplify]: Simplify n into n 226.771 * [backup-simplify]: Simplify (log n) into (log n) 226.771 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 226.771 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 226.771 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 226.772 * [backup-simplify]: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) 226.772 * [backup-simplify]: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) 226.772 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 226.773 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 226.774 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0 226.774 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 226.775 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 226.775 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 226.775 * [backup-simplify]: Simplify (+ 0 0) into 0 226.776 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 226.776 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -2) (log n)))) into 0 226.777 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 226.777 * [taylor]: Taking taylor expansion of 0 in k 226.777 * [backup-simplify]: Simplify 0 into 0 226.777 * [backup-simplify]: Simplify 0 into 0 226.777 * [backup-simplify]: Simplify 0 into 0 226.778 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 226.780 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 226.780 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 226.781 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 226.781 * [backup-simplify]: Simplify (+ 0 0) into 0 226.782 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 226.782 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 226.783 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 226.783 * [taylor]: Taking taylor expansion of 0 in k 226.783 * [backup-simplify]: Simplify 0 into 0 226.784 * [backup-simplify]: Simplify 0 into 0 226.784 * [backup-simplify]: Simplify 0 into 0 226.784 * [backup-simplify]: Simplify 0 into 0 226.784 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 226.788 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -2 1)))) 6) into 0 226.788 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 226.789 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 226.789 * [backup-simplify]: Simplify (+ 0 0) into 0 226.789 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 226.790 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -2) (log n)))))) into 0 226.791 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 226.792 * [taylor]: Taking taylor expansion of 0 in k 226.792 * [backup-simplify]: Simplify 0 into 0 226.792 * [backup-simplify]: Simplify 0 into 0 226.792 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) 226.792 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1 2) 226.792 * [backup-simplify]: Simplify (pow PI (- 1/2 (/ k 2))) into (pow PI (- 1/2 (* 1/2 k))) 226.792 * [approximate]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in (k) around 0 226.792 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 226.792 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 226.792 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 226.792 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 226.792 * [taylor]: Taking taylor expansion of 1/2 in k 226.792 * [backup-simplify]: Simplify 1/2 into 1/2 226.792 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 226.792 * [taylor]: Taking taylor expansion of 1/2 in k 226.792 * [backup-simplify]: Simplify 1/2 into 1/2 226.792 * [taylor]: Taking taylor expansion of k in k 226.792 * [backup-simplify]: Simplify 0 into 0 226.792 * [backup-simplify]: Simplify 1 into 1 226.792 * [taylor]: Taking taylor expansion of (log PI) in k 226.792 * [taylor]: Taking taylor expansion of PI in k 226.792 * [backup-simplify]: Simplify PI into PI 226.793 * [backup-simplify]: Simplify (log PI) into (log PI) 226.793 * [backup-simplify]: Simplify (* 1/2 0) into 0 226.793 * [backup-simplify]: Simplify (- 0) into 0 226.794 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 226.794 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 226.795 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 226.795 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 226.795 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 226.795 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 226.795 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 226.795 * [taylor]: Taking taylor expansion of 1/2 in k 226.795 * [backup-simplify]: Simplify 1/2 into 1/2 226.795 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 226.795 * [taylor]: Taking taylor expansion of 1/2 in k 226.795 * [backup-simplify]: Simplify 1/2 into 1/2 226.795 * [taylor]: Taking taylor expansion of k in k 226.796 * [backup-simplify]: Simplify 0 into 0 226.796 * [backup-simplify]: Simplify 1 into 1 226.796 * [taylor]: Taking taylor expansion of (log PI) in k 226.796 * [taylor]: Taking taylor expansion of PI in k 226.796 * [backup-simplify]: Simplify PI into PI 226.796 * [backup-simplify]: Simplify (log PI) into (log PI) 226.796 * [backup-simplify]: Simplify (* 1/2 0) into 0 226.796 * [backup-simplify]: Simplify (- 0) into 0 226.797 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 226.798 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 226.799 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 226.800 * [backup-simplify]: Simplify (pow PI 1/2) into (pow PI 1/2) 226.802 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 226.803 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 226.803 * [backup-simplify]: Simplify (- 1/2) into -1/2 226.804 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 226.806 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 226.817 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 226.820 * [backup-simplify]: Simplify (* -1/2 (* (log PI) (sqrt PI))) into (* -1/2 (* (log PI) (sqrt PI))) 226.822 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 226.823 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 226.823 * [backup-simplify]: Simplify (- 0) into 0 226.823 * [backup-simplify]: Simplify (+ 0 0) into 0 226.824 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 226.831 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 226.833 * [backup-simplify]: Simplify (* 1/8 (* (pow (log PI) 2) (sqrt PI))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 226.837 * [backup-simplify]: Simplify (+ (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (log PI) (sqrt PI))) k) (pow PI 1/2))) into (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) 226.837 * [backup-simplify]: Simplify (pow PI (- 1/2 (/ (/ 1 k) 2))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 226.837 * [approximate]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in (k) around 0 226.837 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 226.837 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 226.837 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 226.837 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 226.837 * [taylor]: Taking taylor expansion of 1/2 in k 226.837 * [backup-simplify]: Simplify 1/2 into 1/2 226.838 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 226.838 * [taylor]: Taking taylor expansion of 1/2 in k 226.838 * [backup-simplify]: Simplify 1/2 into 1/2 226.838 * [taylor]: Taking taylor expansion of (/ 1 k) in k 226.838 * [taylor]: Taking taylor expansion of k in k 226.838 * [backup-simplify]: Simplify 0 into 0 226.838 * [backup-simplify]: Simplify 1 into 1 226.838 * [backup-simplify]: Simplify (/ 1 1) into 1 226.838 * [taylor]: Taking taylor expansion of (log PI) in k 226.838 * [taylor]: Taking taylor expansion of PI in k 226.838 * [backup-simplify]: Simplify PI into PI 226.838 * [backup-simplify]: Simplify (log PI) into (log PI) 226.838 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 226.839 * [backup-simplify]: Simplify (- 1/2) into -1/2 226.839 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 226.840 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 226.840 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 226.840 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 226.840 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 226.840 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 226.840 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 226.840 * [taylor]: Taking taylor expansion of 1/2 in k 226.840 * [backup-simplify]: Simplify 1/2 into 1/2 226.840 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 226.840 * [taylor]: Taking taylor expansion of 1/2 in k 226.840 * [backup-simplify]: Simplify 1/2 into 1/2 226.840 * [taylor]: Taking taylor expansion of (/ 1 k) in k 226.840 * [taylor]: Taking taylor expansion of k in k 226.840 * [backup-simplify]: Simplify 0 into 0 226.840 * [backup-simplify]: Simplify 1 into 1 226.840 * [backup-simplify]: Simplify (/ 1 1) into 1 226.840 * [taylor]: Taking taylor expansion of (log PI) in k 226.840 * [taylor]: Taking taylor expansion of PI in k 226.840 * [backup-simplify]: Simplify PI into PI 226.841 * [backup-simplify]: Simplify (log PI) into (log PI) 226.841 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 226.841 * [backup-simplify]: Simplify (- 1/2) into -1/2 226.842 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 226.842 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 226.843 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 226.843 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 k)))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 226.843 * [backup-simplify]: Simplify 0 into 0 226.843 * [backup-simplify]: Simplify 0 into 0 226.843 * [backup-simplify]: Simplify 0 into 0 226.843 * [backup-simplify]: Simplify 0 into 0 226.843 * [backup-simplify]: Simplify 0 into 0 226.843 * [backup-simplify]: Simplify 0 into 0 226.843 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) into (pow PI (- 1/2 (* 1/2 k))) 226.843 * [backup-simplify]: Simplify (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 226.843 * [approximate]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in (k) around 0 226.843 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 226.843 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 226.843 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 226.843 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 226.843 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 226.843 * [taylor]: Taking taylor expansion of 1/2 in k 226.843 * [backup-simplify]: Simplify 1/2 into 1/2 226.843 * [taylor]: Taking taylor expansion of (/ 1 k) in k 226.843 * [taylor]: Taking taylor expansion of k in k 226.843 * [backup-simplify]: Simplify 0 into 0 226.843 * [backup-simplify]: Simplify 1 into 1 226.844 * [backup-simplify]: Simplify (/ 1 1) into 1 226.844 * [taylor]: Taking taylor expansion of 1/2 in k 226.844 * [backup-simplify]: Simplify 1/2 into 1/2 226.844 * [taylor]: Taking taylor expansion of (log PI) in k 226.844 * [taylor]: Taking taylor expansion of PI in k 226.844 * [backup-simplify]: Simplify PI into PI 226.844 * [backup-simplify]: Simplify (log PI) into (log PI) 226.844 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 226.844 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 226.845 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 226.845 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 226.845 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 226.845 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 226.846 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 226.846 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 226.846 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 226.846 * [taylor]: Taking taylor expansion of 1/2 in k 226.846 * [backup-simplify]: Simplify 1/2 into 1/2 226.846 * [taylor]: Taking taylor expansion of (/ 1 k) in k 226.846 * [taylor]: Taking taylor expansion of k in k 226.846 * [backup-simplify]: Simplify 0 into 0 226.846 * [backup-simplify]: Simplify 1 into 1 226.846 * [backup-simplify]: Simplify (/ 1 1) into 1 226.846 * [taylor]: Taking taylor expansion of 1/2 in k 226.846 * [backup-simplify]: Simplify 1/2 into 1/2 226.846 * [taylor]: Taking taylor expansion of (log PI) in k 226.846 * [taylor]: Taking taylor expansion of PI in k 226.846 * [backup-simplify]: Simplify PI into PI 226.846 * [backup-simplify]: Simplify (log PI) into (log PI) 226.847 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 226.847 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 226.847 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 226.848 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 226.848 * [backup-simplify]: Simplify (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 226.848 * [backup-simplify]: Simplify 0 into 0 226.848 * [backup-simplify]: Simplify 0 into 0 226.848 * [backup-simplify]: Simplify 0 into 0 226.848 * [backup-simplify]: Simplify 0 into 0 226.848 * [backup-simplify]: Simplify 0 into 0 226.848 * [backup-simplify]: Simplify 0 into 0 226.848 * [backup-simplify]: Simplify (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) into (pow PI (- 1/2 (* 1/2 k))) 226.848 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2) 226.848 * [backup-simplify]: Simplify (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))) into (* (/ 1 (pow (* 2 n) (- 1/2 (* 1/2 k)))) (sqrt k)) 226.848 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 n) (- 1/2 (* 1/2 k)))) (sqrt k)) in (k n) around 0 226.848 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 n) (- 1/2 (* 1/2 k)))) (sqrt k)) in n 226.848 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 n) (- 1/2 (* 1/2 k)))) in n 226.848 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 226.848 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 226.848 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 226.849 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 226.849 * [taylor]: Taking taylor expansion of 1/2 in n 226.849 * [backup-simplify]: Simplify 1/2 into 1/2 226.849 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 226.849 * [taylor]: Taking taylor expansion of 1/2 in n 226.849 * [backup-simplify]: Simplify 1/2 into 1/2 226.849 * [taylor]: Taking taylor expansion of k in n 226.849 * [backup-simplify]: Simplify k into k 226.849 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 226.849 * [taylor]: Taking taylor expansion of (* 2 n) in n 226.849 * [taylor]: Taking taylor expansion of 2 in n 226.849 * [backup-simplify]: Simplify 2 into 2 226.849 * [taylor]: Taking taylor expansion of n in n 226.849 * [backup-simplify]: Simplify 0 into 0 226.849 * [backup-simplify]: Simplify 1 into 1 226.849 * [backup-simplify]: Simplify (* 2 0) into 0 226.850 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 226.850 * [backup-simplify]: Simplify (log 2) into (log 2) 226.850 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 226.850 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 226.850 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 226.851 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 226.851 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 226.851 * [backup-simplify]: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 226.852 * [backup-simplify]: Simplify (/ 1 (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))))) into (/ 1 (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))))) 226.852 * [taylor]: Taking taylor expansion of (sqrt k) in n 226.852 * [taylor]: Taking taylor expansion of k in n 226.852 * [backup-simplify]: Simplify k into k 226.852 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 226.852 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 226.852 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 n) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 226.852 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 n) (- 1/2 (* 1/2 k)))) in k 226.852 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 226.852 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 226.852 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 226.852 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 226.852 * [taylor]: Taking taylor expansion of 1/2 in k 226.852 * [backup-simplify]: Simplify 1/2 into 1/2 226.852 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 226.852 * [taylor]: Taking taylor expansion of 1/2 in k 226.852 * [backup-simplify]: Simplify 1/2 into 1/2 226.852 * [taylor]: Taking taylor expansion of k in k 226.852 * [backup-simplify]: Simplify 0 into 0 226.852 * [backup-simplify]: Simplify 1 into 1 226.852 * [taylor]: Taking taylor expansion of (log (* 2 n)) in k 226.852 * [taylor]: Taking taylor expansion of (* 2 n) in k 226.852 * [taylor]: Taking taylor expansion of 2 in k 226.852 * [backup-simplify]: Simplify 2 into 2 226.852 * [taylor]: Taking taylor expansion of n in k 226.852 * [backup-simplify]: Simplify n into n 226.852 * [backup-simplify]: Simplify (* 2 n) into (* 2 n) 226.852 * [backup-simplify]: Simplify (log (* 2 n)) into (log (* 2 n)) 226.853 * [backup-simplify]: Simplify (* 1/2 0) into 0 226.853 * [backup-simplify]: Simplify (- 0) into 0 226.853 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 226.854 * [backup-simplify]: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 226.854 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 226.854 * [backup-simplify]: Simplify (/ 1 (pow (* 2 n) 1/2)) into (sqrt (/ 1 (* n 2))) 226.854 * [taylor]: Taking taylor expansion of (sqrt k) in k 226.854 * [taylor]: Taking taylor expansion of k in k 226.854 * [backup-simplify]: Simplify 0 into 0 226.854 * [backup-simplify]: Simplify 1 into 1 226.854 * [backup-simplify]: Simplify (sqrt 0) into 0 226.856 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 226.856 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 n) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 226.856 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 n) (- 1/2 (* 1/2 k)))) in k 226.856 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 226.856 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 226.856 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 226.856 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 226.856 * [taylor]: Taking taylor expansion of 1/2 in k 226.857 * [backup-simplify]: Simplify 1/2 into 1/2 226.857 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 226.857 * [taylor]: Taking taylor expansion of 1/2 in k 226.857 * [backup-simplify]: Simplify 1/2 into 1/2 226.857 * [taylor]: Taking taylor expansion of k in k 226.857 * [backup-simplify]: Simplify 0 into 0 226.857 * [backup-simplify]: Simplify 1 into 1 226.857 * [taylor]: Taking taylor expansion of (log (* 2 n)) in k 226.857 * [taylor]: Taking taylor expansion of (* 2 n) in k 226.857 * [taylor]: Taking taylor expansion of 2 in k 226.857 * [backup-simplify]: Simplify 2 into 2 226.857 * [taylor]: Taking taylor expansion of n in k 226.857 * [backup-simplify]: Simplify n into n 226.857 * [backup-simplify]: Simplify (* 2 n) into (* 2 n) 226.857 * [backup-simplify]: Simplify (log (* 2 n)) into (log (* 2 n)) 226.857 * [backup-simplify]: Simplify (* 1/2 0) into 0 226.857 * [backup-simplify]: Simplify (- 0) into 0 226.858 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 226.858 * [backup-simplify]: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 226.858 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 226.858 * [backup-simplify]: Simplify (/ 1 (pow (* 2 n) 1/2)) into (sqrt (/ 1 (* n 2))) 226.858 * [taylor]: Taking taylor expansion of (sqrt k) in k 226.858 * [taylor]: Taking taylor expansion of k in k 226.858 * [backup-simplify]: Simplify 0 into 0 226.858 * [backup-simplify]: Simplify 1 into 1 226.858 * [backup-simplify]: Simplify (sqrt 0) into 0 226.859 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 226.859 * [backup-simplify]: Simplify (* (sqrt (/ 1 (* n 2))) 0) into 0 226.859 * [taylor]: Taking taylor expansion of 0 in n 226.859 * [backup-simplify]: Simplify 0 into 0 226.859 * [backup-simplify]: Simplify 0 into 0 226.860 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 n)) into 0 226.860 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 n) 1)))) 1) into 0 226.861 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 226.861 * [backup-simplify]: Simplify (- 1/2) into -1/2 226.861 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 226.862 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 n)))) into (- (* 1/2 (log (* 2 n)))) 226.862 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 n)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 n)))) 1) 1)))) into (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) 226.862 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 (* n 2))) (/ (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) (pow (* 2 n) 1/2))))) into (* 1/2 (* (* (sqrt 2) (* (log (* 2 n)) (pow (sqrt 1/2) 2))) (sqrt (/ 1 n)))) 226.863 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (* n 2))) +nan.0) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 n)) (pow (sqrt 1/2) 2))) (sqrt (/ 1 n)))) 0)) into (- (* +nan.0 (* (sqrt (/ 1 n)) (sqrt 1/2)))) 226.863 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 n)) (sqrt 1/2)))) in n 226.863 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 n)) (sqrt 1/2))) in n 226.863 * [taylor]: Taking taylor expansion of +nan.0 in n 226.863 * [backup-simplify]: Simplify +nan.0 into +nan.0 226.863 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 n)) (sqrt 1/2)) in n 226.863 * [taylor]: Taking taylor expansion of (sqrt (/ 1 n)) in n 226.863 * [taylor]: Taking taylor expansion of (/ 1 n) in n 226.863 * [taylor]: Taking taylor expansion of n in n 226.863 * [backup-simplify]: Simplify 0 into 0 226.863 * [backup-simplify]: Simplify 1 into 1 226.864 * [backup-simplify]: Simplify (/ 1 1) into 1 226.864 * [backup-simplify]: Simplify (sqrt 0) into 0 226.865 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 226.865 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 226.865 * [taylor]: Taking taylor expansion of 1/2 in n 226.865 * [backup-simplify]: Simplify 1/2 into 1/2 226.865 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 226.865 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 226.867 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (sqrt 1/2))) into (- (* +nan.0 (sqrt 1/2))) 226.867 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0 226.870 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (sqrt 1/2)))) (* 0 0)) into (- (* +nan.0 (sqrt 1/2))) 226.871 * [backup-simplify]: Simplify (- (- (* +nan.0 (sqrt 1/2)))) into (- (* +nan.0 (sqrt 1/2))) 226.875 * [backup-simplify]: Simplify (- (* +nan.0 (sqrt 1/2))) into (- (* +nan.0 (sqrt 1/2))) 226.875 * [backup-simplify]: Simplify 0 into 0 226.877 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 226.878 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 n))) into 0 226.879 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 n) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 n) 1)))) 2) into 0 226.880 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 226.880 * [backup-simplify]: Simplify (- 0) into 0 226.880 * [backup-simplify]: Simplify (+ 0 0) into 0 226.881 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 n))))) into 0 226.881 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 n)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* n 2)) (pow (log (* 2 n)) 2))) 226.883 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 (* n 2))) (/ (* 1/8 (* (sqrt (* n 2)) (pow (log (* 2 n)) 2))) (pow (* 2 n) 1/2))) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 n)) (pow (sqrt 1/2) 2))) (sqrt (/ 1 n)))) (/ (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) (pow (* 2 n) 1/2))))) into (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 n)) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 n)))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 n)) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 n))))) 226.887 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (* n 2))) +nan.0) (+ (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 n)) (pow (sqrt 1/2) 2))) (sqrt (/ 1 n)))) +nan.0) (* (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 n)) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 n)))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 n)) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 n))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (pow (sqrt 1/2) 2))) (sqrt (/ 1 n)))) (- (* +nan.0 (* (sqrt (/ 1 n)) (sqrt 1/2)))))) 226.887 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (pow (sqrt 1/2) 2))) (sqrt (/ 1 n)))) (- (* +nan.0 (* (sqrt (/ 1 n)) (sqrt 1/2)))))) in n 226.887 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (pow (sqrt 1/2) 2))) (sqrt (/ 1 n)))) (- (* +nan.0 (* (sqrt (/ 1 n)) (sqrt 1/2))))) in n 226.887 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (pow (sqrt 1/2) 2))) (sqrt (/ 1 n)))) in n 226.887 * [taylor]: Taking taylor expansion of +nan.0 in n 226.887 * [backup-simplify]: Simplify +nan.0 into +nan.0 226.887 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (* (log (* 2 n)) (pow (sqrt 1/2) 2))) (sqrt (/ 1 n))) in n 226.887 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 n)) (pow (sqrt 1/2) 2))) in n 226.887 * [taylor]: Taking taylor expansion of (sqrt 2) in n 226.887 * [taylor]: Taking taylor expansion of 2 in n 226.887 * [backup-simplify]: Simplify 2 into 2 226.887 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 226.888 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 226.888 * [taylor]: Taking taylor expansion of (* (log (* 2 n)) (pow (sqrt 1/2) 2)) in n 226.888 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 226.888 * [taylor]: Taking taylor expansion of (* 2 n) in n 226.888 * [taylor]: Taking taylor expansion of 2 in n 226.888 * [backup-simplify]: Simplify 2 into 2 226.888 * [taylor]: Taking taylor expansion of n in n 226.888 * [backup-simplify]: Simplify 0 into 0 226.888 * [backup-simplify]: Simplify 1 into 1 226.888 * [backup-simplify]: Simplify (* 2 0) into 0 226.888 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 226.889 * [backup-simplify]: Simplify (log 2) into (log 2) 226.889 * [taylor]: Taking taylor expansion of (pow (sqrt 1/2) 2) in n 226.889 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 226.889 * [taylor]: Taking taylor expansion of 1/2 in n 226.889 * [backup-simplify]: Simplify 1/2 into 1/2 226.889 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 226.890 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 226.890 * [taylor]: Taking taylor expansion of (sqrt (/ 1 n)) in n 226.890 * [taylor]: Taking taylor expansion of (/ 1 n) in n 226.890 * [taylor]: Taking taylor expansion of n in n 226.890 * [backup-simplify]: Simplify 0 into 0 226.890 * [backup-simplify]: Simplify 1 into 1 226.891 * [backup-simplify]: Simplify (/ 1 1) into 1 226.891 * [backup-simplify]: Simplify (sqrt 0) into 0 226.893 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 226.893 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 n)) (sqrt 1/2)))) in n 226.893 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 n)) (sqrt 1/2))) in n 226.893 * [taylor]: Taking taylor expansion of +nan.0 in n 226.893 * [backup-simplify]: Simplify +nan.0 into +nan.0 226.893 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 n)) (sqrt 1/2)) in n 226.893 * [taylor]: Taking taylor expansion of (sqrt (/ 1 n)) in n 226.893 * [taylor]: Taking taylor expansion of (/ 1 n) in n 226.893 * [taylor]: Taking taylor expansion of n in n 226.893 * [backup-simplify]: Simplify 0 into 0 226.893 * [backup-simplify]: Simplify 1 into 1 226.893 * [backup-simplify]: Simplify (/ 1 1) into 1 226.894 * [backup-simplify]: Simplify (sqrt 0) into 0 226.895 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 226.895 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 226.895 * [taylor]: Taking taylor expansion of 1/2 in n 226.895 * [backup-simplify]: Simplify 1/2 into 1/2 226.896 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 226.896 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 226.897 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 226.899 * [backup-simplify]: Simplify (* (sqrt 1/2) (sqrt 1/2)) into (pow (sqrt 1/2) 2) 226.900 * [backup-simplify]: Simplify (* (+ (log 2) (log n)) (pow (sqrt 1/2) 2)) into (* (+ (log 2) (log n)) (pow (sqrt 1/2) 2)) 226.902 * [backup-simplify]: Simplify (* (sqrt 2) (* (+ (log 2) (log n)) (pow (sqrt 1/2) 2))) into (* (+ (log 2) (log n)) (* (sqrt 2) (pow (sqrt 1/2) 2))) 226.903 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 226.903 * [backup-simplify]: Simplify (+ (* (sqrt 1/2) 0) (* 0 (sqrt 1/2))) into 0 226.905 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0 226.906 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 226.908 * [backup-simplify]: Simplify (+ (* (+ (log 2) (log n)) 0) (* 0 (pow (sqrt 1/2) 2))) into 0 226.910 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (* (+ (log 2) (log n)) (pow (sqrt 1/2) 2)))) into 0 226.913 * [backup-simplify]: Simplify (+ (* (* (+ (log 2) (log n)) (* (sqrt 2) (pow (sqrt 1/2) 2))) +nan.0) (* 0 0)) into (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) (- (* +nan.0 (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))))))) 226.914 * [backup-simplify]: Simplify (* (* (+ (log 2) (log n)) (* (sqrt 2) (pow (sqrt 1/2) 2))) 0) into 0 226.919 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) (- (* +nan.0 (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n)))))))) (* 0 0)) into (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) (- (* +nan.0 (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))))))) 226.920 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (sqrt 1/2))) into (- (* +nan.0 (sqrt 1/2))) 226.921 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0 226.923 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (sqrt 1/2)))) (* 0 0)) into (- (* +nan.0 (sqrt 1/2))) 226.924 * [backup-simplify]: Simplify (- (- (* +nan.0 (sqrt 1/2)))) into (- (* +nan.0 (sqrt 1/2))) 226.929 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) (- (* +nan.0 (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))))))) (- (* +nan.0 (sqrt 1/2)))) into (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) (- (+ (* +nan.0 (sqrt 1/2)) (- (* +nan.0 (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))))))))) 226.934 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) (- (+ (* +nan.0 (sqrt 1/2)) (- (* +nan.0 (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n)))))))))) into (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) (- (+ (* +nan.0 (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n)))) (- (* +nan.0 (sqrt 1/2))))))) 226.939 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) (- (+ (* +nan.0 (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n)))) (- (* +nan.0 (sqrt 1/2))))))) into (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) (- (+ (* +nan.0 (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n)))) (- (* +nan.0 (sqrt 1/2))))))) 226.940 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1/2))) into 0 226.940 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 226.942 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 226.944 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (sqrt 1/2)))) into (- (* +nan.0 (sqrt 1/2))) 226.947 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (sqrt 1/2)))) (+ (* 0 (- (* +nan.0 (sqrt 1/2)))) (* 0 0))) into (- (* +nan.0 (sqrt 1/2))) 226.949 * [backup-simplify]: Simplify (- (- (* +nan.0 (sqrt 1/2)))) into (- (* +nan.0 (sqrt 1/2))) 226.949 * [backup-simplify]: Simplify (- (* +nan.0 (sqrt 1/2))) into (- (* +nan.0 (sqrt 1/2))) 226.957 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (sqrt 1/2))) (* n k)) (+ (* (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) (- (+ (* +nan.0 (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n)))) (- (* +nan.0 (sqrt 1/2))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (sqrt 1/2))) (* 1 k)))) into (- (+ (* +nan.0 (* (sqrt 1/2) k)) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2))))) (- (+ (* +nan.0 (* n (* (sqrt 1/2) k))) (- (+ (* +nan.0 (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log n))))) (- (* +nan.0 (* (sqrt 1/2) (pow k 2)))))))))))) 226.957 * [backup-simplify]: Simplify (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) 2) (- 1/2 (/ (/ 1 k) 2)))) into (* (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) 226.957 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in (k n) around 0 226.957 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in n 226.957 * [taylor]: Taking taylor expansion of (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 226.957 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 226.957 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 226.957 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 226.957 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 226.957 * [taylor]: Taking taylor expansion of 1/2 in n 226.957 * [backup-simplify]: Simplify 1/2 into 1/2 226.957 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 226.957 * [taylor]: Taking taylor expansion of 1/2 in n 226.957 * [backup-simplify]: Simplify 1/2 into 1/2 226.957 * [taylor]: Taking taylor expansion of (/ 1 k) in n 226.957 * [taylor]: Taking taylor expansion of k in n 226.957 * [backup-simplify]: Simplify k into k 226.957 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 226.958 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 226.958 * [taylor]: Taking taylor expansion of (/ 2 n) in n 226.958 * [taylor]: Taking taylor expansion of 2 in n 226.958 * [backup-simplify]: Simplify 2 into 2 226.958 * [taylor]: Taking taylor expansion of n in n 226.958 * [backup-simplify]: Simplify 0 into 0 226.958 * [backup-simplify]: Simplify 1 into 1 226.958 * [backup-simplify]: Simplify (/ 2 1) into 2 226.959 * [backup-simplify]: Simplify (log 2) into (log 2) 226.959 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 226.959 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 226.959 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 226.959 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 226.960 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 226.960 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 226.960 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 226.960 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 226.960 * [taylor]: Taking taylor expansion of (/ 1 k) in n 226.961 * [taylor]: Taking taylor expansion of k in n 226.961 * [backup-simplify]: Simplify k into k 226.961 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 226.961 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 226.961 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 226.961 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 226.961 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 226.961 * [taylor]: Taking taylor expansion of (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 226.961 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 226.961 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 226.961 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 226.961 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 226.961 * [taylor]: Taking taylor expansion of 1/2 in k 226.961 * [backup-simplify]: Simplify 1/2 into 1/2 226.961 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 226.961 * [taylor]: Taking taylor expansion of 1/2 in k 226.961 * [backup-simplify]: Simplify 1/2 into 1/2 226.961 * [taylor]: Taking taylor expansion of (/ 1 k) in k 226.961 * [taylor]: Taking taylor expansion of k in k 226.961 * [backup-simplify]: Simplify 0 into 0 226.961 * [backup-simplify]: Simplify 1 into 1 226.961 * [backup-simplify]: Simplify (/ 1 1) into 1 226.961 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in k 226.961 * [taylor]: Taking taylor expansion of (/ 2 n) in k 226.961 * [taylor]: Taking taylor expansion of 2 in k 226.961 * [backup-simplify]: Simplify 2 into 2 226.961 * [taylor]: Taking taylor expansion of n in k 226.961 * [backup-simplify]: Simplify n into n 226.961 * [backup-simplify]: Simplify (/ 2 n) into (/ 2 n) 226.962 * [backup-simplify]: Simplify (log (/ 2 n)) into (log (/ 2 n)) 226.962 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 226.962 * [backup-simplify]: Simplify (- 1/2) into -1/2 226.962 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 226.962 * [backup-simplify]: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 226.963 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 226.963 * [backup-simplify]: Simplify (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) 226.963 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 226.963 * [taylor]: Taking taylor expansion of (/ 1 k) in k 226.963 * [taylor]: Taking taylor expansion of k in k 226.963 * [backup-simplify]: Simplify 0 into 0 226.963 * [backup-simplify]: Simplify 1 into 1 226.963 * [backup-simplify]: Simplify (/ 1 1) into 1 226.963 * [backup-simplify]: Simplify (sqrt 0) into 0 226.964 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 226.964 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 226.964 * [taylor]: Taking taylor expansion of (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 226.964 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 226.964 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 226.964 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 226.964 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 226.964 * [taylor]: Taking taylor expansion of 1/2 in k 226.964 * [backup-simplify]: Simplify 1/2 into 1/2 226.964 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 226.964 * [taylor]: Taking taylor expansion of 1/2 in k 226.964 * [backup-simplify]: Simplify 1/2 into 1/2 226.964 * [taylor]: Taking taylor expansion of (/ 1 k) in k 226.964 * [taylor]: Taking taylor expansion of k in k 226.964 * [backup-simplify]: Simplify 0 into 0 226.964 * [backup-simplify]: Simplify 1 into 1 226.965 * [backup-simplify]: Simplify (/ 1 1) into 1 226.965 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in k 226.965 * [taylor]: Taking taylor expansion of (/ 2 n) in k 226.965 * [taylor]: Taking taylor expansion of 2 in k 226.965 * [backup-simplify]: Simplify 2 into 2 226.965 * [taylor]: Taking taylor expansion of n in k 226.965 * [backup-simplify]: Simplify n into n 226.965 * [backup-simplify]: Simplify (/ 2 n) into (/ 2 n) 226.965 * [backup-simplify]: Simplify (log (/ 2 n)) into (log (/ 2 n)) 226.965 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 226.965 * [backup-simplify]: Simplify (- 1/2) into -1/2 226.966 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 226.966 * [backup-simplify]: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 226.966 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 226.966 * [backup-simplify]: Simplify (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) 226.966 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 226.966 * [taylor]: Taking taylor expansion of (/ 1 k) in k 226.966 * [taylor]: Taking taylor expansion of k in k 226.966 * [backup-simplify]: Simplify 0 into 0 226.966 * [backup-simplify]: Simplify 1 into 1 226.966 * [backup-simplify]: Simplify (/ 1 1) into 1 226.967 * [backup-simplify]: Simplify (sqrt 0) into 0 226.968 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 226.968 * [backup-simplify]: Simplify (* (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 226.968 * [taylor]: Taking taylor expansion of 0 in n 226.968 * [backup-simplify]: Simplify 0 into 0 226.968 * [backup-simplify]: Simplify 0 into 0 226.968 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 226.969 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) 226.969 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 226.969 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 226.969 * [taylor]: Taking taylor expansion of +nan.0 in n 226.969 * [backup-simplify]: Simplify +nan.0 into +nan.0 226.969 * [taylor]: Taking taylor expansion of (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 226.969 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 226.969 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 226.969 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 226.969 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 226.969 * [taylor]: Taking taylor expansion of 1/2 in n 226.969 * [backup-simplify]: Simplify 1/2 into 1/2 226.969 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 226.969 * [taylor]: Taking taylor expansion of 1/2 in n 226.969 * [backup-simplify]: Simplify 1/2 into 1/2 226.969 * [taylor]: Taking taylor expansion of (/ 1 k) in n 226.969 * [taylor]: Taking taylor expansion of k in n 226.969 * [backup-simplify]: Simplify k into k 226.969 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 226.969 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 226.969 * [taylor]: Taking taylor expansion of (/ 2 n) in n 226.969 * [taylor]: Taking taylor expansion of 2 in n 226.969 * [backup-simplify]: Simplify 2 into 2 226.969 * [taylor]: Taking taylor expansion of n in n 226.969 * [backup-simplify]: Simplify 0 into 0 226.969 * [backup-simplify]: Simplify 1 into 1 226.969 * [backup-simplify]: Simplify (/ 2 1) into 2 226.970 * [backup-simplify]: Simplify (log 2) into (log 2) 226.970 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 226.970 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 226.970 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 226.973 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 226.973 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 226.974 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 226.974 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 226.975 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 226.975 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 226.975 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 226.975 * [backup-simplify]: Simplify 0 into 0 226.976 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 226.978 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 226.979 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 226.979 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) 226.979 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 226.979 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 226.979 * [taylor]: Taking taylor expansion of +nan.0 in n 226.979 * [backup-simplify]: Simplify +nan.0 into +nan.0 226.979 * [taylor]: Taking taylor expansion of (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 226.979 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 226.979 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 226.979 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 226.979 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 226.979 * [taylor]: Taking taylor expansion of 1/2 in n 226.979 * [backup-simplify]: Simplify 1/2 into 1/2 226.979 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 226.979 * [taylor]: Taking taylor expansion of 1/2 in n 226.979 * [backup-simplify]: Simplify 1/2 into 1/2 226.979 * [taylor]: Taking taylor expansion of (/ 1 k) in n 226.979 * [taylor]: Taking taylor expansion of k in n 226.979 * [backup-simplify]: Simplify k into k 226.979 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 226.979 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 226.979 * [taylor]: Taking taylor expansion of (/ 2 n) in n 226.979 * [taylor]: Taking taylor expansion of 2 in n 226.979 * [backup-simplify]: Simplify 2 into 2 226.980 * [taylor]: Taking taylor expansion of n in n 226.980 * [backup-simplify]: Simplify 0 into 0 226.980 * [backup-simplify]: Simplify 1 into 1 226.980 * [backup-simplify]: Simplify (/ 2 1) into 2 226.980 * [backup-simplify]: Simplify (log 2) into (log 2) 226.980 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 226.980 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 226.980 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 226.981 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 226.981 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 226.982 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 226.982 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 226.982 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 226.983 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 226.983 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 226.984 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0 226.985 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 226.985 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 226.985 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 226.985 * [backup-simplify]: Simplify (- 0) into 0 226.986 * [backup-simplify]: Simplify (+ 0 0) into 0 226.986 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 226.986 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 226.987 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 226.988 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))))) into 0 226.989 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into 0 226.989 * [backup-simplify]: Simplify (- 0) into 0 226.989 * [backup-simplify]: Simplify 0 into 0 226.989 * [backup-simplify]: Simplify 0 into 0 226.990 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 226.992 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 226.992 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 226.993 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) 226.993 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 226.993 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 226.993 * [taylor]: Taking taylor expansion of +nan.0 in n 226.993 * [backup-simplify]: Simplify +nan.0 into +nan.0 226.993 * [taylor]: Taking taylor expansion of (/ 1 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 226.993 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 226.993 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 226.993 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 226.993 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 226.993 * [taylor]: Taking taylor expansion of 1/2 in n 226.993 * [backup-simplify]: Simplify 1/2 into 1/2 226.993 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 226.993 * [taylor]: Taking taylor expansion of 1/2 in n 226.993 * [backup-simplify]: Simplify 1/2 into 1/2 226.993 * [taylor]: Taking taylor expansion of (/ 1 k) in n 226.993 * [taylor]: Taking taylor expansion of k in n 226.993 * [backup-simplify]: Simplify k into k 226.993 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 226.993 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 226.993 * [taylor]: Taking taylor expansion of (/ 2 n) in n 226.993 * [taylor]: Taking taylor expansion of 2 in n 226.993 * [backup-simplify]: Simplify 2 into 2 226.993 * [taylor]: Taking taylor expansion of n in n 226.993 * [backup-simplify]: Simplify 0 into 0 226.993 * [backup-simplify]: Simplify 1 into 1 226.994 * [backup-simplify]: Simplify (/ 2 1) into 2 226.994 * [backup-simplify]: Simplify (log 2) into (log 2) 226.994 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 226.994 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 226.994 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 226.995 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 226.995 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 226.995 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 226.996 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 226.996 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 226.996 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 226.997 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 226.998 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n)))))))) (* 1 (/ 1 k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n)))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) k))) (- (* +nan.0 (/ 1 (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k))))))))))) 226.998 * [backup-simplify]: Simplify (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) 2) (- 1/2 (/ (/ 1 (- k)) 2)))) into (/ (sqrt (/ -1 k)) (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) 226.998 * [approximate]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) in (k n) around 0 226.998 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) in n 226.999 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 226.999 * [taylor]: Taking taylor expansion of (/ -1 k) in n 226.999 * [taylor]: Taking taylor expansion of -1 in n 226.999 * [backup-simplify]: Simplify -1 into -1 226.999 * [taylor]: Taking taylor expansion of k in n 226.999 * [backup-simplify]: Simplify k into k 226.999 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 226.999 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 226.999 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 226.999 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 226.999 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 226.999 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 226.999 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 226.999 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 226.999 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 226.999 * [taylor]: Taking taylor expansion of 1/2 in n 226.999 * [backup-simplify]: Simplify 1/2 into 1/2 226.999 * [taylor]: Taking taylor expansion of (/ 1 k) in n 226.999 * [taylor]: Taking taylor expansion of k in n 226.999 * [backup-simplify]: Simplify k into k 226.999 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 226.999 * [taylor]: Taking taylor expansion of 1/2 in n 226.999 * [backup-simplify]: Simplify 1/2 into 1/2 226.999 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 226.999 * [taylor]: Taking taylor expansion of (/ -2 n) in n 226.999 * [taylor]: Taking taylor expansion of -2 in n 226.999 * [backup-simplify]: Simplify -2 into -2 226.999 * [taylor]: Taking taylor expansion of n in n 226.999 * [backup-simplify]: Simplify 0 into 0 226.999 * [backup-simplify]: Simplify 1 into 1 226.999 * [backup-simplify]: Simplify (/ -2 1) into -2 227.000 * [backup-simplify]: Simplify (log -2) into (log -2) 227.000 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 227.000 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 227.000 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 227.001 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 227.001 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 227.001 * [backup-simplify]: Simplify (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) into (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) 227.001 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) in k 227.002 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 227.002 * [taylor]: Taking taylor expansion of (/ -1 k) in k 227.002 * [taylor]: Taking taylor expansion of -1 in k 227.002 * [backup-simplify]: Simplify -1 into -1 227.002 * [taylor]: Taking taylor expansion of k in k 227.002 * [backup-simplify]: Simplify 0 into 0 227.002 * [backup-simplify]: Simplify 1 into 1 227.002 * [backup-simplify]: Simplify (/ -1 1) into -1 227.002 * [backup-simplify]: Simplify (sqrt 0) into 0 227.003 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 227.003 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 227.003 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 227.003 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 227.003 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 227.003 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 227.003 * [taylor]: Taking taylor expansion of 1/2 in k 227.003 * [backup-simplify]: Simplify 1/2 into 1/2 227.003 * [taylor]: Taking taylor expansion of (/ 1 k) in k 227.003 * [taylor]: Taking taylor expansion of k in k 227.003 * [backup-simplify]: Simplify 0 into 0 227.003 * [backup-simplify]: Simplify 1 into 1 227.003 * [backup-simplify]: Simplify (/ 1 1) into 1 227.003 * [taylor]: Taking taylor expansion of 1/2 in k 227.003 * [backup-simplify]: Simplify 1/2 into 1/2 227.003 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in k 227.003 * [taylor]: Taking taylor expansion of (/ -2 n) in k 227.003 * [taylor]: Taking taylor expansion of -2 in k 227.004 * [backup-simplify]: Simplify -2 into -2 227.004 * [taylor]: Taking taylor expansion of n in k 227.004 * [backup-simplify]: Simplify n into n 227.004 * [backup-simplify]: Simplify (/ -2 n) into (/ -2 n) 227.004 * [backup-simplify]: Simplify (log (/ -2 n)) into (log (/ -2 n)) 227.004 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 227.004 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 227.004 * [backup-simplify]: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 227.004 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 227.004 * [backup-simplify]: Simplify (/ +nan.0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) into (/ +nan.0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) 227.004 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) in k 227.005 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 227.005 * [taylor]: Taking taylor expansion of (/ -1 k) in k 227.005 * [taylor]: Taking taylor expansion of -1 in k 227.005 * [backup-simplify]: Simplify -1 into -1 227.005 * [taylor]: Taking taylor expansion of k in k 227.005 * [backup-simplify]: Simplify 0 into 0 227.005 * [backup-simplify]: Simplify 1 into 1 227.005 * [backup-simplify]: Simplify (/ -1 1) into -1 227.005 * [backup-simplify]: Simplify (sqrt 0) into 0 227.006 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 227.006 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 227.006 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 227.006 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 227.006 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 227.006 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 227.006 * [taylor]: Taking taylor expansion of 1/2 in k 227.006 * [backup-simplify]: Simplify 1/2 into 1/2 227.006 * [taylor]: Taking taylor expansion of (/ 1 k) in k 227.006 * [taylor]: Taking taylor expansion of k in k 227.006 * [backup-simplify]: Simplify 0 into 0 227.006 * [backup-simplify]: Simplify 1 into 1 227.006 * [backup-simplify]: Simplify (/ 1 1) into 1 227.006 * [taylor]: Taking taylor expansion of 1/2 in k 227.006 * [backup-simplify]: Simplify 1/2 into 1/2 227.006 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in k 227.006 * [taylor]: Taking taylor expansion of (/ -2 n) in k 227.007 * [taylor]: Taking taylor expansion of -2 in k 227.007 * [backup-simplify]: Simplify -2 into -2 227.007 * [taylor]: Taking taylor expansion of n in k 227.007 * [backup-simplify]: Simplify n into n 227.007 * [backup-simplify]: Simplify (/ -2 n) into (/ -2 n) 227.007 * [backup-simplify]: Simplify (log (/ -2 n)) into (log (/ -2 n)) 227.007 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 227.007 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 227.007 * [backup-simplify]: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 227.007 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 227.007 * [backup-simplify]: Simplify (/ +nan.0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) into (/ +nan.0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) 227.008 * [taylor]: Taking taylor expansion of (/ +nan.0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) in n 227.008 * [taylor]: Taking taylor expansion of +nan.0 in n 227.008 * [backup-simplify]: Simplify +nan.0 into +nan.0 227.008 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 227.008 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 227.008 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 227.008 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 227.008 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 227.008 * [taylor]: Taking taylor expansion of 1/2 in n 227.008 * [backup-simplify]: Simplify 1/2 into 1/2 227.008 * [taylor]: Taking taylor expansion of (/ 1 k) in n 227.008 * [taylor]: Taking taylor expansion of k in n 227.008 * [backup-simplify]: Simplify k into k 227.008 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 227.008 * [taylor]: Taking taylor expansion of 1/2 in n 227.008 * [backup-simplify]: Simplify 1/2 into 1/2 227.008 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 227.008 * [taylor]: Taking taylor expansion of (/ -2 n) in n 227.008 * [taylor]: Taking taylor expansion of -2 in n 227.008 * [backup-simplify]: Simplify -2 into -2 227.008 * [taylor]: Taking taylor expansion of n in n 227.008 * [backup-simplify]: Simplify 0 into 0 227.008 * [backup-simplify]: Simplify 1 into 1 227.008 * [backup-simplify]: Simplify (/ -2 1) into -2 227.009 * [backup-simplify]: Simplify (log -2) into (log -2) 227.009 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 227.009 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 227.009 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 227.010 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 227.010 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 227.010 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) 227.011 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) 227.011 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 227.013 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 227.013 * [backup-simplify]: Simplify (- (/ +nan.0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) (+ (* (/ +nan.0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) (/ 0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (/ 1 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))))) 227.013 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 227.013 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 227.013 * [taylor]: Taking taylor expansion of +nan.0 in n 227.013 * [backup-simplify]: Simplify +nan.0 into +nan.0 227.013 * [taylor]: Taking taylor expansion of (/ 1 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) in n 227.013 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 227.013 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 227.013 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 227.014 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 227.014 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 227.014 * [taylor]: Taking taylor expansion of 1/2 in n 227.014 * [backup-simplify]: Simplify 1/2 into 1/2 227.014 * [taylor]: Taking taylor expansion of (/ 1 k) in n 227.014 * [taylor]: Taking taylor expansion of k in n 227.014 * [backup-simplify]: Simplify k into k 227.014 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 227.014 * [taylor]: Taking taylor expansion of 1/2 in n 227.014 * [backup-simplify]: Simplify 1/2 into 1/2 227.014 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 227.014 * [taylor]: Taking taylor expansion of (/ -2 n) in n 227.014 * [taylor]: Taking taylor expansion of -2 in n 227.014 * [backup-simplify]: Simplify -2 into -2 227.014 * [taylor]: Taking taylor expansion of n in n 227.014 * [backup-simplify]: Simplify 0 into 0 227.014 * [backup-simplify]: Simplify 1 into 1 227.014 * [backup-simplify]: Simplify (/ -2 1) into -2 227.014 * [backup-simplify]: Simplify (log -2) into (log -2) 227.014 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 227.014 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 227.015 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 227.015 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 227.016 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 227.016 * [backup-simplify]: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) 227.016 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) 227.017 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))))) 227.017 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))))) 227.018 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0 227.019 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 227.019 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 227.019 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 227.020 * [backup-simplify]: Simplify (+ 0 0) into 0 227.020 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 227.021 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -2) (log n)))) into 0 227.021 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 227.022 * [backup-simplify]: Simplify (- (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) (+ (* (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))))) into 0 227.022 * [backup-simplify]: Simplify 0 into 0 227.023 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 227.026 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 227.027 * [backup-simplify]: Simplify (- (/ +nan.0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) (+ (* (/ +nan.0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) (/ 0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)))) (* (- (* +nan.0 (/ 1 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))))) (/ 0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (/ 1 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))))) 227.027 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 227.027 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 227.027 * [taylor]: Taking taylor expansion of +nan.0 in n 227.027 * [backup-simplify]: Simplify +nan.0 into +nan.0 227.027 * [taylor]: Taking taylor expansion of (/ 1 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) in n 227.027 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 227.027 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 227.027 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 227.027 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 227.027 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 227.027 * [taylor]: Taking taylor expansion of 1/2 in n 227.027 * [backup-simplify]: Simplify 1/2 into 1/2 227.027 * [taylor]: Taking taylor expansion of (/ 1 k) in n 227.027 * [taylor]: Taking taylor expansion of k in n 227.027 * [backup-simplify]: Simplify k into k 227.027 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 227.028 * [taylor]: Taking taylor expansion of 1/2 in n 227.028 * [backup-simplify]: Simplify 1/2 into 1/2 227.028 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 227.028 * [taylor]: Taking taylor expansion of (/ -2 n) in n 227.028 * [taylor]: Taking taylor expansion of -2 in n 227.028 * [backup-simplify]: Simplify -2 into -2 227.028 * [taylor]: Taking taylor expansion of n in n 227.028 * [backup-simplify]: Simplify 0 into 0 227.028 * [backup-simplify]: Simplify 1 into 1 227.028 * [backup-simplify]: Simplify (/ -2 1) into -2 227.029 * [backup-simplify]: Simplify (log -2) into (log -2) 227.029 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 227.029 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 227.030 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 227.030 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 227.031 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 227.031 * [backup-simplify]: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) 227.032 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) 227.033 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))))) 227.033 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))))) 227.035 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) k))) (- (+ (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))))) (- (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow k 2))))))))) 227.036 * * * * [progress]: [ 4 / 4 ] generating series at (2 2) 227.036 * [backup-simplify]: Simplify (* (/ 1 (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) into (* (/ 1 (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) (sqrt k)) 227.036 * [approximate]: Taking taylor expansion of (* (/ 1 (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) (sqrt k)) in (k n) around 0 227.036 * [taylor]: Taking taylor expansion of (* (/ 1 (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) (sqrt k)) in n 227.036 * [taylor]: Taking taylor expansion of (/ 1 (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) in n 227.036 * [taylor]: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in n 227.036 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 227.036 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 227.036 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 227.036 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 227.036 * [taylor]: Taking taylor expansion of 1/2 in n 227.036 * [backup-simplify]: Simplify 1/2 into 1/2 227.036 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 227.036 * [taylor]: Taking taylor expansion of 1/2 in n 227.036 * [backup-simplify]: Simplify 1/2 into 1/2 227.036 * [taylor]: Taking taylor expansion of k in n 227.036 * [backup-simplify]: Simplify k into k 227.036 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 227.036 * [taylor]: Taking taylor expansion of (* 2 n) in n 227.036 * [taylor]: Taking taylor expansion of 2 in n 227.036 * [backup-simplify]: Simplify 2 into 2 227.036 * [taylor]: Taking taylor expansion of n in n 227.037 * [backup-simplify]: Simplify 0 into 0 227.037 * [backup-simplify]: Simplify 1 into 1 227.037 * [backup-simplify]: Simplify (* 2 0) into 0 227.038 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 227.038 * [backup-simplify]: Simplify (log 2) into (log 2) 227.038 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 227.038 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 227.039 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 227.039 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 227.040 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 227.040 * [backup-simplify]: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 227.040 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in n 227.040 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in n 227.040 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in n 227.041 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 227.041 * [taylor]: Taking taylor expansion of 1/2 in n 227.041 * [backup-simplify]: Simplify 1/2 into 1/2 227.041 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 227.041 * [taylor]: Taking taylor expansion of 1/2 in n 227.041 * [backup-simplify]: Simplify 1/2 into 1/2 227.041 * [taylor]: Taking taylor expansion of k in n 227.041 * [backup-simplify]: Simplify k into k 227.041 * [taylor]: Taking taylor expansion of (log PI) in n 227.041 * [taylor]: Taking taylor expansion of PI in n 227.041 * [backup-simplify]: Simplify PI into PI 227.041 * [backup-simplify]: Simplify (log PI) into (log PI) 227.041 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 227.041 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 227.042 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 227.042 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log PI)) into (* (- 1/2 (* 1/2 k)) (log PI)) 227.043 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log PI))) into (pow PI (- 1/2 (* 1/2 k))) 227.043 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) into (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) 227.044 * [backup-simplify]: Simplify (/ 1 (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) into (/ 1 (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) 227.044 * [taylor]: Taking taylor expansion of (sqrt k) in n 227.044 * [taylor]: Taking taylor expansion of k in n 227.044 * [backup-simplify]: Simplify k into k 227.044 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 227.044 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 227.044 * [taylor]: Taking taylor expansion of (* (/ 1 (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) (sqrt k)) in k 227.044 * [taylor]: Taking taylor expansion of (/ 1 (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) in k 227.044 * [taylor]: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in k 227.044 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 227.044 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 227.044 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 227.044 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 227.044 * [taylor]: Taking taylor expansion of 1/2 in k 227.044 * [backup-simplify]: Simplify 1/2 into 1/2 227.044 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 227.044 * [taylor]: Taking taylor expansion of 1/2 in k 227.044 * [backup-simplify]: Simplify 1/2 into 1/2 227.044 * [taylor]: Taking taylor expansion of k in k 227.044 * [backup-simplify]: Simplify 0 into 0 227.044 * [backup-simplify]: Simplify 1 into 1 227.044 * [taylor]: Taking taylor expansion of (log (* 2 n)) in k 227.044 * [taylor]: Taking taylor expansion of (* 2 n) in k 227.045 * [taylor]: Taking taylor expansion of 2 in k 227.045 * [backup-simplify]: Simplify 2 into 2 227.045 * [taylor]: Taking taylor expansion of n in k 227.045 * [backup-simplify]: Simplify n into n 227.045 * [backup-simplify]: Simplify (* 2 n) into (* 2 n) 227.045 * [backup-simplify]: Simplify (log (* 2 n)) into (log (* 2 n)) 227.045 * [backup-simplify]: Simplify (* 1/2 0) into 0 227.046 * [backup-simplify]: Simplify (- 0) into 0 227.046 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 227.046 * [backup-simplify]: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 227.046 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 227.046 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 227.046 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 227.046 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 227.046 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 227.046 * [taylor]: Taking taylor expansion of 1/2 in k 227.046 * [backup-simplify]: Simplify 1/2 into 1/2 227.046 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 227.047 * [taylor]: Taking taylor expansion of 1/2 in k 227.047 * [backup-simplify]: Simplify 1/2 into 1/2 227.047 * [taylor]: Taking taylor expansion of k in k 227.047 * [backup-simplify]: Simplify 0 into 0 227.047 * [backup-simplify]: Simplify 1 into 1 227.047 * [taylor]: Taking taylor expansion of (log PI) in k 227.047 * [taylor]: Taking taylor expansion of PI in k 227.047 * [backup-simplify]: Simplify PI into PI 227.047 * [backup-simplify]: Simplify (log PI) into (log PI) 227.048 * [backup-simplify]: Simplify (* 1/2 0) into 0 227.048 * [backup-simplify]: Simplify (- 0) into 0 227.049 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 227.050 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 227.051 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 227.052 * [backup-simplify]: Simplify (* (pow (* 2 n) 1/2) (pow PI 1/2)) into (sqrt (* PI (* n 2))) 227.052 * [backup-simplify]: Simplify (/ 1 (sqrt (* PI (* n 2)))) into (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))) 227.052 * [taylor]: Taking taylor expansion of (sqrt k) in k 227.052 * [taylor]: Taking taylor expansion of k in k 227.052 * [backup-simplify]: Simplify 0 into 0 227.052 * [backup-simplify]: Simplify 1 into 1 227.053 * [backup-simplify]: Simplify (sqrt 0) into 0 227.054 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 227.054 * [taylor]: Taking taylor expansion of (* (/ 1 (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) (sqrt k)) in k 227.054 * [taylor]: Taking taylor expansion of (/ 1 (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) in k 227.054 * [taylor]: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in k 227.054 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 227.054 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 227.054 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 227.054 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 227.054 * [taylor]: Taking taylor expansion of 1/2 in k 227.054 * [backup-simplify]: Simplify 1/2 into 1/2 227.054 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 227.054 * [taylor]: Taking taylor expansion of 1/2 in k 227.055 * [backup-simplify]: Simplify 1/2 into 1/2 227.055 * [taylor]: Taking taylor expansion of k in k 227.055 * [backup-simplify]: Simplify 0 into 0 227.055 * [backup-simplify]: Simplify 1 into 1 227.055 * [taylor]: Taking taylor expansion of (log (* 2 n)) in k 227.055 * [taylor]: Taking taylor expansion of (* 2 n) in k 227.055 * [taylor]: Taking taylor expansion of 2 in k 227.055 * [backup-simplify]: Simplify 2 into 2 227.055 * [taylor]: Taking taylor expansion of n in k 227.055 * [backup-simplify]: Simplify n into n 227.055 * [backup-simplify]: Simplify (* 2 n) into (* 2 n) 227.055 * [backup-simplify]: Simplify (log (* 2 n)) into (log (* 2 n)) 227.055 * [backup-simplify]: Simplify (* 1/2 0) into 0 227.056 * [backup-simplify]: Simplify (- 0) into 0 227.056 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 227.056 * [backup-simplify]: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 227.056 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 227.056 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 227.056 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 227.056 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 227.057 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 227.057 * [taylor]: Taking taylor expansion of 1/2 in k 227.057 * [backup-simplify]: Simplify 1/2 into 1/2 227.057 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 227.057 * [taylor]: Taking taylor expansion of 1/2 in k 227.057 * [backup-simplify]: Simplify 1/2 into 1/2 227.057 * [taylor]: Taking taylor expansion of k in k 227.057 * [backup-simplify]: Simplify 0 into 0 227.057 * [backup-simplify]: Simplify 1 into 1 227.057 * [taylor]: Taking taylor expansion of (log PI) in k 227.057 * [taylor]: Taking taylor expansion of PI in k 227.057 * [backup-simplify]: Simplify PI into PI 227.057 * [backup-simplify]: Simplify (log PI) into (log PI) 227.057 * [backup-simplify]: Simplify (* 1/2 0) into 0 227.058 * [backup-simplify]: Simplify (- 0) into 0 227.058 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 227.059 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 227.060 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 227.060 * [backup-simplify]: Simplify (* (pow (* 2 n) 1/2) (pow PI 1/2)) into (sqrt (* PI (* n 2))) 227.060 * [backup-simplify]: Simplify (/ 1 (sqrt (* PI (* n 2)))) into (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))) 227.060 * [taylor]: Taking taylor expansion of (sqrt k) in k 227.060 * [taylor]: Taking taylor expansion of k in k 227.060 * [backup-simplify]: Simplify 0 into 0 227.060 * [backup-simplify]: Simplify 1 into 1 227.060 * [backup-simplify]: Simplify (sqrt 0) into 0 227.061 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 227.062 * [backup-simplify]: Simplify (* (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))) 0) into 0 227.062 * [taylor]: Taking taylor expansion of 0 in n 227.062 * [backup-simplify]: Simplify 0 into 0 227.062 * [backup-simplify]: Simplify 0 into 0 227.063 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 227.064 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 227.064 * [backup-simplify]: Simplify (- 1/2) into -1/2 227.064 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 227.066 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 227.072 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 227.072 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 n)) into 0 227.073 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 n) 1)))) 1) into 0 227.073 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 227.074 * [backup-simplify]: Simplify (- 1/2) into -1/2 227.074 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 227.074 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 n)))) into (- (* 1/2 (log (* 2 n)))) 227.074 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 n)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 n)))) 1) 1)))) into (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) 227.076 * [backup-simplify]: Simplify (+ (* (pow (* 2 n) 1/2) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) (pow PI 1/2))) into (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) 227.081 * [backup-simplify]: Simplify (- (+ (* (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))) (/ (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) (sqrt (* PI (* n 2))))))) into (+ (* 1/2 (* (/ (log PI) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (* 1/2 (* (/ (log (* 2 n)) (sqrt 2)) (sqrt (/ 1 (* PI n)))))) 227.083 * [backup-simplify]: Simplify (+ (* (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))) +nan.0) (* (+ (* 1/2 (* (/ (log PI) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (* 1/2 (* (/ (log (* 2 n)) (sqrt 2)) (sqrt (/ 1 (* PI n)))))) 0)) into (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))))) 227.084 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))))) in n 227.084 * [taylor]: Taking taylor expansion of (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI))))) in n 227.084 * [taylor]: Taking taylor expansion of +nan.0 in n 227.084 * [backup-simplify]: Simplify +nan.0 into +nan.0 227.084 * [taylor]: Taking taylor expansion of (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))) in n 227.084 * [taylor]: Taking taylor expansion of (/ 1 (sqrt 2)) in n 227.084 * [taylor]: Taking taylor expansion of (sqrt 2) in n 227.084 * [taylor]: Taking taylor expansion of 2 in n 227.084 * [backup-simplify]: Simplify 2 into 2 227.084 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 227.084 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 227.085 * [backup-simplify]: Simplify (/ 1 (sqrt 2)) into (/ 1 (sqrt 2)) 227.085 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 227.085 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 227.085 * [taylor]: Taking taylor expansion of (* n PI) in n 227.085 * [taylor]: Taking taylor expansion of n in n 227.085 * [backup-simplify]: Simplify 0 into 0 227.085 * [backup-simplify]: Simplify 1 into 1 227.085 * [taylor]: Taking taylor expansion of PI in n 227.085 * [backup-simplify]: Simplify PI into PI 227.085 * [backup-simplify]: Simplify (* 0 PI) into 0 227.086 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 227.087 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 227.087 * [backup-simplify]: Simplify (sqrt 0) into 0 227.088 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 227.089 * [backup-simplify]: Simplify (- (+ (* (/ 1 (sqrt 2)) (/ 0 (sqrt 2))))) into 0 227.092 * [backup-simplify]: Simplify (+ (* (/ 1 (sqrt 2)) (/ +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (/ 1 (* (sqrt 2) PI)))) 227.092 * [backup-simplify]: Simplify (* (/ 1 (sqrt 2)) 0) into 0 227.097 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ 1 (* (sqrt 2) PI))))) (* 0 0)) into (- (* +nan.0 (/ 1 (* (sqrt 2) PI)))) 227.102 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ 1 (* (sqrt 2) PI))))) into (- (* +nan.0 (/ 1 (* (sqrt 2) PI)))) 227.107 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (* (sqrt 2) PI)))) into (- (* +nan.0 (/ 1 (* (sqrt 2) PI)))) 227.107 * [backup-simplify]: Simplify 0 into 0 227.110 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 227.114 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 227.115 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 227.116 * [backup-simplify]: Simplify (- 0) into 0 227.116 * [backup-simplify]: Simplify (+ 0 0) into 0 227.118 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 227.131 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 227.132 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 n))) into 0 227.134 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 n) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 n) 1)))) 2) into 0 227.135 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 227.136 * [backup-simplify]: Simplify (- 0) into 0 227.136 * [backup-simplify]: Simplify (+ 0 0) into 0 227.137 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 n))))) into 0 227.138 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 n)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* n 2)) (pow (log (* 2 n)) 2))) 227.145 * [backup-simplify]: Simplify (+ (* (pow (* 2 n) 1/2) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* 1/8 (* (sqrt (* n 2)) (pow (log (* 2 n)) 2))) (pow PI 1/2)))) into (+ (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (* 1/4 (* (sqrt (* PI n)) (* (sqrt 2) (* (log (* 2 n)) (log PI))))))) 227.157 * [backup-simplify]: Simplify (- (+ (* (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))) (/ (+ (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (* 1/4 (* (sqrt (* PI n)) (* (sqrt 2) (* (log (* 2 n)) (log PI))))))) (sqrt (* PI (* n 2))))) (* (+ (* 1/2 (* (/ (log PI) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (* 1/2 (* (/ (log (* 2 n)) (sqrt 2)) (sqrt (/ 1 (* PI n)))))) (/ (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) (sqrt (* PI (* n 2))))))) into (- (+ (* 1/4 (* (sqrt (/ 1 (* PI n))) (/ (* (log PI) (log (* 2 n))) (sqrt 2)))) (+ (* 1/8 (* (/ (pow (log PI) 2) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (+ (* 1/8 (* (/ (pow (log (* 2 n)) 2) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (* 1/4 (* (sqrt (/ 1 (* PI n))) (/ (* (log (* 2 n)) (log PI)) (sqrt 2))))))) (* 1/4 (* (/ (* (log (* 2 n)) (log PI)) (sqrt 2)) (sqrt (/ 1 (* n PI)))))) 227.169 * [backup-simplify]: Simplify (+ (* (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))) +nan.0) (+ (* (+ (* 1/2 (* (/ (log PI) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (* 1/2 (* (/ (log (* 2 n)) (sqrt 2)) (sqrt (/ 1 (* PI n)))))) +nan.0) (* (- (+ (* 1/4 (* (sqrt (/ 1 (* PI n))) (/ (* (log PI) (log (* 2 n))) (sqrt 2)))) (+ (* 1/8 (* (/ (pow (log PI) 2) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (+ (* 1/8 (* (/ (pow (log (* 2 n)) 2) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (* 1/4 (* (sqrt (/ 1 (* PI n))) (/ (* (log (* 2 n)) (log PI)) (sqrt 2))))))) (* 1/4 (* (/ (* (log (* 2 n)) (log PI)) (sqrt 2)) (sqrt (/ 1 (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (/ (log PI) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (- (+ (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (/ (log (* 2 n)) (sqrt 2)) (sqrt (/ 1 (* PI n)))))))))) 227.169 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (/ (log PI) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (- (+ (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (/ (log (* 2 n)) (sqrt 2)) (sqrt (/ 1 (* PI n)))))))))) in n 227.169 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (/ (log PI) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (- (+ (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (/ (log (* 2 n)) (sqrt 2)) (sqrt (/ 1 (* PI n))))))))) in n 227.169 * [taylor]: Taking taylor expansion of (* +nan.0 (* (/ (log PI) (sqrt 2)) (sqrt (/ 1 (* PI n))))) in n 227.169 * [taylor]: Taking taylor expansion of +nan.0 in n 227.169 * [backup-simplify]: Simplify +nan.0 into +nan.0 227.169 * [taylor]: Taking taylor expansion of (* (/ (log PI) (sqrt 2)) (sqrt (/ 1 (* PI n)))) in n 227.169 * [taylor]: Taking taylor expansion of (/ (log PI) (sqrt 2)) in n 227.169 * [taylor]: Taking taylor expansion of (log PI) in n 227.169 * [taylor]: Taking taylor expansion of PI in n 227.169 * [backup-simplify]: Simplify PI into PI 227.170 * [backup-simplify]: Simplify (log PI) into (log PI) 227.170 * [taylor]: Taking taylor expansion of (sqrt 2) in n 227.170 * [taylor]: Taking taylor expansion of 2 in n 227.170 * [backup-simplify]: Simplify 2 into 2 227.171 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 227.171 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 227.173 * [backup-simplify]: Simplify (/ (log PI) (sqrt 2)) into (/ (log PI) (sqrt 2)) 227.173 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* PI n))) in n 227.173 * [taylor]: Taking taylor expansion of (/ 1 (* PI n)) in n 227.173 * [taylor]: Taking taylor expansion of (* PI n) in n 227.173 * [taylor]: Taking taylor expansion of PI in n 227.173 * [backup-simplify]: Simplify PI into PI 227.173 * [taylor]: Taking taylor expansion of n in n 227.173 * [backup-simplify]: Simplify 0 into 0 227.173 * [backup-simplify]: Simplify 1 into 1 227.174 * [backup-simplify]: Simplify (* PI 0) into 0 227.175 * [backup-simplify]: Simplify (+ (* PI 1) (* 0 0)) into PI 227.176 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 227.176 * [backup-simplify]: Simplify (sqrt 0) into 0 227.179 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 227.179 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (/ (log (* 2 n)) (sqrt 2)) (sqrt (/ 1 (* PI n)))))))) in n 227.179 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (/ (log (* 2 n)) (sqrt 2)) (sqrt (/ 1 (* PI n))))))) in n 227.179 * [taylor]: Taking taylor expansion of (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI))))) in n 227.179 * [taylor]: Taking taylor expansion of +nan.0 in n 227.179 * [backup-simplify]: Simplify +nan.0 into +nan.0 227.179 * [taylor]: Taking taylor expansion of (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))) in n 227.179 * [taylor]: Taking taylor expansion of (/ 1 (sqrt 2)) in n 227.179 * [taylor]: Taking taylor expansion of (sqrt 2) in n 227.179 * [taylor]: Taking taylor expansion of 2 in n 227.179 * [backup-simplify]: Simplify 2 into 2 227.180 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 227.180 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 227.181 * [backup-simplify]: Simplify (/ 1 (sqrt 2)) into (/ 1 (sqrt 2)) 227.181 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 227.182 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 227.182 * [taylor]: Taking taylor expansion of (* n PI) in n 227.182 * [taylor]: Taking taylor expansion of n in n 227.182 * [backup-simplify]: Simplify 0 into 0 227.182 * [backup-simplify]: Simplify 1 into 1 227.182 * [taylor]: Taking taylor expansion of PI in n 227.182 * [backup-simplify]: Simplify PI into PI 227.182 * [backup-simplify]: Simplify (* 0 PI) into 0 227.184 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 227.184 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 227.185 * [backup-simplify]: Simplify (sqrt 0) into 0 227.187 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 227.187 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (/ (log (* 2 n)) (sqrt 2)) (sqrt (/ 1 (* PI n)))))) in n 227.187 * [taylor]: Taking taylor expansion of (* +nan.0 (* (/ (log (* 2 n)) (sqrt 2)) (sqrt (/ 1 (* PI n))))) in n 227.187 * [taylor]: Taking taylor expansion of +nan.0 in n 227.187 * [backup-simplify]: Simplify +nan.0 into +nan.0 227.187 * [taylor]: Taking taylor expansion of (* (/ (log (* 2 n)) (sqrt 2)) (sqrt (/ 1 (* PI n)))) in n 227.187 * [taylor]: Taking taylor expansion of (/ (log (* 2 n)) (sqrt 2)) in n 227.187 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 227.187 * [taylor]: Taking taylor expansion of (* 2 n) in n 227.187 * [taylor]: Taking taylor expansion of 2 in n 227.188 * [backup-simplify]: Simplify 2 into 2 227.188 * [taylor]: Taking taylor expansion of n in n 227.188 * [backup-simplify]: Simplify 0 into 0 227.188 * [backup-simplify]: Simplify 1 into 1 227.188 * [backup-simplify]: Simplify (* 2 0) into 0 227.189 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 227.189 * [backup-simplify]: Simplify (log 2) into (log 2) 227.189 * [taylor]: Taking taylor expansion of (sqrt 2) in n 227.189 * [taylor]: Taking taylor expansion of 2 in n 227.189 * [backup-simplify]: Simplify 2 into 2 227.190 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 227.190 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 227.191 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 227.192 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 227.193 * [backup-simplify]: Simplify (/ (+ (log 2) (log n)) (sqrt 2)) into (/ (+ (log 2) (log n)) (sqrt 2)) 227.193 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* PI n))) in n 227.193 * [taylor]: Taking taylor expansion of (/ 1 (* PI n)) in n 227.193 * [taylor]: Taking taylor expansion of (* PI n) in n 227.193 * [taylor]: Taking taylor expansion of PI in n 227.193 * [backup-simplify]: Simplify PI into PI 227.193 * [taylor]: Taking taylor expansion of n in n 227.193 * [backup-simplify]: Simplify 0 into 0 227.193 * [backup-simplify]: Simplify 1 into 1 227.194 * [backup-simplify]: Simplify (* PI 0) into 0 227.195 * [backup-simplify]: Simplify (+ (* PI 1) (* 0 0)) into PI 227.196 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 227.196 * [backup-simplify]: Simplify (sqrt 0) into 0 227.199 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 227.201 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 227.202 * [backup-simplify]: Simplify (- (/ 0 (sqrt 2)) (+ (* (/ (log PI) (sqrt 2)) (/ 0 (sqrt 2))))) into 0 227.207 * [backup-simplify]: Simplify (+ (* (/ (log PI) (sqrt 2)) (/ +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (/ (log PI) (* (sqrt 2) PI)))) 227.208 * [backup-simplify]: Simplify (* (/ (log PI) (sqrt 2)) 0) into 0 227.221 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (log PI) (* (sqrt 2) PI))))) (* 0 0)) into (- (* +nan.0 (/ (log PI) (* (sqrt 2) PI)))) 227.222 * [backup-simplify]: Simplify (- (+ (* (/ 1 (sqrt 2)) (/ 0 (sqrt 2))))) into 0 227.227 * [backup-simplify]: Simplify (+ (* (/ 1 (sqrt 2)) (/ +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (/ 1 (* (sqrt 2) PI)))) 227.227 * [backup-simplify]: Simplify (* (/ 1 (sqrt 2)) 0) into 0 227.233 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ 1 (* (sqrt 2) PI))))) (* 0 0)) into (- (* +nan.0 (/ 1 (* (sqrt 2) PI)))) 227.233 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0 227.234 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 227.236 * [backup-simplify]: Simplify (- (/ 0 (sqrt 2)) (+ (* (/ (+ (log 2) (log n)) (sqrt 2)) (/ 0 (sqrt 2))))) into 0 227.237 * [backup-simplify]: Simplify (+ (* (/ (+ (log 2) (log n)) (sqrt 2)) (/ +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (/ (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI)))))) 227.237 * [backup-simplify]: Simplify (* (/ (+ (log 2) (log n)) (sqrt 2)) 0) into 0 227.240 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (/ (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI))))))) (* 0 0)) into (- (+ (* +nan.0 (/ (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI)))))) 227.243 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (/ (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (/ (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI)))))) 227.248 * [backup-simplify]: Simplify (+ (- (* +nan.0 (/ 1 (* (sqrt 2) PI)))) (- (+ (* +nan.0 (/ (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (/ (log 2) (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ 1 (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI)))))))) 227.253 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (/ (log 2) (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ 1 (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI))))))))) into (- (+ (* +nan.0 (/ (log 2) (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ 1 (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI)))))))) 227.260 * [backup-simplify]: Simplify (+ (- (* +nan.0 (/ (log PI) (* (sqrt 2) PI)))) (- (+ (* +nan.0 (/ (log 2) (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ 1 (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI))))))))) into (- (+ (* +nan.0 (/ (log 2) (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ 1 (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ (log PI) (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI)))))))))) 227.266 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (/ (log 2) (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ 1 (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ (log PI) (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI))))))))))) into (- (+ (* +nan.0 (/ (log 2) (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ 1 (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ (log PI) (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI)))))))))) 227.273 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ (log 2) (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ 1 (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ (log PI) (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI)))))))))) into (- (+ (* +nan.0 (/ (log 2) (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ 1 (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ (log PI) (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI)))))))))) 227.274 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 227.274 * [backup-simplify]: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)))) into 0 227.277 * [backup-simplify]: Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2)) 227.278 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 227.278 * [backup-simplify]: Simplify (- (+ (* (/ 1 (sqrt 2)) (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))))) into 0 227.283 * [backup-simplify]: Simplify (+ (* (/ 1 (sqrt 2)) (/ +nan.0 (pow PI 2))) (+ (* 0 (/ +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (/ 1 (* (sqrt 2) (pow PI 2))))) 227.289 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ 1 (* (sqrt 2) (pow PI 2)))))) (+ (* 0 (- (* +nan.0 (/ 1 (* (sqrt 2) PI))))) (* 0 0))) into (- (* +nan.0 (/ 1 (* (sqrt 2) (pow PI 2))))) 227.293 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ 1 (* (sqrt 2) (pow PI 2)))))) into (- (* +nan.0 (/ 1 (* (sqrt 2) (pow PI 2))))) 227.296 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (/ 1 (* (sqrt 2) (pow PI 2))))) 227.311 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (* (sqrt 2) (pow PI 2))))) (* n k)) (+ (* (- (+ (* +nan.0 (/ (log 2) (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ 1 (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ (log PI) (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI)))))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (/ 1 (* (sqrt 2) PI)))) (* 1 k)))) into (- (+ (* +nan.0 (/ k (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ (* (log n) (pow k 2)) (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ (* (log PI) (pow k 2)) (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ (* n k) (* (sqrt 2) (pow PI 2)))) (- (+ (* +nan.0 (/ (pow k 2) (* (sqrt 2) PI))) (- (* +nan.0 (/ (* (log 2) (pow k 2)) (* (sqrt 2) PI)))))))))))))) 227.312 * [backup-simplify]: Simplify (* (/ 1 (pow PI (- 1/2 (/ (/ 1 k) 2)))) (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) 2) (- 1/2 (/ (/ 1 k) 2))))) into (* (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) (sqrt (/ 1 k))) 227.312 * [approximate]: Taking taylor expansion of (* (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) (sqrt (/ 1 k))) in (k n) around 0 227.312 * [taylor]: Taking taylor expansion of (* (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) (sqrt (/ 1 k))) in n 227.312 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 227.312 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 227.312 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 227.312 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 227.312 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 227.312 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 227.312 * [taylor]: Taking taylor expansion of 1/2 in n 227.312 * [backup-simplify]: Simplify 1/2 into 1/2 227.312 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 227.312 * [taylor]: Taking taylor expansion of 1/2 in n 227.312 * [backup-simplify]: Simplify 1/2 into 1/2 227.312 * [taylor]: Taking taylor expansion of (/ 1 k) in n 227.312 * [taylor]: Taking taylor expansion of k in n 227.312 * [backup-simplify]: Simplify k into k 227.312 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 227.312 * [taylor]: Taking taylor expansion of (log PI) in n 227.312 * [taylor]: Taking taylor expansion of PI in n 227.312 * [backup-simplify]: Simplify PI into PI 227.313 * [backup-simplify]: Simplify (log PI) into (log PI) 227.313 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 227.313 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 227.313 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 227.313 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 227.313 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 227.313 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 227.313 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 227.313 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 227.314 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 227.314 * [taylor]: Taking taylor expansion of 1/2 in n 227.314 * [backup-simplify]: Simplify 1/2 into 1/2 227.314 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 227.314 * [taylor]: Taking taylor expansion of 1/2 in n 227.314 * [backup-simplify]: Simplify 1/2 into 1/2 227.314 * [taylor]: Taking taylor expansion of (/ 1 k) in n 227.314 * [taylor]: Taking taylor expansion of k in n 227.314 * [backup-simplify]: Simplify k into k 227.314 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 227.314 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 227.314 * [taylor]: Taking taylor expansion of (/ 2 n) in n 227.314 * [taylor]: Taking taylor expansion of 2 in n 227.314 * [backup-simplify]: Simplify 2 into 2 227.314 * [taylor]: Taking taylor expansion of n in n 227.314 * [backup-simplify]: Simplify 0 into 0 227.314 * [backup-simplify]: Simplify 1 into 1 227.314 * [backup-simplify]: Simplify (/ 2 1) into 2 227.314 * [backup-simplify]: Simplify (log 2) into (log 2) 227.314 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 227.314 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 227.314 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 227.315 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 227.315 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 227.316 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 227.316 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 227.316 * [backup-simplify]: Simplify (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 227.316 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 227.317 * [taylor]: Taking taylor expansion of (/ 1 k) in n 227.317 * [taylor]: Taking taylor expansion of k in n 227.317 * [backup-simplify]: Simplify k into k 227.317 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 227.317 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 227.317 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 227.317 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 227.317 * [taylor]: Taking taylor expansion of (* (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) (sqrt (/ 1 k))) in k 227.317 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) in k 227.317 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 227.317 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 227.317 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 227.317 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 227.317 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 227.317 * [taylor]: Taking taylor expansion of 1/2 in k 227.317 * [backup-simplify]: Simplify 1/2 into 1/2 227.317 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 227.317 * [taylor]: Taking taylor expansion of 1/2 in k 227.317 * [backup-simplify]: Simplify 1/2 into 1/2 227.317 * [taylor]: Taking taylor expansion of (/ 1 k) in k 227.317 * [taylor]: Taking taylor expansion of k in k 227.317 * [backup-simplify]: Simplify 0 into 0 227.317 * [backup-simplify]: Simplify 1 into 1 227.317 * [backup-simplify]: Simplify (/ 1 1) into 1 227.317 * [taylor]: Taking taylor expansion of (log PI) in k 227.317 * [taylor]: Taking taylor expansion of PI in k 227.317 * [backup-simplify]: Simplify PI into PI 227.318 * [backup-simplify]: Simplify (log PI) into (log PI) 227.318 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 227.318 * [backup-simplify]: Simplify (- 1/2) into -1/2 227.318 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 227.319 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 227.319 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 227.319 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 227.320 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 227.320 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 227.320 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 227.320 * [taylor]: Taking taylor expansion of 1/2 in k 227.320 * [backup-simplify]: Simplify 1/2 into 1/2 227.320 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 227.320 * [taylor]: Taking taylor expansion of 1/2 in k 227.320 * [backup-simplify]: Simplify 1/2 into 1/2 227.320 * [taylor]: Taking taylor expansion of (/ 1 k) in k 227.320 * [taylor]: Taking taylor expansion of k in k 227.320 * [backup-simplify]: Simplify 0 into 0 227.320 * [backup-simplify]: Simplify 1 into 1 227.320 * [backup-simplify]: Simplify (/ 1 1) into 1 227.320 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in k 227.320 * [taylor]: Taking taylor expansion of (/ 2 n) in k 227.320 * [taylor]: Taking taylor expansion of 2 in k 227.320 * [backup-simplify]: Simplify 2 into 2 227.320 * [taylor]: Taking taylor expansion of n in k 227.320 * [backup-simplify]: Simplify n into n 227.320 * [backup-simplify]: Simplify (/ 2 n) into (/ 2 n) 227.320 * [backup-simplify]: Simplify (log (/ 2 n)) into (log (/ 2 n)) 227.320 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 227.321 * [backup-simplify]: Simplify (- 1/2) into -1/2 227.321 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 227.321 * [backup-simplify]: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 227.321 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 227.321 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) 227.321 * [backup-simplify]: Simplify (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) into (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) 227.321 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 227.321 * [taylor]: Taking taylor expansion of (/ 1 k) in k 227.321 * [taylor]: Taking taylor expansion of k in k 227.321 * [backup-simplify]: Simplify 0 into 0 227.321 * [backup-simplify]: Simplify 1 into 1 227.322 * [backup-simplify]: Simplify (/ 1 1) into 1 227.322 * [backup-simplify]: Simplify (sqrt 0) into 0 227.323 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 227.323 * [taylor]: Taking taylor expansion of (* (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) (sqrt (/ 1 k))) in k 227.323 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) in k 227.323 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 227.323 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 227.323 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 227.323 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 227.323 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 227.323 * [taylor]: Taking taylor expansion of 1/2 in k 227.323 * [backup-simplify]: Simplify 1/2 into 1/2 227.323 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 227.323 * [taylor]: Taking taylor expansion of 1/2 in k 227.323 * [backup-simplify]: Simplify 1/2 into 1/2 227.323 * [taylor]: Taking taylor expansion of (/ 1 k) in k 227.323 * [taylor]: Taking taylor expansion of k in k 227.323 * [backup-simplify]: Simplify 0 into 0 227.323 * [backup-simplify]: Simplify 1 into 1 227.324 * [backup-simplify]: Simplify (/ 1 1) into 1 227.324 * [taylor]: Taking taylor expansion of (log PI) in k 227.324 * [taylor]: Taking taylor expansion of PI in k 227.324 * [backup-simplify]: Simplify PI into PI 227.324 * [backup-simplify]: Simplify (log PI) into (log PI) 227.324 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 227.324 * [backup-simplify]: Simplify (- 1/2) into -1/2 227.325 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 227.325 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 227.326 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 227.326 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 227.326 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 227.326 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 227.326 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 227.326 * [taylor]: Taking taylor expansion of 1/2 in k 227.326 * [backup-simplify]: Simplify 1/2 into 1/2 227.326 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 227.326 * [taylor]: Taking taylor expansion of 1/2 in k 227.326 * [backup-simplify]: Simplify 1/2 into 1/2 227.326 * [taylor]: Taking taylor expansion of (/ 1 k) in k 227.326 * [taylor]: Taking taylor expansion of k in k 227.326 * [backup-simplify]: Simplify 0 into 0 227.326 * [backup-simplify]: Simplify 1 into 1 227.326 * [backup-simplify]: Simplify (/ 1 1) into 1 227.326 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in k 227.326 * [taylor]: Taking taylor expansion of (/ 2 n) in k 227.326 * [taylor]: Taking taylor expansion of 2 in k 227.326 * [backup-simplify]: Simplify 2 into 2 227.326 * [taylor]: Taking taylor expansion of n in k 227.326 * [backup-simplify]: Simplify n into n 227.326 * [backup-simplify]: Simplify (/ 2 n) into (/ 2 n) 227.326 * [backup-simplify]: Simplify (log (/ 2 n)) into (log (/ 2 n)) 227.327 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 227.327 * [backup-simplify]: Simplify (- 1/2) into -1/2 227.327 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 227.327 * [backup-simplify]: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 227.327 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 227.327 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) 227.328 * [backup-simplify]: Simplify (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) into (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) 227.328 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 227.328 * [taylor]: Taking taylor expansion of (/ 1 k) in k 227.328 * [taylor]: Taking taylor expansion of k in k 227.328 * [backup-simplify]: Simplify 0 into 0 227.328 * [backup-simplify]: Simplify 1 into 1 227.328 * [backup-simplify]: Simplify (/ 1 1) into 1 227.328 * [backup-simplify]: Simplify (sqrt 0) into 0 227.329 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 227.329 * [backup-simplify]: Simplify (* (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) 0) into 0 227.330 * [taylor]: Taking taylor expansion of 0 in n 227.330 * [backup-simplify]: Simplify 0 into 0 227.330 * [backup-simplify]: Simplify 0 into 0 227.330 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) into 0 227.330 * [backup-simplify]: Simplify (- (+ (* (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) (/ 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))))) into 0 227.331 * [backup-simplify]: Simplify (+ (* (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))))) 227.331 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))))) in n 227.331 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 227.331 * [taylor]: Taking taylor expansion of +nan.0 in n 227.331 * [backup-simplify]: Simplify +nan.0 into +nan.0 227.331 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 227.331 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 227.331 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 227.331 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 227.331 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 227.331 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 227.331 * [taylor]: Taking taylor expansion of 1/2 in n 227.331 * [backup-simplify]: Simplify 1/2 into 1/2 227.331 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 227.331 * [taylor]: Taking taylor expansion of 1/2 in n 227.331 * [backup-simplify]: Simplify 1/2 into 1/2 227.331 * [taylor]: Taking taylor expansion of (/ 1 k) in n 227.331 * [taylor]: Taking taylor expansion of k in n 227.331 * [backup-simplify]: Simplify k into k 227.331 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 227.331 * [taylor]: Taking taylor expansion of (log PI) in n 227.331 * [taylor]: Taking taylor expansion of PI in n 227.331 * [backup-simplify]: Simplify PI into PI 227.331 * [backup-simplify]: Simplify (log PI) into (log PI) 227.331 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 227.331 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 227.331 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 227.332 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 227.332 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 227.332 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 227.332 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 227.332 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 227.332 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 227.332 * [taylor]: Taking taylor expansion of 1/2 in n 227.332 * [backup-simplify]: Simplify 1/2 into 1/2 227.332 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 227.332 * [taylor]: Taking taylor expansion of 1/2 in n 227.332 * [backup-simplify]: Simplify 1/2 into 1/2 227.332 * [taylor]: Taking taylor expansion of (/ 1 k) in n 227.332 * [taylor]: Taking taylor expansion of k in n 227.332 * [backup-simplify]: Simplify k into k 227.332 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 227.332 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 227.332 * [taylor]: Taking taylor expansion of (/ 2 n) in n 227.332 * [taylor]: Taking taylor expansion of 2 in n 227.332 * [backup-simplify]: Simplify 2 into 2 227.332 * [taylor]: Taking taylor expansion of n in n 227.333 * [backup-simplify]: Simplify 0 into 0 227.333 * [backup-simplify]: Simplify 1 into 1 227.333 * [backup-simplify]: Simplify (/ 2 1) into 2 227.333 * [backup-simplify]: Simplify (log 2) into (log 2) 227.333 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 227.333 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 227.334 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 227.334 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 227.335 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 227.335 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 227.336 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 227.337 * [backup-simplify]: Simplify (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 227.338 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (/ +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 227.338 * [backup-simplify]: Simplify (- (/ +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))))) 227.339 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))))) into (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))))) 227.339 * [backup-simplify]: Simplify 0 into 0 227.340 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 227.343 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 227.344 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) into 0 227.345 * [backup-simplify]: Simplify (- (+ (* (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) (/ 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) (* 0 (/ 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))))) into 0 227.346 * [backup-simplify]: Simplify (+ (* (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))))) 227.346 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))))) in n 227.346 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 227.346 * [taylor]: Taking taylor expansion of +nan.0 in n 227.346 * [backup-simplify]: Simplify +nan.0 into +nan.0 227.346 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 227.346 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 227.346 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 227.346 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 227.346 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 227.346 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 227.346 * [taylor]: Taking taylor expansion of 1/2 in n 227.346 * [backup-simplify]: Simplify 1/2 into 1/2 227.346 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 227.346 * [taylor]: Taking taylor expansion of 1/2 in n 227.346 * [backup-simplify]: Simplify 1/2 into 1/2 227.347 * [taylor]: Taking taylor expansion of (/ 1 k) in n 227.347 * [taylor]: Taking taylor expansion of k in n 227.347 * [backup-simplify]: Simplify k into k 227.347 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 227.347 * [taylor]: Taking taylor expansion of (log PI) in n 227.347 * [taylor]: Taking taylor expansion of PI in n 227.347 * [backup-simplify]: Simplify PI into PI 227.347 * [backup-simplify]: Simplify (log PI) into (log PI) 227.347 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 227.347 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 227.348 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 227.348 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 227.349 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 227.349 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 227.349 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 227.349 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 227.349 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 227.349 * [taylor]: Taking taylor expansion of 1/2 in n 227.349 * [backup-simplify]: Simplify 1/2 into 1/2 227.349 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 227.349 * [taylor]: Taking taylor expansion of 1/2 in n 227.349 * [backup-simplify]: Simplify 1/2 into 1/2 227.349 * [taylor]: Taking taylor expansion of (/ 1 k) in n 227.349 * [taylor]: Taking taylor expansion of k in n 227.349 * [backup-simplify]: Simplify k into k 227.349 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 227.349 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 227.349 * [taylor]: Taking taylor expansion of (/ 2 n) in n 227.349 * [taylor]: Taking taylor expansion of 2 in n 227.349 * [backup-simplify]: Simplify 2 into 2 227.349 * [taylor]: Taking taylor expansion of n in n 227.349 * [backup-simplify]: Simplify 0 into 0 227.349 * [backup-simplify]: Simplify 1 into 1 227.350 * [backup-simplify]: Simplify (/ 2 1) into 2 227.350 * [backup-simplify]: Simplify (log 2) into (log 2) 227.350 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 227.350 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 227.350 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 227.351 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 227.352 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 227.352 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 227.353 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 227.354 * [backup-simplify]: Simplify (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 227.354 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (/ +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 227.355 * [backup-simplify]: Simplify (- (/ +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))))) 227.356 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))))) into (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))))) 227.357 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0 227.359 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 227.359 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 227.359 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 227.360 * [backup-simplify]: Simplify (- 0) into 0 227.360 * [backup-simplify]: Simplify (+ 0 0) into 0 227.361 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 227.361 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 227.363 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 227.365 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 227.365 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 227.366 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 227.366 * [backup-simplify]: Simplify (- 0) into 0 227.366 * [backup-simplify]: Simplify (+ 0 0) into 0 227.367 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (log PI))) into 0 227.369 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 227.369 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into 0 227.371 * [backup-simplify]: Simplify (- (+ (* (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) (/ 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))))) into 0 227.372 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))))) into 0 227.372 * [backup-simplify]: Simplify (- 0) into 0 227.372 * [backup-simplify]: Simplify 0 into 0 227.373 * [backup-simplify]: Simplify 0 into 0 227.373 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 227.378 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 227.379 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 227.380 * [backup-simplify]: Simplify (- (+ (* (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) (/ 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) (* 0 (/ 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) (* 0 (/ 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))))) into 0 227.382 * [backup-simplify]: Simplify (+ (* (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))))) 227.382 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))))) in n 227.382 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 227.382 * [taylor]: Taking taylor expansion of +nan.0 in n 227.382 * [backup-simplify]: Simplify +nan.0 into +nan.0 227.382 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 227.382 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 227.382 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 227.382 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 227.382 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 227.382 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 227.382 * [taylor]: Taking taylor expansion of 1/2 in n 227.382 * [backup-simplify]: Simplify 1/2 into 1/2 227.382 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 227.382 * [taylor]: Taking taylor expansion of 1/2 in n 227.382 * [backup-simplify]: Simplify 1/2 into 1/2 227.382 * [taylor]: Taking taylor expansion of (/ 1 k) in n 227.382 * [taylor]: Taking taylor expansion of k in n 227.382 * [backup-simplify]: Simplify k into k 227.382 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 227.382 * [taylor]: Taking taylor expansion of (log PI) in n 227.382 * [taylor]: Taking taylor expansion of PI in n 227.382 * [backup-simplify]: Simplify PI into PI 227.383 * [backup-simplify]: Simplify (log PI) into (log PI) 227.383 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 227.383 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 227.383 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 227.384 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 227.384 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 227.385 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 227.385 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 227.385 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 227.385 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 227.385 * [taylor]: Taking taylor expansion of 1/2 in n 227.385 * [backup-simplify]: Simplify 1/2 into 1/2 227.385 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 227.385 * [taylor]: Taking taylor expansion of 1/2 in n 227.385 * [backup-simplify]: Simplify 1/2 into 1/2 227.385 * [taylor]: Taking taylor expansion of (/ 1 k) in n 227.385 * [taylor]: Taking taylor expansion of k in n 227.385 * [backup-simplify]: Simplify k into k 227.385 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 227.385 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 227.385 * [taylor]: Taking taylor expansion of (/ 2 n) in n 227.385 * [taylor]: Taking taylor expansion of 2 in n 227.385 * [backup-simplify]: Simplify 2 into 2 227.385 * [taylor]: Taking taylor expansion of n in n 227.385 * [backup-simplify]: Simplify 0 into 0 227.385 * [backup-simplify]: Simplify 1 into 1 227.386 * [backup-simplify]: Simplify (/ 2 1) into 2 227.386 * [backup-simplify]: Simplify (log 2) into (log 2) 227.386 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 227.386 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 227.386 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 227.387 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 227.388 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 227.388 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 227.389 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 227.390 * [backup-simplify]: Simplify (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 227.391 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (/ +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 227.391 * [backup-simplify]: Simplify (- (/ +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))))) 227.392 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))))) into (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))))) 227.395 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))))))) (* 1 (/ 1 k))) (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))))))))) into (- (+ (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 k))) (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) k)))) (- (+ (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 k))) (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k))))))) (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 k))) (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow k 2)))))))))) 227.396 * [backup-simplify]: Simplify (* (/ 1 (pow PI (- 1/2 (/ (/ 1 (- k)) 2)))) (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) 2) (- 1/2 (/ (/ 1 (- k)) 2))))) into (/ (sqrt (/ -1 k)) (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 227.396 * [approximate]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in (k n) around 0 227.396 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 227.396 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 227.396 * [taylor]: Taking taylor expansion of (/ -1 k) in n 227.396 * [taylor]: Taking taylor expansion of -1 in n 227.396 * [backup-simplify]: Simplify -1 into -1 227.396 * [taylor]: Taking taylor expansion of k in n 227.396 * [backup-simplify]: Simplify k into k 227.396 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 227.396 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 227.396 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 227.396 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 227.396 * [taylor]: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 227.396 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 227.396 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 227.396 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 227.396 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 227.396 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 227.396 * [taylor]: Taking taylor expansion of 1/2 in n 227.396 * [backup-simplify]: Simplify 1/2 into 1/2 227.396 * [taylor]: Taking taylor expansion of (/ 1 k) in n 227.396 * [taylor]: Taking taylor expansion of k in n 227.396 * [backup-simplify]: Simplify k into k 227.396 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 227.397 * [taylor]: Taking taylor expansion of 1/2 in n 227.397 * [backup-simplify]: Simplify 1/2 into 1/2 227.397 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 227.397 * [taylor]: Taking taylor expansion of (/ -2 n) in n 227.397 * [taylor]: Taking taylor expansion of -2 in n 227.397 * [backup-simplify]: Simplify -2 into -2 227.397 * [taylor]: Taking taylor expansion of n in n 227.397 * [backup-simplify]: Simplify 0 into 0 227.397 * [backup-simplify]: Simplify 1 into 1 227.397 * [backup-simplify]: Simplify (/ -2 1) into -2 227.398 * [backup-simplify]: Simplify (log -2) into (log -2) 227.398 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 227.398 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 227.399 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 227.399 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 227.400 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 227.400 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 227.400 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 227.400 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 227.400 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 227.400 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 227.400 * [taylor]: Taking taylor expansion of 1/2 in n 227.400 * [backup-simplify]: Simplify 1/2 into 1/2 227.400 * [taylor]: Taking taylor expansion of (/ 1 k) in n 227.400 * [taylor]: Taking taylor expansion of k in n 227.400 * [backup-simplify]: Simplify k into k 227.400 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 227.400 * [taylor]: Taking taylor expansion of 1/2 in n 227.400 * [backup-simplify]: Simplify 1/2 into 1/2 227.400 * [taylor]: Taking taylor expansion of (log PI) in n 227.400 * [taylor]: Taking taylor expansion of PI in n 227.400 * [backup-simplify]: Simplify PI into PI 227.401 * [backup-simplify]: Simplify (log PI) into (log PI) 227.401 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 227.401 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 227.402 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 227.402 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 227.403 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 227.404 * [backup-simplify]: Simplify (/ (sqrt (/ -1 k)) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ (sqrt (/ -1 k)) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 227.404 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in k 227.404 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 227.404 * [taylor]: Taking taylor expansion of (/ -1 k) in k 227.404 * [taylor]: Taking taylor expansion of -1 in k 227.404 * [backup-simplify]: Simplify -1 into -1 227.404 * [taylor]: Taking taylor expansion of k in k 227.404 * [backup-simplify]: Simplify 0 into 0 227.404 * [backup-simplify]: Simplify 1 into 1 227.404 * [backup-simplify]: Simplify (/ -1 1) into -1 227.405 * [backup-simplify]: Simplify (sqrt 0) into 0 227.406 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 227.406 * [taylor]: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 227.406 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 227.406 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 227.406 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 227.406 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 227.406 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 227.406 * [taylor]: Taking taylor expansion of 1/2 in k 227.406 * [backup-simplify]: Simplify 1/2 into 1/2 227.406 * [taylor]: Taking taylor expansion of (/ 1 k) in k 227.406 * [taylor]: Taking taylor expansion of k in k 227.407 * [backup-simplify]: Simplify 0 into 0 227.407 * [backup-simplify]: Simplify 1 into 1 227.407 * [backup-simplify]: Simplify (/ 1 1) into 1 227.407 * [taylor]: Taking taylor expansion of 1/2 in k 227.407 * [backup-simplify]: Simplify 1/2 into 1/2 227.407 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in k 227.407 * [taylor]: Taking taylor expansion of (/ -2 n) in k 227.407 * [taylor]: Taking taylor expansion of -2 in k 227.407 * [backup-simplify]: Simplify -2 into -2 227.407 * [taylor]: Taking taylor expansion of n in k 227.407 * [backup-simplify]: Simplify n into n 227.407 * [backup-simplify]: Simplify (/ -2 n) into (/ -2 n) 227.407 * [backup-simplify]: Simplify (log (/ -2 n)) into (log (/ -2 n)) 227.408 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 227.408 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 227.408 * [backup-simplify]: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 227.409 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 227.409 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 227.409 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 227.409 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 227.409 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 227.409 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 227.409 * [taylor]: Taking taylor expansion of 1/2 in k 227.409 * [backup-simplify]: Simplify 1/2 into 1/2 227.409 * [taylor]: Taking taylor expansion of (/ 1 k) in k 227.409 * [taylor]: Taking taylor expansion of k in k 227.409 * [backup-simplify]: Simplify 0 into 0 227.409 * [backup-simplify]: Simplify 1 into 1 227.409 * [backup-simplify]: Simplify (/ 1 1) into 1 227.409 * [taylor]: Taking taylor expansion of 1/2 in k 227.409 * [backup-simplify]: Simplify 1/2 into 1/2 227.409 * [taylor]: Taking taylor expansion of (log PI) in k 227.409 * [taylor]: Taking taylor expansion of PI in k 227.409 * [backup-simplify]: Simplify PI into PI 227.410 * [backup-simplify]: Simplify (log PI) into (log PI) 227.410 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 227.411 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 227.412 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 227.412 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 227.413 * [backup-simplify]: Simplify (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 227.413 * [backup-simplify]: Simplify (/ +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 227.413 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in k 227.413 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 227.413 * [taylor]: Taking taylor expansion of (/ -1 k) in k 227.413 * [taylor]: Taking taylor expansion of -1 in k 227.413 * [backup-simplify]: Simplify -1 into -1 227.413 * [taylor]: Taking taylor expansion of k in k 227.413 * [backup-simplify]: Simplify 0 into 0 227.413 * [backup-simplify]: Simplify 1 into 1 227.414 * [backup-simplify]: Simplify (/ -1 1) into -1 227.414 * [backup-simplify]: Simplify (sqrt 0) into 0 227.415 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 227.415 * [taylor]: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 227.415 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 227.416 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 227.416 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 227.416 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 227.416 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 227.416 * [taylor]: Taking taylor expansion of 1/2 in k 227.416 * [backup-simplify]: Simplify 1/2 into 1/2 227.416 * [taylor]: Taking taylor expansion of (/ 1 k) in k 227.416 * [taylor]: Taking taylor expansion of k in k 227.416 * [backup-simplify]: Simplify 0 into 0 227.416 * [backup-simplify]: Simplify 1 into 1 227.416 * [backup-simplify]: Simplify (/ 1 1) into 1 227.416 * [taylor]: Taking taylor expansion of 1/2 in k 227.416 * [backup-simplify]: Simplify 1/2 into 1/2 227.416 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in k 227.416 * [taylor]: Taking taylor expansion of (/ -2 n) in k 227.416 * [taylor]: Taking taylor expansion of -2 in k 227.416 * [backup-simplify]: Simplify -2 into -2 227.416 * [taylor]: Taking taylor expansion of n in k 227.416 * [backup-simplify]: Simplify n into n 227.416 * [backup-simplify]: Simplify (/ -2 n) into (/ -2 n) 227.417 * [backup-simplify]: Simplify (log (/ -2 n)) into (log (/ -2 n)) 227.417 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 227.417 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 227.418 * [backup-simplify]: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 227.418 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 227.418 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 227.418 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 227.418 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 227.418 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 227.418 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 227.418 * [taylor]: Taking taylor expansion of 1/2 in k 227.418 * [backup-simplify]: Simplify 1/2 into 1/2 227.418 * [taylor]: Taking taylor expansion of (/ 1 k) in k 227.418 * [taylor]: Taking taylor expansion of k in k 227.418 * [backup-simplify]: Simplify 0 into 0 227.418 * [backup-simplify]: Simplify 1 into 1 227.418 * [backup-simplify]: Simplify (/ 1 1) into 1 227.419 * [taylor]: Taking taylor expansion of 1/2 in k 227.419 * [backup-simplify]: Simplify 1/2 into 1/2 227.419 * [taylor]: Taking taylor expansion of (log PI) in k 227.419 * [taylor]: Taking taylor expansion of PI in k 227.419 * [backup-simplify]: Simplify PI into PI 227.419 * [backup-simplify]: Simplify (log PI) into (log PI) 227.420 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 227.420 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 227.421 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 227.422 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 227.422 * [backup-simplify]: Simplify (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 227.422 * [backup-simplify]: Simplify (/ +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 227.422 * [taylor]: Taking taylor expansion of (/ +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 227.422 * [taylor]: Taking taylor expansion of +nan.0 in n 227.422 * [backup-simplify]: Simplify +nan.0 into +nan.0 227.422 * [taylor]: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 227.422 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 227.422 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 227.422 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 227.422 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 227.422 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 227.422 * [taylor]: Taking taylor expansion of 1/2 in n 227.422 * [backup-simplify]: Simplify 1/2 into 1/2 227.423 * [taylor]: Taking taylor expansion of (/ 1 k) in n 227.423 * [taylor]: Taking taylor expansion of k in n 227.423 * [backup-simplify]: Simplify k into k 227.423 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 227.423 * [taylor]: Taking taylor expansion of 1/2 in n 227.423 * [backup-simplify]: Simplify 1/2 into 1/2 227.423 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 227.423 * [taylor]: Taking taylor expansion of (/ -2 n) in n 227.423 * [taylor]: Taking taylor expansion of -2 in n 227.423 * [backup-simplify]: Simplify -2 into -2 227.423 * [taylor]: Taking taylor expansion of n in n 227.423 * [backup-simplify]: Simplify 0 into 0 227.423 * [backup-simplify]: Simplify 1 into 1 227.423 * [backup-simplify]: Simplify (/ -2 1) into -2 227.424 * [backup-simplify]: Simplify (log -2) into (log -2) 227.424 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 227.424 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 227.425 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 227.425 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 227.426 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 227.426 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 227.426 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 227.426 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 227.426 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 227.426 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 227.426 * [taylor]: Taking taylor expansion of 1/2 in n 227.426 * [backup-simplify]: Simplify 1/2 into 1/2 227.426 * [taylor]: Taking taylor expansion of (/ 1 k) in n 227.426 * [taylor]: Taking taylor expansion of k in n 227.426 * [backup-simplify]: Simplify k into k 227.426 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 227.426 * [taylor]: Taking taylor expansion of 1/2 in n 227.426 * [backup-simplify]: Simplify 1/2 into 1/2 227.426 * [taylor]: Taking taylor expansion of (log PI) in n 227.426 * [taylor]: Taking taylor expansion of PI in n 227.426 * [backup-simplify]: Simplify PI into PI 227.427 * [backup-simplify]: Simplify (log PI) into (log PI) 227.427 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 227.427 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 227.428 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 227.428 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 227.429 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 227.429 * [backup-simplify]: Simplify (/ +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 227.430 * [backup-simplify]: Simplify (/ +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 227.431 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 227.434 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 227.434 * [backup-simplify]: Simplify (+ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 227.435 * [backup-simplify]: Simplify (- (/ +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 227.435 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 227.435 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 227.435 * [taylor]: Taking taylor expansion of +nan.0 in n 227.435 * [backup-simplify]: Simplify +nan.0 into +nan.0 227.435 * [taylor]: Taking taylor expansion of (/ 1 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 227.436 * [taylor]: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 227.436 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 227.436 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 227.436 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 227.436 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 227.436 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 227.436 * [taylor]: Taking taylor expansion of 1/2 in n 227.436 * [backup-simplify]: Simplify 1/2 into 1/2 227.436 * [taylor]: Taking taylor expansion of (/ 1 k) in n 227.436 * [taylor]: Taking taylor expansion of k in n 227.436 * [backup-simplify]: Simplify k into k 227.436 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 227.436 * [taylor]: Taking taylor expansion of 1/2 in n 227.436 * [backup-simplify]: Simplify 1/2 into 1/2 227.436 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 227.436 * [taylor]: Taking taylor expansion of (/ -2 n) in n 227.436 * [taylor]: Taking taylor expansion of -2 in n 227.436 * [backup-simplify]: Simplify -2 into -2 227.436 * [taylor]: Taking taylor expansion of n in n 227.436 * [backup-simplify]: Simplify 0 into 0 227.436 * [backup-simplify]: Simplify 1 into 1 227.437 * [backup-simplify]: Simplify (/ -2 1) into -2 227.437 * [backup-simplify]: Simplify (log -2) into (log -2) 227.437 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 227.437 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 227.438 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 227.439 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 227.440 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 227.440 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 227.440 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 227.440 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 227.440 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 227.440 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 227.440 * [taylor]: Taking taylor expansion of 1/2 in n 227.440 * [backup-simplify]: Simplify 1/2 into 1/2 227.440 * [taylor]: Taking taylor expansion of (/ 1 k) in n 227.440 * [taylor]: Taking taylor expansion of k in n 227.440 * [backup-simplify]: Simplify k into k 227.440 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 227.440 * [taylor]: Taking taylor expansion of 1/2 in n 227.440 * [backup-simplify]: Simplify 1/2 into 1/2 227.440 * [taylor]: Taking taylor expansion of (log PI) in n 227.440 * [taylor]: Taking taylor expansion of PI in n 227.440 * [backup-simplify]: Simplify PI into PI 227.441 * [backup-simplify]: Simplify (log PI) into (log PI) 227.441 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 227.441 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 227.442 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 227.442 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 227.443 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 227.444 * [backup-simplify]: Simplify (/ 1 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ 1 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 227.444 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (/ +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 227.445 * [backup-simplify]: Simplify (- (/ +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (/ 1 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 227.449 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (/ 1 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 227.451 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 227.451 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 227.452 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 227.452 * [backup-simplify]: Simplify (+ 0 0) into 0 227.453 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log PI))) into 0 227.455 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 227.456 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0 227.457 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 227.458 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 227.458 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 227.459 * [backup-simplify]: Simplify (+ 0 0) into 0 227.459 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 227.460 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -2) (log n)))) into 0 227.461 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 227.462 * [backup-simplify]: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 227.464 * [backup-simplify]: Simplify (- (/ 0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) into 0 227.464 * [backup-simplify]: Simplify 0 into 0 227.465 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 227.470 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 227.471 * [backup-simplify]: Simplify (+ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 227.472 * [backup-simplify]: Simplify (- (/ +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (* (- (* +nan.0 (/ 1 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) (/ 0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 227.472 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 227.472 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 227.472 * [taylor]: Taking taylor expansion of +nan.0 in n 227.472 * [backup-simplify]: Simplify +nan.0 into +nan.0 227.472 * [taylor]: Taking taylor expansion of (/ 1 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 227.472 * [taylor]: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 227.472 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 227.472 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 227.472 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 227.472 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 227.472 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 227.472 * [taylor]: Taking taylor expansion of 1/2 in n 227.472 * [backup-simplify]: Simplify 1/2 into 1/2 227.472 * [taylor]: Taking taylor expansion of (/ 1 k) in n 227.472 * [taylor]: Taking taylor expansion of k in n 227.472 * [backup-simplify]: Simplify k into k 227.472 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 227.473 * [taylor]: Taking taylor expansion of 1/2 in n 227.473 * [backup-simplify]: Simplify 1/2 into 1/2 227.473 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 227.473 * [taylor]: Taking taylor expansion of (/ -2 n) in n 227.473 * [taylor]: Taking taylor expansion of -2 in n 227.473 * [backup-simplify]: Simplify -2 into -2 227.473 * [taylor]: Taking taylor expansion of n in n 227.473 * [backup-simplify]: Simplify 0 into 0 227.473 * [backup-simplify]: Simplify 1 into 1 227.473 * [backup-simplify]: Simplify (/ -2 1) into -2 227.474 * [backup-simplify]: Simplify (log -2) into (log -2) 227.474 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 227.474 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 227.475 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 227.475 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 227.476 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 227.476 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 227.476 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 227.476 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 227.476 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 227.476 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 227.476 * [taylor]: Taking taylor expansion of 1/2 in n 227.476 * [backup-simplify]: Simplify 1/2 into 1/2 227.476 * [taylor]: Taking taylor expansion of (/ 1 k) in n 227.476 * [taylor]: Taking taylor expansion of k in n 227.476 * [backup-simplify]: Simplify k into k 227.476 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 227.476 * [taylor]: Taking taylor expansion of 1/2 in n 227.476 * [backup-simplify]: Simplify 1/2 into 1/2 227.476 * [taylor]: Taking taylor expansion of (log PI) in n 227.476 * [taylor]: Taking taylor expansion of PI in n 227.476 * [backup-simplify]: Simplify PI into PI 227.477 * [backup-simplify]: Simplify (log PI) into (log PI) 227.477 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 227.477 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 227.477 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 227.478 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 227.479 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 227.479 * [backup-simplify]: Simplify (/ 1 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ 1 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 227.480 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (/ +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 227.481 * [backup-simplify]: Simplify (- (/ +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (/ 1 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 227.481 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (/ 1 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 227.483 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ 1 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))))) (* 1 (/ 1 (- k)))) (/ +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))))) into (- (+ (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 k))) (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow k 2))))) (- (+ (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 k))) (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) k)))) (- (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k))))))))))) 227.483 * * * [progress]: simplifying candidates 227.483 * * * * [progress]: [ 1 / 1023 ] simplifiying candidate # 227.483 * * * * [progress]: [ 2 / 1023 ] simplifiying candidate # 227.483 * * * * [progress]: [ 3 / 1023 ] simplifiying candidate # 227.484 * * * * [progress]: [ 4 / 1023 ] simplifiying candidate # 227.484 * * * * [progress]: [ 5 / 1023 ] simplifiying candidate # 227.484 * * * * [progress]: [ 6 / 1023 ] simplifiying candidate # 227.484 * * * * [progress]: [ 7 / 1023 ] 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1023 ] simplifiying candidate # 227.487 * * * * [progress]: [ 67 / 1023 ] simplifiying candidate # 227.487 * * * * [progress]: [ 68 / 1023 ] simplifiying candidate # 227.487 * * * * [progress]: [ 69 / 1023 ] simplifiying candidate # 227.487 * * * * [progress]: [ 70 / 1023 ] simplifiying candidate # 227.487 * * * * [progress]: [ 71 / 1023 ] simplifiying candidate # 227.487 * * * * [progress]: [ 72 / 1023 ] simplifiying candidate # 227.487 * * * * [progress]: [ 73 / 1023 ] simplifiying candidate # 227.487 * * * * [progress]: [ 74 / 1023 ] simplifiying candidate # 227.487 * * * * [progress]: [ 75 / 1023 ] simplifiying candidate # 227.487 * * * * [progress]: [ 76 / 1023 ] simplifiying candidate # 227.487 * * * * [progress]: [ 77 / 1023 ] simplifiying candidate # 227.487 * * * * [progress]: [ 78 / 1023 ] simplifiying candidate # 227.487 * * * * [progress]: [ 79 / 1023 ] simplifiying candidate # 227.487 * * * * [progress]: [ 80 / 1023 ] simplifiying candidate # 227.487 * * * * [progress]: [ 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227.489 * * * * [progress]: [ 111 / 1023 ] simplifiying candidate # 227.489 * * * * [progress]: [ 112 / 1023 ] simplifiying candidate # 227.489 * * * * [progress]: [ 113 / 1023 ] simplifiying candidate # 227.489 * * * * [progress]: [ 114 / 1023 ] simplifiying candidate # 227.489 * * * * [progress]: [ 115 / 1023 ] simplifiying candidate # 227.489 * * * * [progress]: [ 116 / 1023 ] simplifiying candidate # 227.489 * * * * [progress]: [ 117 / 1023 ] simplifiying candidate # 227.489 * * * * [progress]: [ 118 / 1023 ] simplifiying candidate # 227.489 * * * * [progress]: [ 119 / 1023 ] simplifiying candidate # 227.489 * * * * [progress]: [ 120 / 1023 ] simplifiying candidate # 227.489 * * * * [progress]: [ 121 / 1023 ] simplifiying candidate # 227.489 * * * * [progress]: [ 122 / 1023 ] simplifiying candidate # 227.489 * * * * [progress]: [ 123 / 1023 ] simplifiying candidate # 227.489 * * * * [progress]: [ 124 / 1023 ] simplifiying candidate # 227.489 * * * * [progress]: [ 125 / 1023 ] simplifiying candidate # 227.490 * * * * [progress]: [ 126 / 1023 ] simplifiying candidate # 227.490 * * * * [progress]: [ 127 / 1023 ] simplifiying candidate # 227.490 * * * * [progress]: [ 128 / 1023 ] simplifiying candidate # 227.490 * * * * [progress]: [ 129 / 1023 ] simplifiying candidate # 227.490 * * * * [progress]: [ 130 / 1023 ] simplifiying candidate #real (real->posit16 (pow PI (- 1/2 (/ k 2)))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))))> 227.490 * * * * [progress]: [ 131 / 1023 ] simplifiying candidate # 227.490 * * * * [progress]: [ 132 / 1023 ] simplifiying candidate # 227.490 * * * * [progress]: [ 133 / 1023 ] simplifiying candidate # 227.490 * * * * [progress]: [ 134 / 1023 ] simplifiying candidate # 227.490 * * * * [progress]: [ 135 / 1023 ] simplifiying candidate # 227.490 * * * * [progress]: [ 136 / 1023 ] simplifiying candidate # 227.490 * * * * [progress]: [ 137 / 1023 ] simplifiying candidate # 227.490 * * * * [progress]: [ 138 / 1023 ] simplifiying candidate # 227.490 * * * * [progress]: [ 139 / 1023 ] simplifiying candidate # 227.490 * * * * [progress]: [ 140 / 1023 ] simplifiying candidate # 227.490 * * * * [progress]: [ 141 / 1023 ] simplifiying candidate # 227.490 * * * * [progress]: [ 142 / 1023 ] simplifiying candidate # 227.490 * * * * [progress]: [ 143 / 1023 ] simplifiying candidate # 227.490 * * * * [progress]: [ 144 / 1023 ] simplifiying candidate # 227.491 * * * * [progress]: [ 145 / 1023 ] simplifiying candidate # 227.491 * * * * [progress]: [ 146 / 1023 ] simplifiying candidate # 227.491 * * * * [progress]: [ 147 / 1023 ] simplifiying candidate # 227.491 * * * * [progress]: [ 148 / 1023 ] simplifiying candidate # 227.491 * * * * [progress]: [ 149 / 1023 ] simplifiying candidate # 227.491 * * * * [progress]: [ 150 / 1023 ] simplifiying candidate # 227.491 * * * * [progress]: [ 151 / 1023 ] simplifiying candidate # 227.491 * * * * [progress]: [ 152 / 1023 ] simplifiying candidate # 227.491 * * * * [progress]: [ 153 / 1023 ] 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(cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (pow (* n 2) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow (* n 2) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* n 2) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (pow (* n 2) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 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(sqrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (pow (* n 2) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (pow (* n 2) (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) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* n 2) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (pow (* n 2) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow (* n 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(fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ (sqrt 1) (pow PI (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ (sqrt 1) (pow 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))))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ (sqrt 1) (pow PI (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ (sqrt 1) (pow PI (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ (sqrt 1) (pow PI (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ (sqrt 1) (pow PI (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ (sqrt 1) (pow PI (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ (sqrt 1) (pow PI (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ (sqrt 1) (pow PI (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ (sqrt 1) (pow PI (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ (sqrt 1) (pow PI (fma (- (/ k 2)) 1 (* (/ k 2) 1)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ (sqrt 1) (pow PI (fma (- (/ 1 2)) k (* (/ 1 2) k)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ (sqrt 1) (pow PI (- (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ (sqrt 1) (pow PI (- (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ (sqrt 1) (pow (cbrt PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ (sqrt 1) (pow (sqrt PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ (sqrt 1) (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ (sqrt 1) (cbrt (pow PI (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ (sqrt 1) (sqrt (pow PI (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ (sqrt 1) (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ (sqrt 1) (pow PI (/ (- 1/2 (/ k 2)) 2))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ 1 (pow PI (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ 1 (pow PI (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ 1 (pow 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))))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ 1 (pow PI (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ 1 (pow PI (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ 1 (pow PI (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ 1 (pow PI (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ 1 (pow PI (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ 1 (pow PI (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ 1 (pow PI (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ 1 (pow PI (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ 1 (pow PI (fma (- (/ k 2)) 1 (* (/ k 2) 1)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ 1 (pow PI (fma (- (/ 1 2)) k (* (/ 1 2) k)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ 1 (pow PI (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ 1 (pow PI (fma (- (sqrt (/ k 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(/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ 1 (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ 1 (cbrt (pow PI (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ 1 (sqrt (pow PI (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ 1 (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ 1 (pow PI (/ (- 1/2 (/ k 2)) 2))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ 1 (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ 1 (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (pow PI (/ k 2)) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ 1 (pow PI (- 1/2 (/ k 2)))) (sqrt k)) (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (real->posit16 (* (/ 1 (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))) (- (+ (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (+ (* 1/4 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (* 1/8 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k))) (* 1/2 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k))))) (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) (pow PI (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))) (- (+ (* +nan.0 (* (sqrt 1/2) k)) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2))))) (- (+ (* +nan.0 (* n (* (sqrt 1/2) k))) (- (+ (* +nan.0 (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log n))))) (- (* +nan.0 (* (sqrt 1/2) (pow k 2)))))))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) k))) (- (* +nan.0 (/ 1 (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k))))))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) k))) (- (+ (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))))) (- (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow k 2))))))))) (- (+ (* +nan.0 (/ k (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ (* (log n) (pow k 2)) (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ (* (log PI) (pow k 2)) (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ (* n k) (* (sqrt 2) (pow PI 2)))) (- (+ (* +nan.0 (/ (pow k 2) (* (sqrt 2) PI))) (- (* +nan.0 (/ (* (log 2) (pow k 2)) (* (sqrt 2) PI)))))))))))))) (- (+ (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 k))) (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) k)))) (- (+ (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 k))) (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k))))))) (- (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 k))) (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow k 2)))))))))) (- (+ (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 k))) (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow k 2))))) (- (+ (* +nan.0 (/ 1 (* (pow PI (- 1/2 (* 1/2 k))) (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) k)))) (- (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k))))))))))) 227.591 * * [simplify]: iteration 1: (1264 enodes) 229.501 * * [simplify]: Extracting #0: cost 638 inf + 0 229.506 * * [simplify]: Extracting #1: cost 1557 inf + 2 229.512 * * [simplify]: Extracting #2: cost 1747 inf + 1959 229.522 * * [simplify]: Extracting #3: cost 1713 inf + 41518 229.557 * * [simplify]: Extracting #4: cost 1381 inf + 193337 229.610 * * [simplify]: Extracting #5: cost 861 inf + 453760 229.734 * * [simplify]: Extracting #6: cost 501 inf + 692691 229.852 * * [simplify]: Extracting #7: cost 142 inf + 952000 229.999 * * [simplify]: Extracting #8: cost 36 inf + 1029466 230.140 * * [simplify]: Extracting #9: cost 13 inf + 1042601 230.289 * * [simplify]: Extracting #10: cost 2 inf + 1053369 230.450 * * [simplify]: Extracting #11: cost 0 inf + 1055124 230.637 * [simplify]: Simplified to: (expm1 (pow (* n 2) (- 1/2 (/ k 2)))) (log1p (pow (* n 2) (- 1/2 (/ k 2)))) (* (log (* n 2)) (- 1/2 (/ k 2))) (* (log (* n 2)) (- 1/2 (/ k 2))) (* (log (* n 2)) (- 1/2 (/ k 2))) (- 1/2 (/ k 2)) (- 1/2 (/ k 2)) (sqrt (* n 2)) (pow (* n 2) (/ k 2)) (pow (* n 2) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* n 2) (sqrt (- 1/2 (/ k 2)))) (* n 2) (pow (* n 2) (+ (sqrt (/ k 2)) (sqrt 1/2))) (pow (* n 2) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2))) (* n 2) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (* (cbrt (/ k 2)) (cbrt (/ k 2))) (cbrt (/ k 2)))))) (pow (* n 2) (+ (- (* (* (cbrt (/ k 2)) (cbrt (/ k 2))) (cbrt (/ k 2)))) (* (* (cbrt (/ k 2)) (cbrt (/ k 2))) (cbrt (/ k 2))))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (/ k 2)))) (pow (* n 2) (+ (- (/ k 2)) (/ k 2))) (pow (* n 2) (fma (* (cbrt 1/2) 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k 2))))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (+ (- (* (* (cbrt (/ k 2)) (cbrt (/ k 2))) (cbrt (/ k 2)))) (* (* (cbrt (/ k 2)) (cbrt (/ k 2))) (cbrt (/ k 2)))))) (/ (* (/ 1 (pow PI (+ (- (/ k 2)) (/ k 2)))) (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (+ (- (* (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))) (/ (cbrt k) (cbrt 2)))) (* (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))) (/ (cbrt k) (cbrt 2)))))) (* (/ 1 (pow PI (fma (/ (- (cbrt k)) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (/ (cbrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (fma (- (/ (cbrt k) 2)) (* (cbrt k) (cbrt k)) (* (* (cbrt k) (cbrt k)) (/ (cbrt k) 2))))) (* (/ 1 (pow PI (+ (* (/ (sqrt k) (cbrt 2)) (- (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)))) (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (/ (sqrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* n 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(/ 1 (pow PI (- (/ k 2))))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow (cbrt PI) (- 1/2 (/ k 2)))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (- 1/2 (/ k 2)))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (cbrt (pow PI (- 1/2 (/ k 2))))) (* (/ 1 (sqrt (pow PI (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (- 1/2 (/ k 2)))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (- 1/4 (/ (/ k 2) 2)))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (+ (- (* (* (cbrt (/ k 2)) (cbrt (/ k 2))) (cbrt (/ k 2)))) (* (* (cbrt (/ k 2)) (cbrt (/ k 2))) (cbrt (/ k 2)))))) (/ (* (/ 1 (pow PI (+ (- (/ k 2)) (/ k 2)))) (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (+ (- (* (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))) (/ (cbrt k) (cbrt 2)))) (* (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))) (/ (cbrt k) (cbrt 2)))))) (* (/ 1 (pow PI (fma (/ (- (cbrt k)) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (/ (cbrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (fma (- (/ (cbrt k) 2)) (* (cbrt k) (cbrt k)) (* (* (cbrt k) (cbrt k)) (/ (cbrt k) 2))))) (* (/ 1 (pow PI (+ (* (/ (sqrt k) (cbrt 2)) (- (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)))) (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (/ (sqrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (fma (- (/ (sqrt k) 2)) (sqrt k) (/ (* (sqrt k) (sqrt k)) 2)))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (+ (* (/ k (cbrt 2)) (- (/ (/ 1 (cbrt 2)) (cbrt 2)))) (* (/ (/ 1 (cbrt 2)) (cbrt 2)) (/ k (cbrt 2)))))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (/ (* (/ 1 (pow PI (fma (- (/ k 2)) 1 (/ k 2)))) (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) (/ (* (/ 1 (pow PI (fma (- (/ k 2)) 1 (/ k 2)))) (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) (* (/ 1 (pow PI (+ (- (* k 1/2)) (* k 1/2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (+ (- (* (* (cbrt (/ k 2)) (cbrt (/ k 2))) (cbrt (/ k 2)))) (* (* (cbrt (/ k 2)) (cbrt (/ k 2))) (cbrt (/ k 2)))))) (/ (* (/ 1 (pow PI (+ (- (/ k 2)) (/ k 2)))) (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (+ (- (* (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))) (/ (cbrt k) (cbrt 2)))) (* (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))) (/ (cbrt k) (cbrt 2)))))) (* (/ 1 (pow PI (fma (/ (- (cbrt k)) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (/ (cbrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (fma (- (/ (cbrt k) 2)) (* (cbrt k) (cbrt k)) (* (* (cbrt k) (cbrt k)) (/ (cbrt k) 2))))) (* (/ 1 (pow PI (+ (* (/ (sqrt k) (cbrt 2)) (- (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)))) (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (/ (sqrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (fma (- (/ (sqrt k) 2)) (sqrt k) (/ (* (sqrt k) (sqrt k)) 2)))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (+ (* (/ k (cbrt 2)) (- (/ (/ 1 (cbrt 2)) (cbrt 2)))) (* (/ (/ 1 (cbrt 2)) (cbrt 2)) (/ k (cbrt 2)))))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (/ (* (/ 1 (pow PI (fma (- (/ k 2)) 1 (/ k 2)))) (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) (/ (* (/ 1 (pow PI (fma (- (/ k 2)) 1 (/ k 2)))) (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) (* (/ 1 (pow PI (+ (- (* k 1/2)) (* k 1/2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (+ (- (* (* (cbrt (/ k 2)) (cbrt (/ k 2))) (cbrt (/ k 2)))) (* (* (cbrt (/ k 2)) (cbrt (/ k 2))) (cbrt (/ k 2)))))) (/ (* (/ 1 (pow PI (+ (- (/ k 2)) (/ k 2)))) (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (+ (- (* (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))) (/ (cbrt k) (cbrt 2)))) (* (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))) (/ (cbrt k) (cbrt 2)))))) (* (/ 1 (pow PI (fma (/ (- (cbrt k)) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (/ (cbrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (fma (- (/ (cbrt k) 2)) (* (cbrt k) (cbrt k)) (* (* (cbrt k) (cbrt k)) (/ (cbrt k) 2))))) (* (/ 1 (pow PI (+ (* (/ (sqrt k) (cbrt 2)) (- (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)))) (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (/ (sqrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (fma (- (/ (sqrt k) 2)) (sqrt k) (/ (* (sqrt k) (sqrt k)) 2)))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (+ (* (/ k (cbrt 2)) (- (/ (/ 1 (cbrt 2)) (cbrt 2)))) (* (/ (/ 1 (cbrt 2)) (cbrt 2)) (/ k (cbrt 2)))))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (/ (* (/ 1 (pow PI (fma (- (/ k 2)) 1 (/ k 2)))) (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) (/ (* (/ 1 (pow PI (fma (- (/ k 2)) 1 (/ k 2)))) (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) (* (/ 1 (pow PI (+ (- (* k 1/2)) (* k 1/2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (* (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))) (/ 1 (pow PI (- (/ k 2))))) (* (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))) (/ 1 (pow PI (- (/ k 2))))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow (cbrt PI) (- 1/2 (/ k 2)))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (- 1/2 (/ k 2)))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (cbrt (pow PI (- 1/2 (/ k 2))))) (* (/ 1 (sqrt (pow PI (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (- 1/2 (/ k 2)))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (- 1/4 (/ (/ k 2) 2)))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (- 1/2 (/ k 2)))) (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (- 1/2 (/ k 2)))) (/ (* (pow PI (/ k 2)) (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) (/ (* 1 (sqrt k)) (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))) (real->posit16 (/ (* 1 (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))) (pow PI (- 1/2 (/ k 2))))) (- (+ (fma 1/8 (* (* (log 2) (log 2)) (* (exp (* (log (* n 2)) 1/2)) (* k k))) (fma 1/4 (* (* (log 2) (exp (* (log (* n 2)) 1/2))) (* (log n) (* k k))) (* (* (exp (* (log (* n 2)) 1/2)) (* (* k k) (* (log n) (log n)))) 1/8))) (exp (* (log (* n 2)) 1/2))) (* 1/2 (+ (* (exp (* (log (* n 2)) 1/2)) (* k (log n))) (* (* (exp (* (log (* n 2)) 1/2)) k) (log 2))))) (exp (* (- (log 2) (- (log n))) (- 1/2 (* k 1/2)))) (exp (* (- 1/2 (* k 1/2)) (- (log -2) (log (/ -1 n))))) (- (+ (* (* (* (log PI) (log PI)) (* (* k k) (sqrt PI))) 1/8) (sqrt PI)) (* 1/2 (* (sqrt PI) (* k (log PI))))) (pow PI (- 1/2 (* k 1/2))) (pow PI (- 1/2 (* k 1/2))) (- (- (* (* k (sqrt 1/2)) +nan.0) (- (* (* (* (log 2) (sqrt 2)) (* (* k k) (* (sqrt 1/2) (sqrt 1/2)))) +nan.0) (- (* (* (* k (sqrt 1/2)) n) +nan.0) (- (* (* +nan.0 (sqrt 2)) (* (* (* (sqrt 1/2) (sqrt 1/2)) (log n)) (* k k))) (* (* +nan.0 (sqrt 1/2)) (* k k))))))) (- (- (* +nan.0 (/ (exp (- (* (- (log 2) (- (log n))) (- 1/2 (* k 1/2))))) (* k k))) (- (* (/ (exp (- (* (- (log 2) (- (log n))) (- 1/2 (* k 1/2))))) k) +nan.0) (* (exp (- (* (- (log 2) (- (log n))) (- 1/2 (* k 1/2))))) +nan.0)))) (- (- (* +nan.0 (/ (exp (- (* (- 1/2 (* k 1/2)) (- (log -2) (log (/ -1 n)))))) k)) (- (* +nan.0 (exp (- (* (- 1/2 (* k 1/2)) (- (log -2) (log (/ -1 n))))))) (* +nan.0 (/ (exp (- (* (- 1/2 (* k 1/2)) (- (log -2) (log (/ -1 n)))))) (* k k)))))) (- (- (* (/ (/ k (sqrt 2)) PI) +nan.0) (- (* +nan.0 (/ (* (log n) (* k k)) (* PI (sqrt 2)))) (- (* +nan.0 (* (/ (log PI) (sqrt 2)) (/ (* k k) PI))) (- (* (/ (/ (* k n) (sqrt 2)) (* PI PI)) +nan.0) (- (* +nan.0 (/ (* k k) (* PI (sqrt 2)))) (* (/ (log 2) (/ (* PI (sqrt 2)) (* k k))) +nan.0))))))) (- (- (* +nan.0 (/ (/ 1 (pow PI (- 1/2 (* k 1/2)))) (* (exp (* (- (log 2) (- (log n))) (- 1/2 (* k 1/2)))) k))) (- (/ (* +nan.0 1) (* (exp (* (- (log 2) (- (log n))) (- 1/2 (* k 1/2)))) (pow PI (- 1/2 (* k 1/2))))) (/ (* +nan.0 1) (* (* (* k k) (exp (* (- (log 2) (- (log n))) (- 1/2 (* k 1/2))))) (pow PI (- 1/2 (* k 1/2)))))))) (- (- (* (/ (/ 1 (pow PI (- 1/2 (* k 1/2)))) (* (* k k) (exp (* (- 1/2 (* k 1/2)) (- (log -2) (log (/ -1 n))))))) +nan.0) (- (/ (* +nan.0 1) (* (* k (exp (* (- 1/2 (* k 1/2)) (- (log -2) (log (/ -1 n)))))) (pow PI (- 1/2 (* k 1/2))))) (* +nan.0 (/ (exp (- (* (- 1/2 (* k 1/2)) (- (log -2) (log (/ -1 n)))))) (pow PI (- 1/2 (* k 1/2)))))))) 230.883 * * * [progress]: adding candidates to table 245.074 * * [progress]: iteration 4 / 4 245.074 * * * [progress]: picking best candidate 245.105 * * * * [pick]: Picked # 245.105 * * * [progress]: localizing error 245.140 * * * [progress]: generating rewritten candidates 245.140 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 1 2 2) 245.147 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1 2) 245.153 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2) 245.170 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2) 245.289 * * * [progress]: generating series expansions 245.289 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 1 2 2) 245.289 * [backup-simplify]: Simplify (pow n (- 1/2 (/ k 2))) into (pow n (- 1/2 (* 1/2 k))) 245.289 * [approximate]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in (n k) around 0 245.289 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 245.289 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 245.289 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 245.289 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 245.289 * [taylor]: Taking taylor expansion of 1/2 in k 245.289 * [backup-simplify]: Simplify 1/2 into 1/2 245.289 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 245.289 * [taylor]: Taking taylor expansion of 1/2 in k 245.289 * [backup-simplify]: Simplify 1/2 into 1/2 245.289 * [taylor]: Taking taylor expansion of k in k 245.289 * [backup-simplify]: Simplify 0 into 0 245.289 * [backup-simplify]: Simplify 1 into 1 245.289 * [taylor]: Taking taylor expansion of (log n) in k 245.289 * [taylor]: Taking taylor expansion of n in k 245.289 * [backup-simplify]: Simplify n into n 245.289 * [backup-simplify]: Simplify (log n) into (log n) 245.290 * [backup-simplify]: Simplify (* 1/2 0) into 0 245.290 * [backup-simplify]: Simplify (- 0) into 0 245.290 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 245.290 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 245.290 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 245.290 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 245.290 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 245.290 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 245.290 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 245.290 * [taylor]: Taking taylor expansion of 1/2 in n 245.290 * [backup-simplify]: Simplify 1/2 into 1/2 245.290 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 245.290 * [taylor]: Taking taylor expansion of 1/2 in n 245.290 * [backup-simplify]: Simplify 1/2 into 1/2 245.290 * [taylor]: Taking taylor expansion of k in n 245.290 * [backup-simplify]: Simplify k into k 245.291 * [taylor]: Taking taylor expansion of (log n) in n 245.291 * [taylor]: Taking taylor expansion of n in n 245.291 * [backup-simplify]: Simplify 0 into 0 245.291 * [backup-simplify]: Simplify 1 into 1 245.291 * [backup-simplify]: Simplify (log 1) into 0 245.291 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 245.291 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 245.291 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 245.291 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 245.291 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 245.291 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 245.291 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 245.291 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 245.291 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 245.291 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 245.291 * [taylor]: Taking taylor expansion of 1/2 in n 245.291 * [backup-simplify]: Simplify 1/2 into 1/2 245.291 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 245.291 * [taylor]: Taking taylor expansion of 1/2 in n 245.292 * [backup-simplify]: Simplify 1/2 into 1/2 245.292 * [taylor]: Taking taylor expansion of k in n 245.292 * [backup-simplify]: Simplify k into k 245.292 * [taylor]: Taking taylor expansion of (log n) in n 245.292 * [taylor]: Taking taylor expansion of n in n 245.292 * [backup-simplify]: Simplify 0 into 0 245.292 * [backup-simplify]: Simplify 1 into 1 245.292 * [backup-simplify]: Simplify (log 1) into 0 245.292 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 245.292 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 245.292 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 245.292 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 245.292 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 245.292 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 245.292 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 245.293 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 245.293 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 245.293 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 245.293 * [taylor]: Taking taylor expansion of 1/2 in k 245.293 * [backup-simplify]: Simplify 1/2 into 1/2 245.293 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 245.293 * [taylor]: Taking taylor expansion of 1/2 in k 245.293 * [backup-simplify]: Simplify 1/2 into 1/2 245.293 * [taylor]: Taking taylor expansion of k in k 245.293 * [backup-simplify]: Simplify 0 into 0 245.293 * [backup-simplify]: Simplify 1 into 1 245.293 * [taylor]: Taking taylor expansion of (log n) in k 245.293 * [taylor]: Taking taylor expansion of n in k 245.293 * [backup-simplify]: Simplify n into n 245.293 * [backup-simplify]: Simplify (log n) into (log n) 245.293 * [backup-simplify]: Simplify (* 1/2 0) into 0 245.294 * [backup-simplify]: Simplify (- 0) into 0 245.294 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 245.294 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 245.294 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 245.294 * [backup-simplify]: Simplify (pow n 1/2) into (pow n 1/2) 245.295 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 245.295 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 245.295 * [backup-simplify]: Simplify (- 0) into 0 245.296 * [backup-simplify]: Simplify (+ 0 0) into 0 245.296 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 245.296 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log n))) into 0 245.296 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 245.296 * [taylor]: Taking taylor expansion of 0 in k 245.296 * [backup-simplify]: Simplify 0 into 0 245.296 * [backup-simplify]: Simplify 0 into 0 245.297 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 245.297 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 245.298 * [backup-simplify]: Simplify (- 1/2) into -1/2 245.298 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 245.298 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log n))) into (- (* 1/2 (log n))) 245.298 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n))) 245.298 * [backup-simplify]: Simplify (* -1/2 (* (sqrt n) (log n))) into (* -1/2 (* (sqrt n) (log n))) 245.300 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 245.301 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 245.301 * [backup-simplify]: Simplify (- 0) into 0 245.301 * [backup-simplify]: Simplify (+ 0 0) into 0 245.301 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 245.302 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0 245.303 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 245.303 * [taylor]: Taking taylor expansion of 0 in k 245.303 * [backup-simplify]: Simplify 0 into 0 245.303 * [backup-simplify]: Simplify 0 into 0 245.303 * [backup-simplify]: Simplify 0 into 0 245.304 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 245.304 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 245.305 * [backup-simplify]: Simplify (- 0) into 0 245.305 * [backup-simplify]: Simplify (+ 0 0) into 0 245.305 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log n)))) into 0 245.306 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2))) 245.306 * [backup-simplify]: Simplify (* 1/8 (* (sqrt n) (pow (log n) 2))) into (* 1/8 (* (sqrt n) (pow (log n) 2))) 245.306 * [backup-simplify]: Simplify (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (pow (* k 1) 2)) (+ (* (* -1/2 (* (sqrt n) (log n))) (* k 1)) (pow n 1/2))) into (- (+ (pow n 1/2) (* 1/8 (* (sqrt n) (* (pow (log n) 2) (pow k 2))))) (* 1/2 (* (sqrt n) (* (log n) k)))) 245.307 * [backup-simplify]: Simplify (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 245.307 * [approximate]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 245.307 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 245.307 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in k 245.307 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in k 245.307 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 245.307 * [taylor]: Taking taylor expansion of 1/2 in k 245.307 * [backup-simplify]: Simplify 1/2 into 1/2 245.307 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 245.307 * [taylor]: Taking taylor expansion of 1/2 in k 245.307 * [backup-simplify]: Simplify 1/2 into 1/2 245.307 * [taylor]: Taking taylor expansion of (/ 1 k) in k 245.307 * [taylor]: Taking taylor expansion of k in k 245.307 * [backup-simplify]: Simplify 0 into 0 245.307 * [backup-simplify]: Simplify 1 into 1 245.307 * [backup-simplify]: Simplify (/ 1 1) into 1 245.307 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k 245.307 * [taylor]: Taking taylor expansion of (/ 1 n) in k 245.307 * [taylor]: Taking taylor expansion of n in k 245.307 * [backup-simplify]: Simplify n into n 245.307 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n) 245.307 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n)) 245.308 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 245.308 * [backup-simplify]: Simplify (- 1/2) into -1/2 245.308 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 245.308 * [backup-simplify]: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) 245.308 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 245.308 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 245.308 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 245.308 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 245.308 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 245.308 * [taylor]: Taking taylor expansion of 1/2 in n 245.308 * [backup-simplify]: Simplify 1/2 into 1/2 245.308 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 245.308 * [taylor]: Taking taylor expansion of 1/2 in n 245.308 * [backup-simplify]: Simplify 1/2 into 1/2 245.308 * [taylor]: Taking taylor expansion of (/ 1 k) in n 245.308 * [taylor]: Taking taylor expansion of k in n 245.308 * [backup-simplify]: Simplify k into k 245.308 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 245.309 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 245.309 * [taylor]: Taking taylor expansion of (/ 1 n) in n 245.309 * [taylor]: Taking taylor expansion of n in n 245.309 * [backup-simplify]: Simplify 0 into 0 245.309 * [backup-simplify]: Simplify 1 into 1 245.309 * [backup-simplify]: Simplify (/ 1 1) into 1 245.309 * [backup-simplify]: Simplify (log 1) into 0 245.309 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 245.309 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 245.309 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 245.310 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 245.310 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 245.310 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 245.310 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 245.310 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 245.310 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 245.310 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 245.310 * [taylor]: Taking taylor expansion of 1/2 in n 245.310 * [backup-simplify]: Simplify 1/2 into 1/2 245.310 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 245.310 * [taylor]: Taking taylor expansion of 1/2 in n 245.310 * [backup-simplify]: Simplify 1/2 into 1/2 245.310 * [taylor]: Taking taylor expansion of (/ 1 k) in n 245.310 * [taylor]: Taking taylor expansion of k in n 245.310 * [backup-simplify]: Simplify k into k 245.310 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 245.310 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 245.310 * [taylor]: Taking taylor expansion of (/ 1 n) in n 245.310 * [taylor]: Taking taylor expansion of n in n 245.310 * [backup-simplify]: Simplify 0 into 0 245.310 * [backup-simplify]: Simplify 1 into 1 245.310 * [backup-simplify]: Simplify (/ 1 1) into 1 245.311 * [backup-simplify]: Simplify (log 1) into 0 245.311 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 245.311 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 245.311 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 245.311 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 245.311 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 245.311 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 245.311 * [taylor]: Taking taylor expansion of (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) in k 245.311 * [taylor]: Taking taylor expansion of (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) in k 245.311 * [taylor]: Taking taylor expansion of -1 in k 245.311 * [backup-simplify]: Simplify -1 into -1 245.311 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log n)) in k 245.311 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 245.311 * [taylor]: Taking taylor expansion of 1/2 in k 245.311 * [backup-simplify]: Simplify 1/2 into 1/2 245.311 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 245.311 * [taylor]: Taking taylor expansion of 1/2 in k 245.311 * [backup-simplify]: Simplify 1/2 into 1/2 245.311 * [taylor]: Taking taylor expansion of (/ 1 k) in k 245.311 * [taylor]: Taking taylor expansion of k in k 245.311 * [backup-simplify]: Simplify 0 into 0 245.311 * [backup-simplify]: Simplify 1 into 1 245.312 * [backup-simplify]: Simplify (/ 1 1) into 1 245.312 * [taylor]: Taking taylor expansion of (log n) in k 245.312 * [taylor]: Taking taylor expansion of n in k 245.312 * [backup-simplify]: Simplify n into n 245.312 * [backup-simplify]: Simplify (log n) into (log n) 245.312 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 245.312 * [backup-simplify]: Simplify (- 1/2) into -1/2 245.313 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 245.313 * [backup-simplify]: Simplify (* -1/2 (log n)) into (* -1/2 (log n)) 245.313 * [backup-simplify]: Simplify (* -1 (* -1/2 (log n))) into (* 1/2 (log n)) 245.313 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 245.313 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 245.313 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 245.314 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 245.314 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 245.315 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 245.315 * [backup-simplify]: Simplify (- 0) into 0 245.315 * [backup-simplify]: Simplify (+ 0 0) into 0 245.315 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 245.316 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 245.316 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 245.316 * [taylor]: Taking taylor expansion of 0 in k 245.316 * [backup-simplify]: Simplify 0 into 0 245.316 * [backup-simplify]: Simplify 0 into 0 245.316 * [backup-simplify]: Simplify 0 into 0 245.317 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 245.318 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 245.319 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 245.319 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 245.319 * [backup-simplify]: Simplify (- 0) into 0 245.320 * [backup-simplify]: Simplify (+ 0 0) into 0 245.320 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 245.320 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 245.321 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 245.321 * [taylor]: Taking taylor expansion of 0 in k 245.321 * [backup-simplify]: Simplify 0 into 0 245.321 * [backup-simplify]: Simplify 0 into 0 245.321 * [backup-simplify]: Simplify 0 into 0 245.321 * [backup-simplify]: Simplify 0 into 0 245.322 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 245.325 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 245.325 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 245.326 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 245.326 * [backup-simplify]: Simplify (- 0) into 0 245.326 * [backup-simplify]: Simplify (+ 0 0) into 0 245.327 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 245.327 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 245.328 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 245.328 * [taylor]: Taking taylor expansion of 0 in k 245.328 * [backup-simplify]: Simplify 0 into 0 245.328 * [backup-simplify]: Simplify 0 into 0 245.329 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) into (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) 245.329 * [backup-simplify]: Simplify (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 245.329 * [approximate]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 245.329 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 245.329 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in k 245.329 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in k 245.329 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 245.329 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 245.329 * [taylor]: Taking taylor expansion of 1/2 in k 245.329 * [backup-simplify]: Simplify 1/2 into 1/2 245.329 * [taylor]: Taking taylor expansion of (/ 1 k) in k 245.329 * [taylor]: Taking taylor expansion of k in k 245.329 * [backup-simplify]: Simplify 0 into 0 245.329 * [backup-simplify]: Simplify 1 into 1 245.329 * [backup-simplify]: Simplify (/ 1 1) into 1 245.329 * [taylor]: Taking taylor expansion of 1/2 in k 245.329 * [backup-simplify]: Simplify 1/2 into 1/2 245.329 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k 245.329 * [taylor]: Taking taylor expansion of (/ -1 n) in k 245.329 * [taylor]: Taking taylor expansion of -1 in k 245.329 * [backup-simplify]: Simplify -1 into -1 245.329 * [taylor]: Taking taylor expansion of n in k 245.329 * [backup-simplify]: Simplify n into n 245.329 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n) 245.329 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n)) 245.330 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 245.330 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 245.330 * [backup-simplify]: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) 245.330 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 245.330 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 245.330 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 245.330 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 245.330 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 245.330 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 245.330 * [taylor]: Taking taylor expansion of 1/2 in n 245.330 * [backup-simplify]: Simplify 1/2 into 1/2 245.330 * [taylor]: Taking taylor expansion of (/ 1 k) in n 245.330 * [taylor]: Taking taylor expansion of k in n 245.330 * [backup-simplify]: Simplify k into k 245.330 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 245.330 * [taylor]: Taking taylor expansion of 1/2 in n 245.330 * [backup-simplify]: Simplify 1/2 into 1/2 245.330 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 245.330 * [taylor]: Taking taylor expansion of (/ -1 n) in n 245.330 * [taylor]: Taking taylor expansion of -1 in n 245.330 * [backup-simplify]: Simplify -1 into -1 245.330 * [taylor]: Taking taylor expansion of n in n 245.330 * [backup-simplify]: Simplify 0 into 0 245.330 * [backup-simplify]: Simplify 1 into 1 245.331 * [backup-simplify]: Simplify (/ -1 1) into -1 245.331 * [backup-simplify]: Simplify (log -1) into (log -1) 245.331 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 245.331 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 245.332 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 245.332 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 245.332 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 245.332 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 245.332 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 245.332 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 245.332 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 245.332 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 245.332 * [taylor]: Taking taylor expansion of 1/2 in n 245.333 * [backup-simplify]: Simplify 1/2 into 1/2 245.333 * [taylor]: Taking taylor expansion of (/ 1 k) in n 245.333 * [taylor]: Taking taylor expansion of k in n 245.333 * [backup-simplify]: Simplify k into k 245.333 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 245.333 * [taylor]: Taking taylor expansion of 1/2 in n 245.333 * [backup-simplify]: Simplify 1/2 into 1/2 245.333 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 245.333 * [taylor]: Taking taylor expansion of (/ -1 n) in n 245.333 * [taylor]: Taking taylor expansion of -1 in n 245.333 * [backup-simplify]: Simplify -1 into -1 245.333 * [taylor]: Taking taylor expansion of n in n 245.333 * [backup-simplify]: Simplify 0 into 0 245.333 * [backup-simplify]: Simplify 1 into 1 245.333 * [backup-simplify]: Simplify (/ -1 1) into -1 245.333 * [backup-simplify]: Simplify (log -1) into (log -1) 245.333 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 245.333 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 245.334 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 245.334 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 245.335 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 245.335 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) in k 245.335 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) in k 245.335 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 245.335 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 245.335 * [taylor]: Taking taylor expansion of 1/2 in k 245.335 * [backup-simplify]: Simplify 1/2 into 1/2 245.335 * [taylor]: Taking taylor expansion of (/ 1 k) in k 245.335 * [taylor]: Taking taylor expansion of k in k 245.335 * [backup-simplify]: Simplify 0 into 0 245.335 * [backup-simplify]: Simplify 1 into 1 245.335 * [backup-simplify]: Simplify (/ 1 1) into 1 245.335 * [taylor]: Taking taylor expansion of 1/2 in k 245.335 * [backup-simplify]: Simplify 1/2 into 1/2 245.335 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k 245.335 * [taylor]: Taking taylor expansion of (log -1) in k 245.335 * [taylor]: Taking taylor expansion of -1 in k 245.335 * [backup-simplify]: Simplify -1 into -1 245.336 * [backup-simplify]: Simplify (log -1) into (log -1) 245.336 * [taylor]: Taking taylor expansion of (log n) in k 245.336 * [taylor]: Taking taylor expansion of n in k 245.336 * [backup-simplify]: Simplify n into n 245.336 * [backup-simplify]: Simplify (log n) into (log n) 245.336 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 245.336 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 245.336 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 245.337 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n)) 245.337 * [backup-simplify]: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n))) 245.337 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 245.338 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 245.338 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 245.339 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 245.339 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 245.339 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 245.340 * [backup-simplify]: Simplify (+ 0 0) into 0 245.340 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 245.341 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -1) (log n)))) into 0 245.342 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 245.342 * [taylor]: Taking taylor expansion of 0 in k 245.342 * [backup-simplify]: Simplify 0 into 0 245.342 * [backup-simplify]: Simplify 0 into 0 245.342 * [backup-simplify]: Simplify 0 into 0 245.342 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 245.345 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0 245.345 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 245.345 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 245.346 * [backup-simplify]: Simplify (+ 0 0) into 0 245.346 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 245.347 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0 245.348 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 245.348 * [taylor]: Taking taylor expansion of 0 in k 245.348 * [backup-simplify]: Simplify 0 into 0 245.348 * [backup-simplify]: Simplify 0 into 0 245.348 * [backup-simplify]: Simplify 0 into 0 245.348 * [backup-simplify]: Simplify 0 into 0 245.349 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 245.352 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -1 1)))) 6) into 0 245.352 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 245.353 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 245.354 * [backup-simplify]: Simplify (+ 0 0) into 0 245.354 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 245.355 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -1) (log n)))))) into 0 245.357 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 245.357 * [taylor]: Taking taylor expansion of 0 in k 245.357 * [backup-simplify]: Simplify 0 into 0 245.357 * [backup-simplify]: Simplify 0 into 0 245.357 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) 245.357 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1 2) 245.357 * [backup-simplify]: Simplify (pow PI (- 1/2 (/ k 2))) into (pow PI (- 1/2 (* 1/2 k))) 245.357 * [approximate]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in (k) around 0 245.357 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 245.357 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 245.357 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 245.357 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 245.357 * [taylor]: Taking taylor expansion of 1/2 in k 245.357 * [backup-simplify]: Simplify 1/2 into 1/2 245.357 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 245.357 * [taylor]: Taking taylor expansion of 1/2 in k 245.357 * [backup-simplify]: Simplify 1/2 into 1/2 245.357 * [taylor]: Taking taylor expansion of k in k 245.358 * [backup-simplify]: Simplify 0 into 0 245.358 * [backup-simplify]: Simplify 1 into 1 245.358 * [taylor]: Taking taylor expansion of (log PI) in k 245.358 * [taylor]: Taking taylor expansion of PI in k 245.358 * [backup-simplify]: Simplify PI into PI 245.358 * [backup-simplify]: Simplify (log PI) into (log PI) 245.358 * [backup-simplify]: Simplify (* 1/2 0) into 0 245.359 * [backup-simplify]: Simplify (- 0) into 0 245.359 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 245.360 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 245.361 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 245.361 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 245.361 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 245.361 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 245.361 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 245.361 * [taylor]: Taking taylor expansion of 1/2 in k 245.361 * [backup-simplify]: Simplify 1/2 into 1/2 245.361 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 245.361 * [taylor]: Taking taylor expansion of 1/2 in k 245.361 * [backup-simplify]: Simplify 1/2 into 1/2 245.361 * [taylor]: Taking taylor expansion of k in k 245.361 * [backup-simplify]: Simplify 0 into 0 245.361 * [backup-simplify]: Simplify 1 into 1 245.361 * [taylor]: Taking taylor expansion of (log PI) in k 245.361 * [taylor]: Taking taylor expansion of PI in k 245.361 * [backup-simplify]: Simplify PI into PI 245.361 * [backup-simplify]: Simplify (log PI) into (log PI) 245.362 * [backup-simplify]: Simplify (* 1/2 0) into 0 245.362 * [backup-simplify]: Simplify (- 0) into 0 245.362 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 245.363 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 245.364 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 245.364 * [backup-simplify]: Simplify (pow PI 1/2) into (pow PI 1/2) 245.365 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 245.366 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 245.366 * [backup-simplify]: Simplify (- 1/2) into -1/2 245.366 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 245.377 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 245.383 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 245.385 * [backup-simplify]: Simplify (* -1/2 (* (log PI) (sqrt PI))) into (* -1/2 (* (log PI) (sqrt PI))) 245.387 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 245.388 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 245.388 * [backup-simplify]: Simplify (- 0) into 0 245.388 * [backup-simplify]: Simplify (+ 0 0) into 0 245.389 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 245.397 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 245.400 * [backup-simplify]: Simplify (* 1/8 (* (pow (log PI) 2) (sqrt PI))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 245.404 * [backup-simplify]: Simplify (+ (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (log PI) (sqrt PI))) k) (pow PI 1/2))) into (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) 245.404 * [backup-simplify]: Simplify (pow PI (- 1/2 (/ (/ 1 k) 2))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 245.404 * [approximate]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in (k) around 0 245.404 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 245.404 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 245.404 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 245.404 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 245.404 * [taylor]: Taking taylor expansion of 1/2 in k 245.404 * [backup-simplify]: Simplify 1/2 into 1/2 245.404 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 245.404 * [taylor]: Taking taylor expansion of 1/2 in k 245.404 * [backup-simplify]: Simplify 1/2 into 1/2 245.404 * [taylor]: Taking taylor expansion of (/ 1 k) in k 245.404 * [taylor]: Taking taylor expansion of k in k 245.404 * [backup-simplify]: Simplify 0 into 0 245.404 * [backup-simplify]: Simplify 1 into 1 245.405 * [backup-simplify]: Simplify (/ 1 1) into 1 245.405 * [taylor]: Taking taylor expansion of (log PI) in k 245.405 * [taylor]: Taking taylor expansion of PI in k 245.405 * [backup-simplify]: Simplify PI into PI 245.405 * [backup-simplify]: Simplify (log PI) into (log PI) 245.405 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 245.406 * [backup-simplify]: Simplify (- 1/2) into -1/2 245.406 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 245.407 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 245.407 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 245.407 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 245.407 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 245.407 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 245.407 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 245.407 * [taylor]: Taking taylor expansion of 1/2 in k 245.407 * [backup-simplify]: Simplify 1/2 into 1/2 245.407 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 245.407 * [taylor]: Taking taylor expansion of 1/2 in k 245.407 * [backup-simplify]: Simplify 1/2 into 1/2 245.407 * [taylor]: Taking taylor expansion of (/ 1 k) in k 245.407 * [taylor]: Taking taylor expansion of k in k 245.407 * [backup-simplify]: Simplify 0 into 0 245.407 * [backup-simplify]: Simplify 1 into 1 245.407 * [backup-simplify]: Simplify (/ 1 1) into 1 245.408 * [taylor]: Taking taylor expansion of (log PI) in k 245.408 * [taylor]: Taking taylor expansion of PI in k 245.408 * [backup-simplify]: Simplify PI into PI 245.408 * [backup-simplify]: Simplify (log PI) into (log PI) 245.408 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 245.408 * [backup-simplify]: Simplify (- 1/2) into -1/2 245.409 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 245.409 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 245.410 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 245.410 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 k)))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 245.410 * [backup-simplify]: Simplify 0 into 0 245.410 * [backup-simplify]: Simplify 0 into 0 245.410 * [backup-simplify]: Simplify 0 into 0 245.410 * [backup-simplify]: Simplify 0 into 0 245.410 * [backup-simplify]: Simplify 0 into 0 245.410 * [backup-simplify]: Simplify 0 into 0 245.410 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) into (pow PI (- 1/2 (* 1/2 k))) 245.410 * [backup-simplify]: Simplify (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 245.410 * [approximate]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in (k) around 0 245.410 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 245.410 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 245.410 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 245.410 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 245.410 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 245.410 * [taylor]: Taking taylor expansion of 1/2 in k 245.410 * [backup-simplify]: Simplify 1/2 into 1/2 245.410 * [taylor]: Taking taylor expansion of (/ 1 k) in k 245.410 * [taylor]: Taking taylor expansion of k in k 245.410 * [backup-simplify]: Simplify 0 into 0 245.410 * [backup-simplify]: Simplify 1 into 1 245.411 * [backup-simplify]: Simplify (/ 1 1) into 1 245.411 * [taylor]: Taking taylor expansion of 1/2 in k 245.411 * [backup-simplify]: Simplify 1/2 into 1/2 245.411 * [taylor]: Taking taylor expansion of (log PI) in k 245.411 * [taylor]: Taking taylor expansion of PI in k 245.411 * [backup-simplify]: Simplify PI into PI 245.411 * [backup-simplify]: Simplify (log PI) into (log PI) 245.411 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 245.412 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 245.412 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 245.413 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 245.413 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 245.413 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 245.413 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 245.413 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 245.413 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 245.413 * [taylor]: Taking taylor expansion of 1/2 in k 245.413 * [backup-simplify]: Simplify 1/2 into 1/2 245.413 * [taylor]: Taking taylor expansion of (/ 1 k) in k 245.413 * [taylor]: Taking taylor expansion of k in k 245.413 * [backup-simplify]: Simplify 0 into 0 245.413 * [backup-simplify]: Simplify 1 into 1 245.413 * [backup-simplify]: Simplify (/ 1 1) into 1 245.413 * [taylor]: Taking taylor expansion of 1/2 in k 245.413 * [backup-simplify]: Simplify 1/2 into 1/2 245.413 * [taylor]: Taking taylor expansion of (log PI) in k 245.413 * [taylor]: Taking taylor expansion of PI in k 245.413 * [backup-simplify]: Simplify PI into PI 245.414 * [backup-simplify]: Simplify (log PI) into (log PI) 245.414 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 245.414 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 245.415 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 245.415 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 245.415 * [backup-simplify]: Simplify (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 245.416 * [backup-simplify]: Simplify 0 into 0 245.416 * [backup-simplify]: Simplify 0 into 0 245.416 * [backup-simplify]: Simplify 0 into 0 245.416 * [backup-simplify]: Simplify 0 into 0 245.416 * [backup-simplify]: Simplify 0 into 0 245.416 * [backup-simplify]: Simplify 0 into 0 245.416 * [backup-simplify]: Simplify (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) into (pow PI (- 1/2 (* 1/2 k))) 245.416 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2) 245.416 * [backup-simplify]: Simplify (/ (sqrt k) (pow 2 (- 1/2 (/ k 2)))) into (* (/ 1 (pow 2 (- 1/2 (* 1/2 k)))) (sqrt k)) 245.416 * [approximate]: Taking taylor expansion of (* (/ 1 (pow 2 (- 1/2 (* 1/2 k)))) (sqrt k)) in (k) around 0 245.416 * [taylor]: Taking taylor expansion of (* (/ 1 (pow 2 (- 1/2 (* 1/2 k)))) (sqrt k)) in k 245.416 * [taylor]: Taking taylor expansion of (/ 1 (pow 2 (- 1/2 (* 1/2 k)))) in k 245.416 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in k 245.416 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in k 245.416 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in k 245.416 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 245.416 * [taylor]: Taking taylor expansion of 1/2 in k 245.416 * [backup-simplify]: Simplify 1/2 into 1/2 245.416 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 245.416 * [taylor]: Taking taylor expansion of 1/2 in k 245.416 * [backup-simplify]: Simplify 1/2 into 1/2 245.416 * [taylor]: Taking taylor expansion of k in k 245.416 * [backup-simplify]: Simplify 0 into 0 245.416 * [backup-simplify]: Simplify 1 into 1 245.416 * [taylor]: Taking taylor expansion of (log 2) in k 245.416 * [taylor]: Taking taylor expansion of 2 in k 245.416 * [backup-simplify]: Simplify 2 into 2 245.417 * [backup-simplify]: Simplify (log 2) into (log 2) 245.417 * [backup-simplify]: Simplify (* 1/2 0) into 0 245.417 * [backup-simplify]: Simplify (- 0) into 0 245.417 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 245.418 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 245.419 * [backup-simplify]: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2) 245.420 * [backup-simplify]: Simplify (/ 1 (pow 2 1/2)) into (sqrt (/ 1 2)) 245.420 * [taylor]: Taking taylor expansion of (sqrt k) in k 245.420 * [taylor]: Taking taylor expansion of k in k 245.420 * [backup-simplify]: Simplify 0 into 0 245.420 * [backup-simplify]: Simplify 1 into 1 245.420 * [backup-simplify]: Simplify (sqrt 0) into 0 245.421 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 245.421 * [taylor]: Taking taylor expansion of (* (/ 1 (pow 2 (- 1/2 (* 1/2 k)))) (sqrt k)) in k 245.421 * [taylor]: Taking taylor expansion of (/ 1 (pow 2 (- 1/2 (* 1/2 k)))) in k 245.421 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in k 245.421 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in k 245.421 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in k 245.421 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 245.421 * [taylor]: Taking taylor expansion of 1/2 in k 245.421 * [backup-simplify]: Simplify 1/2 into 1/2 245.421 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 245.421 * [taylor]: Taking taylor expansion of 1/2 in k 245.421 * [backup-simplify]: Simplify 1/2 into 1/2 245.421 * [taylor]: Taking taylor expansion of k in k 245.421 * [backup-simplify]: Simplify 0 into 0 245.421 * [backup-simplify]: Simplify 1 into 1 245.421 * [taylor]: Taking taylor expansion of (log 2) in k 245.421 * [taylor]: Taking taylor expansion of 2 in k 245.421 * [backup-simplify]: Simplify 2 into 2 245.421 * [backup-simplify]: Simplify (log 2) into (log 2) 245.422 * [backup-simplify]: Simplify (* 1/2 0) into 0 245.422 * [backup-simplify]: Simplify (- 0) into 0 245.422 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 245.423 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 245.424 * [backup-simplify]: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2) 245.424 * [backup-simplify]: Simplify (/ 1 (pow 2 1/2)) into (sqrt (/ 1 2)) 245.424 * [taylor]: Taking taylor expansion of (sqrt k) in k 245.424 * [taylor]: Taking taylor expansion of k in k 245.424 * [backup-simplify]: Simplify 0 into 0 245.424 * [backup-simplify]: Simplify 1 into 1 245.425 * [backup-simplify]: Simplify (sqrt 0) into 0 245.425 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 245.426 * [backup-simplify]: Simplify (* (sqrt (/ 1 2)) 0) into 0 245.426 * [backup-simplify]: Simplify 0 into 0 245.427 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 245.427 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 245.428 * [backup-simplify]: Simplify (- 1/2) into -1/2 245.428 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 245.429 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log 2))) into (- (* 1/2 (log 2))) 245.435 * [backup-simplify]: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 1) 1)))) into (* -1/2 (* (log 2) (sqrt 2))) 245.441 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 2)) (/ (* -1/2 (* (log 2) (sqrt 2))) (pow 2 1/2))))) into (* 1/2 (* (log 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) 245.445 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 2)) +nan.0) (* (* 1/2 (* (log 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) 0)) into (- (* +nan.0 (sqrt 1/2))) 245.446 * [backup-simplify]: Simplify (- (* +nan.0 (sqrt 1/2))) into (- (* +nan.0 (sqrt 1/2))) 245.448 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 245.450 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 245.451 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 245.451 * [backup-simplify]: Simplify (- 0) into 0 245.451 * [backup-simplify]: Simplify (+ 0 0) into 0 245.452 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log 2)))) into 0 245.459 * [backup-simplify]: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log 2) 2) (sqrt 2))) 245.480 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 2)) (/ (* 1/8 (* (pow (log 2) 2) (sqrt 2))) (pow 2 1/2))) (* (* 1/2 (* (log 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) (/ (* -1/2 (* (log 2) (sqrt 2))) (pow 2 1/2))))) into (- (* 1/4 (* (pow (log 2) 2) (* (pow (sqrt 2) 2) (pow (sqrt 1/2) 3)))) (* 1/8 (* (pow (log 2) 2) (* (sqrt 2) (pow (sqrt 1/2) 2))))) 245.493 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 2)) +nan.0) (+ (* (* 1/2 (* (log 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) +nan.0) (* (- (* 1/4 (* (pow (log 2) 2) (* (pow (sqrt 2) 2) (pow (sqrt 1/2) 3)))) (* 1/8 (* (pow (log 2) 2) (* (sqrt 2) (pow (sqrt 1/2) 2))))) 0))) into (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) (- (* +nan.0 (sqrt 1/2))))) 245.499 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) (- (* +nan.0 (sqrt 1/2))))) into (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) (- (* +nan.0 (sqrt 1/2))))) 245.502 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 245.505 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 245.506 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 245.506 * [backup-simplify]: Simplify (- 0) into 0 245.506 * [backup-simplify]: Simplify (+ 0 0) into 0 245.507 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log 2))))) into 0 245.516 * [backup-simplify]: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 3) 6)) (* (/ (pow (- (* 1/2 (log 2))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log 2) 3) (sqrt 2))) 245.553 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 2)) (/ (* -1/48 (* (pow (log 2) 3) (sqrt 2))) (pow 2 1/2))) (* (* 1/2 (* (log 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) (/ (* 1/8 (* (pow (log 2) 2) (sqrt 2))) (pow 2 1/2))) (* (- (* 1/4 (* (pow (log 2) 2) (* (pow (sqrt 2) 2) (pow (sqrt 1/2) 3)))) (* 1/8 (* (pow (log 2) 2) (* (sqrt 2) (pow (sqrt 1/2) 2))))) (/ (* -1/2 (* (log 2) (sqrt 2))) (pow 2 1/2))))) into (- (+ (* 1/8 (* (pow (log 2) 3) (* (pow (sqrt 2) 3) (pow (sqrt 1/2) 4)))) (* 1/48 (* (pow (log 2) 3) (* (sqrt 2) (pow (sqrt 1/2) 2))))) (* 1/8 (* (pow (log 2) 3) (* (pow (sqrt 2) 2) (pow (sqrt 1/2) 3))))) 245.597 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 2)) +nan.0) (+ (* (* 1/2 (* (log 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) +nan.0) (+ (* (- (* 1/4 (* (pow (log 2) 2) (* (pow (sqrt 2) 2) (pow (sqrt 1/2) 3)))) (* 1/8 (* (pow (log 2) 2) (* (sqrt 2) (pow (sqrt 1/2) 2))))) +nan.0) (* (- (+ (* 1/8 (* (pow (log 2) 3) (* (pow (sqrt 2) 3) (pow (sqrt 1/2) 4)))) (* 1/48 (* (pow (log 2) 3) (* (sqrt 2) (pow (sqrt 1/2) 2))))) (* 1/8 (* (pow (log 2) 3) (* (pow (sqrt 2) 2) (pow (sqrt 1/2) 3))))) 0)))) into (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) (- (+ (* +nan.0 (* (pow (log 2) 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) (- (+ (* +nan.0 (* (pow (log 2) 2) (* (pow (sqrt 2) 2) (pow (sqrt 1/2) 3)))) (- (* +nan.0 (sqrt 1/2))))))))) 245.624 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) (- (+ (* +nan.0 (* (pow (log 2) 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) (- (+ (* +nan.0 (* (pow (log 2) 2) (* (pow (sqrt 2) 2) (pow (sqrt 1/2) 3)))) (- (* +nan.0 (sqrt 1/2))))))))) into (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) (- (+ (* +nan.0 (* (pow (log 2) 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) (- (+ (* +nan.0 (* (pow (log 2) 2) (* (pow (sqrt 2) 2) (pow (sqrt 1/2) 3)))) (- (* +nan.0 (sqrt 1/2))))))))) 245.662 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) (- (+ (* +nan.0 (* (pow (log 2) 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) (- (+ (* +nan.0 (* (pow (log 2) 2) (* (pow (sqrt 2) 2) (pow (sqrt 1/2) 3)))) (- (* +nan.0 (sqrt 1/2))))))))) (pow k 3)) (+ (* (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (pow (sqrt 1/2) 2)))) (- (* +nan.0 (sqrt 1/2))))) (pow k 2)) (* (- (* +nan.0 (sqrt 1/2))) k))) into (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 3))))) (- (+ (* +nan.0 (* (pow (log 2) 2) (* (pow (sqrt 2) 2) (* (pow (sqrt 1/2) 3) (pow k 3))))) (- (+ (* +nan.0 (* (sqrt 1/2) (pow k 3))) (- (+ (* +nan.0 (* (sqrt 1/2) k)) (- (+ (* +nan.0 (* (pow (log 2) 2) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 3))))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2))))) (- (* +nan.0 (* (sqrt 1/2) (pow k 2)))))))))))))))) 245.663 * [backup-simplify]: Simplify (/ (sqrt (/ 1 k)) (pow 2 (- 1/2 (/ (/ 1 k) 2)))) into (* (/ 1 (pow 2 (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) 245.663 * [approximate]: Taking taylor expansion of (* (/ 1 (pow 2 (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in (k) around 0 245.663 * [taylor]: Taking taylor expansion of (* (/ 1 (pow 2 (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 245.663 * [taylor]: Taking taylor expansion of (/ 1 (pow 2 (- 1/2 (* 1/2 (/ 1 k))))) in k 245.663 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in k 245.663 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in k 245.663 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in k 245.663 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 245.663 * [taylor]: Taking taylor expansion of 1/2 in k 245.663 * [backup-simplify]: Simplify 1/2 into 1/2 245.663 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 245.663 * [taylor]: Taking taylor expansion of 1/2 in k 245.663 * [backup-simplify]: Simplify 1/2 into 1/2 245.663 * [taylor]: Taking taylor expansion of (/ 1 k) in k 245.663 * [taylor]: Taking taylor expansion of k in k 245.663 * [backup-simplify]: Simplify 0 into 0 245.663 * [backup-simplify]: Simplify 1 into 1 245.663 * [backup-simplify]: Simplify (/ 1 1) into 1 245.663 * [taylor]: Taking taylor expansion of (log 2) in k 245.663 * [taylor]: Taking taylor expansion of 2 in k 245.663 * [backup-simplify]: Simplify 2 into 2 245.663 * [backup-simplify]: Simplify (log 2) into (log 2) 245.664 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 245.664 * [backup-simplify]: Simplify (- 1/2) into -1/2 245.664 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 245.665 * [backup-simplify]: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2)) 245.665 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 245.665 * [backup-simplify]: Simplify (/ 1 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))) into (/ 1 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))) 245.665 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 245.665 * [taylor]: Taking taylor expansion of (/ 1 k) in k 245.665 * [taylor]: Taking taylor expansion of k in k 245.665 * [backup-simplify]: Simplify 0 into 0 245.665 * [backup-simplify]: Simplify 1 into 1 245.666 * [backup-simplify]: Simplify (/ 1 1) into 1 245.666 * [backup-simplify]: Simplify (sqrt 0) into 0 245.667 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 245.667 * [taylor]: Taking taylor expansion of (* (/ 1 (pow 2 (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 245.667 * [taylor]: Taking taylor expansion of (/ 1 (pow 2 (- 1/2 (* 1/2 (/ 1 k))))) in k 245.667 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in k 245.667 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in k 245.667 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in k 245.667 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 245.667 * [taylor]: Taking taylor expansion of 1/2 in k 245.667 * [backup-simplify]: Simplify 1/2 into 1/2 245.667 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 245.667 * [taylor]: Taking taylor expansion of 1/2 in k 245.667 * [backup-simplify]: Simplify 1/2 into 1/2 245.667 * [taylor]: Taking taylor expansion of (/ 1 k) in k 245.667 * [taylor]: Taking taylor expansion of k in k 245.667 * [backup-simplify]: Simplify 0 into 0 245.667 * [backup-simplify]: Simplify 1 into 1 245.667 * [backup-simplify]: Simplify (/ 1 1) into 1 245.667 * [taylor]: Taking taylor expansion of (log 2) in k 245.667 * [taylor]: Taking taylor expansion of 2 in k 245.668 * [backup-simplify]: Simplify 2 into 2 245.668 * [backup-simplify]: Simplify (log 2) into (log 2) 245.668 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 245.668 * [backup-simplify]: Simplify (- 1/2) into -1/2 245.669 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 245.669 * [backup-simplify]: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2)) 245.669 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 245.670 * [backup-simplify]: Simplify (/ 1 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))) into (/ 1 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))) 245.670 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 245.670 * [taylor]: Taking taylor expansion of (/ 1 k) in k 245.670 * [taylor]: Taking taylor expansion of k in k 245.670 * [backup-simplify]: Simplify 0 into 0 245.670 * [backup-simplify]: Simplify 1 into 1 245.670 * [backup-simplify]: Simplify (/ 1 1) into 1 245.670 * [backup-simplify]: Simplify (sqrt 0) into 0 245.671 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 245.672 * [backup-simplify]: Simplify (* (/ 1 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))) 0) into 0 245.672 * [backup-simplify]: Simplify 0 into 0 245.672 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))) (/ 0 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))))))) into 0 245.673 * [backup-simplify]: Simplify (+ (* (/ 1 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))))) 245.673 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (/ 1 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))))) 245.674 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 245.675 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 245.676 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))) (/ 0 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))))) (* 0 (/ 0 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))))))) into 0 245.677 * [backup-simplify]: Simplify (+ (* (/ 1 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ 1 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))))) 245.677 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (/ 1 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))))) 245.678 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 245.680 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 245.682 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))) (/ 0 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))))) (* 0 (/ 0 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))))) (* 0 (/ 0 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))))))) into 0 245.682 * [backup-simplify]: Simplify (+ (* (/ 1 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ 1 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))))) 245.683 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (/ 1 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))))) 245.684 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (pow (/ 1 k) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (/ 1 k)) (- (* +nan.0 (/ 1 (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (exp (* (log 2) (- 1/2 (* 1/2 k)))))) (- (* +nan.0 (/ 1 (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) k)))))))) 245.684 * [backup-simplify]: Simplify (/ (sqrt (/ 1 (- k))) (pow 2 (- 1/2 (/ (/ 1 (- k)) 2)))) into (/ (sqrt (/ -1 k)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) 245.684 * [approximate]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) in (k) around 0 245.684 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) in k 245.684 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 245.684 * [taylor]: Taking taylor expansion of (/ -1 k) in k 245.684 * [taylor]: Taking taylor expansion of -1 in k 245.684 * [backup-simplify]: Simplify -1 into -1 245.684 * [taylor]: Taking taylor expansion of k in k 245.684 * [backup-simplify]: Simplify 0 into 0 245.684 * [backup-simplify]: Simplify 1 into 1 245.685 * [backup-simplify]: Simplify (/ -1 1) into -1 245.685 * [backup-simplify]: Simplify (sqrt 0) into 0 245.686 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 245.686 * [taylor]: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in k 245.686 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in k 245.686 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in k 245.686 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 245.686 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 245.686 * [taylor]: Taking taylor expansion of 1/2 in k 245.686 * [backup-simplify]: Simplify 1/2 into 1/2 245.686 * [taylor]: Taking taylor expansion of (/ 1 k) in k 245.686 * [taylor]: Taking taylor expansion of k in k 245.686 * [backup-simplify]: Simplify 0 into 0 245.686 * [backup-simplify]: Simplify 1 into 1 245.686 * [backup-simplify]: Simplify (/ 1 1) into 1 245.686 * [taylor]: Taking taylor expansion of 1/2 in k 245.686 * [backup-simplify]: Simplify 1/2 into 1/2 245.686 * [taylor]: Taking taylor expansion of (log 2) in k 245.686 * [taylor]: Taking taylor expansion of 2 in k 245.686 * [backup-simplify]: Simplify 2 into 2 245.686 * [backup-simplify]: Simplify (log 2) into (log 2) 245.687 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 245.687 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 245.688 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 245.688 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 245.688 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) 245.688 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) in k 245.688 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 245.688 * [taylor]: Taking taylor expansion of (/ -1 k) in k 245.688 * [taylor]: Taking taylor expansion of -1 in k 245.688 * [backup-simplify]: Simplify -1 into -1 245.688 * [taylor]: Taking taylor expansion of k in k 245.688 * [backup-simplify]: Simplify 0 into 0 245.688 * [backup-simplify]: Simplify 1 into 1 245.689 * [backup-simplify]: Simplify (/ -1 1) into -1 245.689 * [backup-simplify]: Simplify (sqrt 0) into 0 245.690 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 245.690 * [taylor]: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in k 245.690 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in k 245.690 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in k 245.690 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 245.690 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 245.690 * [taylor]: Taking taylor expansion of 1/2 in k 245.690 * [backup-simplify]: Simplify 1/2 into 1/2 245.690 * [taylor]: Taking taylor expansion of (/ 1 k) in k 245.690 * [taylor]: Taking taylor expansion of k in k 245.690 * [backup-simplify]: Simplify 0 into 0 245.690 * [backup-simplify]: Simplify 1 into 1 245.690 * [backup-simplify]: Simplify (/ 1 1) into 1 245.690 * [taylor]: Taking taylor expansion of 1/2 in k 245.690 * [backup-simplify]: Simplify 1/2 into 1/2 245.690 * [taylor]: Taking taylor expansion of (log 2) in k 245.690 * [taylor]: Taking taylor expansion of 2 in k 245.690 * [backup-simplify]: Simplify 2 into 2 245.690 * [backup-simplify]: Simplify (log 2) into (log 2) 245.691 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 245.691 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 245.691 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 245.692 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 245.692 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) 245.693 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) 245.693 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 245.695 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 245.696 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) 245.696 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (/ 1 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) 245.697 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 245.699 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 245.701 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) (* (- (* +nan.0 (/ 1 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) (/ 0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) 245.701 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (/ 1 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) 245.702 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))))) (/ 1 (- k))) (/ +nan.0 (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (exp (* (log 2) (- 1/2 (* 1/2 k)))))) (- (* +nan.0 (/ 1 (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) k)))))))) 245.702 * * * * [progress]: [ 4 / 4 ] generating series at (2 2) 245.703 * [backup-simplify]: Simplify (* (/ (* 1 (/ 1 (pow n (- 1/2 (/ k 2))))) (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (pow 2 (- 1/2 (/ k 2))))) into (* (/ 1 (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))))) (sqrt k)) 245.703 * [approximate]: Taking taylor expansion of (* (/ 1 (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))))) (sqrt k)) in (n k) around 0 245.703 * [taylor]: Taking taylor expansion of (* (/ 1 (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))))) (sqrt k)) in k 245.703 * [taylor]: Taking taylor expansion of (/ 1 (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))))) in k 245.703 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) in k 245.703 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 245.703 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 245.703 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 245.703 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 245.703 * [taylor]: Taking taylor expansion of 1/2 in k 245.703 * [backup-simplify]: Simplify 1/2 into 1/2 245.703 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 245.703 * [taylor]: Taking taylor expansion of 1/2 in k 245.703 * [backup-simplify]: Simplify 1/2 into 1/2 245.703 * [taylor]: Taking taylor expansion of k in k 245.703 * [backup-simplify]: Simplify 0 into 0 245.703 * [backup-simplify]: Simplify 1 into 1 245.703 * [taylor]: Taking taylor expansion of (log n) in k 245.703 * [taylor]: Taking taylor expansion of n in k 245.703 * [backup-simplify]: Simplify n into n 245.703 * [backup-simplify]: Simplify (log n) into (log n) 245.703 * [backup-simplify]: Simplify (* 1/2 0) into 0 245.704 * [backup-simplify]: Simplify (- 0) into 0 245.704 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 245.704 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 245.704 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 245.704 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in k 245.704 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in k 245.704 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in k 245.704 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in k 245.704 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 245.704 * [taylor]: Taking taylor expansion of 1/2 in k 245.704 * [backup-simplify]: Simplify 1/2 into 1/2 245.704 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 245.704 * [taylor]: Taking taylor expansion of 1/2 in k 245.704 * [backup-simplify]: Simplify 1/2 into 1/2 245.704 * [taylor]: Taking taylor expansion of k in k 245.704 * [backup-simplify]: Simplify 0 into 0 245.704 * [backup-simplify]: Simplify 1 into 1 245.704 * [taylor]: Taking taylor expansion of (log 2) in k 245.704 * [taylor]: Taking taylor expansion of 2 in k 245.704 * [backup-simplify]: Simplify 2 into 2 245.704 * [backup-simplify]: Simplify (log 2) into (log 2) 245.705 * [backup-simplify]: Simplify (* 1/2 0) into 0 245.705 * [backup-simplify]: Simplify (- 0) into 0 245.705 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 245.706 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 245.707 * [backup-simplify]: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2) 245.707 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 245.707 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 245.707 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 245.707 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 245.707 * [taylor]: Taking taylor expansion of 1/2 in k 245.707 * [backup-simplify]: Simplify 1/2 into 1/2 245.707 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 245.707 * [taylor]: Taking taylor expansion of 1/2 in k 245.707 * [backup-simplify]: Simplify 1/2 into 1/2 245.707 * [taylor]: Taking taylor expansion of k in k 245.707 * [backup-simplify]: Simplify 0 into 0 245.707 * [backup-simplify]: Simplify 1 into 1 245.707 * [taylor]: Taking taylor expansion of (log PI) in k 245.707 * [taylor]: Taking taylor expansion of PI in k 245.707 * [backup-simplify]: Simplify PI into PI 245.707 * [backup-simplify]: Simplify (log PI) into (log PI) 245.708 * [backup-simplify]: Simplify (* 1/2 0) into 0 245.708 * [backup-simplify]: Simplify (- 0) into 0 245.708 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 245.709 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 245.710 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 245.711 * [backup-simplify]: Simplify (* (pow 2 1/2) (pow PI 1/2)) into (sqrt (* PI 2)) 245.712 * [backup-simplify]: Simplify (* (pow n 1/2) (sqrt (* PI 2))) into (* (sqrt 2) (sqrt (* n PI))) 245.712 * [backup-simplify]: Simplify (/ 1 (* (sqrt 2) (sqrt (* n PI)))) into (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))) 245.712 * [taylor]: Taking taylor expansion of (sqrt k) in k 245.712 * [taylor]: Taking taylor expansion of k in k 245.712 * [backup-simplify]: Simplify 0 into 0 245.712 * [backup-simplify]: Simplify 1 into 1 245.712 * [backup-simplify]: Simplify (sqrt 0) into 0 245.713 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 245.713 * [taylor]: Taking taylor expansion of (* (/ 1 (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))))) (sqrt k)) in n 245.713 * [taylor]: Taking taylor expansion of (/ 1 (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))))) in n 245.713 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) in n 245.713 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 245.713 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 245.713 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 245.713 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 245.713 * [taylor]: Taking taylor expansion of 1/2 in n 245.713 * [backup-simplify]: Simplify 1/2 into 1/2 245.713 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 245.713 * [taylor]: Taking taylor expansion of 1/2 in n 245.713 * [backup-simplify]: Simplify 1/2 into 1/2 245.713 * [taylor]: Taking taylor expansion of k in n 245.713 * [backup-simplify]: Simplify k into k 245.713 * [taylor]: Taking taylor expansion of (log n) in n 245.713 * [taylor]: Taking taylor expansion of n in n 245.713 * [backup-simplify]: Simplify 0 into 0 245.713 * [backup-simplify]: Simplify 1 into 1 245.713 * [backup-simplify]: Simplify (log 1) into 0 245.714 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 245.714 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 245.714 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 245.714 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 245.714 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 245.714 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 245.714 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in n 245.714 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in n 245.714 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in n 245.714 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in n 245.714 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 245.714 * [taylor]: Taking taylor expansion of 1/2 in n 245.714 * [backup-simplify]: Simplify 1/2 into 1/2 245.714 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 245.714 * [taylor]: Taking taylor expansion of 1/2 in n 245.714 * [backup-simplify]: Simplify 1/2 into 1/2 245.714 * [taylor]: Taking taylor expansion of k in n 245.714 * [backup-simplify]: Simplify k into k 245.714 * [taylor]: Taking taylor expansion of (log 2) in n 245.714 * [taylor]: Taking taylor expansion of 2 in n 245.714 * [backup-simplify]: Simplify 2 into 2 245.715 * [backup-simplify]: Simplify (log 2) into (log 2) 245.715 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 245.715 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 245.715 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 245.715 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log 2)) into (* (log 2) (- 1/2 (* 1/2 k))) 245.715 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 k)))) into (exp (* (log 2) (- 1/2 (* 1/2 k)))) 245.715 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in n 245.715 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in n 245.715 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in n 245.715 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 245.715 * [taylor]: Taking taylor expansion of 1/2 in n 245.715 * [backup-simplify]: Simplify 1/2 into 1/2 245.715 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 245.715 * [taylor]: Taking taylor expansion of 1/2 in n 245.715 * [backup-simplify]: Simplify 1/2 into 1/2 245.715 * [taylor]: Taking taylor expansion of k in n 245.715 * [backup-simplify]: Simplify k into k 245.715 * [taylor]: Taking taylor expansion of (log PI) in n 245.716 * [taylor]: Taking taylor expansion of PI in n 245.716 * [backup-simplify]: Simplify PI into PI 245.716 * [backup-simplify]: Simplify (log PI) into (log PI) 245.716 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 245.716 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 245.716 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 245.716 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log PI)) into (* (- 1/2 (* 1/2 k)) (log PI)) 245.717 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log PI))) into (pow PI (- 1/2 (* 1/2 k))) 245.717 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) into (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) 245.717 * [backup-simplify]: Simplify (* (pow n (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) into (* (pow n (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) 245.718 * [backup-simplify]: Simplify (/ 1 (* (pow n (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) into (/ 1 (* (pow n (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) 245.718 * [taylor]: Taking taylor expansion of (sqrt k) in n 245.718 * [taylor]: Taking taylor expansion of k in n 245.718 * [backup-simplify]: Simplify k into k 245.718 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 245.718 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 245.718 * [taylor]: Taking taylor expansion of (* (/ 1 (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))))) (sqrt k)) in n 245.718 * [taylor]: Taking taylor expansion of (/ 1 (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))))) in n 245.718 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) in n 245.718 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 245.718 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 245.718 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 245.718 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 245.718 * [taylor]: Taking taylor expansion of 1/2 in n 245.718 * [backup-simplify]: Simplify 1/2 into 1/2 245.718 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 245.718 * [taylor]: Taking taylor expansion of 1/2 in n 245.718 * [backup-simplify]: Simplify 1/2 into 1/2 245.718 * [taylor]: Taking taylor expansion of k in n 245.718 * [backup-simplify]: Simplify k into k 245.718 * [taylor]: Taking taylor expansion of (log n) in n 245.718 * [taylor]: Taking taylor expansion of n in n 245.718 * [backup-simplify]: Simplify 0 into 0 245.718 * [backup-simplify]: Simplify 1 into 1 245.718 * [backup-simplify]: Simplify (log 1) into 0 245.719 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 245.719 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 245.719 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 245.719 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 245.719 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 245.719 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 245.719 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in n 245.719 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in n 245.719 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in n 245.719 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in n 245.719 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 245.719 * [taylor]: Taking taylor expansion of 1/2 in n 245.719 * [backup-simplify]: Simplify 1/2 into 1/2 245.719 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 245.719 * [taylor]: Taking taylor expansion of 1/2 in n 245.719 * [backup-simplify]: Simplify 1/2 into 1/2 245.719 * [taylor]: Taking taylor expansion of k in n 245.719 * [backup-simplify]: Simplify k into k 245.719 * [taylor]: Taking taylor expansion of (log 2) in n 245.719 * [taylor]: Taking taylor expansion of 2 in n 245.719 * [backup-simplify]: Simplify 2 into 2 245.720 * [backup-simplify]: Simplify (log 2) into (log 2) 245.720 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 245.720 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 245.720 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 245.720 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log 2)) into (* (log 2) (- 1/2 (* 1/2 k))) 245.720 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 k)))) into (exp (* (log 2) (- 1/2 (* 1/2 k)))) 245.720 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in n 245.720 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in n 245.720 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in n 245.720 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 245.720 * [taylor]: Taking taylor expansion of 1/2 in n 245.720 * [backup-simplify]: Simplify 1/2 into 1/2 245.720 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 245.720 * [taylor]: Taking taylor expansion of 1/2 in n 245.720 * [backup-simplify]: Simplify 1/2 into 1/2 245.720 * [taylor]: Taking taylor expansion of k in n 245.720 * [backup-simplify]: Simplify k into k 245.720 * [taylor]: Taking taylor expansion of (log PI) in n 245.720 * [taylor]: Taking taylor expansion of PI in n 245.721 * [backup-simplify]: Simplify PI into PI 245.721 * [backup-simplify]: Simplify (log PI) into (log PI) 245.721 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 245.721 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 245.721 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 245.721 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log PI)) into (* (- 1/2 (* 1/2 k)) (log PI)) 245.722 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log PI))) into (pow PI (- 1/2 (* 1/2 k))) 245.722 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) into (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) 245.722 * [backup-simplify]: Simplify (* (pow n (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) into (* (pow n (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) 245.723 * [backup-simplify]: Simplify (/ 1 (* (pow n (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) into (/ 1 (* (pow n (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) 245.723 * [taylor]: Taking taylor expansion of (sqrt k) in n 245.723 * [taylor]: Taking taylor expansion of k in n 245.723 * [backup-simplify]: Simplify k into k 245.723 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 245.723 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 245.723 * [backup-simplify]: Simplify (* (/ 1 (* (pow n (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) (sqrt k)) into (* (/ 1 (* (pow n (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) (sqrt k)) 245.723 * [taylor]: Taking taylor expansion of (* (/ 1 (* (pow n (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) (sqrt k)) in k 245.723 * [taylor]: Taking taylor expansion of (/ 1 (* (pow n (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) in k 245.724 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) in k 245.724 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 245.724 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 245.724 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 245.724 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 245.724 * [taylor]: Taking taylor expansion of 1/2 in k 245.724 * [backup-simplify]: Simplify 1/2 into 1/2 245.724 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 245.724 * [taylor]: Taking taylor expansion of 1/2 in k 245.724 * [backup-simplify]: Simplify 1/2 into 1/2 245.724 * [taylor]: Taking taylor expansion of k in k 245.724 * [backup-simplify]: Simplify 0 into 0 245.724 * [backup-simplify]: Simplify 1 into 1 245.724 * [taylor]: Taking taylor expansion of (log n) in k 245.724 * [taylor]: Taking taylor expansion of n in k 245.724 * [backup-simplify]: Simplify n into n 245.724 * [backup-simplify]: Simplify (log n) into (log n) 245.724 * [backup-simplify]: Simplify (* 1/2 0) into 0 245.724 * [backup-simplify]: Simplify (- 0) into 0 245.725 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 245.725 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 245.725 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 245.725 * [taylor]: Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) in k 245.725 * [taylor]: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 k)))) in k 245.725 * [taylor]: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 k))) in k 245.725 * [taylor]: Taking taylor expansion of (log 2) in k 245.725 * [taylor]: Taking taylor expansion of 2 in k 245.725 * [backup-simplify]: Simplify 2 into 2 245.725 * [backup-simplify]: Simplify (log 2) into (log 2) 245.725 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 245.725 * [taylor]: Taking taylor expansion of 1/2 in k 245.725 * [backup-simplify]: Simplify 1/2 into 1/2 245.725 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 245.725 * [taylor]: Taking taylor expansion of 1/2 in k 245.725 * [backup-simplify]: Simplify 1/2 into 1/2 245.725 * [taylor]: Taking taylor expansion of k in k 245.725 * [backup-simplify]: Simplify 0 into 0 245.725 * [backup-simplify]: Simplify 1 into 1 245.725 * [backup-simplify]: Simplify (* 1/2 0) into 0 245.726 * [backup-simplify]: Simplify (- 0) into 0 245.726 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 245.726 * [backup-simplify]: Simplify (* (log 2) 1/2) into (* 1/2 (log 2)) 245.727 * [backup-simplify]: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2) 245.727 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 245.727 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 245.727 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 245.727 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 245.728 * [taylor]: Taking taylor expansion of 1/2 in k 245.728 * [backup-simplify]: Simplify 1/2 into 1/2 245.728 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 245.728 * [taylor]: Taking taylor expansion of 1/2 in k 245.728 * [backup-simplify]: Simplify 1/2 into 1/2 245.728 * [taylor]: Taking taylor expansion of k in k 245.728 * [backup-simplify]: Simplify 0 into 0 245.728 * [backup-simplify]: Simplify 1 into 1 245.728 * [taylor]: Taking taylor expansion of (log PI) in k 245.728 * [taylor]: Taking taylor expansion of PI in k 245.728 * [backup-simplify]: Simplify PI into PI 245.728 * [backup-simplify]: Simplify (log PI) into (log PI) 245.728 * [backup-simplify]: Simplify (* 1/2 0) into 0 245.728 * [backup-simplify]: Simplify (- 0) into 0 245.729 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 245.729 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 245.730 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 245.731 * [backup-simplify]: Simplify (* (pow 2 1/2) (pow PI 1/2)) into (sqrt (* PI 2)) 245.732 * [backup-simplify]: Simplify (* (pow n 1/2) (sqrt (* PI 2))) into (* (sqrt 2) (sqrt (* n PI))) 245.732 * [backup-simplify]: Simplify (/ 1 (* (sqrt 2) (sqrt (* n PI)))) into (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))) 245.732 * [taylor]: Taking taylor expansion of (sqrt k) in k 245.732 * [taylor]: Taking taylor expansion of k in k 245.732 * [backup-simplify]: Simplify 0 into 0 245.732 * [backup-simplify]: Simplify 1 into 1 245.733 * [backup-simplify]: Simplify (sqrt 0) into 0 245.733 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 245.734 * [backup-simplify]: Simplify (* (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))) 0) into 0 245.734 * [backup-simplify]: Simplify 0 into 0 245.735 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 245.735 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 245.736 * [backup-simplify]: Simplify (- 0) into 0 245.736 * [backup-simplify]: Simplify (+ 0 0) into 0 245.736 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log PI))) into 0 245.737 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 245.738 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 245.738 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 245.738 * [backup-simplify]: Simplify (- 0) into 0 245.739 * [backup-simplify]: Simplify (+ 0 0) into 0 245.739 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log 2))) into 0 245.740 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 245.740 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) 0) (* 0 (pow PI (- 1/2 (* 1/2 k))))) into 0 245.741 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 245.741 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 245.742 * [backup-simplify]: Simplify (- 0) into 0 245.742 * [backup-simplify]: Simplify (+ 0 0) into 0 245.742 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 245.742 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log n))) into 0 245.743 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 245.743 * [backup-simplify]: Simplify (+ (* (pow n (- 1/2 (* 1/2 k))) 0) (* 0 (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) into 0 245.750 * [backup-simplify]: Simplify (- (+ (* (/ 1 (* (pow n (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) (/ 0 (* (pow n (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))))))) into 0 245.750 * [backup-simplify]: Simplify (+ (* (/ 1 (* (pow n (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) 0) (* 0 (sqrt k))) into 0 245.750 * [taylor]: Taking taylor expansion of 0 in k 245.750 * [backup-simplify]: Simplify 0 into 0 245.750 * [backup-simplify]: Simplify 0 into 0 245.751 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 245.752 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 245.752 * [backup-simplify]: Simplify (- 1/2) into -1/2 245.752 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 245.754 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 245.759 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 245.760 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 245.760 * [backup-simplify]: Simplify (- 1/2) into -1/2 245.760 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 245.761 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 245.763 * [backup-simplify]: Simplify (+ (* (log 2) -1/2) (* 0 1/2)) into (- (* 1/2 (log 2))) 245.768 * [backup-simplify]: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 1) 1)))) into (* -1/2 (* (log 2) (sqrt 2))) 245.774 * [backup-simplify]: Simplify (+ (* (pow 2 1/2) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1/2 (* (log 2) (sqrt 2))) (pow PI 1/2))) into (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt PI))) (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt PI))))) 245.774 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 245.775 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 245.775 * [backup-simplify]: Simplify (- 1/2) into -1/2 245.775 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 245.776 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log n))) into (- (* 1/2 (log n))) 245.776 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n))) 245.784 * [backup-simplify]: Simplify (+ (* (pow n 1/2) (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt PI))) (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt PI)))))) (* (* -1/2 (* (sqrt n) (log n))) (sqrt (* PI 2)))) into (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))) 245.788 * [backup-simplify]: Simplify (- (+ (* (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))) (/ (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))) (* (sqrt 2) (sqrt (* n PI))))))) into (+ (* 1/2 (* (/ (log PI) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (+ (* 1/2 (* (/ (log 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (* 1/2 (* (/ (log n) (sqrt 2)) (sqrt (/ 1 (* n PI))))))) 245.791 * [backup-simplify]: Simplify (+ (* (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))) +nan.0) (* (+ (* 1/2 (* (/ (log PI) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (+ (* 1/2 (* (/ (log 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (* 1/2 (* (/ (log n) (sqrt 2)) (sqrt (/ 1 (* n PI))))))) 0)) into (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))))) 245.791 * [backup-simplify]: Simplify (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))))) into (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))))) 245.792 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 245.794 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 245.794 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 245.795 * [backup-simplify]: Simplify (- 0) into 0 245.795 * [backup-simplify]: Simplify (+ 0 0) into 0 245.795 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (log PI)))) into 0 245.796 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log PI))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 245.798 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 245.799 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 245.799 * [backup-simplify]: Simplify (- 0) into 0 245.799 * [backup-simplify]: Simplify (+ 0 0) into 0 245.800 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (log 2)))) into 0 245.801 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 245.801 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) 0) (+ (* 0 0) (* 0 (pow PI (- 1/2 (* 1/2 k)))))) into 0 245.803 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 245.803 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 245.804 * [backup-simplify]: Simplify (- 0) into 0 245.804 * [backup-simplify]: Simplify (+ 0 0) into 0 245.804 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 245.805 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0 245.805 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 245.806 * [backup-simplify]: Simplify (+ (* (pow n (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))))) into 0 245.807 * [backup-simplify]: Simplify (- (+ (* (/ 1 (* (pow n (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) (/ 0 (* (pow n (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))))) (* 0 (/ 0 (* (pow n (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))))))) into 0 245.808 * [backup-simplify]: Simplify (+ (* (/ 1 (* (pow n (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0 245.808 * [taylor]: Taking taylor expansion of 0 in k 245.808 * [backup-simplify]: Simplify 0 into 0 245.808 * [backup-simplify]: Simplify 0 into 0 245.808 * [backup-simplify]: Simplify 0 into 0 245.810 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 245.812 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 245.813 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 245.813 * [backup-simplify]: Simplify (- 0) into 0 245.813 * [backup-simplify]: Simplify (+ 0 0) into 0 245.814 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 245.821 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 245.822 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 245.822 * [backup-simplify]: Simplify (- 0) into 0 245.822 * [backup-simplify]: Simplify (+ 0 0) into 0 245.824 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 245.824 * [backup-simplify]: Simplify (+ (* (log 2) 0) (+ (* 0 -1/2) (* 0 1/2))) into 0 245.831 * [backup-simplify]: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log 2) 2) (sqrt 2))) 245.851 * [backup-simplify]: Simplify (+ (* (pow 2 1/2) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* -1/2 (* (log 2) (sqrt 2))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* 1/8 (* (pow (log 2) 2) (sqrt 2))) (pow PI 1/2)))) into (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt PI))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt PI))) (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt PI))))) 245.852 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 245.853 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 245.853 * [backup-simplify]: Simplify (- 0) into 0 245.854 * [backup-simplify]: Simplify (+ 0 0) into 0 245.854 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log n)))) into 0 245.855 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2))) 245.877 * [backup-simplify]: Simplify (+ (* (pow n 1/2) (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt PI))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt PI))) (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt PI)))))) (+ (* (* -1/2 (* (sqrt n) (log n))) (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt PI))) (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt PI)))))) (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (sqrt (* PI 2))))) into (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (+ (* 1/8 (* (sqrt (* PI n)) (* (sqrt 2) (pow (log PI) 2)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (* 1/4 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n))))))))) 245.890 * [backup-simplify]: Simplify (- (+ (* (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))) (/ (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (+ (* 1/8 (* (sqrt (* PI n)) (* (sqrt 2) (pow (log PI) 2)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (* 1/4 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n))))))))) (* (sqrt 2) (sqrt (* n PI))))) (* (+ (* 1/2 (* (/ (log PI) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (+ (* 1/2 (* (/ (log 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (* 1/2 (* (/ (log n) (sqrt 2)) (sqrt (/ 1 (* n PI))))))) (/ (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))) (* (sqrt 2) (sqrt (* n PI))))))) into (+ (* 1/8 (* (/ (pow (log n) 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (+ (* 1/8 (* (/ (pow (log 2) 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (+ (* 1/4 (* (/ (* (log 2) (log n)) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (+ (* 1/8 (* (/ (pow (log PI) 2) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (+ (* 1/4 (* (/ (* (log PI) (log n)) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (* 1/4 (* (/ (* (log 2) (log PI)) (sqrt 2)) (sqrt (/ 1 (* PI n)))))))))) 245.900 * [backup-simplify]: Simplify (+ (* (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))) +nan.0) (+ (* (+ (* 1/2 (* (/ (log PI) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (+ (* 1/2 (* (/ (log 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (* 1/2 (* (/ (log n) (sqrt 2)) (sqrt (/ 1 (* n PI))))))) +nan.0) (* (+ (* 1/8 (* (/ (pow (log n) 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (+ (* 1/8 (* (/ (pow (log 2) 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (+ (* 1/4 (* (/ (* (log 2) (log n)) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (+ (* 1/8 (* (/ (pow (log PI) 2) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (+ (* 1/4 (* (/ (* (log PI) (log n)) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (* 1/4 (* (/ (* (log 2) (log PI)) (sqrt 2)) (sqrt (/ 1 (* PI n)))))))))) 0))) into (- (+ (* +nan.0 (* (/ (log PI) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (- (+ (* +nan.0 (* (/ (log 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (log n) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))))))))))) 245.904 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (/ (log PI) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (- (+ (* +nan.0 (* (/ (log 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (log n) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))))))))))) into (- (+ (* +nan.0 (* (/ (log PI) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (- (+ (* +nan.0 (* (/ (log 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (log n) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))))))))))) 245.905 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 245.908 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 245.909 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 245.909 * [backup-simplify]: Simplify (- 0) into 0 245.909 * [backup-simplify]: Simplify (+ 0 0) into 0 245.910 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))) into 0 245.911 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log PI))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 245.914 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 245.915 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 245.915 * [backup-simplify]: Simplify (- 0) into 0 245.915 * [backup-simplify]: Simplify (+ 0 0) into 0 245.916 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log 2))))) into 0 245.917 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 245.918 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow PI (- 1/2 (* 1/2 k))))))) into 0 245.927 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 245.928 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 245.928 * [backup-simplify]: Simplify (- 0) into 0 245.928 * [backup-simplify]: Simplify (+ 0 0) into 0 245.929 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 245.929 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0 245.930 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 245.931 * [backup-simplify]: Simplify (+ (* (pow n (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))))) into 0 245.933 * [backup-simplify]: Simplify (- (+ (* (/ 1 (* (pow n (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) (/ 0 (* (pow n (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))))) (* 0 (/ 0 (* (pow n (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))))) (* 0 (/ 0 (* (pow n (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))))))) into 0 245.934 * [backup-simplify]: Simplify (+ (* (/ 1 (* (pow n (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0 245.934 * [taylor]: Taking taylor expansion of 0 in k 245.934 * [backup-simplify]: Simplify 0 into 0 245.934 * [backup-simplify]: Simplify 0 into 0 245.934 * [backup-simplify]: Simplify 0 into 0 245.934 * [backup-simplify]: Simplify 0 into 0 245.936 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 245.940 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 245.940 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 245.941 * [backup-simplify]: Simplify (- 0) into 0 245.941 * [backup-simplify]: Simplify (+ 0 0) into 0 245.942 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log PI))))) into 0 245.951 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 3) 6)) (* (/ (pow (- (* 1/2 (log PI))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log PI) 3) (sqrt PI))) 245.952 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 245.952 * [backup-simplify]: Simplify (- 0) into 0 245.952 * [backup-simplify]: Simplify (+ 0 0) into 0 245.955 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 245.956 * [backup-simplify]: Simplify (+ (* (log 2) 0) (+ (* 0 0) (+ (* 0 -1/2) (* 0 1/2)))) into 0 245.965 * [backup-simplify]: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 3) 6)) (* (/ (pow (- (* 1/2 (log 2))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log 2) 3) (sqrt 2))) 245.994 * [backup-simplify]: Simplify (+ (* (pow 2 1/2) (* -1/48 (* (pow (log PI) 3) (sqrt PI)))) (+ (* (* -1/2 (* (log 2) (sqrt 2))) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* 1/8 (* (pow (log 2) 2) (sqrt 2))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1/48 (* (pow (log 2) 3) (sqrt 2))) (pow PI 1/2))))) into (- (+ (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt PI))) (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt PI))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log PI) 2))) (sqrt PI))) (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log PI))) (sqrt PI))))))) 245.996 * [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 0 245.997 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 245.997 * [backup-simplify]: Simplify (- 0) into 0 245.997 * [backup-simplify]: Simplify (+ 0 0) into 0 245.998 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log n))))) into 0 245.999 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 3) 6)) (* (/ (pow (- (* 1/2 (log n))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt n) (pow (log n) 3))) 246.058 * [backup-simplify]: Simplify (+ (* (pow n 1/2) (- (+ (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt PI))) (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt PI))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log PI) 2))) (sqrt PI))) (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log PI))) (sqrt PI)))))))) (+ (* (* -1/2 (* (sqrt n) (log n))) (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt PI))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt PI))) (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt PI)))))) (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt PI))) (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt PI)))))) (* (* -1/48 (* (sqrt n) (pow (log n) 3))) (sqrt (* PI 2)))))) into (- (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log n) 2))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (log PI) (pow (log n) 2))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log PI) 2))) (sqrt (* PI n)))) (+ (* 1/48 (* (* (sqrt 2) (pow (log n) 3)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (log 2) (* (sqrt 2) (* (log PI) (log n)))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (sqrt 2) (* (pow (log PI) 2) (log n))) (sqrt (* PI n)))) (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt (* PI n)))))))))))))) 246.097 * [backup-simplify]: Simplify (- (+ (* (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))) (/ (- (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log n) 2))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (log PI) (pow (log n) 2))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log PI) 2))) (sqrt (* PI n)))) (+ (* 1/48 (* (* (sqrt 2) (pow (log n) 3)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (log 2) (* (sqrt 2) (* (log PI) (log n)))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (sqrt 2) (* (pow (log PI) 2) (log n))) (sqrt (* PI n)))) (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt (* PI n)))))))))))))) (* (sqrt 2) (sqrt (* n PI))))) (* (+ (* 1/2 (* (/ (log PI) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (+ (* 1/2 (* (/ (log 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (* 1/2 (* (/ (log n) (sqrt 2)) (sqrt (/ 1 (* n PI))))))) (/ (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (+ (* 1/8 (* (sqrt (* PI n)) (* (sqrt 2) (pow (log PI) 2)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (* 1/4 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n))))))))) (* (sqrt 2) (sqrt (* n PI))))) (* (+ (* 1/8 (* (/ (pow (log n) 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (+ (* 1/8 (* (/ (pow (log 2) 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (+ (* 1/4 (* (/ (* (log 2) (log n)) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (+ (* 1/8 (* (/ (pow (log PI) 2) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (+ (* 1/4 (* (/ (* (log PI) (log n)) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (* 1/4 (* (/ (* (log 2) (log PI)) (sqrt 2)) (sqrt (/ 1 (* PI n)))))))))) (/ (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))) (* (sqrt 2) (sqrt (* n PI))))))) into (+ (* 1/16 (* (/ (* (pow (log 2) 2) (log n)) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (+ (* 1/48 (* (/ (pow (log PI) 3) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (+ (* 1/16 (* (/ (* (log 2) (pow (log PI) 2)) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (+ (* 1/48 (* (/ (pow (log n) 3) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (+ (* 1/16 (* (/ (* (pow (log PI) 2) (log n)) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (+ (* 1/16 (* (/ (* (pow (log 2) 2) (log PI)) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (+ (* 1/8 (* (/ (* (log 2) (* (log PI) (log n))) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (+ (* 1/16 (* (/ (* (log PI) (pow (log n) 2)) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (+ (* 1/48 (* (/ (pow (log 2) 3) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (* 1/16 (* (/ (* (log 2) (pow (log n) 2)) (sqrt 2)) (sqrt (/ 1 (* n PI)))))))))))))) 246.129 * [backup-simplify]: Simplify (+ (* (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))) +nan.0) (+ (* (+ (* 1/2 (* (/ (log PI) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (+ (* 1/2 (* (/ (log 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (* 1/2 (* (/ (log n) (sqrt 2)) (sqrt (/ 1 (* n PI))))))) +nan.0) (+ (* (+ (* 1/8 (* (/ (pow (log n) 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (+ (* 1/8 (* (/ (pow (log 2) 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (+ (* 1/4 (* (/ (* (log 2) (log n)) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (+ (* 1/8 (* (/ (pow (log PI) 2) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (+ (* 1/4 (* (/ (* (log PI) (log n)) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (* 1/4 (* (/ (* (log 2) (log PI)) (sqrt 2)) (sqrt (/ 1 (* PI n)))))))))) +nan.0) (* (+ (* 1/16 (* (/ (* (pow (log 2) 2) (log n)) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (+ (* 1/48 (* (/ (pow (log PI) 3) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (+ (* 1/16 (* (/ (* (log 2) (pow (log PI) 2)) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (+ (* 1/48 (* (/ (pow (log n) 3) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (+ (* 1/16 (* (/ (* (pow (log PI) 2) (log n)) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (+ (* 1/16 (* (/ (* (pow (log 2) 2) (log PI)) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (+ (* 1/8 (* (/ (* (log 2) (* (log PI) (log n))) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (+ (* 1/16 (* (/ (* (log PI) (pow (log n) 2)) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (+ (* 1/48 (* (/ (pow (log 2) 3) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (* 1/16 (* (/ (* (log 2) (pow (log n) 2)) (sqrt 2)) (sqrt (/ 1 (* n PI)))))))))))))) 0)))) into (- (+ (* +nan.0 (* (/ (log PI) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (- (+ (* +nan.0 (* (/ (* (log 2) (log n)) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (log n) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (* (log PI) (log n)) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (- (+ (* +nan.0 (* (/ (pow (log n) 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (pow (log 2) 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (log 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (pow (log PI) 2) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (- (* +nan.0 (* (/ (* (log 2) (log PI)) (sqrt 2)) (sqrt (/ 1 (* PI n)))))))))))))))))))))))) 246.143 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (/ (log PI) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (- (+ (* +nan.0 (* (/ (* (log 2) (log n)) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (log n) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (* (log PI) (log n)) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (- (+ (* +nan.0 (* (/ (pow (log n) 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (pow (log 2) 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (log 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (pow (log PI) 2) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (- (* +nan.0 (* (/ (* (log 2) (log PI)) (sqrt 2)) (sqrt (/ 1 (* PI n)))))))))))))))))))))))) into (- (+ (* +nan.0 (* (/ (log 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (* (log 2) (log n)) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (log PI) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (- (+ (* +nan.0 (* (/ (* (log PI) (log n)) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (- (+ (* +nan.0 (* (/ (pow (log n) 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (pow (log 2) 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (log n) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (pow (log PI) 2) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (- (* +nan.0 (* (/ (* (log 2) (log PI)) (sqrt 2)) (sqrt (/ 1 (* PI n)))))))))))))))))))))))) 246.163 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (/ (log 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (* (log 2) (log n)) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (log PI) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (- (+ (* +nan.0 (* (/ (* (log PI) (log n)) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (- (+ (* +nan.0 (* (/ (pow (log n) 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (pow (log 2) 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (log n) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (pow (log PI) 2) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (- (* +nan.0 (* (/ (* (log 2) (log PI)) (sqrt 2)) (sqrt (/ 1 (* PI n)))))))))))))))))))))))) (pow (* k 1) 3)) (+ (* (- (+ (* +nan.0 (* (/ (log PI) (sqrt 2)) (sqrt (/ 1 (* PI n))))) (- (+ (* +nan.0 (* (/ (log 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (log n) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))))))))))) (pow (* k 1) 2)) (* (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (* n PI)))))) (* k 1)))) into (- (+ (* +nan.0 (* (/ (* (log PI) (pow k 2)) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (* (log n) (pow k 3)) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (* (pow (log n) 2) (pow k 3)) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (* (log 2) (* (log n) (pow k 3))) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (pow k 2) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (* (log 2) (* (log PI) (pow k 3))) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (* (pow (log 2) 2) (pow k 3)) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (* (pow (log PI) 2) (pow k 3)) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (* (log PI) (* (log n) (pow k 3))) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (pow k 3) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ k (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (* (log 2) (pow k 3)) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (* (log n) (pow k 2)) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (* (log 2) (pow k 2)) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (/ (* (log PI) (pow k 3)) (sqrt 2)) (sqrt (/ 1 (* n PI)))))))))))))))))))))))))))))))))) 246.163 * [backup-simplify]: Simplify (* (/ (* 1 (/ 1 (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))))) (pow PI (- 1/2 (/ (/ 1 k) 2)))) (/ (sqrt (/ 1 k)) (pow 2 (- 1/2 (/ (/ 1 k) 2))))) into (* (/ 1 (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) (sqrt (/ 1 k))) 246.163 * [approximate]: Taking taylor expansion of (* (/ 1 (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) (sqrt (/ 1 k))) in (n k) around 0 246.163 * [taylor]: Taking taylor expansion of (* (/ 1 (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) (sqrt (/ 1 k))) in k 246.163 * [taylor]: Taking taylor expansion of (/ 1 (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) in k 246.163 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in k 246.163 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in k 246.163 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in k 246.163 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in k 246.163 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 246.163 * [taylor]: Taking taylor expansion of 1/2 in k 246.163 * [backup-simplify]: Simplify 1/2 into 1/2 246.163 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 246.163 * [taylor]: Taking taylor expansion of 1/2 in k 246.163 * [backup-simplify]: Simplify 1/2 into 1/2 246.163 * [taylor]: Taking taylor expansion of (/ 1 k) in k 246.163 * [taylor]: Taking taylor expansion of k in k 246.163 * [backup-simplify]: Simplify 0 into 0 246.163 * [backup-simplify]: Simplify 1 into 1 246.164 * [backup-simplify]: Simplify (/ 1 1) into 1 246.164 * [taylor]: Taking taylor expansion of (log 2) in k 246.164 * [taylor]: Taking taylor expansion of 2 in k 246.164 * [backup-simplify]: Simplify 2 into 2 246.164 * [backup-simplify]: Simplify (log 2) into (log 2) 246.164 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 246.165 * [backup-simplify]: Simplify (- 1/2) into -1/2 246.165 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 246.165 * [backup-simplify]: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2)) 246.166 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 246.166 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 246.166 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 246.166 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 246.166 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 246.166 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 246.166 * [taylor]: Taking taylor expansion of 1/2 in k 246.166 * [backup-simplify]: Simplify 1/2 into 1/2 246.166 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 246.166 * [taylor]: Taking taylor expansion of 1/2 in k 246.166 * [backup-simplify]: Simplify 1/2 into 1/2 246.166 * [taylor]: Taking taylor expansion of (/ 1 k) in k 246.166 * [taylor]: Taking taylor expansion of k in k 246.166 * [backup-simplify]: Simplify 0 into 0 246.166 * [backup-simplify]: Simplify 1 into 1 246.166 * [backup-simplify]: Simplify (/ 1 1) into 1 246.166 * [taylor]: Taking taylor expansion of (log PI) in k 246.166 * [taylor]: Taking taylor expansion of PI in k 246.166 * [backup-simplify]: Simplify PI into PI 246.167 * [backup-simplify]: Simplify (log PI) into (log PI) 246.167 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 246.167 * [backup-simplify]: Simplify (- 1/2) into -1/2 246.167 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 246.168 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 246.168 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 246.169 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 246.169 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in k 246.169 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in k 246.169 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 246.169 * [taylor]: Taking taylor expansion of 1/2 in k 246.169 * [backup-simplify]: Simplify 1/2 into 1/2 246.169 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 246.169 * [taylor]: Taking taylor expansion of 1/2 in k 246.169 * [backup-simplify]: Simplify 1/2 into 1/2 246.169 * [taylor]: Taking taylor expansion of (/ 1 k) in k 246.169 * [taylor]: Taking taylor expansion of k in k 246.169 * [backup-simplify]: Simplify 0 into 0 246.169 * [backup-simplify]: Simplify 1 into 1 246.169 * [backup-simplify]: Simplify (/ 1 1) into 1 246.169 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k 246.169 * [taylor]: Taking taylor expansion of (/ 1 n) in k 246.169 * [taylor]: Taking taylor expansion of n in k 246.169 * [backup-simplify]: Simplify n into n 246.169 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n) 246.169 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n)) 246.169 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 246.170 * [backup-simplify]: Simplify (- 1/2) into -1/2 246.170 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 246.170 * [backup-simplify]: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) 246.170 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 246.170 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) 246.171 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) 246.171 * [backup-simplify]: Simplify (/ 1 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) into (/ 1 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) 246.171 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 246.171 * [taylor]: Taking taylor expansion of (/ 1 k) in k 246.171 * [taylor]: Taking taylor expansion of k in k 246.171 * [backup-simplify]: Simplify 0 into 0 246.171 * [backup-simplify]: Simplify 1 into 1 246.171 * [backup-simplify]: Simplify (/ 1 1) into 1 246.172 * [backup-simplify]: Simplify (sqrt 0) into 0 246.173 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 246.173 * [taylor]: Taking taylor expansion of (* (/ 1 (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) (sqrt (/ 1 k))) in n 246.173 * [taylor]: Taking taylor expansion of (/ 1 (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 246.173 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 246.173 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in n 246.173 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in n 246.173 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in n 246.173 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 246.173 * [taylor]: Taking taylor expansion of 1/2 in n 246.173 * [backup-simplify]: Simplify 1/2 into 1/2 246.173 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 246.173 * [taylor]: Taking taylor expansion of 1/2 in n 246.173 * [backup-simplify]: Simplify 1/2 into 1/2 246.173 * [taylor]: Taking taylor expansion of (/ 1 k) in n 246.173 * [taylor]: Taking taylor expansion of k in n 246.173 * [backup-simplify]: Simplify k into k 246.173 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 246.173 * [taylor]: Taking taylor expansion of (log 2) in n 246.173 * [taylor]: Taking taylor expansion of 2 in n 246.173 * [backup-simplify]: Simplify 2 into 2 246.173 * [backup-simplify]: Simplify (log 2) into (log 2) 246.173 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 246.173 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 246.173 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 246.174 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 246.174 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 246.174 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 246.174 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 246.174 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 246.174 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 246.174 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 246.174 * [taylor]: Taking taylor expansion of 1/2 in n 246.174 * [backup-simplify]: Simplify 1/2 into 1/2 246.174 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 246.174 * [taylor]: Taking taylor expansion of 1/2 in n 246.174 * [backup-simplify]: Simplify 1/2 into 1/2 246.174 * [taylor]: Taking taylor expansion of (/ 1 k) in n 246.174 * [taylor]: Taking taylor expansion of k in n 246.174 * [backup-simplify]: Simplify k into k 246.174 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 246.174 * [taylor]: Taking taylor expansion of (log PI) in n 246.174 * [taylor]: Taking taylor expansion of PI in n 246.174 * [backup-simplify]: Simplify PI into PI 246.175 * [backup-simplify]: Simplify (log PI) into (log PI) 246.175 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 246.175 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 246.175 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 246.175 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 246.175 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 246.175 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 246.176 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 246.176 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 246.176 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 246.176 * [taylor]: Taking taylor expansion of 1/2 in n 246.176 * [backup-simplify]: Simplify 1/2 into 1/2 246.176 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 246.176 * [taylor]: Taking taylor expansion of 1/2 in n 246.176 * [backup-simplify]: Simplify 1/2 into 1/2 246.176 * [taylor]: Taking taylor expansion of (/ 1 k) in n 246.176 * [taylor]: Taking taylor expansion of k in n 246.176 * [backup-simplify]: Simplify k into k 246.176 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 246.176 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 246.176 * [taylor]: Taking taylor expansion of (/ 1 n) in n 246.176 * [taylor]: Taking taylor expansion of n in n 246.176 * [backup-simplify]: Simplify 0 into 0 246.176 * [backup-simplify]: Simplify 1 into 1 246.176 * [backup-simplify]: Simplify (/ 1 1) into 1 246.181 * [backup-simplify]: Simplify (log 1) into 0 246.181 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 246.181 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 246.181 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 246.182 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 246.182 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 246.182 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 246.182 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 246.182 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) 246.183 * [backup-simplify]: Simplify (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 246.183 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 246.183 * [taylor]: Taking taylor expansion of (/ 1 k) in n 246.183 * [taylor]: Taking taylor expansion of k in n 246.183 * [backup-simplify]: Simplify k into k 246.183 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 246.183 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 246.183 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 246.183 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 246.183 * [taylor]: Taking taylor expansion of (* (/ 1 (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) (sqrt (/ 1 k))) in n 246.183 * [taylor]: Taking taylor expansion of (/ 1 (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 246.183 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 246.183 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in n 246.183 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in n 246.183 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in n 246.183 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 246.183 * [taylor]: Taking taylor expansion of 1/2 in n 246.183 * [backup-simplify]: Simplify 1/2 into 1/2 246.183 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 246.183 * [taylor]: Taking taylor expansion of 1/2 in n 246.183 * [backup-simplify]: Simplify 1/2 into 1/2 246.183 * [taylor]: Taking taylor expansion of (/ 1 k) in n 246.183 * [taylor]: Taking taylor expansion of k in n 246.183 * [backup-simplify]: Simplify k into k 246.183 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 246.183 * [taylor]: Taking taylor expansion of (log 2) in n 246.183 * [taylor]: Taking taylor expansion of 2 in n 246.184 * [backup-simplify]: Simplify 2 into 2 246.184 * [backup-simplify]: Simplify (log 2) into (log 2) 246.184 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 246.184 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 246.184 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 246.184 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 246.185 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 246.185 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 246.185 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 246.185 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 246.185 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 246.185 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 246.185 * [taylor]: Taking taylor expansion of 1/2 in n 246.185 * [backup-simplify]: Simplify 1/2 into 1/2 246.185 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 246.185 * [taylor]: Taking taylor expansion of 1/2 in n 246.185 * [backup-simplify]: Simplify 1/2 into 1/2 246.185 * [taylor]: Taking taylor expansion of (/ 1 k) in n 246.185 * [taylor]: Taking taylor expansion of k in n 246.185 * [backup-simplify]: Simplify k into k 246.185 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 246.185 * [taylor]: Taking taylor expansion of (log PI) in n 246.185 * [taylor]: Taking taylor expansion of PI in n 246.185 * [backup-simplify]: Simplify PI into PI 246.185 * [backup-simplify]: Simplify (log PI) into (log PI) 246.185 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 246.185 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 246.185 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 246.186 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 246.186 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 246.186 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 246.186 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 246.186 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 246.186 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 246.186 * [taylor]: Taking taylor expansion of 1/2 in n 246.186 * [backup-simplify]: Simplify 1/2 into 1/2 246.186 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 246.186 * [taylor]: Taking taylor expansion of 1/2 in n 246.186 * [backup-simplify]: Simplify 1/2 into 1/2 246.186 * [taylor]: Taking taylor expansion of (/ 1 k) in n 246.186 * [taylor]: Taking taylor expansion of k in n 246.186 * [backup-simplify]: Simplify k into k 246.186 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 246.186 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 246.186 * [taylor]: Taking taylor expansion of (/ 1 n) in n 246.186 * [taylor]: Taking taylor expansion of n in n 246.186 * [backup-simplify]: Simplify 0 into 0 246.186 * [backup-simplify]: Simplify 1 into 1 246.187 * [backup-simplify]: Simplify (/ 1 1) into 1 246.187 * [backup-simplify]: Simplify (log 1) into 0 246.187 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 246.187 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 246.187 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 246.187 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 246.187 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 246.187 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 246.188 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 246.188 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) 246.189 * [backup-simplify]: Simplify (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 246.189 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 246.189 * [taylor]: Taking taylor expansion of (/ 1 k) in n 246.189 * [taylor]: Taking taylor expansion of k in n 246.189 * [backup-simplify]: Simplify k into k 246.189 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 246.189 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 246.189 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 246.189 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 246.189 * [backup-simplify]: Simplify (* (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) (sqrt (/ 1 k))) into (* (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) (sqrt (/ 1 k))) 246.189 * [taylor]: Taking taylor expansion of (* (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) (sqrt (/ 1 k))) in k 246.190 * [taylor]: Taking taylor expansion of (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) in k 246.190 * [taylor]: Taking taylor expansion of (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) in k 246.190 * [taylor]: Taking taylor expansion of (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) in k 246.190 * [taylor]: Taking taylor expansion of (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) in k 246.190 * [taylor]: Taking taylor expansion of -1 in k 246.190 * [backup-simplify]: Simplify -1 into -1 246.190 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log n)) in k 246.190 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 246.190 * [taylor]: Taking taylor expansion of 1/2 in k 246.190 * [backup-simplify]: Simplify 1/2 into 1/2 246.190 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 246.190 * [taylor]: Taking taylor expansion of 1/2 in k 246.190 * [backup-simplify]: Simplify 1/2 into 1/2 246.190 * [taylor]: Taking taylor expansion of (/ 1 k) in k 246.190 * [taylor]: Taking taylor expansion of k in k 246.190 * [backup-simplify]: Simplify 0 into 0 246.190 * [backup-simplify]: Simplify 1 into 1 246.190 * [backup-simplify]: Simplify (/ 1 1) into 1 246.190 * [taylor]: Taking taylor expansion of (log n) in k 246.190 * [taylor]: Taking taylor expansion of n in k 246.190 * [backup-simplify]: Simplify n into n 246.190 * [backup-simplify]: Simplify (log n) into (log n) 246.190 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 246.191 * [backup-simplify]: Simplify (- 1/2) into -1/2 246.191 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 246.191 * [backup-simplify]: Simplify (* -1/2 (log n)) into (* -1/2 (log n)) 246.191 * [backup-simplify]: Simplify (* -1 (* -1/2 (log n))) into (* 1/2 (log n)) 246.191 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 246.191 * [taylor]: Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) in k 246.191 * [taylor]: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in k 246.191 * [taylor]: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in k 246.191 * [taylor]: Taking taylor expansion of (log 2) in k 246.191 * [taylor]: Taking taylor expansion of 2 in k 246.191 * [backup-simplify]: Simplify 2 into 2 246.191 * [backup-simplify]: Simplify (log 2) into (log 2) 246.192 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 246.192 * [taylor]: Taking taylor expansion of 1/2 in k 246.192 * [backup-simplify]: Simplify 1/2 into 1/2 246.192 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 246.192 * [taylor]: Taking taylor expansion of 1/2 in k 246.192 * [backup-simplify]: Simplify 1/2 into 1/2 246.192 * [taylor]: Taking taylor expansion of (/ 1 k) in k 246.192 * [taylor]: Taking taylor expansion of k in k 246.192 * [backup-simplify]: Simplify 0 into 0 246.192 * [backup-simplify]: Simplify 1 into 1 246.192 * [backup-simplify]: Simplify (/ 1 1) into 1 246.192 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 246.192 * [backup-simplify]: Simplify (- 1/2) into -1/2 246.193 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 246.193 * [backup-simplify]: Simplify (* (log 2) -1/2) into (* -1/2 (log 2)) 246.194 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 246.194 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 246.194 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 246.194 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 246.194 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 246.194 * [taylor]: Taking taylor expansion of 1/2 in k 246.194 * [backup-simplify]: Simplify 1/2 into 1/2 246.194 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 246.194 * [taylor]: Taking taylor expansion of 1/2 in k 246.194 * [backup-simplify]: Simplify 1/2 into 1/2 246.194 * [taylor]: Taking taylor expansion of (/ 1 k) in k 246.194 * [taylor]: Taking taylor expansion of k in k 246.194 * [backup-simplify]: Simplify 0 into 0 246.194 * [backup-simplify]: Simplify 1 into 1 246.194 * [backup-simplify]: Simplify (/ 1 1) into 1 246.194 * [taylor]: Taking taylor expansion of (log PI) in k 246.194 * [taylor]: Taking taylor expansion of PI in k 246.194 * [backup-simplify]: Simplify PI into PI 246.194 * [backup-simplify]: Simplify (log PI) into (log PI) 246.195 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 246.195 * [backup-simplify]: Simplify (- 1/2) into -1/2 246.195 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 246.196 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 246.196 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 246.196 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 246.197 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) 246.197 * [backup-simplify]: Simplify (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 246.197 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 246.197 * [taylor]: Taking taylor expansion of (/ 1 k) in k 246.197 * [taylor]: Taking taylor expansion of k in k 246.197 * [backup-simplify]: Simplify 0 into 0 246.198 * [backup-simplify]: Simplify 1 into 1 246.198 * [backup-simplify]: Simplify (/ 1 1) into 1 246.198 * [backup-simplify]: Simplify (sqrt 0) into 0 246.199 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 246.199 * [backup-simplify]: Simplify (* (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 0) into 0 246.199 * [backup-simplify]: Simplify 0 into 0 246.200 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 246.201 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 246.201 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 246.201 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 246.201 * [backup-simplify]: Simplify (- 0) into 0 246.202 * [backup-simplify]: Simplify (+ 0 0) into 0 246.202 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 246.202 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 246.203 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 246.203 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 246.204 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 246.204 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 246.204 * [backup-simplify]: Simplify (- 0) into 0 246.204 * [backup-simplify]: Simplify (+ 0 0) into 0 246.205 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (log PI))) into 0 246.206 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 246.206 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))))) into 0 246.207 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 246.207 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 246.207 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 246.207 * [backup-simplify]: Simplify (- 0) into 0 246.207 * [backup-simplify]: Simplify (+ 0 0) into 0 246.208 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (log 2))) into 0 246.209 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 246.209 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into 0 246.210 * [backup-simplify]: Simplify (- (+ (* (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) (/ 0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))))) into 0 246.211 * [backup-simplify]: Simplify (+ (* (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 0) (* 0 (sqrt (/ 1 k)))) into 0 246.211 * [taylor]: Taking taylor expansion of 0 in k 246.211 * [backup-simplify]: Simplify 0 into 0 246.211 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into 0 246.212 * [backup-simplify]: Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (* 0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into 0 246.213 * [backup-simplify]: Simplify (- (+ (* (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) (/ 0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))))) into 0 246.214 * [backup-simplify]: Simplify (+ (* (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))))) 246.214 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))))) into (- (* +nan.0 (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))))) 246.214 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 246.215 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 246.215 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 246.217 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 246.217 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 246.218 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 246.218 * [backup-simplify]: Simplify (- 0) into 0 246.218 * [backup-simplify]: Simplify (+ 0 0) into 0 246.218 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 246.219 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 246.220 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 246.221 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 246.222 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 246.222 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 246.222 * [backup-simplify]: Simplify (- 0) into 0 246.223 * [backup-simplify]: Simplify (+ 0 0) into 0 246.223 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (log PI)))) into 0 246.224 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 246.225 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))))) into 0 246.227 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 246.227 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 246.227 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 246.228 * [backup-simplify]: Simplify (- 0) into 0 246.228 * [backup-simplify]: Simplify (+ 0 0) into 0 246.228 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (log 2)))) into 0 246.229 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 246.230 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 246.232 * [backup-simplify]: Simplify (- (+ (* (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) (/ 0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) (* 0 (/ 0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))))) into 0 246.232 * [backup-simplify]: Simplify (+ (* (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 246.233 * [taylor]: Taking taylor expansion of 0 in k 246.233 * [backup-simplify]: Simplify 0 into 0 246.233 * [backup-simplify]: Simplify 0 into 0 246.233 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 246.235 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 246.236 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into 0 246.236 * [backup-simplify]: Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (+ (* 0 0) (* 0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 246.238 * [backup-simplify]: Simplify (- (+ (* (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) (/ 0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) (* 0 (/ 0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))))) into 0 246.239 * [backup-simplify]: Simplify (+ (* (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))))) 246.239 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))))) into (- (* +nan.0 (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))))) 246.239 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 246.240 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 246.241 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 246.243 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 246.244 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 246.244 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 246.245 * [backup-simplify]: Simplify (- 0) into 0 246.245 * [backup-simplify]: Simplify (+ 0 0) into 0 246.245 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 246.246 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 246.247 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 246.250 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 246.250 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 246.251 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 246.251 * [backup-simplify]: Simplify (- 0) into 0 246.252 * [backup-simplify]: Simplify (+ 0 0) into 0 246.252 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))) into 0 246.254 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 246.254 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))))))) into 0 246.257 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 246.257 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 246.258 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 246.258 * [backup-simplify]: Simplify (- 0) into 0 246.259 * [backup-simplify]: Simplify (+ 0 0) into 0 246.259 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log 2))))) into 0 246.260 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 246.262 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))))) into 0 246.264 * [backup-simplify]: Simplify (- (+ (* (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) (/ 0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) (* 0 (/ 0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) (* 0 (/ 0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))))) into 0 246.265 * [backup-simplify]: Simplify (+ (* (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0 246.265 * [taylor]: Taking taylor expansion of 0 in k 246.265 * [backup-simplify]: Simplify 0 into 0 246.265 * [backup-simplify]: Simplify 0 into 0 246.265 * [backup-simplify]: Simplify 0 into 0 246.265 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 246.273 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 246.274 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 246.275 * [backup-simplify]: Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))))) into 0 246.277 * [backup-simplify]: Simplify (- (+ (* (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) (/ 0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) (* 0 (/ 0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) (* 0 (/ 0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))))) into 0 246.278 * [backup-simplify]: Simplify (+ (* (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))))) 246.279 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))))) into (- (* +nan.0 (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))))) 246.281 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))))) (pow (* (/ 1 k) 1) 2)) (+ (* (- (* +nan.0 (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))))) (* (/ 1 k) 1)) (- (* +nan.0 (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (pow PI (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) k))))) (- (+ (* +nan.0 (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))))) (- (* +nan.0 (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (pow PI (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow k 2))))))))))) 246.281 * [backup-simplify]: Simplify (* (/ (* 1 (/ 1 (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))))) (pow PI (- 1/2 (/ (/ 1 (- k)) 2)))) (/ (sqrt (/ 1 (- k))) (pow 2 (- 1/2 (/ (/ 1 (- k)) 2))))) into (/ (sqrt (/ -1 k)) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 246.281 * [approximate]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in (n k) around 0 246.281 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in k 246.281 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 246.281 * [taylor]: Taking taylor expansion of (/ -1 k) in k 246.281 * [taylor]: Taking taylor expansion of -1 in k 246.281 * [backup-simplify]: Simplify -1 into -1 246.281 * [taylor]: Taking taylor expansion of k in k 246.281 * [backup-simplify]: Simplify 0 into 0 246.281 * [backup-simplify]: Simplify 1 into 1 246.282 * [backup-simplify]: Simplify (/ -1 1) into -1 246.282 * [backup-simplify]: Simplify (sqrt 0) into 0 246.283 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 246.283 * [taylor]: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in k 246.283 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 246.283 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in k 246.283 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in k 246.283 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 246.283 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 246.283 * [taylor]: Taking taylor expansion of 1/2 in k 246.283 * [backup-simplify]: Simplify 1/2 into 1/2 246.283 * [taylor]: Taking taylor expansion of (/ 1 k) in k 246.283 * [taylor]: Taking taylor expansion of k in k 246.283 * [backup-simplify]: Simplify 0 into 0 246.283 * [backup-simplify]: Simplify 1 into 1 246.283 * [backup-simplify]: Simplify (/ 1 1) into 1 246.283 * [taylor]: Taking taylor expansion of 1/2 in k 246.283 * [backup-simplify]: Simplify 1/2 into 1/2 246.283 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k 246.283 * [taylor]: Taking taylor expansion of (/ -1 n) in k 246.283 * [taylor]: Taking taylor expansion of -1 in k 246.283 * [backup-simplify]: Simplify -1 into -1 246.283 * [taylor]: Taking taylor expansion of n in k 246.283 * [backup-simplify]: Simplify n into n 246.283 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n) 246.284 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n)) 246.284 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 246.284 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 246.284 * [backup-simplify]: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) 246.284 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 246.284 * [taylor]: Taking taylor expansion of (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 246.284 * [taylor]: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in k 246.284 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in k 246.284 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in k 246.284 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 246.284 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 246.284 * [taylor]: Taking taylor expansion of 1/2 in k 246.284 * [backup-simplify]: Simplify 1/2 into 1/2 246.284 * [taylor]: Taking taylor expansion of (/ 1 k) in k 246.284 * [taylor]: Taking taylor expansion of k in k 246.284 * [backup-simplify]: Simplify 0 into 0 246.284 * [backup-simplify]: Simplify 1 into 1 246.285 * [backup-simplify]: Simplify (/ 1 1) into 1 246.285 * [taylor]: Taking taylor expansion of 1/2 in k 246.285 * [backup-simplify]: Simplify 1/2 into 1/2 246.285 * [taylor]: Taking taylor expansion of (log 2) in k 246.285 * [taylor]: Taking taylor expansion of 2 in k 246.285 * [backup-simplify]: Simplify 2 into 2 246.285 * [backup-simplify]: Simplify (log 2) into (log 2) 246.285 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 246.286 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 246.286 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 246.286 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 246.287 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 246.287 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 246.287 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 246.287 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 246.287 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 246.287 * [taylor]: Taking taylor expansion of 1/2 in k 246.287 * [backup-simplify]: Simplify 1/2 into 1/2 246.287 * [taylor]: Taking taylor expansion of (/ 1 k) in k 246.287 * [taylor]: Taking taylor expansion of k in k 246.287 * [backup-simplify]: Simplify 0 into 0 246.287 * [backup-simplify]: Simplify 1 into 1 246.287 * [backup-simplify]: Simplify (/ 1 1) into 1 246.287 * [taylor]: Taking taylor expansion of 1/2 in k 246.287 * [backup-simplify]: Simplify 1/2 into 1/2 246.287 * [taylor]: Taking taylor expansion of (log PI) in k 246.287 * [taylor]: Taking taylor expansion of PI in k 246.287 * [backup-simplify]: Simplify PI into PI 246.287 * [backup-simplify]: Simplify (log PI) into (log PI) 246.288 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 246.288 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 246.288 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 246.289 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 246.289 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 246.290 * [backup-simplify]: Simplify (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 246.290 * [backup-simplify]: Simplify (/ +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (/ +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 246.290 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 246.290 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 246.290 * [taylor]: Taking taylor expansion of (/ -1 k) in n 246.290 * [taylor]: Taking taylor expansion of -1 in n 246.290 * [backup-simplify]: Simplify -1 into -1 246.290 * [taylor]: Taking taylor expansion of k in n 246.290 * [backup-simplify]: Simplify k into k 246.290 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 246.290 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 246.290 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 246.290 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 246.290 * [taylor]: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 246.290 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 246.291 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 246.291 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 246.291 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 246.291 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 246.291 * [taylor]: Taking taylor expansion of 1/2 in n 246.291 * [backup-simplify]: Simplify 1/2 into 1/2 246.291 * [taylor]: Taking taylor expansion of (/ 1 k) in n 246.291 * [taylor]: Taking taylor expansion of k in n 246.291 * [backup-simplify]: Simplify k into k 246.291 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 246.291 * [taylor]: Taking taylor expansion of 1/2 in n 246.291 * [backup-simplify]: Simplify 1/2 into 1/2 246.291 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 246.291 * [taylor]: Taking taylor expansion of (/ -1 n) in n 246.291 * [taylor]: Taking taylor expansion of -1 in n 246.291 * [backup-simplify]: Simplify -1 into -1 246.291 * [taylor]: Taking taylor expansion of n in n 246.291 * [backup-simplify]: Simplify 0 into 0 246.291 * [backup-simplify]: Simplify 1 into 1 246.291 * [backup-simplify]: Simplify (/ -1 1) into -1 246.291 * [backup-simplify]: Simplify (log -1) into (log -1) 246.291 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 246.292 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 246.292 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 246.292 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 246.293 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 246.293 * [taylor]: Taking taylor expansion of (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 246.293 * [taylor]: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in n 246.293 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in n 246.293 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in n 246.293 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 246.293 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 246.293 * [taylor]: Taking taylor expansion of 1/2 in n 246.293 * [backup-simplify]: Simplify 1/2 into 1/2 246.293 * [taylor]: Taking taylor expansion of (/ 1 k) in n 246.293 * [taylor]: Taking taylor expansion of k in n 246.293 * [backup-simplify]: Simplify k into k 246.293 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 246.293 * [taylor]: Taking taylor expansion of 1/2 in n 246.293 * [backup-simplify]: Simplify 1/2 into 1/2 246.293 * [taylor]: Taking taylor expansion of (log 2) in n 246.293 * [taylor]: Taking taylor expansion of 2 in n 246.293 * [backup-simplify]: Simplify 2 into 2 246.293 * [backup-simplify]: Simplify (log 2) into (log 2) 246.293 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 246.293 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 246.294 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 246.294 * [backup-simplify]: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 246.294 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 246.294 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 246.294 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 246.294 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 246.294 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 246.294 * [taylor]: Taking taylor expansion of 1/2 in n 246.294 * [backup-simplify]: Simplify 1/2 into 1/2 246.294 * [taylor]: Taking taylor expansion of (/ 1 k) in n 246.294 * [taylor]: Taking taylor expansion of k in n 246.294 * [backup-simplify]: Simplify k into k 246.294 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 246.294 * [taylor]: Taking taylor expansion of 1/2 in n 246.294 * [backup-simplify]: Simplify 1/2 into 1/2 246.294 * [taylor]: Taking taylor expansion of (log PI) in n 246.294 * [taylor]: Taking taylor expansion of PI in n 246.294 * [backup-simplify]: Simplify PI into PI 246.295 * [backup-simplify]: Simplify (log PI) into (log PI) 246.295 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 246.295 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 246.295 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 246.295 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 246.296 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 246.296 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 246.297 * [backup-simplify]: Simplify (/ (sqrt (/ -1 k)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (/ (sqrt (/ -1 k)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 246.297 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 246.297 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 246.297 * [taylor]: Taking taylor expansion of (/ -1 k) in n 246.297 * [taylor]: Taking taylor expansion of -1 in n 246.297 * [backup-simplify]: Simplify -1 into -1 246.297 * [taylor]: Taking taylor expansion of k in n 246.297 * [backup-simplify]: Simplify k into k 246.297 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 246.297 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 246.297 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 246.298 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 246.298 * [taylor]: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 246.298 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 246.298 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 246.298 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 246.298 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 246.298 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 246.298 * [taylor]: Taking taylor expansion of 1/2 in n 246.298 * [backup-simplify]: Simplify 1/2 into 1/2 246.298 * [taylor]: Taking taylor expansion of (/ 1 k) in n 246.298 * [taylor]: Taking taylor expansion of k in n 246.298 * [backup-simplify]: Simplify k into k 246.298 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 246.298 * [taylor]: Taking taylor expansion of 1/2 in n 246.298 * [backup-simplify]: Simplify 1/2 into 1/2 246.298 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 246.298 * [taylor]: Taking taylor expansion of (/ -1 n) in n 246.298 * [taylor]: Taking taylor expansion of -1 in n 246.298 * [backup-simplify]: Simplify -1 into -1 246.298 * [taylor]: Taking taylor expansion of n in n 246.298 * [backup-simplify]: Simplify 0 into 0 246.298 * [backup-simplify]: Simplify 1 into 1 246.298 * [backup-simplify]: Simplify (/ -1 1) into -1 246.298 * [backup-simplify]: Simplify (log -1) into (log -1) 246.299 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 246.299 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 246.299 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 246.299 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 246.300 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 246.300 * [taylor]: Taking taylor expansion of (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 246.300 * [taylor]: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in n 246.300 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in n 246.300 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in n 246.300 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 246.300 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 246.300 * [taylor]: Taking taylor expansion of 1/2 in n 246.300 * [backup-simplify]: Simplify 1/2 into 1/2 246.300 * [taylor]: Taking taylor expansion of (/ 1 k) in n 246.300 * [taylor]: Taking taylor expansion of k in n 246.300 * [backup-simplify]: Simplify k into k 246.300 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 246.300 * [taylor]: Taking taylor expansion of 1/2 in n 246.300 * [backup-simplify]: Simplify 1/2 into 1/2 246.300 * [taylor]: Taking taylor expansion of (log 2) in n 246.300 * [taylor]: Taking taylor expansion of 2 in n 246.300 * [backup-simplify]: Simplify 2 into 2 246.300 * [backup-simplify]: Simplify (log 2) into (log 2) 246.300 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 246.300 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 246.301 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 246.301 * [backup-simplify]: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 246.301 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 246.301 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 246.301 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 246.301 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 246.301 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 246.301 * [taylor]: Taking taylor expansion of 1/2 in n 246.301 * [backup-simplify]: Simplify 1/2 into 1/2 246.301 * [taylor]: Taking taylor expansion of (/ 1 k) in n 246.301 * [taylor]: Taking taylor expansion of k in n 246.301 * [backup-simplify]: Simplify k into k 246.301 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 246.301 * [taylor]: Taking taylor expansion of 1/2 in n 246.301 * [backup-simplify]: Simplify 1/2 into 1/2 246.301 * [taylor]: Taking taylor expansion of (log PI) in n 246.301 * [taylor]: Taking taylor expansion of PI in n 246.301 * [backup-simplify]: Simplify PI into PI 246.302 * [backup-simplify]: Simplify (log PI) into (log PI) 246.302 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 246.302 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 246.302 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 246.302 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 246.303 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 246.303 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 246.304 * [backup-simplify]: Simplify (/ (sqrt (/ -1 k)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (/ (sqrt (/ -1 k)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 246.304 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in k 246.304 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 246.304 * [taylor]: Taking taylor expansion of (/ -1 k) in k 246.304 * [taylor]: Taking taylor expansion of -1 in k 246.304 * [backup-simplify]: Simplify -1 into -1 246.304 * [taylor]: Taking taylor expansion of k in k 246.304 * [backup-simplify]: Simplify 0 into 0 246.304 * [backup-simplify]: Simplify 1 into 1 246.305 * [backup-simplify]: Simplify (/ -1 1) into -1 246.305 * [backup-simplify]: Simplify (sqrt 0) into 0 246.306 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 246.306 * [taylor]: Taking taylor expansion of (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in k 246.306 * [taylor]: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in k 246.306 * [taylor]: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in k 246.306 * [taylor]: Taking taylor expansion of (log 2) in k 246.306 * [taylor]: Taking taylor expansion of 2 in k 246.306 * [backup-simplify]: Simplify 2 into 2 246.306 * [backup-simplify]: Simplify (log 2) into (log 2) 246.306 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 246.306 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 246.306 * [taylor]: Taking taylor expansion of 1/2 in k 246.306 * [backup-simplify]: Simplify 1/2 into 1/2 246.306 * [taylor]: Taking taylor expansion of (/ 1 k) in k 246.306 * [taylor]: Taking taylor expansion of k in k 246.306 * [backup-simplify]: Simplify 0 into 0 246.306 * [backup-simplify]: Simplify 1 into 1 246.307 * [backup-simplify]: Simplify (/ 1 1) into 1 246.307 * [taylor]: Taking taylor expansion of 1/2 in k 246.307 * [backup-simplify]: Simplify 1/2 into 1/2 246.307 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 246.307 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 246.308 * [backup-simplify]: Simplify (* (log 2) 1/2) into (* 1/2 (log 2)) 246.308 * [backup-simplify]: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 246.308 * [taylor]: Taking taylor expansion of (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 246.308 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) in k 246.308 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) in k 246.308 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 246.308 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 246.308 * [taylor]: Taking taylor expansion of 1/2 in k 246.308 * [backup-simplify]: Simplify 1/2 into 1/2 246.308 * [taylor]: Taking taylor expansion of (/ 1 k) in k 246.308 * [taylor]: Taking taylor expansion of k in k 246.308 * [backup-simplify]: Simplify 0 into 0 246.308 * [backup-simplify]: Simplify 1 into 1 246.308 * [backup-simplify]: Simplify (/ 1 1) into 1 246.308 * [taylor]: Taking taylor expansion of 1/2 in k 246.308 * [backup-simplify]: Simplify 1/2 into 1/2 246.308 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k 246.309 * [taylor]: Taking taylor expansion of (log -1) in k 246.309 * [taylor]: Taking taylor expansion of -1 in k 246.309 * [backup-simplify]: Simplify -1 into -1 246.309 * [backup-simplify]: Simplify (log -1) into (log -1) 246.309 * [taylor]: Taking taylor expansion of (log n) in k 246.309 * [taylor]: Taking taylor expansion of n in k 246.309 * [backup-simplify]: Simplify n into n 246.309 * [backup-simplify]: Simplify (log n) into (log n) 246.309 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 246.309 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 246.309 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 246.310 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n)) 246.310 * [backup-simplify]: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n))) 246.310 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 246.310 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 246.310 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 246.310 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 246.310 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 246.310 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 246.310 * [taylor]: Taking taylor expansion of 1/2 in k 246.310 * [backup-simplify]: Simplify 1/2 into 1/2 246.310 * [taylor]: Taking taylor expansion of (/ 1 k) in k 246.311 * [taylor]: Taking taylor expansion of k in k 246.311 * [backup-simplify]: Simplify 0 into 0 246.311 * [backup-simplify]: Simplify 1 into 1 246.311 * [backup-simplify]: Simplify (/ 1 1) into 1 246.311 * [taylor]: Taking taylor expansion of 1/2 in k 246.311 * [backup-simplify]: Simplify 1/2 into 1/2 246.311 * [taylor]: Taking taylor expansion of (log PI) in k 246.311 * [taylor]: Taking taylor expansion of PI in k 246.311 * [backup-simplify]: Simplify PI into PI 246.311 * [backup-simplify]: Simplify (log PI) into (log PI) 246.312 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 246.312 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 246.313 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 246.313 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 246.313 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 246.314 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 246.315 * [backup-simplify]: Simplify (/ +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (/ +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 246.315 * [backup-simplify]: Simplify (/ +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (/ +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 246.317 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 246.317 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 246.317 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 246.317 * [backup-simplify]: Simplify (+ 0 0) into 0 246.318 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log PI))) into 0 246.318 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 246.319 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 246.319 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 246.320 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 246.320 * [backup-simplify]: Simplify (+ 0 0) into 0 246.320 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log 2))) into 0 246.321 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (+ (* (/ (pow 0 1) 1)))) into 0 246.322 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 246.322 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 246.323 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 246.323 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 246.323 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 246.324 * [backup-simplify]: Simplify (+ 0 0) into 0 246.324 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 246.324 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -1) (log n)))) into 0 246.325 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 246.326 * [backup-simplify]: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 0) (* 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 246.328 * [backup-simplify]: Simplify (- (/ 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (+ (* (/ (sqrt (/ -1 k)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (/ 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))))) into 0 246.328 * [taylor]: Taking taylor expansion of 0 in k 246.328 * [backup-simplify]: Simplify 0 into 0 246.328 * [backup-simplify]: Simplify 0 into 0 246.329 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 246.331 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 246.331 * [backup-simplify]: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 246.332 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 0) (* 0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 246.334 * [backup-simplify]: Simplify (- (/ +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (+ (* (/ +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (/ 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))))) into (- (* +nan.0 (/ 1 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) 246.335 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) 246.335 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 246.336 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 246.337 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 246.338 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 246.338 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 246.338 * [backup-simplify]: Simplify (+ 0 0) into 0 246.339 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (log PI)))) into 0 246.340 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 246.342 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 246.342 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 246.342 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 246.343 * [backup-simplify]: Simplify (+ 0 0) into 0 246.343 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (log 2)))) into 0 246.344 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 246.345 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 0) (+ (* 0 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 246.346 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 246.347 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0 246.347 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 246.348 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 246.348 * [backup-simplify]: Simplify (+ 0 0) into 0 246.349 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 246.349 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0 246.350 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 246.351 * [backup-simplify]: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 0) (+ (* 0 0) (* 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into 0 246.354 * [backup-simplify]: Simplify (- (/ 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (+ (* (/ (sqrt (/ -1 k)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (/ 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) (* 0 (/ 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))))) into 0 246.354 * [taylor]: Taking taylor expansion of 0 in k 246.354 * [backup-simplify]: Simplify 0 into 0 246.354 * [backup-simplify]: Simplify 0 into 0 246.354 * [backup-simplify]: Simplify 0 into 0 246.355 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 246.362 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 246.363 * [backup-simplify]: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 0) (+ (* 0 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 246.364 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 0) (+ (* 0 0) (* 0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into 0 246.368 * [backup-simplify]: Simplify (- (/ +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (+ (* (/ +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (/ 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) (* (- (* +nan.0 (/ 1 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) (/ 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))))) into (- (* +nan.0 (/ 1 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) 246.369 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) 246.372 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (/ 1 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))))) (* (/ 1 (- k)) 1)) (/ +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (pow PI (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) k))))) (- (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (pow PI (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow k 2))))))))))) 246.372 * * * [progress]: simplifying candidates 246.372 * * * * [progress]: [ 1 / 1134 ] simplifiying candidate # 246.372 * * * * [progress]: [ 2 / 1134 ] simplifiying candidate # 246.372 * * * * [progress]: [ 3 / 1134 ] simplifiying candidate # 246.372 * * * * [progress]: [ 4 / 1134 ] simplifiying candidate # 246.372 * * * * [progress]: [ 5 / 1134 ] simplifiying candidate # 246.372 * * * * [progress]: [ 6 / 1134 ] simplifiying candidate # 246.372 * * * * [progress]: [ 7 / 1134 ] simplifiying candidate # 246.372 * * * * [progress]: [ 8 / 1134 ] simplifiying candidate # 246.372 * * * * [progress]: [ 9 / 1134 ] simplifiying candidate # 246.372 * * * * [progress]: [ 10 / 1134 ] simplifiying candidate # 246.372 * * * * [progress]: [ 11 / 1134 ] simplifiying candidate # 246.372 * * * * [progress]: [ 12 / 1134 ] simplifiying candidate # 246.372 * * * * [progress]: [ 13 / 1134 ] simplifiying candidate # 246.372 * * * * [progress]: [ 14 / 1134 ] simplifiying candidate # 246.372 * * * * [progress]: [ 15 / 1134 ] simplifiying candidate # 246.373 * * * * [progress]: [ 16 / 1134 ] simplifiying candidate # 246.373 * * * * [progress]: [ 17 / 1134 ] simplifiying candidate # 246.373 * * * * [progress]: [ 18 / 1134 ] simplifiying candidate # 246.373 * * * * [progress]: [ 19 / 1134 ] simplifiying candidate # 246.373 * * * * [progress]: [ 20 / 1134 ] simplifiying candidate # 246.373 * * * * [progress]: [ 21 / 1134 ] simplifiying candidate # 246.373 * * * * [progress]: [ 22 / 1134 ] simplifiying candidate # 246.373 * * * * [progress]: [ 23 / 1134 ] simplifiying candidate # 246.373 * * * * [progress]: [ 24 / 1134 ] simplifiying candidate # 246.373 * * * * [progress]: [ 25 / 1134 ] simplifiying candidate # 246.373 * * * * [progress]: [ 26 / 1134 ] simplifiying candidate # 246.373 * * * * [progress]: [ 27 / 1134 ] simplifiying candidate # 246.373 * * * * [progress]: [ 28 / 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[progress]: [ 58 / 1134 ] simplifiying candidate # 246.375 * * * * [progress]: [ 59 / 1134 ] simplifiying candidate # 246.375 * * * * [progress]: [ 60 / 1134 ] simplifiying candidate # 246.375 * * * * [progress]: [ 61 / 1134 ] simplifiying candidate # 246.375 * * * * [progress]: [ 62 / 1134 ] simplifiying candidate # 246.375 * * * * [progress]: [ 63 / 1134 ] simplifiying candidate # 246.375 * * * * [progress]: [ 64 / 1134 ] simplifiying candidate # 246.375 * * * * [progress]: [ 65 / 1134 ] simplifiying candidate #real (real->posit16 (pow n (- 1/2 (/ k 2))))))) (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (pow 2 (- 1/2 (/ k 2)))))))> 246.375 * * * * [progress]: [ 66 / 1134 ] simplifiying candidate # 246.375 * * * * [progress]: [ 67 / 1134 ] simplifiying candidate # 246.375 * * * * [progress]: [ 68 / 1134 ] simplifiying candidate # 246.375 * * * * [progress]: [ 69 / 1134 ] simplifiying candidate # 246.375 * * * * [progress]: [ 70 / 1134 ] simplifiying candidate # 246.375 * * * * [progress]: [ 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[progress]: [ 86 / 1134 ] simplifiying candidate # 246.376 * * * * [progress]: [ 87 / 1134 ] simplifiying candidate # 246.376 * * * * [progress]: [ 88 / 1134 ] simplifiying candidate # 246.376 * * * * [progress]: [ 89 / 1134 ] simplifiying candidate # 246.376 * * * * [progress]: [ 90 / 1134 ] simplifiying candidate # 246.376 * * * * [progress]: [ 91 / 1134 ] simplifiying candidate # 246.376 * * * * [progress]: [ 92 / 1134 ] simplifiying candidate # 246.376 * * * * [progress]: [ 93 / 1134 ] simplifiying candidate # 246.376 * * * * [progress]: [ 94 / 1134 ] simplifiying candidate # 246.377 * * * * [progress]: [ 95 / 1134 ] simplifiying candidate # 246.377 * * * * [progress]: [ 96 / 1134 ] simplifiying candidate # 246.377 * * * * [progress]: [ 97 / 1134 ] simplifiying candidate # 246.377 * * * * [progress]: [ 98 / 1134 ] simplifiying candidate # 246.377 * * * * [progress]: [ 99 / 1134 ] simplifiying candidate # 246.377 * * * * [progress]: [ 100 / 1134 ] simplifiying candidate # 246.377 * * * * [progress]: [ 101 / 1134 ] simplifiying candidate # 246.377 * * * * [progress]: [ 102 / 1134 ] simplifiying candidate # 246.377 * * * * [progress]: [ 103 / 1134 ] simplifiying candidate # 246.377 * * * * [progress]: [ 104 / 1134 ] simplifiying candidate # 246.377 * * * * [progress]: [ 105 / 1134 ] simplifiying candidate # 246.377 * * * * [progress]: [ 106 / 1134 ] simplifiying candidate # 246.377 * * * * [progress]: [ 107 / 1134 ] simplifiying candidate # 246.377 * * * * [progress]: [ 108 / 1134 ] simplifiying candidate # 246.377 * * * * [progress]: [ 109 / 1134 ] simplifiying candidate # 246.377 * * * * [progress]: [ 110 / 1134 ] simplifiying candidate # 246.377 * * * * [progress]: [ 111 / 1134 ] simplifiying candidate # 246.377 * * * * [progress]: [ 112 / 1134 ] simplifiying candidate # 246.378 * * * * [progress]: [ 113 / 1134 ] simplifiying candidate # 246.378 * * * * [progress]: [ 114 / 1134 ] simplifiying candidate # 246.378 * * * * [progress]: [ 115 / 1134 ] simplifiying candidate # 246.378 * * * * [progress]: [ 116 / 1134 ] simplifiying candidate # 246.378 * * * * [progress]: [ 117 / 1134 ] simplifiying candidate # 246.378 * * * * [progress]: [ 118 / 1134 ] simplifiying candidate # 246.378 * * * * [progress]: [ 119 / 1134 ] simplifiying candidate # 246.378 * * * * [progress]: [ 120 / 1134 ] simplifiying candidate # 246.378 * * * * [progress]: [ 121 / 1134 ] simplifiying candidate # 246.378 * * * * [progress]: [ 122 / 1134 ] simplifiying candidate # 246.378 * * * * [progress]: [ 123 / 1134 ] simplifiying candidate # 246.378 * * * * [progress]: [ 124 / 1134 ] simplifiying candidate # 246.378 * * * * [progress]: [ 125 / 1134 ] simplifiying candidate # 246.378 * * * * [progress]: [ 126 / 1134 ] simplifiying candidate # 246.378 * * * * [progress]: [ 127 / 1134 ] simplifiying candidate # 246.378 * * * * [progress]: [ 128 / 1134 ] simplifiying candidate # 246.378 * * * * [progress]: [ 129 / 1134 ] simplifiying candidate # 246.378 * * * * [progress]: [ 130 / 1134 ] simplifiying candidate #real (real->posit16 (pow PI (- 1/2 (/ k 2)))))) (/ (sqrt k) (pow 2 (- 1/2 (/ k 2)))))))> 246.378 * * * * [progress]: [ 131 / 1134 ] simplifiying candidate # 246.378 * * * * [progress]: [ 132 / 1134 ] simplifiying candidate # 246.378 * * * * [progress]: [ 133 / 1134 ] simplifiying candidate # 246.378 * * * * [progress]: [ 134 / 1134 ] simplifiying candidate # 246.379 * * * * [progress]: [ 135 / 1134 ] simplifiying candidate # 246.379 * * * * [progress]: [ 136 / 1134 ] simplifiying candidate # 246.379 * * * * [progress]: [ 137 / 1134 ] simplifiying candidate # 246.379 * * * * [progress]: [ 138 / 1134 ] simplifiying candidate # 246.379 * * * * [progress]: [ 139 / 1134 ] simplifiying candidate # 246.379 * * * * [progress]: [ 140 / 1134 ] simplifiying candidate # 246.379 * * * * [progress]: [ 141 / 1134 ] simplifiying candidate # 246.379 * * * * [progress]: [ 142 / 1134 ] simplifiying candidate # 246.379 * * * * [progress]: [ 143 / 1134 ] simplifiying 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[progress]: [ 1122 / 1134 ] simplifiying candidate # 246.430 * * * * [progress]: [ 1123 / 1134 ] simplifiying candidate # 246.430 * * * * [progress]: [ 1124 / 1134 ] simplifiying candidate # 246.430 * * * * [progress]: [ 1125 / 1134 ] simplifiying candidate # 246.430 * * * * [progress]: [ 1126 / 1134 ] simplifiying candidate # 246.430 * * * * [progress]: [ 1127 / 1134 ] simplifiying candidate # 246.430 * * * * [progress]: [ 1128 / 1134 ] simplifiying candidate # 246.430 * * * * [progress]: [ 1129 / 1134 ] simplifiying candidate # 246.430 * * * * [progress]: [ 1130 / 1134 ] simplifiying candidate # 246.430 * * * * [progress]: [ 1131 / 1134 ] simplifiying candidate # 246.430 * * * * [progress]: [ 1132 / 1134 ] simplifiying candidate # 246.430 * * * * [progress]: [ 1133 / 1134 ] simplifiying candidate # 246.430 * * * * [progress]: [ 1134 / 1134 ] simplifiying candidate # 246.454 * [simplify]: Simplifying: (expm1 (pow n (- 1/2 (/ k 2)))) (log1p (pow n (- 1/2 (/ k 2)))) (* (log n) (- 1/2 (/ k 2))) (* (log n) (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (pow n 1/2) (pow n (/ k 2)) (pow n (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow n (sqrt (- 1/2 (/ k 2)))) (pow n 1) (pow n (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow n (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (pow n 1) (pow n (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow n (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow n (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (pow n (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (pow n (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (pow n (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 (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow n (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (pow n (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (pow n (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (pow n (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow n (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (pow n (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow n (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow n (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (pow n (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (pow n (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (pow n (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (pow n (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (pow n (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (pow n (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) (/ 1 1))))) (pow n (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (pow n (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) 1)))) (pow n (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (pow n (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1 2) k)))) (pow n (fma (- (/ 1 2)) k (* (/ 1 2) k))) (pow n (fma (sqrt 1/2) (sqrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow n (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow n (fma (sqrt 1/2) (sqrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (pow n (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (pow n (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (pow n (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 (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow n (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (pow n (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (pow n (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (pow n (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow n (fma (- (/ 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(/ (* (log PI) (* (log n) (pow k 3))) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (pow k 3) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ k (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (* (log 2) (pow k 3)) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (* (log n) (pow k 2)) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (/ (* (log 2) (pow k 2)) (sqrt 2)) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (/ (* (log PI) (pow k 3)) (sqrt 2)) (sqrt (/ 1 (* n PI)))))))))))))))))))))))))))))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (pow PI (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) k))))) (- (+ (* +nan.0 (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))))) (- (* +nan.0 (/ 1 (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (pow PI (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow k 2))))))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (pow PI (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) k))))) (- (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (pow PI (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow k 2))))))))))) 246.491 * * [simplify]: iteration 1: (1432 enodes) 247.616 * * [simplify]: Extracting #0: cost 652 inf + 0 247.621 * * [simplify]: Extracting #1: cost 1542 inf + 85 247.628 * * [simplify]: Extracting #2: cost 1863 inf + 512 247.641 * * [simplify]: Extracting #3: cost 1969 inf + 3022 247.651 * * [simplify]: Extracting #4: cost 1893 inf + 25055 247.672 * * [simplify]: Extracting #5: cost 1537 inf + 150866 247.725 * * [simplify]: Extracting #6: cost 924 inf + 506405 247.827 * * [simplify]: Extracting #7: cost 321 inf + 1003589 247.962 * * [simplify]: Extracting #8: cost 78 inf + 1232506 248.103 * * [simplify]: Extracting #9: cost 64 inf + 1249866 248.243 * * [simplify]: Extracting #10: cost 73 inf + 1251302 248.385 * * [simplify]: Extracting #11: cost 70 inf + 1256956 248.528 * * [simplify]: Extracting #12: cost 66 inf + 1265678 248.674 * * [simplify]: Extracting #13: cost 58 inf + 1275919 248.821 * * [simplify]: Extracting #14: cost 51 inf + 1284224 248.969 * * [simplify]: Extracting #15: cost 61 inf + 1284780 249.116 * * [simplify]: Extracting #16: cost 66 inf + 1285406 249.261 * * [simplify]: Extracting #17: cost 63 inf + 1287330 249.406 * * [simplify]: Extracting #18: cost 53 inf + 1291239 249.551 * * [simplify]: Extracting #19: cost 43 inf + 1295116 249.698 * * [simplify]: Extracting #20: cost 36 inf + 1300685 249.847 * * [simplify]: Extracting #21: cost 29 inf + 1309847 250.000 * * [simplify]: Extracting #22: cost 20 inf + 1327831 250.163 * * [simplify]: Extracting #23: cost 9 inf + 1354247 250.333 * * [simplify]: Extracting #24: cost 2 inf + 1375759 250.510 * * [simplify]: Extracting #25: cost 0 inf + 1382271 250.700 * [simplify]: Simplified to: (expm1 (pow n (- 1/2 (/ k 2)))) (log1p (pow n (- 1/2 (/ k 2)))) (* (log n) (- 1/2 (/ k 2))) (* (log n) (- 1/2 (/ k 2))) (- 1/2 (/ k 2)) (sqrt n) (pow n (/ k 2)) (pow n (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow n (sqrt (- 1/2 (/ k 2)))) n (pow n (+ (sqrt (/ k 2)) (sqrt 1/2))) (pow n (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) n (pow n (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow n (+ (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow n (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (/ k 2)))) (pow n (+ (- (/ k 2)) (/ k 2))) (pow n (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (pow n (+ (- (* (/ (cbrt k) (cbrt 2)) (* (/ (cbrt k) (cbrt 2)) 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(* (* (* (exp (* (- 1/2 (* 1/2 k)) (log 2))) (pow PI (- 1/2 (* 1/2 k)))) (* k k)) (exp (- (* (- (log n)) (- 1/2 (* 1/2 k)))))))))) (- (- (/ (* +nan.0 1) (* (* (exp (* (- 1/2 (* 1/2 k)) (log 2))) (pow PI (- 1/2 (* 1/2 k)))) (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (- (log -1) (log n))))))) (- (* (/ (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (- (log -1) (log n)))))) (* (pow PI (- 1/2 (* 1/2 k))) (* (exp (* (- 1/2 (* 1/2 k)) (log 2))) k))) +nan.0) (* +nan.0 (/ (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (- (log -1) (log n)))))) (* (* (exp (* (- 1/2 (* 1/2 k)) (log 2))) (pow PI (- 1/2 (* 1/2 k)))) (* k k))))))) 250.922 * * * [progress]: adding candidates to table 266.157 * [progress]: [Phase 3 of 3] Extracting. 266.157 * * [regime]: Finding splitpoints for: (# # # # # # # #) 266.159 * * * [regime-changes]: Trying 2 branch expressions: (n k) 266.159 * * * * [regimes]: Trying to branch on n from (# # # # # # # #) 266.209 * * * * [regimes]: Trying to branch on k from (# # # # # # # #) 266.259 * * * [regime]: Found split indices: #