53.435 * [progress]: [Phase 1 of 3] Setting up. 0.002 * * * [progress]: [1/2] Preparing points 0.214 * * * [progress]: [2/2] Setting up program. 0.218 * [progress]: [Phase 2 of 3] Improving. 0.218 * * * * [progress]: [ 1 / 1 ] simplifiying candidate # 0.219 * [simplify]: Simplifying: (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 0.219 * * [simplify]: iteration 1: (13 enodes) 0.222 * * [simplify]: iteration 2: (29 enodes) 0.228 * * [simplify]: iteration 3: (60 enodes) 0.246 * * [simplify]: iteration 4: (123 enodes) 0.323 * * [simplify]: iteration 5: (322 enodes) 0.518 * * [simplify]: iteration 6: (817 enodes) 1.551 * * [simplify]: Extracting #0: cost 1 inf + 0 1.551 * * [simplify]: Extracting #1: cost 58 inf + 0 1.552 * * [simplify]: Extracting #2: cost 198 inf + 1 1.553 * * [simplify]: Extracting #3: cost 265 inf + 46 1.555 * * [simplify]: Extracting #4: cost 245 inf + 1713 1.560 * * [simplify]: Extracting #5: cost 180 inf + 14173 1.583 * * [simplify]: Extracting #6: cost 61 inf + 110645 1.631 * * [simplify]: Extracting #7: cost 0 inf + 167860 1.696 * * [simplify]: Extracting #8: cost 0 inf + 164570 1.761 * [simplify]: Simplified to: (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) 1.774 * * [progress]: iteration 1 / 4 1.774 * * * [progress]: picking best candidate 1.784 * * * * [pick]: Picked # 1.785 * * * [progress]: localizing error 1.835 * * * [progress]: generating rewritten candidates 1.835 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1) 1.867 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1) 1.894 * * * * [progress]: [ 3 / 3 ] rewriting at (2) 1.922 * * * [progress]: generating series expansions 1.922 * * * * [progress]: [ 1 / 3 ] generating series at (2 1) 1.924 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1.924 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1.924 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1.924 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1.924 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1.924 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1.924 * [taylor]: Taking taylor expansion of 1/2 in k 1.924 * [backup-simplify]: Simplify 1/2 into 1/2 1.924 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 1.924 * [taylor]: Taking taylor expansion of 1/2 in k 1.924 * [backup-simplify]: Simplify 1/2 into 1/2 1.924 * [taylor]: Taking taylor expansion of k in k 1.924 * [backup-simplify]: Simplify 0 into 0 1.924 * [backup-simplify]: Simplify 1 into 1 1.924 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 1.928 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 1.929 * [taylor]: Taking taylor expansion of 2 in k 1.929 * [backup-simplify]: Simplify 2 into 2 1.929 * [taylor]: Taking taylor expansion of (* n PI) in k 1.929 * [taylor]: Taking taylor expansion of n in k 1.929 * [backup-simplify]: Simplify n into n 1.929 * [taylor]: Taking taylor expansion of PI in k 1.929 * [backup-simplify]: Simplify PI into PI 1.929 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.929 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1.929 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1.930 * [backup-simplify]: Simplify (* 1/2 0) into 0 1.930 * [backup-simplify]: Simplify (- 0) into 0 1.931 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 1.931 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1.931 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1.931 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1.931 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1.931 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1.931 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1.931 * [taylor]: Taking taylor expansion of 1/2 in n 1.931 * [backup-simplify]: Simplify 1/2 into 1/2 1.931 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 1.931 * [taylor]: Taking taylor expansion of 1/2 in n 1.931 * [backup-simplify]: Simplify 1/2 into 1/2 1.931 * [taylor]: Taking taylor expansion of k in n 1.931 * [backup-simplify]: Simplify k into k 1.931 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.931 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.931 * [taylor]: Taking taylor expansion of 2 in n 1.931 * [backup-simplify]: Simplify 2 into 2 1.931 * [taylor]: Taking taylor expansion of (* n PI) in n 1.931 * [taylor]: Taking taylor expansion of n in n 1.931 * [backup-simplify]: Simplify 0 into 0 1.931 * [backup-simplify]: Simplify 1 into 1 1.931 * [taylor]: Taking taylor expansion of PI in n 1.931 * [backup-simplify]: Simplify PI into PI 1.932 * [backup-simplify]: Simplify (* 0 PI) into 0 1.932 * [backup-simplify]: Simplify (* 2 0) into 0 1.934 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.935 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1.936 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.937 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 1.937 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1.937 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1.938 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.939 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1.941 * [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))))) 1.941 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1.941 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1.941 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1.941 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1.941 * [taylor]: Taking taylor expansion of 1/2 in n 1.941 * [backup-simplify]: Simplify 1/2 into 1/2 1.941 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 1.941 * [taylor]: Taking taylor expansion of 1/2 in n 1.941 * [backup-simplify]: Simplify 1/2 into 1/2 1.941 * [taylor]: Taking taylor expansion of k in n 1.941 * [backup-simplify]: Simplify k into k 1.941 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.941 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.941 * [taylor]: Taking taylor expansion of 2 in n 1.941 * [backup-simplify]: Simplify 2 into 2 1.941 * [taylor]: Taking taylor expansion of (* n PI) in n 1.941 * [taylor]: Taking taylor expansion of n in n 1.941 * [backup-simplify]: Simplify 0 into 0 1.941 * [backup-simplify]: Simplify 1 into 1 1.941 * [taylor]: Taking taylor expansion of PI in n 1.941 * [backup-simplify]: Simplify PI into PI 1.942 * [backup-simplify]: Simplify (* 0 PI) into 0 1.942 * [backup-simplify]: Simplify (* 2 0) into 0 1.944 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.945 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1.946 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.946 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 1.946 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1.946 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1.948 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.949 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1.950 * [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))))) 1.950 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1.950 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1.951 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1.951 * [taylor]: Taking taylor expansion of 1/2 in k 1.951 * [backup-simplify]: Simplify 1/2 into 1/2 1.951 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 1.951 * [taylor]: Taking taylor expansion of 1/2 in k 1.951 * [backup-simplify]: Simplify 1/2 into 1/2 1.951 * [taylor]: Taking taylor expansion of k in k 1.951 * [backup-simplify]: Simplify 0 into 0 1.951 * [backup-simplify]: Simplify 1 into 1 1.951 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1.951 * [taylor]: Taking taylor expansion of (log n) in k 1.951 * [taylor]: Taking taylor expansion of n in k 1.951 * [backup-simplify]: Simplify n into n 1.951 * [backup-simplify]: Simplify (log n) into (log n) 1.951 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 1.951 * [taylor]: Taking taylor expansion of (* 2 PI) in k 1.951 * [taylor]: Taking taylor expansion of 2 in k 1.951 * [backup-simplify]: Simplify 2 into 2 1.951 * [taylor]: Taking taylor expansion of PI in k 1.951 * [backup-simplify]: Simplify PI into PI 1.952 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 1.953 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.953 * [backup-simplify]: Simplify (* 1/2 0) into 0 1.953 * [backup-simplify]: Simplify (- 0) into 0 1.954 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 1.955 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.956 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1.957 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1.958 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1.960 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.961 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1.963 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1.963 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1.963 * [backup-simplify]: Simplify (- 0) into 0 1.964 * [backup-simplify]: Simplify (+ 0 0) into 0 1.965 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.966 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1.968 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.968 * [taylor]: Taking taylor expansion of 0 in k 1.968 * [backup-simplify]: Simplify 0 into 0 1.968 * [backup-simplify]: Simplify 0 into 0 1.969 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.970 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 1.972 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1.972 * [backup-simplify]: Simplify (+ 0 0) into 0 1.973 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1.973 * [backup-simplify]: Simplify (- 1/2) into -1/2 1.974 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 1.975 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1.979 * [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))))))) 1.981 * [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))))))) 1.983 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.984 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.988 * [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 1.989 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1.989 * [backup-simplify]: Simplify (- 0) into 0 1.989 * [backup-simplify]: Simplify (+ 0 0) into 0 1.991 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.993 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1.995 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.995 * [taylor]: Taking taylor expansion of 0 in k 1.995 * [backup-simplify]: Simplify 0 into 0 1.995 * [backup-simplify]: Simplify 0 into 0 1.996 * [backup-simplify]: Simplify 0 into 0 1.997 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.998 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.002 * [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 2.003 * [backup-simplify]: Simplify (+ 0 0) into 0 2.004 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 2.004 * [backup-simplify]: Simplify (- 0) into 0 2.004 * [backup-simplify]: Simplify (+ 0 0) into 0 2.006 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.010 * [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))))) 2.015 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 2.025 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 2.026 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 2.026 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 2.026 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 2.026 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 2.026 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 2.026 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.026 * [taylor]: Taking taylor expansion of 1/2 in k 2.026 * [backup-simplify]: Simplify 1/2 into 1/2 2.026 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.026 * [taylor]: Taking taylor expansion of 1/2 in k 2.026 * [backup-simplify]: Simplify 1/2 into 1/2 2.026 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.026 * [taylor]: Taking taylor expansion of k in k 2.026 * [backup-simplify]: Simplify 0 into 0 2.026 * [backup-simplify]: Simplify 1 into 1 2.026 * [backup-simplify]: Simplify (/ 1 1) into 1 2.027 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 2.027 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 2.027 * [taylor]: Taking taylor expansion of 2 in k 2.027 * [backup-simplify]: Simplify 2 into 2 2.027 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.027 * [taylor]: Taking taylor expansion of PI in k 2.027 * [backup-simplify]: Simplify PI into PI 2.027 * [taylor]: Taking taylor expansion of n in k 2.027 * [backup-simplify]: Simplify n into n 2.027 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.027 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 2.027 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 2.027 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.028 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.028 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.028 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 2.028 * [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)))) 2.029 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.029 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.029 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.029 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.029 * [taylor]: Taking taylor expansion of 1/2 in n 2.029 * [backup-simplify]: Simplify 1/2 into 1/2 2.029 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.029 * [taylor]: Taking taylor expansion of 1/2 in n 2.029 * [backup-simplify]: Simplify 1/2 into 1/2 2.029 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.029 * [taylor]: Taking taylor expansion of k in n 2.029 * [backup-simplify]: Simplify k into k 2.029 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.029 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.029 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.029 * [taylor]: Taking taylor expansion of 2 in n 2.029 * [backup-simplify]: Simplify 2 into 2 2.029 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.029 * [taylor]: Taking taylor expansion of PI in n 2.029 * [backup-simplify]: Simplify PI into PI 2.029 * [taylor]: Taking taylor expansion of n in n 2.029 * [backup-simplify]: Simplify 0 into 0 2.029 * [backup-simplify]: Simplify 1 into 1 2.030 * [backup-simplify]: Simplify (/ PI 1) into PI 2.030 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.031 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.031 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.031 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.031 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.032 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.033 * [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))) 2.033 * [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)))) 2.034 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.034 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.034 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.034 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.034 * [taylor]: Taking taylor expansion of 1/2 in n 2.034 * [backup-simplify]: Simplify 1/2 into 1/2 2.034 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.034 * [taylor]: Taking taylor expansion of 1/2 in n 2.034 * [backup-simplify]: Simplify 1/2 into 1/2 2.034 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.034 * [taylor]: Taking taylor expansion of k in n 2.034 * [backup-simplify]: Simplify k into k 2.034 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.034 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.034 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.034 * [taylor]: Taking taylor expansion of 2 in n 2.034 * [backup-simplify]: Simplify 2 into 2 2.034 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.034 * [taylor]: Taking taylor expansion of PI in n 2.034 * [backup-simplify]: Simplify PI into PI 2.034 * [taylor]: Taking taylor expansion of n in n 2.034 * [backup-simplify]: Simplify 0 into 0 2.034 * [backup-simplify]: Simplify 1 into 1 2.034 * [backup-simplify]: Simplify (/ PI 1) into PI 2.035 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.035 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.035 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.035 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.035 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.036 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.037 * [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))) 2.038 * [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)))) 2.038 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 2.038 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 2.038 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.038 * [taylor]: Taking taylor expansion of 1/2 in k 2.038 * [backup-simplify]: Simplify 1/2 into 1/2 2.038 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.038 * [taylor]: Taking taylor expansion of 1/2 in k 2.038 * [backup-simplify]: Simplify 1/2 into 1/2 2.038 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.038 * [taylor]: Taking taylor expansion of k in k 2.038 * [backup-simplify]: Simplify 0 into 0 2.038 * [backup-simplify]: Simplify 1 into 1 2.038 * [backup-simplify]: Simplify (/ 1 1) into 1 2.039 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 2.039 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.039 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.039 * [taylor]: Taking taylor expansion of 2 in k 2.039 * [backup-simplify]: Simplify 2 into 2 2.039 * [taylor]: Taking taylor expansion of PI in k 2.039 * [backup-simplify]: Simplify PI into PI 2.039 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.040 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.040 * [taylor]: Taking taylor expansion of (log n) in k 2.040 * [taylor]: Taking taylor expansion of n in k 2.040 * [backup-simplify]: Simplify n into n 2.040 * [backup-simplify]: Simplify (log n) into (log n) 2.040 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.040 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.041 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.041 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.041 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 2.042 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 2.043 * [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)))) 2.044 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 2.044 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.045 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.046 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.046 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.046 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.047 * [backup-simplify]: Simplify (- 0) into 0 2.047 * [backup-simplify]: Simplify (+ 0 0) into 0 2.048 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.049 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 2.050 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.050 * [taylor]: Taking taylor expansion of 0 in k 2.050 * [backup-simplify]: Simplify 0 into 0 2.050 * [backup-simplify]: Simplify 0 into 0 2.050 * [backup-simplify]: Simplify 0 into 0 2.051 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.051 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.053 * [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 2.054 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.054 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.055 * [backup-simplify]: Simplify (- 0) into 0 2.055 * [backup-simplify]: Simplify (+ 0 0) into 0 2.058 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.059 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 2.061 * [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 2.061 * [taylor]: Taking taylor expansion of 0 in k 2.061 * [backup-simplify]: Simplify 0 into 0 2.061 * [backup-simplify]: Simplify 0 into 0 2.061 * [backup-simplify]: Simplify 0 into 0 2.061 * [backup-simplify]: Simplify 0 into 0 2.062 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.063 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.066 * [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 2.067 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.068 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 2.068 * [backup-simplify]: Simplify (- 0) into 0 2.068 * [backup-simplify]: Simplify (+ 0 0) into 0 2.070 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.071 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 2.074 * [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 2.074 * [taylor]: Taking taylor expansion of 0 in k 2.074 * [backup-simplify]: Simplify 0 into 0 2.074 * [backup-simplify]: Simplify 0 into 0 2.076 * [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))))) 2.076 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 2.076 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 2.076 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 2.076 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 2.076 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 2.076 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.077 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.077 * [taylor]: Taking taylor expansion of 1/2 in k 2.077 * [backup-simplify]: Simplify 1/2 into 1/2 2.077 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.077 * [taylor]: Taking taylor expansion of k in k 2.077 * [backup-simplify]: Simplify 0 into 0 2.077 * [backup-simplify]: Simplify 1 into 1 2.077 * [backup-simplify]: Simplify (/ 1 1) into 1 2.077 * [taylor]: Taking taylor expansion of 1/2 in k 2.077 * [backup-simplify]: Simplify 1/2 into 1/2 2.077 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 2.077 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 2.077 * [taylor]: Taking taylor expansion of -2 in k 2.077 * [backup-simplify]: Simplify -2 into -2 2.077 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.077 * [taylor]: Taking taylor expansion of PI in k 2.077 * [backup-simplify]: Simplify PI into PI 2.077 * [taylor]: Taking taylor expansion of n in k 2.077 * [backup-simplify]: Simplify n into n 2.077 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.078 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 2.078 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 2.078 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.079 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.079 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 2.079 * [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))) 2.079 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.079 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.079 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.079 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.079 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.079 * [taylor]: Taking taylor expansion of 1/2 in n 2.079 * [backup-simplify]: Simplify 1/2 into 1/2 2.079 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.079 * [taylor]: Taking taylor expansion of k in n 2.079 * [backup-simplify]: Simplify k into k 2.079 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.079 * [taylor]: Taking taylor expansion of 1/2 in n 2.079 * [backup-simplify]: Simplify 1/2 into 1/2 2.079 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.079 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.079 * [taylor]: Taking taylor expansion of -2 in n 2.079 * [backup-simplify]: Simplify -2 into -2 2.079 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.079 * [taylor]: Taking taylor expansion of PI in n 2.079 * [backup-simplify]: Simplify PI into PI 2.079 * [taylor]: Taking taylor expansion of n in n 2.079 * [backup-simplify]: Simplify 0 into 0 2.079 * [backup-simplify]: Simplify 1 into 1 2.080 * [backup-simplify]: Simplify (/ PI 1) into PI 2.081 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.083 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.083 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.083 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.085 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.086 * [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))) 2.088 * [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)))) 2.088 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.088 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.088 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.088 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.088 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.088 * [taylor]: Taking taylor expansion of 1/2 in n 2.088 * [backup-simplify]: Simplify 1/2 into 1/2 2.088 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.088 * [taylor]: Taking taylor expansion of k in n 2.088 * [backup-simplify]: Simplify k into k 2.088 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.088 * [taylor]: Taking taylor expansion of 1/2 in n 2.088 * [backup-simplify]: Simplify 1/2 into 1/2 2.088 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.088 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.088 * [taylor]: Taking taylor expansion of -2 in n 2.088 * [backup-simplify]: Simplify -2 into -2 2.088 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.088 * [taylor]: Taking taylor expansion of PI in n 2.088 * [backup-simplify]: Simplify PI into PI 2.088 * [taylor]: Taking taylor expansion of n in n 2.088 * [backup-simplify]: Simplify 0 into 0 2.088 * [backup-simplify]: Simplify 1 into 1 2.089 * [backup-simplify]: Simplify (/ PI 1) into PI 2.089 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.091 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.091 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.091 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.093 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.094 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 2.096 * [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)))) 2.096 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 2.096 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 2.096 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.096 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.096 * [taylor]: Taking taylor expansion of 1/2 in k 2.096 * [backup-simplify]: Simplify 1/2 into 1/2 2.096 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.096 * [taylor]: Taking taylor expansion of k in k 2.096 * [backup-simplify]: Simplify 0 into 0 2.096 * [backup-simplify]: Simplify 1 into 1 2.097 * [backup-simplify]: Simplify (/ 1 1) into 1 2.097 * [taylor]: Taking taylor expansion of 1/2 in k 2.097 * [backup-simplify]: Simplify 1/2 into 1/2 2.097 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 2.097 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 2.097 * [taylor]: Taking taylor expansion of (* -2 PI) in k 2.097 * [taylor]: Taking taylor expansion of -2 in k 2.097 * [backup-simplify]: Simplify -2 into -2 2.097 * [taylor]: Taking taylor expansion of PI in k 2.097 * [backup-simplify]: Simplify PI into PI 2.097 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.098 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.099 * [taylor]: Taking taylor expansion of (log n) in k 2.099 * [taylor]: Taking taylor expansion of n in k 2.099 * [backup-simplify]: Simplify n into n 2.099 * [backup-simplify]: Simplify (log n) into (log n) 2.099 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.100 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.100 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.101 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 2.102 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 2.103 * [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)))) 2.104 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 2.105 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.106 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.108 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 2.108 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.109 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.109 * [backup-simplify]: Simplify (+ 0 0) into 0 2.111 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.112 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 2.114 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.114 * [taylor]: Taking taylor expansion of 0 in k 2.114 * [backup-simplify]: Simplify 0 into 0 2.114 * [backup-simplify]: Simplify 0 into 0 2.114 * [backup-simplify]: Simplify 0 into 0 2.115 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.116 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.120 * [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 2.120 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.121 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.122 * [backup-simplify]: Simplify (+ 0 0) into 0 2.123 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.125 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 2.127 * [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 2.127 * [taylor]: Taking taylor expansion of 0 in k 2.127 * [backup-simplify]: Simplify 0 into 0 2.127 * [backup-simplify]: Simplify 0 into 0 2.127 * [backup-simplify]: Simplify 0 into 0 2.127 * [backup-simplify]: Simplify 0 into 0 2.129 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.130 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.136 * [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 2.137 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.138 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 2.138 * [backup-simplify]: Simplify (+ 0 0) into 0 2.140 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.142 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 2.145 * [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 2.145 * [taylor]: Taking taylor expansion of 0 in k 2.145 * [backup-simplify]: Simplify 0 into 0 2.145 * [backup-simplify]: Simplify 0 into 0 2.147 * [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))))) 2.147 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1) 2.147 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) 2.147 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 2.148 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.148 * [taylor]: Taking taylor expansion of 2 in n 2.148 * [backup-simplify]: Simplify 2 into 2 2.148 * [taylor]: Taking taylor expansion of (* n PI) in n 2.148 * [taylor]: Taking taylor expansion of n in n 2.148 * [backup-simplify]: Simplify 0 into 0 2.148 * [backup-simplify]: Simplify 1 into 1 2.148 * [taylor]: Taking taylor expansion of PI in n 2.148 * [backup-simplify]: Simplify PI into PI 2.148 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.148 * [taylor]: Taking taylor expansion of 2 in n 2.148 * [backup-simplify]: Simplify 2 into 2 2.148 * [taylor]: Taking taylor expansion of (* n PI) in n 2.148 * [taylor]: Taking taylor expansion of n in n 2.148 * [backup-simplify]: Simplify 0 into 0 2.148 * [backup-simplify]: Simplify 1 into 1 2.148 * [taylor]: Taking taylor expansion of PI in n 2.148 * [backup-simplify]: Simplify PI into PI 2.148 * [backup-simplify]: Simplify (* 0 PI) into 0 2.149 * [backup-simplify]: Simplify (* 2 0) into 0 2.149 * [backup-simplify]: Simplify 0 into 0 2.151 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.152 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.153 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.154 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.155 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 2.155 * [backup-simplify]: Simplify 0 into 0 2.157 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.158 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.158 * [backup-simplify]: Simplify 0 into 0 2.159 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.160 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.160 * [backup-simplify]: Simplify 0 into 0 2.161 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.162 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 2.162 * [backup-simplify]: Simplify 0 into 0 2.163 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.164 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 2.164 * [backup-simplify]: Simplify 0 into 0 2.165 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.166 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.166 * [backup-simplify]: Simplify 0 into 0 2.166 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 2.167 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) 2.167 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 2.167 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.167 * [taylor]: Taking taylor expansion of 2 in n 2.167 * [backup-simplify]: Simplify 2 into 2 2.167 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.167 * [taylor]: Taking taylor expansion of PI in n 2.167 * [backup-simplify]: Simplify PI into PI 2.167 * [taylor]: Taking taylor expansion of n in n 2.167 * [backup-simplify]: Simplify 0 into 0 2.167 * [backup-simplify]: Simplify 1 into 1 2.167 * [backup-simplify]: Simplify (/ PI 1) into PI 2.167 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.167 * [taylor]: Taking taylor expansion of 2 in n 2.167 * [backup-simplify]: Simplify 2 into 2 2.167 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.167 * [taylor]: Taking taylor expansion of PI in n 2.167 * [backup-simplify]: Simplify PI into PI 2.167 * [taylor]: Taking taylor expansion of n in n 2.167 * [backup-simplify]: Simplify 0 into 0 2.167 * [backup-simplify]: Simplify 1 into 1 2.168 * [backup-simplify]: Simplify (/ PI 1) into PI 2.168 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.168 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.169 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.169 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.170 * [backup-simplify]: Simplify 0 into 0 2.170 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.171 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.171 * [backup-simplify]: Simplify 0 into 0 2.171 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.172 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.172 * [backup-simplify]: Simplify 0 into 0 2.173 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.174 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.174 * [backup-simplify]: Simplify 0 into 0 2.174 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.175 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.176 * [backup-simplify]: Simplify 0 into 0 2.176 * [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 2.177 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.177 * [backup-simplify]: Simplify 0 into 0 2.178 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 2.178 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n)) 2.178 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 2.178 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.178 * [taylor]: Taking taylor expansion of -2 in n 2.178 * [backup-simplify]: Simplify -2 into -2 2.178 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.178 * [taylor]: Taking taylor expansion of PI in n 2.178 * [backup-simplify]: Simplify PI into PI 2.178 * [taylor]: Taking taylor expansion of n in n 2.178 * [backup-simplify]: Simplify 0 into 0 2.178 * [backup-simplify]: Simplify 1 into 1 2.179 * [backup-simplify]: Simplify (/ PI 1) into PI 2.179 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.179 * [taylor]: Taking taylor expansion of -2 in n 2.179 * [backup-simplify]: Simplify -2 into -2 2.179 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.179 * [taylor]: Taking taylor expansion of PI in n 2.179 * [backup-simplify]: Simplify PI into PI 2.179 * [taylor]: Taking taylor expansion of n in n 2.179 * [backup-simplify]: Simplify 0 into 0 2.179 * [backup-simplify]: Simplify 1 into 1 2.179 * [backup-simplify]: Simplify (/ PI 1) into PI 2.180 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.180 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.181 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.181 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.181 * [backup-simplify]: Simplify 0 into 0 2.182 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.182 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.182 * [backup-simplify]: Simplify 0 into 0 2.183 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.184 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.184 * [backup-simplify]: Simplify 0 into 0 2.185 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.185 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.185 * [backup-simplify]: Simplify 0 into 0 2.186 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.189 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.189 * [backup-simplify]: Simplify 0 into 0 2.190 * [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 2.191 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.191 * [backup-simplify]: Simplify 0 into 0 2.191 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 2.191 * * * * [progress]: [ 3 / 3 ] generating series at (2) 2.192 * [backup-simplify]: Simplify (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 2.192 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 2.192 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 2.192 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.192 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.192 * [taylor]: Taking taylor expansion of k in k 2.192 * [backup-simplify]: Simplify 0 into 0 2.192 * [backup-simplify]: Simplify 1 into 1 2.192 * [backup-simplify]: Simplify (/ 1 1) into 1 2.192 * [backup-simplify]: Simplify (sqrt 0) into 0 2.193 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.193 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 2.193 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 2.193 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 2.193 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 2.193 * [taylor]: Taking taylor expansion of 1/2 in k 2.193 * [backup-simplify]: Simplify 1/2 into 1/2 2.193 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 2.193 * [taylor]: Taking taylor expansion of 1/2 in k 2.193 * [backup-simplify]: Simplify 1/2 into 1/2 2.193 * [taylor]: Taking taylor expansion of k in k 2.194 * [backup-simplify]: Simplify 0 into 0 2.194 * [backup-simplify]: Simplify 1 into 1 2.194 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 2.194 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 2.194 * [taylor]: Taking taylor expansion of 2 in k 2.194 * [backup-simplify]: Simplify 2 into 2 2.194 * [taylor]: Taking taylor expansion of (* n PI) in k 2.194 * [taylor]: Taking taylor expansion of n in k 2.194 * [backup-simplify]: Simplify n into n 2.194 * [taylor]: Taking taylor expansion of PI in k 2.194 * [backup-simplify]: Simplify PI into PI 2.194 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.194 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 2.194 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 2.194 * [backup-simplify]: Simplify (* 1/2 0) into 0 2.194 * [backup-simplify]: Simplify (- 0) into 0 2.195 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.195 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 2.195 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 2.195 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 2.195 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.195 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.195 * [taylor]: Taking taylor expansion of k in n 2.195 * [backup-simplify]: Simplify k into k 2.195 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.195 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 2.195 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.195 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 2.195 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 2.195 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 2.195 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 2.195 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 2.195 * [taylor]: Taking taylor expansion of 1/2 in n 2.195 * [backup-simplify]: Simplify 1/2 into 1/2 2.195 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 2.195 * [taylor]: Taking taylor expansion of 1/2 in n 2.195 * [backup-simplify]: Simplify 1/2 into 1/2 2.195 * [taylor]: Taking taylor expansion of k in n 2.195 * [backup-simplify]: Simplify k into k 2.195 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 2.196 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.196 * [taylor]: Taking taylor expansion of 2 in n 2.196 * [backup-simplify]: Simplify 2 into 2 2.196 * [taylor]: Taking taylor expansion of (* n PI) in n 2.196 * [taylor]: Taking taylor expansion of n in n 2.196 * [backup-simplify]: Simplify 0 into 0 2.196 * [backup-simplify]: Simplify 1 into 1 2.196 * [taylor]: Taking taylor expansion of PI in n 2.196 * [backup-simplify]: Simplify PI into PI 2.196 * [backup-simplify]: Simplify (* 0 PI) into 0 2.197 * [backup-simplify]: Simplify (* 2 0) into 0 2.198 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.200 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.201 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.201 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 2.201 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 2.201 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 2.203 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.204 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 2.205 * [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))))) 2.205 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 2.205 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.205 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.205 * [taylor]: Taking taylor expansion of k in n 2.205 * [backup-simplify]: Simplify k into k 2.205 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.205 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 2.205 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.205 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 2.205 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 2.205 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 2.206 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 2.206 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 2.206 * [taylor]: Taking taylor expansion of 1/2 in n 2.206 * [backup-simplify]: Simplify 1/2 into 1/2 2.206 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 2.206 * [taylor]: Taking taylor expansion of 1/2 in n 2.206 * [backup-simplify]: Simplify 1/2 into 1/2 2.206 * [taylor]: Taking taylor expansion of k in n 2.206 * [backup-simplify]: Simplify k into k 2.206 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 2.206 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.206 * [taylor]: Taking taylor expansion of 2 in n 2.206 * [backup-simplify]: Simplify 2 into 2 2.206 * [taylor]: Taking taylor expansion of (* n PI) in n 2.206 * [taylor]: Taking taylor expansion of n in n 2.206 * [backup-simplify]: Simplify 0 into 0 2.206 * [backup-simplify]: Simplify 1 into 1 2.206 * [taylor]: Taking taylor expansion of PI in n 2.206 * [backup-simplify]: Simplify PI into PI 2.206 * [backup-simplify]: Simplify (* 0 PI) into 0 2.207 * [backup-simplify]: Simplify (* 2 0) into 0 2.208 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.210 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.211 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.211 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 2.211 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 2.211 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 2.213 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.214 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 2.215 * [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))))) 2.216 * [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))) 2.216 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 2.216 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 2.216 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 2.216 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 2.216 * [taylor]: Taking taylor expansion of 1/2 in k 2.216 * [backup-simplify]: Simplify 1/2 into 1/2 2.216 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 2.216 * [taylor]: Taking taylor expansion of 1/2 in k 2.216 * [backup-simplify]: Simplify 1/2 into 1/2 2.216 * [taylor]: Taking taylor expansion of k in k 2.216 * [backup-simplify]: Simplify 0 into 0 2.217 * [backup-simplify]: Simplify 1 into 1 2.217 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 2.217 * [taylor]: Taking taylor expansion of (log n) in k 2.217 * [taylor]: Taking taylor expansion of n in k 2.217 * [backup-simplify]: Simplify n into n 2.217 * [backup-simplify]: Simplify (log n) into (log n) 2.217 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.217 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.217 * [taylor]: Taking taylor expansion of 2 in k 2.217 * [backup-simplify]: Simplify 2 into 2 2.217 * [taylor]: Taking taylor expansion of PI in k 2.217 * [backup-simplify]: Simplify PI into PI 2.217 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.218 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.219 * [backup-simplify]: Simplify (* 1/2 0) into 0 2.219 * [backup-simplify]: Simplify (- 0) into 0 2.219 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.220 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.222 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 2.223 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 2.223 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.223 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.223 * [taylor]: Taking taylor expansion of k in k 2.223 * [backup-simplify]: Simplify 0 into 0 2.223 * [backup-simplify]: Simplify 1 into 1 2.223 * [backup-simplify]: Simplify (/ 1 1) into 1 2.223 * [backup-simplify]: Simplify (sqrt 0) into 0 2.225 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.226 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 2.226 * [backup-simplify]: Simplify 0 into 0 2.227 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.228 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 2.230 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.230 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 2.231 * [backup-simplify]: Simplify (- 0) into 0 2.231 * [backup-simplify]: Simplify (+ 0 0) into 0 2.232 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.233 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 2.235 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.237 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 2.237 * [taylor]: Taking taylor expansion of 0 in k 2.237 * [backup-simplify]: Simplify 0 into 0 2.237 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.238 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.240 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.241 * [backup-simplify]: Simplify (+ 0 0) into 0 2.241 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 2.242 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.242 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.244 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2.247 * [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))))))) 2.251 * [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))))))) 2.252 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 2.254 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.255 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.257 * [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 2.257 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 2.257 * [backup-simplify]: Simplify (- 0) into 0 2.258 * [backup-simplify]: Simplify (+ 0 0) into 0 2.259 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.260 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.261 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.261 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.262 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 2.263 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 2.263 * [taylor]: Taking taylor expansion of 0 in k 2.263 * [backup-simplify]: Simplify 0 into 0 2.263 * [backup-simplify]: Simplify 0 into 0 2.263 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.265 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.266 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.267 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.269 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 2.269 * [backup-simplify]: Simplify (+ 0 0) into 0 2.270 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 2.270 * [backup-simplify]: Simplify (- 0) into 0 2.271 * [backup-simplify]: Simplify (+ 0 0) into 0 2.272 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.274 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 2.284 * [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)))))))) 2.289 * [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)))))))) 2.291 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.292 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.299 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 2.300 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 2.301 * [backup-simplify]: Simplify (- 0) into 0 2.301 * [backup-simplify]: Simplify (+ 0 0) into 0 2.303 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.305 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 2.308 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.308 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.309 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 2.311 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0 2.311 * [taylor]: Taking taylor expansion of 0 in k 2.311 * [backup-simplify]: Simplify 0 into 0 2.312 * [backup-simplify]: Simplify 0 into 0 2.312 * [backup-simplify]: Simplify 0 into 0 2.313 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.320 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.323 * [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 2.324 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.331 * [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 2.331 * [backup-simplify]: Simplify (+ 0 0) into 0 2.332 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 2.333 * [backup-simplify]: Simplify (- 0) into 0 2.333 * [backup-simplify]: Simplify (+ 0 0) into 0 2.335 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 2.341 * [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))))))) 2.359 * [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)))))))))))))) 2.371 * [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)))))))))))))) 2.391 * [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)))))))))))))))))))))) 2.392 * [backup-simplify]: Simplify (/ (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 2.392 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 2.392 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 2.392 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.392 * [taylor]: Taking taylor expansion of k in k 2.392 * [backup-simplify]: Simplify 0 into 0 2.392 * [backup-simplify]: Simplify 1 into 1 2.393 * [backup-simplify]: Simplify (sqrt 0) into 0 2.394 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.394 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 2.394 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 2.394 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 2.394 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.394 * [taylor]: Taking taylor expansion of 1/2 in k 2.394 * [backup-simplify]: Simplify 1/2 into 1/2 2.394 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.394 * [taylor]: Taking taylor expansion of 1/2 in k 2.395 * [backup-simplify]: Simplify 1/2 into 1/2 2.395 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.395 * [taylor]: Taking taylor expansion of k in k 2.395 * [backup-simplify]: Simplify 0 into 0 2.395 * [backup-simplify]: Simplify 1 into 1 2.395 * [backup-simplify]: Simplify (/ 1 1) into 1 2.395 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 2.395 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 2.395 * [taylor]: Taking taylor expansion of 2 in k 2.395 * [backup-simplify]: Simplify 2 into 2 2.395 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.395 * [taylor]: Taking taylor expansion of PI in k 2.395 * [backup-simplify]: Simplify PI into PI 2.395 * [taylor]: Taking taylor expansion of n in k 2.395 * [backup-simplify]: Simplify n into n 2.395 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.395 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 2.395 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 2.396 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.396 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.397 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.397 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 2.397 * [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)))) 2.397 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 2.397 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.397 * [taylor]: Taking taylor expansion of k in n 2.397 * [backup-simplify]: Simplify k into k 2.397 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.397 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.397 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.397 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.397 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.397 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.397 * [taylor]: Taking taylor expansion of 1/2 in n 2.397 * [backup-simplify]: Simplify 1/2 into 1/2 2.397 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.397 * [taylor]: Taking taylor expansion of 1/2 in n 2.397 * [backup-simplify]: Simplify 1/2 into 1/2 2.397 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.398 * [taylor]: Taking taylor expansion of k in n 2.398 * [backup-simplify]: Simplify k into k 2.398 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.398 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.398 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.398 * [taylor]: Taking taylor expansion of 2 in n 2.398 * [backup-simplify]: Simplify 2 into 2 2.398 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.398 * [taylor]: Taking taylor expansion of PI in n 2.398 * [backup-simplify]: Simplify PI into PI 2.398 * [taylor]: Taking taylor expansion of n in n 2.398 * [backup-simplify]: Simplify 0 into 0 2.398 * [backup-simplify]: Simplify 1 into 1 2.398 * [backup-simplify]: Simplify (/ PI 1) into PI 2.399 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.399 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.400 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.400 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.400 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.401 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.401 * [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))) 2.402 * [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)))) 2.402 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 2.402 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.402 * [taylor]: Taking taylor expansion of k in n 2.402 * [backup-simplify]: Simplify k into k 2.402 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.402 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.402 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.402 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.402 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.402 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.402 * [taylor]: Taking taylor expansion of 1/2 in n 2.402 * [backup-simplify]: Simplify 1/2 into 1/2 2.402 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.402 * [taylor]: Taking taylor expansion of 1/2 in n 2.402 * [backup-simplify]: Simplify 1/2 into 1/2 2.402 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.402 * [taylor]: Taking taylor expansion of k in n 2.402 * [backup-simplify]: Simplify k into k 2.402 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.402 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.402 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.402 * [taylor]: Taking taylor expansion of 2 in n 2.402 * [backup-simplify]: Simplify 2 into 2 2.402 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.402 * [taylor]: Taking taylor expansion of PI in n 2.403 * [backup-simplify]: Simplify PI into PI 2.403 * [taylor]: Taking taylor expansion of n in n 2.403 * [backup-simplify]: Simplify 0 into 0 2.403 * [backup-simplify]: Simplify 1 into 1 2.403 * [backup-simplify]: Simplify (/ PI 1) into PI 2.403 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.404 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.404 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.404 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.404 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.405 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.406 * [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))) 2.406 * [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)))) 2.407 * [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)) 2.407 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 2.407 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 2.407 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 2.407 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.407 * [taylor]: Taking taylor expansion of 1/2 in k 2.407 * [backup-simplify]: Simplify 1/2 into 1/2 2.407 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.407 * [taylor]: Taking taylor expansion of 1/2 in k 2.407 * [backup-simplify]: Simplify 1/2 into 1/2 2.407 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.407 * [taylor]: Taking taylor expansion of k in k 2.407 * [backup-simplify]: Simplify 0 into 0 2.407 * [backup-simplify]: Simplify 1 into 1 2.408 * [backup-simplify]: Simplify (/ 1 1) into 1 2.408 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 2.408 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.408 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.408 * [taylor]: Taking taylor expansion of 2 in k 2.408 * [backup-simplify]: Simplify 2 into 2 2.408 * [taylor]: Taking taylor expansion of PI in k 2.408 * [backup-simplify]: Simplify PI into PI 2.408 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.409 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.409 * [taylor]: Taking taylor expansion of (log n) in k 2.409 * [taylor]: Taking taylor expansion of n in k 2.409 * [backup-simplify]: Simplify n into n 2.409 * [backup-simplify]: Simplify (log n) into (log n) 2.409 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.409 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.410 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.410 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.410 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 2.411 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 2.412 * [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)))) 2.412 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.412 * [taylor]: Taking taylor expansion of k in k 2.412 * [backup-simplify]: Simplify 0 into 0 2.412 * [backup-simplify]: Simplify 1 into 1 2.412 * [backup-simplify]: Simplify (sqrt 0) into 0 2.413 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.414 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 2.414 * [backup-simplify]: Simplify 0 into 0 2.414 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.415 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.416 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.416 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.416 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.416 * [backup-simplify]: Simplify (- 0) into 0 2.417 * [backup-simplify]: Simplify (+ 0 0) into 0 2.418 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.418 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 2.420 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.420 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 2.420 * [taylor]: Taking taylor expansion of 0 in k 2.420 * [backup-simplify]: Simplify 0 into 0 2.420 * [backup-simplify]: Simplify 0 into 0 2.421 * [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)))))) 2.422 * [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)))))) 2.423 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.424 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.426 * [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 2.426 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.426 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.427 * [backup-simplify]: Simplify (- 0) into 0 2.427 * [backup-simplify]: Simplify (+ 0 0) into 0 2.428 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.429 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 2.430 * [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 2.431 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 2.432 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 2.432 * [taylor]: Taking taylor expansion of 0 in k 2.432 * [backup-simplify]: Simplify 0 into 0 2.432 * [backup-simplify]: Simplify 0 into 0 2.432 * [backup-simplify]: Simplify 0 into 0 2.436 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.437 * [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)))))) 2.438 * [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)))))) 2.439 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.439 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.443 * [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 2.443 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.444 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 2.444 * [backup-simplify]: Simplify (- 0) into 0 2.444 * [backup-simplify]: Simplify (+ 0 0) into 0 2.445 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.446 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 2.448 * [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 2.449 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 2.450 * [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 2.450 * [taylor]: Taking taylor expansion of 0 in k 2.450 * [backup-simplify]: Simplify 0 into 0 2.450 * [backup-simplify]: Simplify 0 into 0 2.450 * [backup-simplify]: Simplify 0 into 0 2.450 * [backup-simplify]: Simplify 0 into 0 2.453 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.454 * [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)))))) 2.455 * [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)))))) 2.458 * [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)))))))) 2.458 * [backup-simplify]: Simplify (/ (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 2.458 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 2.458 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 2.458 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 2.458 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 2.458 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 2.458 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.458 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.458 * [taylor]: Taking taylor expansion of 1/2 in k 2.458 * [backup-simplify]: Simplify 1/2 into 1/2 2.458 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.458 * [taylor]: Taking taylor expansion of k in k 2.458 * [backup-simplify]: Simplify 0 into 0 2.458 * [backup-simplify]: Simplify 1 into 1 2.459 * [backup-simplify]: Simplify (/ 1 1) into 1 2.459 * [taylor]: Taking taylor expansion of 1/2 in k 2.459 * [backup-simplify]: Simplify 1/2 into 1/2 2.459 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 2.459 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 2.459 * [taylor]: Taking taylor expansion of -2 in k 2.459 * [backup-simplify]: Simplify -2 into -2 2.459 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.459 * [taylor]: Taking taylor expansion of PI in k 2.459 * [backup-simplify]: Simplify PI into PI 2.459 * [taylor]: Taking taylor expansion of n in k 2.459 * [backup-simplify]: Simplify n into n 2.459 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.459 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 2.459 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 2.459 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.459 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.460 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 2.460 * [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))) 2.460 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.460 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.460 * [taylor]: Taking taylor expansion of -1 in k 2.460 * [backup-simplify]: Simplify -1 into -1 2.460 * [taylor]: Taking taylor expansion of k in k 2.460 * [backup-simplify]: Simplify 0 into 0 2.460 * [backup-simplify]: Simplify 1 into 1 2.460 * [backup-simplify]: Simplify (/ -1 1) into -1 2.460 * [backup-simplify]: Simplify (sqrt 0) into 0 2.461 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.461 * [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)))) 2.461 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 2.461 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.461 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.461 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.461 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.461 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.461 * [taylor]: Taking taylor expansion of 1/2 in n 2.461 * [backup-simplify]: Simplify 1/2 into 1/2 2.461 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.461 * [taylor]: Taking taylor expansion of k in n 2.461 * [backup-simplify]: Simplify k into k 2.461 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.461 * [taylor]: Taking taylor expansion of 1/2 in n 2.461 * [backup-simplify]: Simplify 1/2 into 1/2 2.461 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.461 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.462 * [taylor]: Taking taylor expansion of -2 in n 2.462 * [backup-simplify]: Simplify -2 into -2 2.462 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.462 * [taylor]: Taking taylor expansion of PI in n 2.462 * [backup-simplify]: Simplify PI into PI 2.462 * [taylor]: Taking taylor expansion of n in n 2.462 * [backup-simplify]: Simplify 0 into 0 2.462 * [backup-simplify]: Simplify 1 into 1 2.462 * [backup-simplify]: Simplify (/ PI 1) into PI 2.462 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.463 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.463 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.463 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.464 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.465 * [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))) 2.465 * [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)))) 2.465 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.466 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.466 * [taylor]: Taking taylor expansion of -1 in n 2.466 * [backup-simplify]: Simplify -1 into -1 2.466 * [taylor]: Taking taylor expansion of k in n 2.466 * [backup-simplify]: Simplify k into k 2.466 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.466 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.466 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.466 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.467 * [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))) 2.467 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 2.467 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.467 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.467 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.467 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.467 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.467 * [taylor]: Taking taylor expansion of 1/2 in n 2.467 * [backup-simplify]: Simplify 1/2 into 1/2 2.467 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.467 * [taylor]: Taking taylor expansion of k in n 2.467 * [backup-simplify]: Simplify k into k 2.467 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.467 * [taylor]: Taking taylor expansion of 1/2 in n 2.467 * [backup-simplify]: Simplify 1/2 into 1/2 2.467 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.467 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.467 * [taylor]: Taking taylor expansion of -2 in n 2.467 * [backup-simplify]: Simplify -2 into -2 2.467 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.467 * [taylor]: Taking taylor expansion of PI in n 2.467 * [backup-simplify]: Simplify PI into PI 2.467 * [taylor]: Taking taylor expansion of n in n 2.467 * [backup-simplify]: Simplify 0 into 0 2.467 * [backup-simplify]: Simplify 1 into 1 2.467 * [backup-simplify]: Simplify (/ PI 1) into PI 2.468 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.468 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.468 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.468 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.469 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.470 * [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))) 2.471 * [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)))) 2.471 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.471 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.471 * [taylor]: Taking taylor expansion of -1 in n 2.471 * [backup-simplify]: Simplify -1 into -1 2.471 * [taylor]: Taking taylor expansion of k in n 2.471 * [backup-simplify]: Simplify k into k 2.471 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.471 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.471 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.471 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.472 * [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))) 2.472 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 2.472 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 2.472 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 2.472 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.472 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.472 * [taylor]: Taking taylor expansion of 1/2 in k 2.472 * [backup-simplify]: Simplify 1/2 into 1/2 2.472 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.472 * [taylor]: Taking taylor expansion of k in k 2.472 * [backup-simplify]: Simplify 0 into 0 2.472 * [backup-simplify]: Simplify 1 into 1 2.472 * [backup-simplify]: Simplify (/ 1 1) into 1 2.472 * [taylor]: Taking taylor expansion of 1/2 in k 2.472 * [backup-simplify]: Simplify 1/2 into 1/2 2.472 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 2.472 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 2.472 * [taylor]: Taking taylor expansion of (* -2 PI) in k 2.472 * [taylor]: Taking taylor expansion of -2 in k 2.472 * [backup-simplify]: Simplify -2 into -2 2.472 * [taylor]: Taking taylor expansion of PI in k 2.473 * [backup-simplify]: Simplify PI into PI 2.473 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.474 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.474 * [taylor]: Taking taylor expansion of (log n) in k 2.474 * [taylor]: Taking taylor expansion of n in k 2.474 * [backup-simplify]: Simplify n into n 2.474 * [backup-simplify]: Simplify (log n) into (log n) 2.474 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.474 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.474 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.475 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 2.476 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 2.477 * [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)))) 2.477 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.477 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.477 * [taylor]: Taking taylor expansion of -1 in k 2.477 * [backup-simplify]: Simplify -1 into -1 2.477 * [taylor]: Taking taylor expansion of k in k 2.477 * [backup-simplify]: Simplify 0 into 0 2.477 * [backup-simplify]: Simplify 1 into 1 2.477 * [backup-simplify]: Simplify (/ -1 1) into -1 2.477 * [backup-simplify]: Simplify (sqrt 0) into 0 2.478 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.479 * [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))))) 2.480 * [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))))) 2.480 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.481 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.482 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 2.482 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.482 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.483 * [backup-simplify]: Simplify (+ 0 0) into 0 2.484 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.484 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 2.486 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.486 * [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 2.486 * [taylor]: Taking taylor expansion of 0 in k 2.486 * [backup-simplify]: Simplify 0 into 0 2.487 * [backup-simplify]: Simplify 0 into 0 2.487 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.489 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.490 * [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)))))) 2.491 * [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)))))) 2.492 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.493 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.495 * [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 2.495 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.496 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.496 * [backup-simplify]: Simplify (+ 0 0) into 0 2.497 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.499 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 2.501 * [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 2.501 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.502 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 2.503 * [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 2.503 * [taylor]: Taking taylor expansion of 0 in k 2.503 * [backup-simplify]: Simplify 0 into 0 2.503 * [backup-simplify]: Simplify 0 into 0 2.503 * [backup-simplify]: Simplify 0 into 0 2.504 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.506 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.509 * [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)))))) 2.509 * [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)))))) 2.512 * [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))))))))))) 2.512 * * * [progress]: simplifying candidates 2.512 * * * * [progress]: [ 1 / 127 ] simplifiying candidate # 2.512 * * * * [progress]: [ 2 / 127 ] simplifiying candidate # 2.512 * * * * [progress]: [ 3 / 127 ] simplifiying candidate # 2.512 * * * * [progress]: [ 4 / 127 ] simplifiying candidate # 2.512 * * * * [progress]: [ 5 / 127 ] simplifiying candidate # 2.512 * * * * [progress]: [ 6 / 127 ] simplifiying candidate # 2.512 * * * * [progress]: [ 7 / 127 ] simplifiying candidate # 2.512 * * * * [progress]: [ 8 / 127 ] simplifiying candidate # 2.512 * * * * [progress]: [ 9 / 127 ] simplifiying candidate # 2.512 * * * * [progress]: [ 10 / 127 ] simplifiying candidate # 2.513 * * * * [progress]: [ 11 / 127 ] simplifiying candidate # 2.513 * * * * [progress]: [ 12 / 127 ] simplifiying candidate # 2.513 * * * * [progress]: [ 13 / 127 ] simplifiying candidate # 2.513 * * * * [progress]: [ 14 / 127 ] simplifiying candidate # 2.513 * * * * [progress]: [ 15 / 127 ] simplifiying candidate # 2.513 * * * * [progress]: [ 16 / 127 ] simplifiying candidate # 2.513 * * * * [progress]: [ 17 / 127 ] simplifiying candidate # 2.513 * * * * [progress]: [ 18 / 127 ] simplifiying candidate # 2.513 * * * * [progress]: [ 19 / 127 ] simplifiying candidate # 2.513 * * * * [progress]: [ 20 / 127 ] simplifiying candidate # 2.513 * * * * [progress]: [ 21 / 127 ] simplifiying candidate # 2.513 * * * * [progress]: [ 22 / 127 ] simplifiying candidate # 2.513 * * * * [progress]: [ 23 / 127 ] simplifiying candidate # 2.513 * * * * [progress]: [ 24 / 127 ] simplifiying candidate # 2.513 * * * * [progress]: [ 25 / 127 ] simplifiying candidate # 2.513 * * * * [progress]: [ 26 / 127 ] simplifiying candidate #real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))> 2.513 * * * * [progress]: [ 27 / 127 ] simplifiying candidate # 2.513 * * * * [progress]: [ 28 / 127 ] simplifiying candidate # 2.513 * * * * [progress]: [ 29 / 127 ] simplifiying candidate # 2.513 * * * * [progress]: [ 30 / 127 ] simplifiying candidate # 2.513 * * * * [progress]: [ 31 / 127 ] simplifiying candidate # 2.513 * * * * [progress]: [ 32 / 127 ] simplifiying candidate # 2.513 * * * * [progress]: [ 33 / 127 ] simplifiying candidate # 2.513 * * * * [progress]: [ 34 / 127 ] simplifiying candidate # 2.514 * * * * [progress]: [ 35 / 127 ] simplifiying candidate # 2.514 * * * * [progress]: [ 36 / 127 ] simplifiying candidate # 2.514 * * * * [progress]: [ 37 / 127 ] simplifiying candidate # 2.514 * * * * [progress]: [ 38 / 127 ] simplifiying candidate # 2.514 * * * * [progress]: [ 39 / 127 ] simplifiying candidate # 2.514 * * * * [progress]: [ 40 / 127 ] simplifiying candidate # 2.514 * * * * [progress]: [ 41 / 127 ] simplifiying candidate # 2.514 * * * * [progress]: [ 42 / 127 ] simplifiying candidate # 2.514 * * * * [progress]: [ 43 / 127 ] simplifiying candidate # 2.514 * * * * [progress]: [ 44 / 127 ] simplifiying candidate #real (real->posit16 (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))> 2.514 * * * * [progress]: [ 45 / 127 ] simplifiying candidate # 2.514 * * * * [progress]: [ 46 / 127 ] simplifiying candidate # 2.514 * * * * [progress]: [ 47 / 127 ] simplifiying candidate # 2.514 * * * * [progress]: [ 48 / 127 ] simplifiying candidate # 2.514 * * * * [progress]: [ 49 / 127 ] simplifiying candidate # 2.514 * * * * [progress]: [ 50 / 127 ] simplifiying candidate # 2.514 * * * * [progress]: [ 51 / 127 ] simplifiying candidate # 2.514 * * * * [progress]: [ 52 / 127 ] simplifiying candidate # 2.514 * * * * [progress]: [ 53 / 127 ] simplifiying candidate # 2.514 * * * * [progress]: [ 54 / 127 ] simplifiying candidate # 2.514 * * * * [progress]: [ 55 / 127 ] simplifiying candidate # 2.514 * * * * [progress]: [ 56 / 127 ] simplifiying candidate # 2.514 * * * * [progress]: [ 57 / 127 ] simplifiying candidate # 2.514 * * * * [progress]: [ 58 / 127 ] simplifiying candidate # 2.514 * * * * [progress]: [ 59 / 127 ] simplifiying candidate # 2.514 * * * * [progress]: [ 60 / 127 ] simplifiying candidate # 2.515 * * * * [progress]: [ 61 / 127 ] simplifiying candidate # 2.515 * * * * [progress]: [ 62 / 127 ] simplifiying candidate # 2.515 * * * * [progress]: [ 63 / 127 ] simplifiying candidate # 2.515 * * * * [progress]: [ 64 / 127 ] simplifiying candidate # 2.515 * * * * [progress]: [ 65 / 127 ] simplifiying candidate # 2.515 * * * * [progress]: [ 66 / 127 ] simplifiying candidate # 2.515 * * * * [progress]: [ 67 / 127 ] simplifiying candidate # 2.515 * * * * [progress]: [ 68 / 127 ] simplifiying candidate # 2.515 * * * * [progress]: [ 69 / 127 ] simplifiying candidate # 2.515 * * * * [progress]: [ 70 / 127 ] simplifiying candidate # 2.515 * * * * [progress]: [ 71 / 127 ] simplifiying candidate # 2.515 * * * * [progress]: [ 72 / 127 ] simplifiying candidate # 2.515 * * * * [progress]: [ 73 / 127 ] simplifiying candidate # 2.515 * * * * [progress]: [ 74 / 127 ] simplifiying candidate # 2.515 * * * * [progress]: [ 75 / 127 ] simplifiying candidate # 2.515 * * * * [progress]: [ 76 / 127 ] simplifiying candidate # 2.515 * * * * [progress]: [ 77 / 127 ] simplifiying candidate # 2.515 * * * * [progress]: [ 78 / 127 ] simplifiying candidate # 2.515 * * * * [progress]: [ 79 / 127 ] simplifiying candidate # 2.515 * * * * [progress]: [ 80 / 127 ] simplifiying candidate # 2.515 * * * * [progress]: [ 81 / 127 ] simplifiying candidate # 2.515 * * * * [progress]: [ 82 / 127 ] simplifiying candidate # 2.515 * * * * [progress]: [ 83 / 127 ] simplifiying candidate # 2.515 * * * * [progress]: [ 84 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 85 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 86 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 87 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 88 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 89 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 90 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 91 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 92 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 93 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 94 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 95 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 96 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 97 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 98 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 99 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 100 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 101 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 102 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 103 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 104 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 105 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 106 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 107 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 108 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 109 / 127 ] simplifiying candidate # 2.516 * * * * [progress]: [ 110 / 127 ] simplifiying candidate # 2.517 * * * * [progress]: [ 111 / 127 ] simplifiying candidate # 2.517 * * * * [progress]: [ 112 / 127 ] simplifiying candidate # 2.517 * * * * [progress]: [ 113 / 127 ] simplifiying candidate # 2.517 * * * * [progress]: [ 114 / 127 ] simplifiying candidate # 2.517 * * * * [progress]: [ 115 / 127 ] simplifiying candidate # 2.517 * * * * [progress]: [ 116 / 127 ] simplifiying candidate # 2.517 * * * * [progress]: [ 117 / 127 ] simplifiying candidate # 2.517 * * * * [progress]: [ 118 / 127 ] simplifiying candidate #real (real->posit16 (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))> 2.517 * * * * [progress]: [ 119 / 127 ] simplifiying candidate # 2.517 * * * * [progress]: [ 120 / 127 ] simplifiying candidate # 2.517 * * * * [progress]: [ 121 / 127 ] simplifiying candidate # 2.517 * * * * [progress]: [ 122 / 127 ] simplifiying candidate # 2.517 * * * * [progress]: [ 123 / 127 ] simplifiying candidate # 2.517 * * * * [progress]: [ 124 / 127 ] simplifiying candidate # 2.517 * * * * [progress]: [ 125 / 127 ] simplifiying candidate # 2.517 * * * * [progress]: [ 126 / 127 ] simplifiying candidate # 2.517 * * * * [progress]: [ 127 / 127 ] simplifiying candidate # 2.519 * [simplify]: Simplifying: (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (/ k 2)) (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2))) (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2))) (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))) (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* n (* 2 PI)) (* n (* 2 PI)) (+ (log n) (+ (log 2) (log PI))) (+ (log n) (log (* 2 PI))) (log (* n (* 2 PI))) (exp (* n (* 2 PI))) (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI))) (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI))) (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI))) (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI))) (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI))) (* n 2) (* (cbrt n) (* 2 PI)) (* (sqrt n) (* 2 PI)) (* n (* 2 PI)) (real->posit16 (* n (* 2 PI))) (- (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k))) (- (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k))) (- (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k))) (- (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k))) (- (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (log (sqrt k))) (log (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (exp (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (/ (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (* (* (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (- (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (- (sqrt k)) (/ (pow (* n (* 2 PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (cbrt (sqrt k))) (/ (pow (* n (* 2 PI)) 1/2) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (cbrt k))) (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) 1/2) (sqrt 1)) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k)) (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) 1/2) 1) (/ (pow (* n (* 2 PI)) (- (/ k 2))) 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-1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 2.521 * * [simplify]: iteration 1: (267 enodes) 2.584 * * [simplify]: iteration 2: (644 enodes) 3.166 * * [simplify]: Extracting #0: cost 97 inf + 0 3.167 * * [simplify]: Extracting #1: cost 372 inf + 1 3.173 * * [simplify]: Extracting #2: cost 513 inf + 18891 3.197 * * [simplify]: Extracting #3: cost 411 inf + 87524 3.220 * * [simplify]: Extracting #4: cost 283 inf + 135704 3.258 * * [simplify]: Extracting #5: cost 156 inf + 192203 3.301 * * [simplify]: Extracting #6: cost 96 inf + 227990 3.382 * * [simplify]: Extracting #7: cost 25 inf + 269385 3.461 * * [simplify]: Extracting #8: cost 0 inf + 290477 3.515 * * [simplify]: Extracting #9: cost 0 inf + 287997 3.569 * * [simplify]: Extracting #10: cost 0 inf + 287757 3.632 * [simplify]: Simplified to: (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (* (- 1/2 (/ 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(sqrt (sqrt k))) (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (fabs (cbrt k))) (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* (* PI 2) n) (- (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (- (/ k 2)))) (/ (sqrt k) (pow (* PI 2) (- 1/2 (/ k 2)))) (/ (sqrt k) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (- 1/4 (/ k 4)))) (* (sqrt k) (pow (* (* PI 2) n) (/ k 2))) (real->posit16 (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k))) (+ (* -1/2 (* k (+ (* (sqrt (* (* PI 2) n)) (log n)) (* (sqrt (* (* PI 2) n)) (log (* PI 2)))))) (+ (* (* (* (log n) k) (* (log n) k)) (* (sqrt (* (* PI 2) n)) 1/8)) (+ (+ (* (* (log (* PI 2)) (* (* (sqrt (* (* PI 2) n)) (* k k)) (log (* PI 2)))) 1/8) (sqrt (* (* PI 2) n))) (* (* (sqrt (* (* PI 2) n)) (log (* PI 2))) (* (* (* (log n) k) k) 1/4))))) (exp (* (log (* (* PI 2) n)) (- 1/2 (* k 1/2)))) (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2)))) (* (* PI 2) n) (* (* PI 2) n) (* (* PI 2) n) (- (+ (* (* (* (sqrt (* (* PI 2) n)) (* k k)) (log n)) (* (log (* PI 2)) +nan.0)) (- (* (- +nan.0) (* (* (sqrt (* (* PI 2) n)) (* k k)) (log (* PI 2)))) (+ (+ (- (* (* k (sqrt (* (* PI 2) n))) +nan.0) (* (sqrt (* (* PI 2) n)) +nan.0)) (+ (+ (* (* (log (* PI 2)) (* (* (sqrt (* (* PI 2) n)) (* k k)) (log (* PI 2)))) +nan.0) (* (* (* (sqrt (* (* PI 2) n)) (* k k)) (log n)) (- +nan.0))) (+ (- (* (* k k) (* (sqrt (* (* PI 2) n)) +nan.0)) (* (* (* (log (* PI 2)) +nan.0) (sqrt (* (* PI 2) n))) k)) (* (* (log n) k) (* (sqrt (* (* PI 2) n)) +nan.0))))) (* (* (* (* (log n) k) (* (log n) k)) (sqrt (* (* PI 2) n))) (- +nan.0)))))) (- (+ (- (* (/ +nan.0 (* k k)) (/ (exp (* (log (* (* PI 2) n)) (- 1/2 (* k 1/2)))) k)) (/ (* (exp (* (log (* (* PI 2) n)) (- 1/2 (* k 1/2)))) +nan.0) k)) (/ (/ (* (exp (* (log (* (* PI 2) n)) (- 1/2 (* k 1/2)))) +nan.0) k) k))) (- (- (/ +nan.0 (/ k (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2)))))) (* +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)))))))) 3.651 * * * [progress]: adding candidates to table 5.326 * * [progress]: iteration 2 / 4 5.326 * * * [progress]: picking best candidate 5.372 * * * * [pick]: Picked # 5.373 * * * [progress]: localizing error 5.427 * * * [progress]: generating rewritten candidates 5.428 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1) 5.439 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 5.449 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2) 5.460 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 5.494 * * * [progress]: generating series expansions 5.494 * * * * [progress]: [ 1 / 4 ] generating series at (2 1) 5.495 * [backup-simplify]: Simplify (pow n (- 1/2 (/ k 2))) into (pow n (- 1/2 (* 1/2 k))) 5.495 * [approximate]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in (n k) around 0 5.495 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 5.495 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 5.495 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 5.495 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 5.495 * [taylor]: Taking taylor expansion of 1/2 in k 5.495 * [backup-simplify]: Simplify 1/2 into 1/2 5.495 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 5.495 * [taylor]: Taking taylor expansion of 1/2 in k 5.495 * [backup-simplify]: Simplify 1/2 into 1/2 5.495 * [taylor]: Taking taylor expansion of k in k 5.495 * [backup-simplify]: Simplify 0 into 0 5.495 * [backup-simplify]: Simplify 1 into 1 5.495 * [taylor]: Taking taylor expansion of (log n) in k 5.495 * [taylor]: Taking taylor expansion of n in k 5.495 * [backup-simplify]: Simplify n into n 5.495 * [backup-simplify]: Simplify (log n) into (log n) 5.496 * [backup-simplify]: Simplify (* 1/2 0) into 0 5.496 * [backup-simplify]: Simplify (- 0) into 0 5.497 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 5.497 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 5.497 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 5.497 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 5.497 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 5.497 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 5.497 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 5.497 * [taylor]: Taking taylor expansion of 1/2 in n 5.497 * [backup-simplify]: Simplify 1/2 into 1/2 5.497 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 5.497 * [taylor]: Taking taylor expansion of 1/2 in n 5.497 * [backup-simplify]: Simplify 1/2 into 1/2 5.497 * [taylor]: Taking taylor expansion of k in n 5.497 * [backup-simplify]: Simplify k into k 5.497 * [taylor]: Taking taylor expansion of (log n) in n 5.497 * [taylor]: Taking taylor expansion of n in n 5.497 * [backup-simplify]: Simplify 0 into 0 5.497 * [backup-simplify]: Simplify 1 into 1 5.498 * [backup-simplify]: Simplify (log 1) into 0 5.498 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 5.498 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 5.498 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 5.498 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 5.498 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 5.499 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 5.499 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 5.499 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 5.499 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 5.499 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 5.499 * [taylor]: Taking taylor expansion of 1/2 in n 5.499 * [backup-simplify]: Simplify 1/2 into 1/2 5.499 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 5.499 * [taylor]: Taking taylor expansion of 1/2 in n 5.499 * [backup-simplify]: Simplify 1/2 into 1/2 5.499 * [taylor]: Taking taylor expansion of k in n 5.499 * [backup-simplify]: Simplify k into k 5.499 * [taylor]: Taking taylor expansion of (log n) in n 5.499 * [taylor]: Taking taylor expansion of n in n 5.499 * [backup-simplify]: Simplify 0 into 0 5.499 * [backup-simplify]: Simplify 1 into 1 5.499 * [backup-simplify]: Simplify (log 1) into 0 5.499 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 5.499 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 5.499 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 5.500 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 5.500 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 5.500 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 5.500 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 5.500 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 5.500 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 5.500 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 5.500 * [taylor]: Taking taylor expansion of 1/2 in k 5.500 * [backup-simplify]: Simplify 1/2 into 1/2 5.500 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 5.500 * [taylor]: Taking taylor expansion of 1/2 in k 5.500 * [backup-simplify]: Simplify 1/2 into 1/2 5.500 * [taylor]: Taking taylor expansion of k in k 5.501 * [backup-simplify]: Simplify 0 into 0 5.501 * [backup-simplify]: Simplify 1 into 1 5.501 * [taylor]: Taking taylor expansion of (log n) in k 5.501 * [taylor]: Taking taylor expansion of n in k 5.501 * [backup-simplify]: Simplify n into n 5.501 * [backup-simplify]: Simplify (log n) into (log n) 5.501 * [backup-simplify]: Simplify (* 1/2 0) into 0 5.502 * [backup-simplify]: Simplify (- 0) into 0 5.502 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 5.502 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 5.502 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 5.502 * [backup-simplify]: Simplify (pow n 1/2) into (pow n 1/2) 5.504 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 5.504 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 5.505 * [backup-simplify]: Simplify (- 0) into 0 5.505 * [backup-simplify]: Simplify (+ 0 0) into 0 5.506 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 5.506 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log n))) into 0 5.507 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 5.507 * [taylor]: Taking taylor expansion of 0 in k 5.507 * [backup-simplify]: Simplify 0 into 0 5.507 * [backup-simplify]: Simplify 0 into 0 5.508 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 5.508 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 5.509 * [backup-simplify]: Simplify (- 1/2) into -1/2 5.509 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 5.510 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log n))) into (- (* 1/2 (log n))) 5.510 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n))) 5.510 * [backup-simplify]: Simplify (* -1/2 (* (sqrt n) (log n))) into (* -1/2 (* (sqrt n) (log n))) 5.513 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 5.514 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 5.514 * [backup-simplify]: Simplify (- 0) into 0 5.515 * [backup-simplify]: Simplify (+ 0 0) into 0 5.515 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 5.516 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0 5.517 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 5.517 * [taylor]: Taking taylor expansion of 0 in k 5.517 * [backup-simplify]: Simplify 0 into 0 5.517 * [backup-simplify]: Simplify 0 into 0 5.517 * [backup-simplify]: Simplify 0 into 0 5.519 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 5.520 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 5.521 * [backup-simplify]: Simplify (- 0) into 0 5.521 * [backup-simplify]: Simplify (+ 0 0) into 0 5.522 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log n)))) into 0 5.523 * [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))) 5.523 * [backup-simplify]: Simplify (* 1/8 (* (sqrt n) (pow (log n) 2))) into (* 1/8 (* (sqrt n) (pow (log n) 2))) 5.524 * [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)))) 5.524 * [backup-simplify]: Simplify (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 5.524 * [approximate]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 5.524 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 5.524 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in k 5.524 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in k 5.524 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 5.524 * [taylor]: Taking taylor expansion of 1/2 in k 5.524 * [backup-simplify]: Simplify 1/2 into 1/2 5.524 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 5.524 * [taylor]: Taking taylor expansion of 1/2 in k 5.524 * [backup-simplify]: Simplify 1/2 into 1/2 5.524 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.524 * [taylor]: Taking taylor expansion of k in k 5.524 * [backup-simplify]: Simplify 0 into 0 5.524 * [backup-simplify]: Simplify 1 into 1 5.525 * [backup-simplify]: Simplify (/ 1 1) into 1 5.525 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k 5.525 * [taylor]: Taking taylor expansion of (/ 1 n) in k 5.525 * [taylor]: Taking taylor expansion of n in k 5.525 * [backup-simplify]: Simplify n into n 5.525 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n) 5.525 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n)) 5.526 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 5.526 * [backup-simplify]: Simplify (- 1/2) into -1/2 5.526 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 5.527 * [backup-simplify]: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) 5.527 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 5.527 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 5.527 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 5.527 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 5.527 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 5.527 * [taylor]: Taking taylor expansion of 1/2 in n 5.527 * [backup-simplify]: Simplify 1/2 into 1/2 5.527 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 5.527 * [taylor]: Taking taylor expansion of 1/2 in n 5.527 * [backup-simplify]: Simplify 1/2 into 1/2 5.527 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.527 * [taylor]: Taking taylor expansion of k in n 5.527 * [backup-simplify]: Simplify k into k 5.527 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.527 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 5.527 * [taylor]: Taking taylor expansion of (/ 1 n) in n 5.527 * [taylor]: Taking taylor expansion of n in n 5.527 * [backup-simplify]: Simplify 0 into 0 5.527 * [backup-simplify]: Simplify 1 into 1 5.528 * [backup-simplify]: Simplify (/ 1 1) into 1 5.528 * [backup-simplify]: Simplify (log 1) into 0 5.528 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 5.528 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 5.528 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 5.529 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 5.529 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 5.529 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 5.529 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 5.529 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 5.529 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 5.529 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 5.529 * [taylor]: Taking taylor expansion of 1/2 in n 5.529 * [backup-simplify]: Simplify 1/2 into 1/2 5.529 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 5.529 * [taylor]: Taking taylor expansion of 1/2 in n 5.529 * [backup-simplify]: Simplify 1/2 into 1/2 5.529 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.529 * [taylor]: Taking taylor expansion of k in n 5.529 * [backup-simplify]: Simplify k into k 5.529 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.529 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 5.529 * [taylor]: Taking taylor expansion of (/ 1 n) in n 5.529 * [taylor]: Taking taylor expansion of n in n 5.529 * [backup-simplify]: Simplify 0 into 0 5.529 * [backup-simplify]: Simplify 1 into 1 5.530 * [backup-simplify]: Simplify (/ 1 1) into 1 5.530 * [backup-simplify]: Simplify (log 1) into 0 5.530 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 5.530 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 5.531 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 5.531 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 5.531 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 5.531 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 5.531 * [taylor]: Taking taylor expansion of (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) in k 5.531 * [taylor]: Taking taylor expansion of (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) in k 5.531 * [taylor]: Taking taylor expansion of -1 in k 5.531 * [backup-simplify]: Simplify -1 into -1 5.531 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log n)) in k 5.531 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 5.531 * [taylor]: Taking taylor expansion of 1/2 in k 5.531 * [backup-simplify]: Simplify 1/2 into 1/2 5.531 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 5.531 * [taylor]: Taking taylor expansion of 1/2 in k 5.531 * [backup-simplify]: Simplify 1/2 into 1/2 5.531 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.531 * [taylor]: Taking taylor expansion of k in k 5.531 * [backup-simplify]: Simplify 0 into 0 5.531 * [backup-simplify]: Simplify 1 into 1 5.532 * [backup-simplify]: Simplify (/ 1 1) into 1 5.532 * [taylor]: Taking taylor expansion of (log n) in k 5.532 * [taylor]: Taking taylor expansion of n in k 5.532 * [backup-simplify]: Simplify n into n 5.532 * [backup-simplify]: Simplify (log n) into (log n) 5.532 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 5.532 * [backup-simplify]: Simplify (- 1/2) into -1/2 5.532 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 5.533 * [backup-simplify]: Simplify (* -1/2 (log n)) into (* -1/2 (log n)) 5.533 * [backup-simplify]: Simplify (* -1 (* -1/2 (log n))) into (* 1/2 (log n)) 5.533 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 5.533 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 5.533 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 5.534 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 5.534 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 5.535 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 5.535 * [backup-simplify]: Simplify (- 0) into 0 5.535 * [backup-simplify]: Simplify (+ 0 0) into 0 5.536 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 5.536 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 5.536 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 5.536 * [taylor]: Taking taylor expansion of 0 in k 5.536 * [backup-simplify]: Simplify 0 into 0 5.536 * [backup-simplify]: Simplify 0 into 0 5.536 * [backup-simplify]: Simplify 0 into 0 5.537 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.538 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 5.539 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 5.539 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 5.540 * [backup-simplify]: Simplify (- 0) into 0 5.540 * [backup-simplify]: Simplify (+ 0 0) into 0 5.540 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 5.541 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 5.541 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 5.541 * [taylor]: Taking taylor expansion of 0 in k 5.541 * [backup-simplify]: Simplify 0 into 0 5.542 * [backup-simplify]: Simplify 0 into 0 5.542 * [backup-simplify]: Simplify 0 into 0 5.542 * [backup-simplify]: Simplify 0 into 0 5.542 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.545 * [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 5.545 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 5.546 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 5.546 * [backup-simplify]: Simplify (- 0) into 0 5.547 * [backup-simplify]: Simplify (+ 0 0) into 0 5.547 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 5.547 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 5.549 * [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 5.549 * [taylor]: Taking taylor expansion of 0 in k 5.549 * [backup-simplify]: Simplify 0 into 0 5.549 * [backup-simplify]: Simplify 0 into 0 5.549 * [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))))) 5.549 * [backup-simplify]: Simplify (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 5.549 * [approximate]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 5.549 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 5.549 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in k 5.549 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in k 5.549 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 5.549 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 5.549 * [taylor]: Taking taylor expansion of 1/2 in k 5.549 * [backup-simplify]: Simplify 1/2 into 1/2 5.549 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.549 * [taylor]: Taking taylor expansion of k in k 5.549 * [backup-simplify]: Simplify 0 into 0 5.549 * [backup-simplify]: Simplify 1 into 1 5.549 * [backup-simplify]: Simplify (/ 1 1) into 1 5.549 * [taylor]: Taking taylor expansion of 1/2 in k 5.549 * [backup-simplify]: Simplify 1/2 into 1/2 5.549 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k 5.549 * [taylor]: Taking taylor expansion of (/ -1 n) in k 5.549 * [taylor]: Taking taylor expansion of -1 in k 5.549 * [backup-simplify]: Simplify -1 into -1 5.549 * [taylor]: Taking taylor expansion of n in k 5.549 * [backup-simplify]: Simplify n into n 5.549 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n) 5.550 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n)) 5.550 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 5.550 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 5.550 * [backup-simplify]: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) 5.550 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 5.550 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 5.550 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 5.550 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 5.550 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 5.550 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 5.550 * [taylor]: Taking taylor expansion of 1/2 in n 5.550 * [backup-simplify]: Simplify 1/2 into 1/2 5.550 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.550 * [taylor]: Taking taylor expansion of k in n 5.550 * [backup-simplify]: Simplify k into k 5.550 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.550 * [taylor]: Taking taylor expansion of 1/2 in n 5.551 * [backup-simplify]: Simplify 1/2 into 1/2 5.551 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 5.551 * [taylor]: Taking taylor expansion of (/ -1 n) in n 5.551 * [taylor]: Taking taylor expansion of -1 in n 5.551 * [backup-simplify]: Simplify -1 into -1 5.551 * [taylor]: Taking taylor expansion of n in n 5.551 * [backup-simplify]: Simplify 0 into 0 5.551 * [backup-simplify]: Simplify 1 into 1 5.551 * [backup-simplify]: Simplify (/ -1 1) into -1 5.551 * [backup-simplify]: Simplify (log -1) into (log -1) 5.551 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 5.551 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 5.552 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 5.552 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 5.552 * [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)))) 5.552 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 5.552 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 5.552 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 5.553 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 5.553 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 5.553 * [taylor]: Taking taylor expansion of 1/2 in n 5.553 * [backup-simplify]: Simplify 1/2 into 1/2 5.553 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.553 * [taylor]: Taking taylor expansion of k in n 5.553 * [backup-simplify]: Simplify k into k 5.553 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.553 * [taylor]: Taking taylor expansion of 1/2 in n 5.553 * [backup-simplify]: Simplify 1/2 into 1/2 5.553 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 5.553 * [taylor]: Taking taylor expansion of (/ -1 n) in n 5.553 * [taylor]: Taking taylor expansion of -1 in n 5.553 * [backup-simplify]: Simplify -1 into -1 5.553 * [taylor]: Taking taylor expansion of n in n 5.553 * [backup-simplify]: Simplify 0 into 0 5.553 * [backup-simplify]: Simplify 1 into 1 5.553 * [backup-simplify]: Simplify (/ -1 1) into -1 5.553 * [backup-simplify]: Simplify (log -1) into (log -1) 5.553 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 5.553 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 5.554 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 5.554 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 5.555 * [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)))) 5.555 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) in k 5.555 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) in k 5.555 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 5.555 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 5.555 * [taylor]: Taking taylor expansion of 1/2 in k 5.555 * [backup-simplify]: Simplify 1/2 into 1/2 5.555 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.555 * [taylor]: Taking taylor expansion of k in k 5.555 * [backup-simplify]: Simplify 0 into 0 5.555 * [backup-simplify]: Simplify 1 into 1 5.555 * [backup-simplify]: Simplify (/ 1 1) into 1 5.555 * [taylor]: Taking taylor expansion of 1/2 in k 5.555 * [backup-simplify]: Simplify 1/2 into 1/2 5.555 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k 5.555 * [taylor]: Taking taylor expansion of (log -1) in k 5.555 * [taylor]: Taking taylor expansion of -1 in k 5.555 * [backup-simplify]: Simplify -1 into -1 5.555 * [backup-simplify]: Simplify (log -1) into (log -1) 5.555 * [taylor]: Taking taylor expansion of (log n) in k 5.555 * [taylor]: Taking taylor expansion of n in k 5.556 * [backup-simplify]: Simplify n into n 5.556 * [backup-simplify]: Simplify (log n) into (log n) 5.556 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 5.556 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 5.556 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 5.556 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n)) 5.557 * [backup-simplify]: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n))) 5.557 * [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)))) 5.557 * [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)))) 5.558 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 5.559 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 5.559 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 5.559 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 5.559 * [backup-simplify]: Simplify (+ 0 0) into 0 5.560 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 5.560 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -1) (log n)))) into 0 5.561 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 5.561 * [taylor]: Taking taylor expansion of 0 in k 5.561 * [backup-simplify]: Simplify 0 into 0 5.561 * [backup-simplify]: Simplify 0 into 0 5.561 * [backup-simplify]: Simplify 0 into 0 5.562 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.563 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0 5.564 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 5.564 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 5.564 * [backup-simplify]: Simplify (+ 0 0) into 0 5.565 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 5.565 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0 5.567 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 5.567 * [taylor]: Taking taylor expansion of 0 in k 5.567 * [backup-simplify]: Simplify 0 into 0 5.567 * [backup-simplify]: Simplify 0 into 0 5.567 * [backup-simplify]: Simplify 0 into 0 5.567 * [backup-simplify]: Simplify 0 into 0 5.567 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.570 * [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 5.571 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 5.572 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 5.572 * [backup-simplify]: Simplify (+ 0 0) into 0 5.572 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 5.573 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -1) (log n)))))) into 0 5.575 * [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 5.575 * [taylor]: Taking taylor expansion of 0 in k 5.575 * [backup-simplify]: Simplify 0 into 0 5.575 * [backup-simplify]: Simplify 0 into 0 5.575 * [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))))) 5.575 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 5.576 * [backup-simplify]: Simplify (pow (* 2 PI) (- 1/2 (/ k 2))) into (pow (* 2 PI) (- 1/2 (* 1/2 k))) 5.576 * [approximate]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in (k) around 0 5.576 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in k 5.576 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) in k 5.576 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) in k 5.576 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 5.576 * [taylor]: Taking taylor expansion of 1/2 in k 5.576 * [backup-simplify]: Simplify 1/2 into 1/2 5.576 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 5.576 * [taylor]: Taking taylor expansion of 1/2 in k 5.576 * [backup-simplify]: Simplify 1/2 into 1/2 5.576 * [taylor]: Taking taylor expansion of k in k 5.576 * [backup-simplify]: Simplify 0 into 0 5.576 * [backup-simplify]: Simplify 1 into 1 5.576 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 5.576 * [taylor]: Taking taylor expansion of (* 2 PI) in k 5.576 * [taylor]: Taking taylor expansion of 2 in k 5.576 * [backup-simplify]: Simplify 2 into 2 5.576 * [taylor]: Taking taylor expansion of PI in k 5.576 * [backup-simplify]: Simplify PI into PI 5.576 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 5.577 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 5.577 * [backup-simplify]: Simplify (* 1/2 0) into 0 5.577 * [backup-simplify]: Simplify (- 0) into 0 5.578 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 5.579 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 5.580 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) 5.580 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in k 5.580 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) in k 5.580 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) in k 5.580 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 5.581 * [taylor]: Taking taylor expansion of 1/2 in k 5.581 * [backup-simplify]: Simplify 1/2 into 1/2 5.581 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 5.581 * [taylor]: Taking taylor expansion of 1/2 in k 5.581 * [backup-simplify]: Simplify 1/2 into 1/2 5.581 * [taylor]: Taking taylor expansion of k in k 5.581 * [backup-simplify]: Simplify 0 into 0 5.581 * [backup-simplify]: Simplify 1 into 1 5.581 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 5.581 * [taylor]: Taking taylor expansion of (* 2 PI) in k 5.581 * [taylor]: Taking taylor expansion of 2 in k 5.581 * [backup-simplify]: Simplify 2 into 2 5.581 * [taylor]: Taking taylor expansion of PI in k 5.581 * [backup-simplify]: Simplify PI into PI 5.581 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 5.587 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 5.587 * [backup-simplify]: Simplify (* 1/2 0) into 0 5.587 * [backup-simplify]: Simplify (- 0) into 0 5.588 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 5.589 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 5.591 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) 5.592 * [backup-simplify]: Simplify (pow (* 2 PI) 1/2) into (pow (* 2 PI) 1/2) 5.592 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 5.593 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 5.594 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 5.594 * [backup-simplify]: Simplify (- 1/2) into -1/2 5.594 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 5.596 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 PI)))) into (- (* 1/2 (log (* 2 PI)))) 5.604 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) 5.607 * [backup-simplify]: Simplify (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) into (* -1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) 5.608 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 5.611 * [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 5.613 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 5.613 * [backup-simplify]: Simplify (- 0) into 0 5.613 * [backup-simplify]: Simplify (+ 0 0) into 0 5.615 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 PI))))) into 0 5.631 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) 5.637 * [backup-simplify]: Simplify (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) into (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI))) 5.650 * [backup-simplify]: Simplify (+ (* (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) k) (pow (* 2 PI) 1/2))) into (- (+ (* 1/8 (* (* (sqrt 2) (* (pow k 2) (pow (log (* 2 PI)) 2))) (sqrt PI))) (pow (* 2 PI) 1/2)) (* 1/2 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt PI)))) 5.651 * [backup-simplify]: Simplify (pow (* 2 PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 5.651 * [approximate]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in (k) around 0 5.651 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in k 5.651 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in k 5.651 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in k 5.651 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 5.651 * [taylor]: Taking taylor expansion of 1/2 in k 5.651 * [backup-simplify]: Simplify 1/2 into 1/2 5.651 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 5.651 * [taylor]: Taking taylor expansion of 1/2 in k 5.651 * [backup-simplify]: Simplify 1/2 into 1/2 5.651 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.651 * [taylor]: Taking taylor expansion of k in k 5.651 * [backup-simplify]: Simplify 0 into 0 5.651 * [backup-simplify]: Simplify 1 into 1 5.652 * [backup-simplify]: Simplify (/ 1 1) into 1 5.652 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 5.652 * [taylor]: Taking taylor expansion of (* 2 PI) in k 5.652 * [taylor]: Taking taylor expansion of 2 in k 5.652 * [backup-simplify]: Simplify 2 into 2 5.652 * [taylor]: Taking taylor expansion of PI in k 5.652 * [backup-simplify]: Simplify PI into PI 5.652 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 5.653 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 5.654 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 5.654 * [backup-simplify]: Simplify (- 1/2) into -1/2 5.655 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 5.656 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) 5.657 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 5.658 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in k 5.658 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in k 5.658 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in k 5.658 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 5.658 * [taylor]: Taking taylor expansion of 1/2 in k 5.658 * [backup-simplify]: Simplify 1/2 into 1/2 5.658 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 5.658 * [taylor]: Taking taylor expansion of 1/2 in k 5.658 * [backup-simplify]: Simplify 1/2 into 1/2 5.658 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.658 * [taylor]: Taking taylor expansion of k in k 5.658 * [backup-simplify]: Simplify 0 into 0 5.658 * [backup-simplify]: Simplify 1 into 1 5.658 * [backup-simplify]: Simplify (/ 1 1) into 1 5.658 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 5.658 * [taylor]: Taking taylor expansion of (* 2 PI) in k 5.658 * [taylor]: Taking taylor expansion of 2 in k 5.658 * [backup-simplify]: Simplify 2 into 2 5.658 * [taylor]: Taking taylor expansion of PI in k 5.658 * [backup-simplify]: Simplify PI into PI 5.659 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 5.660 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 5.660 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 5.661 * [backup-simplify]: Simplify (- 1/2) into -1/2 5.661 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 5.663 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) 5.664 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 5.665 * [backup-simplify]: Simplify (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 5.665 * [backup-simplify]: Simplify 0 into 0 5.665 * [backup-simplify]: Simplify 0 into 0 5.665 * [backup-simplify]: Simplify 0 into 0 5.665 * [backup-simplify]: Simplify 0 into 0 5.665 * [backup-simplify]: Simplify 0 into 0 5.665 * [backup-simplify]: Simplify 0 into 0 5.666 * [backup-simplify]: Simplify (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) into (pow (* 2 PI) (- 1/2 (* 1/2 k))) 5.666 * [backup-simplify]: Simplify (pow (* 2 PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 5.666 * [approximate]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in (k) around 0 5.666 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in k 5.666 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in k 5.666 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in k 5.666 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 5.666 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 5.667 * [taylor]: Taking taylor expansion of 1/2 in k 5.667 * [backup-simplify]: Simplify 1/2 into 1/2 5.667 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.667 * [taylor]: Taking taylor expansion of k in k 5.667 * [backup-simplify]: Simplify 0 into 0 5.667 * [backup-simplify]: Simplify 1 into 1 5.667 * [backup-simplify]: Simplify (/ 1 1) into 1 5.667 * [taylor]: Taking taylor expansion of 1/2 in k 5.667 * [backup-simplify]: Simplify 1/2 into 1/2 5.667 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 5.667 * [taylor]: Taking taylor expansion of (* 2 PI) in k 5.667 * [taylor]: Taking taylor expansion of 2 in k 5.667 * [backup-simplify]: Simplify 2 into 2 5.667 * [taylor]: Taking taylor expansion of PI in k 5.667 * [backup-simplify]: Simplify PI into PI 5.668 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 5.669 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 5.669 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 5.670 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 5.671 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 5.672 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 5.673 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in k 5.673 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in k 5.673 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in k 5.673 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 5.673 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 5.673 * [taylor]: Taking taylor expansion of 1/2 in k 5.673 * [backup-simplify]: Simplify 1/2 into 1/2 5.673 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.673 * [taylor]: Taking taylor expansion of k in k 5.673 * [backup-simplify]: Simplify 0 into 0 5.673 * [backup-simplify]: Simplify 1 into 1 5.673 * [backup-simplify]: Simplify (/ 1 1) into 1 5.673 * [taylor]: Taking taylor expansion of 1/2 in k 5.673 * [backup-simplify]: Simplify 1/2 into 1/2 5.673 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 5.673 * [taylor]: Taking taylor expansion of (* 2 PI) in k 5.673 * [taylor]: Taking taylor expansion of 2 in k 5.673 * [backup-simplify]: Simplify 2 into 2 5.673 * [taylor]: Taking taylor expansion of PI in k 5.673 * [backup-simplify]: Simplify PI into PI 5.674 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 5.675 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 5.675 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 5.676 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 5.678 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 5.679 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 5.680 * [backup-simplify]: Simplify (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 5.680 * [backup-simplify]: Simplify 0 into 0 5.680 * [backup-simplify]: Simplify 0 into 0 5.680 * [backup-simplify]: Simplify 0 into 0 5.680 * [backup-simplify]: Simplify 0 into 0 5.680 * [backup-simplify]: Simplify 0 into 0 5.680 * [backup-simplify]: Simplify 0 into 0 5.681 * [backup-simplify]: Simplify (pow (* 2 PI) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) into (pow (* 2 PI) (- 1/2 (* 1/2 k))) 5.681 * * * * [progress]: [ 3 / 4 ] generating series at (2 2) 5.681 * [backup-simplify]: Simplify (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k)) into (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) 5.681 * [approximate]: Taking taylor expansion of (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in (k) around 0 5.681 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in k 5.681 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in k 5.681 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) in k 5.682 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) in k 5.682 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 5.682 * [taylor]: Taking taylor expansion of 1/2 in k 5.682 * [backup-simplify]: Simplify 1/2 into 1/2 5.682 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 5.682 * [taylor]: Taking taylor expansion of 1/2 in k 5.682 * [backup-simplify]: Simplify 1/2 into 1/2 5.682 * [taylor]: Taking taylor expansion of k in k 5.682 * [backup-simplify]: Simplify 0 into 0 5.682 * [backup-simplify]: Simplify 1 into 1 5.682 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 5.682 * [taylor]: Taking taylor expansion of (* 2 PI) in k 5.682 * [taylor]: Taking taylor expansion of 2 in k 5.682 * [backup-simplify]: Simplify 2 into 2 5.682 * [taylor]: Taking taylor expansion of PI in k 5.682 * [backup-simplify]: Simplify PI into PI 5.682 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 5.683 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 5.684 * [backup-simplify]: Simplify (* 1/2 0) into 0 5.684 * [backup-simplify]: Simplify (- 0) into 0 5.685 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 5.686 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 5.689 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) 5.689 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 5.689 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.689 * [taylor]: Taking taylor expansion of k in k 5.689 * [backup-simplify]: Simplify 0 into 0 5.689 * [backup-simplify]: Simplify 1 into 1 5.690 * [backup-simplify]: Simplify (/ 1 1) into 1 5.690 * [backup-simplify]: Simplify (sqrt 0) into 0 5.691 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 5.691 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in k 5.692 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in k 5.692 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) in k 5.692 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) in k 5.692 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 5.692 * [taylor]: Taking taylor expansion of 1/2 in k 5.692 * [backup-simplify]: Simplify 1/2 into 1/2 5.692 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 5.692 * [taylor]: Taking taylor expansion of 1/2 in k 5.692 * [backup-simplify]: Simplify 1/2 into 1/2 5.692 * [taylor]: Taking taylor expansion of k in k 5.692 * [backup-simplify]: Simplify 0 into 0 5.692 * [backup-simplify]: Simplify 1 into 1 5.692 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 5.692 * [taylor]: Taking taylor expansion of (* 2 PI) in k 5.692 * [taylor]: Taking taylor expansion of 2 in k 5.692 * [backup-simplify]: Simplify 2 into 2 5.692 * [taylor]: Taking taylor expansion of PI in k 5.692 * [backup-simplify]: Simplify PI into PI 5.692 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 5.693 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 5.694 * [backup-simplify]: Simplify (* 1/2 0) into 0 5.694 * [backup-simplify]: Simplify (- 0) into 0 5.695 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 5.697 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 5.700 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) 5.700 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 5.700 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.700 * [taylor]: Taking taylor expansion of k in k 5.700 * [backup-simplify]: Simplify 0 into 0 5.700 * [backup-simplify]: Simplify 1 into 1 5.700 * [backup-simplify]: Simplify (/ 1 1) into 1 5.701 * [backup-simplify]: Simplify (sqrt 0) into 0 5.702 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 5.703 * [backup-simplify]: Simplify (* (pow (* 2 PI) 1/2) 0) into 0 5.703 * [backup-simplify]: Simplify 0 into 0 5.704 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 5.706 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 5.707 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 5.707 * [backup-simplify]: Simplify (- 1/2) into -1/2 5.707 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 5.711 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 PI)))) into (- (* 1/2 (log (* 2 PI)))) 5.731 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) 5.738 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) 1/2) +nan.0) (* (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt PI)))) 5.741 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (sqrt PI)))) into (- (* +nan.0 (* (sqrt 2) (sqrt PI)))) 5.742 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 5.745 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 5.747 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 5.750 * [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 5.751 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 5.752 * [backup-simplify]: Simplify (- 0) into 0 5.752 * [backup-simplify]: Simplify (+ 0 0) into 0 5.754 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 PI))))) into 0 5.769 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) 5.787 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) +nan.0) (* (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) 0))) into (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI)))))) 5.801 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI)))))) into (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI)))))) 5.802 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.806 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 5.807 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 5.814 * [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 5.815 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 5.816 * [backup-simplify]: Simplify (- 0) into 0 5.816 * [backup-simplify]: Simplify (+ 0 0) into 0 5.818 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 PI)))))) into 0 5.838 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 3))) 5.869 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) +nan.0) (+ (* (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) +nan.0) (* (* -1/48 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 3))) 0)))) into (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI)))))))) 5.906 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI)))))))) 5.955 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI)))))))) (pow k 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI)))))) k) (- (* +nan.0 (* (sqrt 2) (sqrt PI)))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (pow k 2)) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (log (* 2 PI)) (* (sqrt 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log (* 2 PI)) 2) (* (sqrt 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) k) (sqrt PI)))))))))))))) 5.956 * [backup-simplify]: Simplify (/ (pow (* 2 PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) 5.956 * [approximate]: Taking taylor expansion of (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in (k) around 0 5.956 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 5.956 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in k 5.956 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in k 5.956 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in k 5.956 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 5.956 * [taylor]: Taking taylor expansion of 1/2 in k 5.956 * [backup-simplify]: Simplify 1/2 into 1/2 5.956 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 5.956 * [taylor]: Taking taylor expansion of 1/2 in k 5.956 * [backup-simplify]: Simplify 1/2 into 1/2 5.956 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.956 * [taylor]: Taking taylor expansion of k in k 5.956 * [backup-simplify]: Simplify 0 into 0 5.956 * [backup-simplify]: Simplify 1 into 1 5.957 * [backup-simplify]: Simplify (/ 1 1) into 1 5.957 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 5.957 * [taylor]: Taking taylor expansion of (* 2 PI) in k 5.957 * [taylor]: Taking taylor expansion of 2 in k 5.957 * [backup-simplify]: Simplify 2 into 2 5.957 * [taylor]: Taking taylor expansion of PI in k 5.957 * [backup-simplify]: Simplify PI into PI 5.957 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 5.958 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 5.958 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 5.958 * [backup-simplify]: Simplify (- 1/2) into -1/2 5.959 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 5.960 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) 5.960 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 5.960 * [taylor]: Taking taylor expansion of (sqrt k) in k 5.961 * [taylor]: Taking taylor expansion of k in k 5.961 * [backup-simplify]: Simplify 0 into 0 5.961 * [backup-simplify]: Simplify 1 into 1 5.961 * [backup-simplify]: Simplify (sqrt 0) into 0 5.962 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 5.962 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 5.962 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in k 5.962 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in k 5.962 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in k 5.962 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 5.962 * [taylor]: Taking taylor expansion of 1/2 in k 5.962 * [backup-simplify]: Simplify 1/2 into 1/2 5.962 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 5.962 * [taylor]: Taking taylor expansion of 1/2 in k 5.962 * [backup-simplify]: Simplify 1/2 into 1/2 5.962 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.962 * [taylor]: Taking taylor expansion of k in k 5.962 * [backup-simplify]: Simplify 0 into 0 5.962 * [backup-simplify]: Simplify 1 into 1 5.962 * [backup-simplify]: Simplify (/ 1 1) into 1 5.962 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 5.962 * [taylor]: Taking taylor expansion of (* 2 PI) in k 5.962 * [taylor]: Taking taylor expansion of 2 in k 5.962 * [backup-simplify]: Simplify 2 into 2 5.962 * [taylor]: Taking taylor expansion of PI in k 5.962 * [backup-simplify]: Simplify PI into PI 5.963 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 5.963 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 5.964 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 5.964 * [backup-simplify]: Simplify (- 1/2) into -1/2 5.964 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 5.965 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) 5.966 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 5.966 * [taylor]: Taking taylor expansion of (sqrt k) in k 5.966 * [taylor]: Taking taylor expansion of k in k 5.966 * [backup-simplify]: Simplify 0 into 0 5.966 * [backup-simplify]: Simplify 1 into 1 5.966 * [backup-simplify]: Simplify (sqrt 0) into 0 5.967 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 5.968 * [backup-simplify]: Simplify (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 0) into 0 5.968 * [backup-simplify]: Simplify 0 into 0 5.968 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) (* 0 0)) into (- (* +nan.0 (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))) 5.969 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))) into (- (* +nan.0 (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))) 5.970 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 5.971 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))) 5.972 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))) into (- (* +nan.0 (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))) 5.974 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 5.975 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))) 5.975 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))) into (- (* +nan.0 (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))) 5.977 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))) (pow (/ 1 k) 3)) (+ (* (- (* +nan.0 (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))) (pow (/ 1 k) 2)) (* (- (* +nan.0 (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))) (/ 1 k)))) into (- (+ (* +nan.0 (/ (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow k 3))) (- (+ (* +nan.0 (/ (pow (* 2 PI) (- 1/2 (* 1/2 k))) k)) (- (* +nan.0 (/ (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow k 2)))))))) 5.977 * [backup-simplify]: Simplify (/ (pow (* 2 PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 5.977 * [approximate]: Taking taylor expansion of (/ (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (k) around 0 5.977 * [taylor]: Taking taylor expansion of (/ (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 5.977 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in k 5.977 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in k 5.977 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in k 5.977 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 5.978 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 5.978 * [taylor]: Taking taylor expansion of 1/2 in k 5.978 * [backup-simplify]: Simplify 1/2 into 1/2 5.978 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.978 * [taylor]: Taking taylor expansion of k in k 5.978 * [backup-simplify]: Simplify 0 into 0 5.978 * [backup-simplify]: Simplify 1 into 1 5.978 * [backup-simplify]: Simplify (/ 1 1) into 1 5.978 * [taylor]: Taking taylor expansion of 1/2 in k 5.978 * [backup-simplify]: Simplify 1/2 into 1/2 5.978 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 5.978 * [taylor]: Taking taylor expansion of (* 2 PI) in k 5.978 * [taylor]: Taking taylor expansion of 2 in k 5.978 * [backup-simplify]: Simplify 2 into 2 5.978 * [taylor]: Taking taylor expansion of PI in k 5.978 * [backup-simplify]: Simplify PI into PI 5.978 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 5.979 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 5.979 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 5.980 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 5.981 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 5.982 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 5.982 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 5.982 * [taylor]: Taking taylor expansion of (/ -1 k) in k 5.982 * [taylor]: Taking taylor expansion of -1 in k 5.982 * [backup-simplify]: Simplify -1 into -1 5.982 * [taylor]: Taking taylor expansion of k in k 5.982 * [backup-simplify]: Simplify 0 into 0 5.982 * [backup-simplify]: Simplify 1 into 1 5.982 * [backup-simplify]: Simplify (/ -1 1) into -1 5.982 * [backup-simplify]: Simplify (sqrt 0) into 0 5.983 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 5.984 * [backup-simplify]: Simplify (/ (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) 5.984 * [taylor]: Taking taylor expansion of (/ (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 5.984 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in k 5.984 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in k 5.984 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in k 5.984 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 5.984 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 5.984 * [taylor]: Taking taylor expansion of 1/2 in k 5.984 * [backup-simplify]: Simplify 1/2 into 1/2 5.984 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.984 * [taylor]: Taking taylor expansion of k in k 5.984 * [backup-simplify]: Simplify 0 into 0 5.984 * [backup-simplify]: Simplify 1 into 1 5.985 * [backup-simplify]: Simplify (/ 1 1) into 1 5.985 * [taylor]: Taking taylor expansion of 1/2 in k 5.985 * [backup-simplify]: Simplify 1/2 into 1/2 5.985 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 5.985 * [taylor]: Taking taylor expansion of (* 2 PI) in k 5.985 * [taylor]: Taking taylor expansion of 2 in k 5.985 * [backup-simplify]: Simplify 2 into 2 5.985 * [taylor]: Taking taylor expansion of PI in k 5.985 * [backup-simplify]: Simplify PI into PI 5.985 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 5.986 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 5.986 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 5.986 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 5.987 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 5.988 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 5.988 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 5.988 * [taylor]: Taking taylor expansion of (/ -1 k) in k 5.988 * [taylor]: Taking taylor expansion of -1 in k 5.988 * [backup-simplify]: Simplify -1 into -1 5.988 * [taylor]: Taking taylor expansion of k in k 5.988 * [backup-simplify]: Simplify 0 into 0 5.988 * [backup-simplify]: Simplify 1 into 1 5.988 * [backup-simplify]: Simplify (/ -1 1) into -1 5.989 * [backup-simplify]: Simplify (sqrt 0) into 0 5.989 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 5.990 * [backup-simplify]: Simplify (/ (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) 5.990 * [backup-simplify]: Simplify (* +nan.0 (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) into (* +nan.0 (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) 5.991 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 5.993 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 5.994 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)))) 5.994 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)))) into (- (* +nan.0 (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)))) 5.995 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.997 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 5.999 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)))) 5.999 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)))) into (- (* +nan.0 (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)))) 6.000 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (pow (* 2 PI) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (pow (* 2 PI) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))) (/ 1 (- k))) (* +nan.0 (pow (* 2 PI) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))) into (- (+ (* +nan.0 (/ (pow (* 2 PI) (- 1/2 (* 1/2 k))) k)) (- (+ (* +nan.0 (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (- (* +nan.0 (/ (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow k 2)))))))) 6.000 * * * * [progress]: [ 4 / 4 ] generating series at (2) 6.001 * [backup-simplify]: Simplify (* (pow n (- 1/2 (/ k 2))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))) into (* (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) 6.001 * [approximate]: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in (n k) around 0 6.001 * [taylor]: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k 6.001 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) in k 6.001 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 6.001 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 6.001 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 6.001 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 6.001 * [taylor]: Taking taylor expansion of 1/2 in k 6.001 * [backup-simplify]: Simplify 1/2 into 1/2 6.001 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 6.001 * [taylor]: Taking taylor expansion of 1/2 in k 6.001 * [backup-simplify]: Simplify 1/2 into 1/2 6.001 * [taylor]: Taking taylor expansion of k in k 6.001 * [backup-simplify]: Simplify 0 into 0 6.001 * [backup-simplify]: Simplify 1 into 1 6.001 * [taylor]: Taking taylor expansion of (log n) in k 6.001 * [taylor]: Taking taylor expansion of n in k 6.001 * [backup-simplify]: Simplify n into n 6.001 * [backup-simplify]: Simplify (log n) into (log n) 6.002 * [backup-simplify]: Simplify (* 1/2 0) into 0 6.002 * [backup-simplify]: Simplify (- 0) into 0 6.002 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 6.002 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 6.002 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 6.002 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in k 6.002 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) in k 6.002 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) in k 6.002 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 6.002 * [taylor]: Taking taylor expansion of 1/2 in k 6.002 * [backup-simplify]: Simplify 1/2 into 1/2 6.002 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 6.002 * [taylor]: Taking taylor expansion of 1/2 in k 6.002 * [backup-simplify]: Simplify 1/2 into 1/2 6.002 * [taylor]: Taking taylor expansion of k in k 6.002 * [backup-simplify]: Simplify 0 into 0 6.002 * [backup-simplify]: Simplify 1 into 1 6.002 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 6.002 * [taylor]: Taking taylor expansion of (* 2 PI) in k 6.002 * [taylor]: Taking taylor expansion of 2 in k 6.002 * [backup-simplify]: Simplify 2 into 2 6.002 * [taylor]: Taking taylor expansion of PI in k 6.002 * [backup-simplify]: Simplify PI into PI 6.003 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 6.008 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 6.009 * [backup-simplify]: Simplify (* 1/2 0) into 0 6.009 * [backup-simplify]: Simplify (- 0) into 0 6.009 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 6.010 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 6.012 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) 6.012 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 6.012 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.013 * [taylor]: Taking taylor expansion of k in k 6.013 * [backup-simplify]: Simplify 0 into 0 6.013 * [backup-simplify]: Simplify 1 into 1 6.013 * [backup-simplify]: Simplify (/ 1 1) into 1 6.013 * [backup-simplify]: Simplify (sqrt 0) into 0 6.014 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.014 * [taylor]: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in n 6.014 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) in n 6.014 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 6.014 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 6.014 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 6.014 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 6.014 * [taylor]: Taking taylor expansion of 1/2 in n 6.014 * [backup-simplify]: Simplify 1/2 into 1/2 6.014 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 6.014 * [taylor]: Taking taylor expansion of 1/2 in n 6.014 * [backup-simplify]: Simplify 1/2 into 1/2 6.014 * [taylor]: Taking taylor expansion of k in n 6.014 * [backup-simplify]: Simplify k into k 6.014 * [taylor]: Taking taylor expansion of (log n) in n 6.014 * [taylor]: Taking taylor expansion of n in n 6.014 * [backup-simplify]: Simplify 0 into 0 6.014 * [backup-simplify]: Simplify 1 into 1 6.014 * [backup-simplify]: Simplify (log 1) into 0 6.014 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 6.014 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 6.015 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 6.015 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 6.015 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 6.015 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 6.015 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in n 6.015 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) in n 6.015 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) in n 6.015 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 6.015 * [taylor]: Taking taylor expansion of 1/2 in n 6.015 * [backup-simplify]: Simplify 1/2 into 1/2 6.015 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 6.015 * [taylor]: Taking taylor expansion of 1/2 in n 6.015 * [backup-simplify]: Simplify 1/2 into 1/2 6.015 * [taylor]: Taking taylor expansion of k in n 6.015 * [backup-simplify]: Simplify k into k 6.015 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 6.015 * [taylor]: Taking taylor expansion of (* 2 PI) in n 6.015 * [taylor]: Taking taylor expansion of 2 in n 6.015 * [backup-simplify]: Simplify 2 into 2 6.015 * [taylor]: Taking taylor expansion of PI in n 6.015 * [backup-simplify]: Simplify PI into PI 6.016 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 6.016 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 6.016 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 6.016 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 6.016 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 6.017 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) into (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) 6.018 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 k))) 6.018 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 6.018 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.018 * [taylor]: Taking taylor expansion of k in n 6.018 * [backup-simplify]: Simplify k into k 6.018 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.018 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 6.018 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.018 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 6.018 * [taylor]: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in n 6.018 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) in n 6.018 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 6.018 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 6.018 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 6.018 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 6.018 * [taylor]: Taking taylor expansion of 1/2 in n 6.018 * [backup-simplify]: Simplify 1/2 into 1/2 6.018 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 6.018 * [taylor]: Taking taylor expansion of 1/2 in n 6.018 * [backup-simplify]: Simplify 1/2 into 1/2 6.018 * [taylor]: Taking taylor expansion of k in n 6.018 * [backup-simplify]: Simplify k into k 6.018 * [taylor]: Taking taylor expansion of (log n) in n 6.018 * [taylor]: Taking taylor expansion of n in n 6.018 * [backup-simplify]: Simplify 0 into 0 6.018 * [backup-simplify]: Simplify 1 into 1 6.019 * [backup-simplify]: Simplify (log 1) into 0 6.019 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 6.019 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 6.019 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 6.019 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 6.019 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 6.019 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 6.019 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in n 6.019 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) in n 6.019 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) in n 6.019 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 6.019 * [taylor]: Taking taylor expansion of 1/2 in n 6.019 * [backup-simplify]: Simplify 1/2 into 1/2 6.019 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 6.019 * [taylor]: Taking taylor expansion of 1/2 in n 6.019 * [backup-simplify]: Simplify 1/2 into 1/2 6.019 * [taylor]: Taking taylor expansion of k in n 6.019 * [backup-simplify]: Simplify k into k 6.019 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 6.019 * [taylor]: Taking taylor expansion of (* 2 PI) in n 6.019 * [taylor]: Taking taylor expansion of 2 in n 6.019 * [backup-simplify]: Simplify 2 into 2 6.019 * [taylor]: Taking taylor expansion of PI in n 6.019 * [backup-simplify]: Simplify PI into PI 6.020 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 6.020 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 6.021 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 6.021 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 6.021 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 6.021 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) into (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) 6.022 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 k))) 6.022 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 6.022 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.022 * [taylor]: Taking taylor expansion of k in n 6.022 * [backup-simplify]: Simplify k into k 6.022 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.022 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 6.022 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.022 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 6.023 * [backup-simplify]: Simplify (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) into (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) 6.023 * [backup-simplify]: Simplify (* (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) into (* (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) 6.023 * [taylor]: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k 6.023 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) in k 6.023 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 6.023 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 6.023 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 6.023 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 6.023 * [taylor]: Taking taylor expansion of 1/2 in k 6.023 * [backup-simplify]: Simplify 1/2 into 1/2 6.023 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 6.023 * [taylor]: Taking taylor expansion of 1/2 in k 6.023 * [backup-simplify]: Simplify 1/2 into 1/2 6.023 * [taylor]: Taking taylor expansion of k in k 6.023 * [backup-simplify]: Simplify 0 into 0 6.023 * [backup-simplify]: Simplify 1 into 1 6.024 * [taylor]: Taking taylor expansion of (log n) in k 6.024 * [taylor]: Taking taylor expansion of n in k 6.024 * [backup-simplify]: Simplify n into n 6.024 * [backup-simplify]: Simplify (log n) into (log n) 6.024 * [backup-simplify]: Simplify (* 1/2 0) into 0 6.024 * [backup-simplify]: Simplify (- 0) into 0 6.024 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 6.024 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 6.024 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 6.024 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in k 6.024 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) in k 6.025 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) in k 6.025 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 6.025 * [taylor]: Taking taylor expansion of 1/2 in k 6.025 * [backup-simplify]: Simplify 1/2 into 1/2 6.025 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 6.025 * [taylor]: Taking taylor expansion of 1/2 in k 6.025 * [backup-simplify]: Simplify 1/2 into 1/2 6.025 * [taylor]: Taking taylor expansion of k in k 6.025 * [backup-simplify]: Simplify 0 into 0 6.025 * [backup-simplify]: Simplify 1 into 1 6.025 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 6.025 * [taylor]: Taking taylor expansion of (* 2 PI) in k 6.025 * [taylor]: Taking taylor expansion of 2 in k 6.025 * [backup-simplify]: Simplify 2 into 2 6.025 * [taylor]: Taking taylor expansion of PI in k 6.025 * [backup-simplify]: Simplify PI into PI 6.025 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 6.026 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 6.026 * [backup-simplify]: Simplify (* 1/2 0) into 0 6.026 * [backup-simplify]: Simplify (- 0) into 0 6.026 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 6.028 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 6.030 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) 6.030 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 6.030 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.030 * [taylor]: Taking taylor expansion of k in k 6.030 * [backup-simplify]: Simplify 0 into 0 6.030 * [backup-simplify]: Simplify 1 into 1 6.030 * [backup-simplify]: Simplify (/ 1 1) into 1 6.030 * [backup-simplify]: Simplify (sqrt 0) into 0 6.031 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.032 * [backup-simplify]: Simplify (* (pow n 1/2) (pow (* 2 PI) 1/2)) into (sqrt (* PI (* n 2))) 6.032 * [backup-simplify]: Simplify (* (sqrt (* PI (* n 2))) 0) into 0 6.032 * [backup-simplify]: Simplify 0 into 0 6.033 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 6.034 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 6.034 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 6.034 * [backup-simplify]: Simplify (- 0) into 0 6.035 * [backup-simplify]: Simplify (+ 0 0) into 0 6.035 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log (* 2 PI)))) into 0 6.036 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) (+ (* (/ (pow 0 1) 1)))) into 0 6.037 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 6.037 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 6.038 * [backup-simplify]: Simplify (- 0) into 0 6.038 * [backup-simplify]: Simplify (+ 0 0) into 0 6.038 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 6.038 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log n))) into 0 6.039 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 6.039 * [backup-simplify]: Simplify (+ (* (pow n (- 1/2 (* 1/2 k))) 0) (* 0 (pow (* 2 PI) (- 1/2 (* 1/2 k))))) into 0 6.040 * [backup-simplify]: Simplify (+ (* (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) 0) (* 0 (sqrt (/ 1 k)))) into 0 6.040 * [taylor]: Taking taylor expansion of 0 in k 6.040 * [backup-simplify]: Simplify 0 into 0 6.040 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 6.041 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 6.042 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 6.042 * [backup-simplify]: Simplify (- 1/2) into -1/2 6.042 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 6.046 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 PI)))) into (- (* 1/2 (log (* 2 PI)))) 6.059 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) 6.060 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 6.060 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 6.061 * [backup-simplify]: Simplify (- 1/2) into -1/2 6.061 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 6.062 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log n))) into (- (* 1/2 (log n))) 6.062 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n))) 6.068 * [backup-simplify]: Simplify (+ (* (pow n 1/2) (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI))))) (* (* -1/2 (* (sqrt n) (log n))) (pow (* 2 PI) 1/2))) into (- (+ (* 1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))) 6.071 * [backup-simplify]: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (* (- (+ (* 1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 6.072 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 6.072 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.073 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 6.074 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 6.078 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 6.079 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 6.079 * [backup-simplify]: Simplify (- 0) into 0 6.079 * [backup-simplify]: Simplify (+ 0 0) into 0 6.080 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (log (* 2 PI))))) into 0 6.083 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.086 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 6.086 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 6.087 * [backup-simplify]: Simplify (- 0) into 0 6.087 * [backup-simplify]: Simplify (+ 0 0) into 0 6.088 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 6.088 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0 6.089 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.091 * [backup-simplify]: Simplify (+ (* (pow n (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (pow (* 2 PI) (- 1/2 (* 1/2 k)))))) into 0 6.092 * [backup-simplify]: Simplify (+ (* (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 6.092 * [taylor]: Taking taylor expansion of 0 in k 6.092 * [backup-simplify]: Simplify 0 into 0 6.092 * [backup-simplify]: Simplify 0 into 0 6.093 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 6.096 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 6.097 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 6.101 * [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 6.103 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 6.103 * [backup-simplify]: Simplify (- 0) into 0 6.103 * [backup-simplify]: Simplify (+ 0 0) into 0 6.105 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 PI))))) into 0 6.121 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) 6.123 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 6.124 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 6.125 * [backup-simplify]: Simplify (- 0) into 0 6.125 * [backup-simplify]: Simplify (+ 0 0) into 0 6.126 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log n)))) into 0 6.127 * [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))) 6.146 * [backup-simplify]: Simplify (+ (* (pow n 1/2) (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2)))) (+ (* (* -1/2 (* (sqrt n) (log n))) (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI))))) (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (pow (* 2 PI) 1/2)))) into (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (* 1/4 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))))) 6.154 * [backup-simplify]: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))) +nan.0) (* (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (* 1/4 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))) 6.156 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))) 6.156 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.157 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 6.157 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.161 * [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 6.161 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 6.162 * [backup-simplify]: Simplify (- 0) into 0 6.162 * [backup-simplify]: Simplify (+ 0 0) into 0 6.163 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log (* 2 PI)))))) into 0 6.165 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 6.168 * [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 6.169 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 6.169 * [backup-simplify]: Simplify (- 0) into 0 6.169 * [backup-simplify]: Simplify (+ 0 0) into 0 6.169 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 6.170 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0 6.171 * [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 6.172 * [backup-simplify]: Simplify (+ (* (pow n (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (* 2 PI) (- 1/2 (* 1/2 k))))))) into 0 6.173 * [backup-simplify]: Simplify (+ (* (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0 6.173 * [taylor]: Taking taylor expansion of 0 in k 6.173 * [backup-simplify]: Simplify 0 into 0 6.173 * [backup-simplify]: Simplify 0 into 0 6.173 * [backup-simplify]: Simplify 0 into 0 6.173 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.176 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 6.176 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.180 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 6.181 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 6.181 * [backup-simplify]: Simplify (- 0) into 0 6.181 * [backup-simplify]: Simplify (+ 0 0) into 0 6.182 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 PI)))))) into 0 6.202 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 3))) 6.205 * [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 6.206 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 6.206 * [backup-simplify]: Simplify (- 0) into 0 6.207 * [backup-simplify]: Simplify (+ 0 0) into 0 6.208 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log n))))) into 0 6.209 * [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))) 6.228 * [backup-simplify]: Simplify (+ (* (pow n 1/2) (* -1/48 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 3)))) (+ (* (* -1/2 (* (sqrt n) (log n))) (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2)))) (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI))))) (* (* -1/48 (* (sqrt n) (pow (log n) 3))) (pow (* 2 PI) 1/2))))) into (- (+ (* 1/48 (* (* (sqrt 2) (pow (log n) 3)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (log n) (pow (log (* 2 PI)) 2))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (pow (log n) 2) (log (* 2 PI)))) (sqrt (* n PI)))) (* 1/48 (* (* (sqrt 2) (pow (log (* 2 PI)) 3)) (sqrt (* n PI)))))))) 6.248 * [backup-simplify]: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))) +nan.0) (+ (* (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (* 1/4 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))))) +nan.0) (* (- (+ (* 1/48 (* (* (sqrt 2) (pow (log n) 3)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (log n) (pow (log (* 2 PI)) 2))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (pow (log n) 2) (log (* 2 PI)))) (sqrt (* n PI)))) (* 1/48 (* (* (sqrt 2) (pow (log (* 2 PI)) 3)) (sqrt (* n PI)))))))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI))))))))))))))) 6.265 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI))))))))))))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI))))))))))))))) 6.282 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))) (* k 1)) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (pow k 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) k) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log (* 2 PI)) 2) (* (sqrt 2) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (pow (log n) 2) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) k)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log (* 2 PI)) (* (sqrt 2) (* (log n) (pow k 2)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log (* 2 PI)) (* (sqrt 2) (pow k 2))) (sqrt (* n PI))))))))))))))))))))))) 6.283 * [backup-simplify]: Simplify (* (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) (/ (pow (* 2 PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) into (* (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) 6.283 * [approximate]: Taking taylor expansion of (* (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in (n k) around 0 6.283 * [taylor]: Taking taylor expansion of (* (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k 6.283 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 6.283 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in k 6.283 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in k 6.283 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in k 6.283 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 6.283 * [taylor]: Taking taylor expansion of 1/2 in k 6.283 * [backup-simplify]: Simplify 1/2 into 1/2 6.283 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 6.283 * [taylor]: Taking taylor expansion of 1/2 in k 6.283 * [backup-simplify]: Simplify 1/2 into 1/2 6.283 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.283 * [taylor]: Taking taylor expansion of k in k 6.283 * [backup-simplify]: Simplify 0 into 0 6.283 * [backup-simplify]: Simplify 1 into 1 6.283 * [backup-simplify]: Simplify (/ 1 1) into 1 6.283 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 6.283 * [taylor]: Taking taylor expansion of (* 2 PI) in k 6.283 * [taylor]: Taking taylor expansion of 2 in k 6.283 * [backup-simplify]: Simplify 2 into 2 6.283 * [taylor]: Taking taylor expansion of PI in k 6.283 * [backup-simplify]: Simplify PI into PI 6.284 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 6.284 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 6.284 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 6.285 * [backup-simplify]: Simplify (- 1/2) into -1/2 6.285 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 6.286 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) 6.287 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 6.287 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 6.287 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in k 6.287 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in k 6.287 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 6.287 * [taylor]: Taking taylor expansion of 1/2 in k 6.287 * [backup-simplify]: Simplify 1/2 into 1/2 6.287 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 6.287 * [taylor]: Taking taylor expansion of 1/2 in k 6.287 * [backup-simplify]: Simplify 1/2 into 1/2 6.287 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.287 * [taylor]: Taking taylor expansion of k in k 6.287 * [backup-simplify]: Simplify 0 into 0 6.287 * [backup-simplify]: Simplify 1 into 1 6.287 * [backup-simplify]: Simplify (/ 1 1) into 1 6.287 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k 6.287 * [taylor]: Taking taylor expansion of (/ 1 n) in k 6.287 * [taylor]: Taking taylor expansion of n in k 6.287 * [backup-simplify]: Simplify n into n 6.287 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n) 6.287 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n)) 6.288 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 6.288 * [backup-simplify]: Simplify (- 1/2) into -1/2 6.288 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 6.288 * [backup-simplify]: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) 6.288 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 6.288 * [taylor]: Taking taylor expansion of (sqrt k) in k 6.288 * [taylor]: Taking taylor expansion of k in k 6.288 * [backup-simplify]: Simplify 0 into 0 6.288 * [backup-simplify]: Simplify 1 into 1 6.289 * [backup-simplify]: Simplify (sqrt 0) into 0 6.290 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.290 * [taylor]: Taking taylor expansion of (* (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in n 6.290 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 6.290 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in n 6.290 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in n 6.290 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in n 6.290 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 6.290 * [taylor]: Taking taylor expansion of 1/2 in n 6.290 * [backup-simplify]: Simplify 1/2 into 1/2 6.290 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 6.290 * [taylor]: Taking taylor expansion of 1/2 in n 6.290 * [backup-simplify]: Simplify 1/2 into 1/2 6.290 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.290 * [taylor]: Taking taylor expansion of k in n 6.290 * [backup-simplify]: Simplify k into k 6.290 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.290 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 6.290 * [taylor]: Taking taylor expansion of (* 2 PI) in n 6.290 * [taylor]: Taking taylor expansion of 2 in n 6.290 * [backup-simplify]: Simplify 2 into 2 6.290 * [taylor]: Taking taylor expansion of PI in n 6.290 * [backup-simplify]: Simplify PI into PI 6.290 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 6.291 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 6.291 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 6.291 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 6.291 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 6.292 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) into (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) 6.292 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 6.293 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 6.293 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 6.293 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 6.293 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 6.293 * [taylor]: Taking taylor expansion of 1/2 in n 6.293 * [backup-simplify]: Simplify 1/2 into 1/2 6.293 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 6.293 * [taylor]: Taking taylor expansion of 1/2 in n 6.293 * [backup-simplify]: Simplify 1/2 into 1/2 6.293 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.293 * [taylor]: Taking taylor expansion of k in n 6.293 * [backup-simplify]: Simplify k into k 6.293 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.293 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 6.293 * [taylor]: Taking taylor expansion of (/ 1 n) in n 6.293 * [taylor]: Taking taylor expansion of n in n 6.293 * [backup-simplify]: Simplify 0 into 0 6.293 * [backup-simplify]: Simplify 1 into 1 6.293 * [backup-simplify]: Simplify (/ 1 1) into 1 6.293 * [backup-simplify]: Simplify (log 1) into 0 6.293 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 6.293 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 6.293 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 6.294 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 6.294 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 6.294 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 6.294 * [taylor]: Taking taylor expansion of (sqrt k) in n 6.294 * [taylor]: Taking taylor expansion of k in n 6.294 * [backup-simplify]: Simplify k into k 6.294 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 6.294 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 6.294 * [taylor]: Taking taylor expansion of (* (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in n 6.294 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 6.294 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in n 6.294 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in n 6.294 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in n 6.294 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 6.294 * [taylor]: Taking taylor expansion of 1/2 in n 6.294 * [backup-simplify]: Simplify 1/2 into 1/2 6.294 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 6.294 * [taylor]: Taking taylor expansion of 1/2 in n 6.294 * [backup-simplify]: Simplify 1/2 into 1/2 6.294 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.294 * [taylor]: Taking taylor expansion of k in n 6.294 * [backup-simplify]: Simplify k into k 6.294 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.294 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 6.294 * [taylor]: Taking taylor expansion of (* 2 PI) in n 6.294 * [taylor]: Taking taylor expansion of 2 in n 6.294 * [backup-simplify]: Simplify 2 into 2 6.294 * [taylor]: Taking taylor expansion of PI in n 6.294 * [backup-simplify]: Simplify PI into PI 6.295 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 6.295 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 6.295 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 6.296 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 6.296 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 6.296 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) into (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) 6.297 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 6.297 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 6.297 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 6.297 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 6.297 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 6.297 * [taylor]: Taking taylor expansion of 1/2 in n 6.297 * [backup-simplify]: Simplify 1/2 into 1/2 6.297 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 6.297 * [taylor]: Taking taylor expansion of 1/2 in n 6.297 * [backup-simplify]: Simplify 1/2 into 1/2 6.297 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.297 * [taylor]: Taking taylor expansion of k in n 6.297 * [backup-simplify]: Simplify k into k 6.297 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.297 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 6.297 * [taylor]: Taking taylor expansion of (/ 1 n) in n 6.297 * [taylor]: Taking taylor expansion of n in n 6.297 * [backup-simplify]: Simplify 0 into 0 6.297 * [backup-simplify]: Simplify 1 into 1 6.298 * [backup-simplify]: Simplify (/ 1 1) into 1 6.298 * [backup-simplify]: Simplify (log 1) into 0 6.298 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 6.298 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 6.298 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 6.298 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 6.298 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 6.298 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 6.298 * [taylor]: Taking taylor expansion of (sqrt k) in n 6.298 * [taylor]: Taking taylor expansion of k in n 6.299 * [backup-simplify]: Simplify k into k 6.299 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 6.299 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 6.299 * [backup-simplify]: Simplify (* (pow (* 2 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 (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) 6.300 * [backup-simplify]: Simplify (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) into (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) 6.300 * [taylor]: Taking taylor expansion of (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k 6.300 * [taylor]: Taking taylor expansion of (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) in k 6.300 * [taylor]: Taking taylor expansion of (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) in k 6.300 * [taylor]: Taking taylor expansion of (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) in k 6.300 * [taylor]: Taking taylor expansion of -1 in k 6.300 * [backup-simplify]: Simplify -1 into -1 6.300 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log n)) in k 6.300 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 6.300 * [taylor]: Taking taylor expansion of 1/2 in k 6.300 * [backup-simplify]: Simplify 1/2 into 1/2 6.300 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 6.300 * [taylor]: Taking taylor expansion of 1/2 in k 6.300 * [backup-simplify]: Simplify 1/2 into 1/2 6.300 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.300 * [taylor]: Taking taylor expansion of k in k 6.300 * [backup-simplify]: Simplify 0 into 0 6.300 * [backup-simplify]: Simplify 1 into 1 6.300 * [backup-simplify]: Simplify (/ 1 1) into 1 6.300 * [taylor]: Taking taylor expansion of (log n) in k 6.300 * [taylor]: Taking taylor expansion of n in k 6.300 * [backup-simplify]: Simplify n into n 6.300 * [backup-simplify]: Simplify (log n) into (log n) 6.301 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 6.301 * [backup-simplify]: Simplify (- 1/2) into -1/2 6.301 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 6.301 * [backup-simplify]: Simplify (* -1/2 (log n)) into (* -1/2 (log n)) 6.301 * [backup-simplify]: Simplify (* -1 (* -1/2 (log n))) into (* 1/2 (log n)) 6.301 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 6.301 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in k 6.301 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in k 6.301 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in k 6.301 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 6.301 * [taylor]: Taking taylor expansion of 1/2 in k 6.301 * [backup-simplify]: Simplify 1/2 into 1/2 6.301 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 6.301 * [taylor]: Taking taylor expansion of 1/2 in k 6.301 * [backup-simplify]: Simplify 1/2 into 1/2 6.301 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.301 * [taylor]: Taking taylor expansion of k in k 6.301 * [backup-simplify]: Simplify 0 into 0 6.301 * [backup-simplify]: Simplify 1 into 1 6.302 * [backup-simplify]: Simplify (/ 1 1) into 1 6.302 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 6.302 * [taylor]: Taking taylor expansion of (* 2 PI) in k 6.302 * [taylor]: Taking taylor expansion of 2 in k 6.302 * [backup-simplify]: Simplify 2 into 2 6.302 * [taylor]: Taking taylor expansion of PI in k 6.302 * [backup-simplify]: Simplify PI into PI 6.302 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 6.303 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 6.303 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 6.303 * [backup-simplify]: Simplify (- 1/2) into -1/2 6.304 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 6.305 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) 6.305 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 6.306 * [taylor]: Taking taylor expansion of (sqrt k) in k 6.306 * [taylor]: Taking taylor expansion of k in k 6.306 * [backup-simplify]: Simplify 0 into 0 6.306 * [backup-simplify]: Simplify 1 into 1 6.306 * [backup-simplify]: Simplify (sqrt 0) into 0 6.307 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.308 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) 6.308 * [backup-simplify]: Simplify (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 6.308 * [backup-simplify]: Simplify 0 into 0 6.309 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 6.309 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 6.310 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.310 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 6.310 * [backup-simplify]: Simplify (- 0) into 0 6.310 * [backup-simplify]: Simplify (+ 0 0) into 0 6.311 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 6.311 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 6.311 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 6.312 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 6.313 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 6.313 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.313 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 6.313 * [backup-simplify]: Simplify (- 0) into 0 6.314 * [backup-simplify]: Simplify (+ 0 0) into 0 6.314 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (log (* 2 PI)))) into 0 6.315 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) (+ (* (/ (pow 0 1) 1)))) into 0 6.316 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))))) into 0 6.316 * [backup-simplify]: Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (sqrt k))) into 0 6.316 * [taylor]: Taking taylor expansion of 0 in k 6.316 * [backup-simplify]: Simplify 0 into 0 6.316 * [backup-simplify]: Simplify 0 into 0 6.317 * [backup-simplify]: Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (* 0 (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))) into 0 6.318 * [backup-simplify]: Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) 6.318 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) 6.319 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 6.320 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.321 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 6.321 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.322 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 6.322 * [backup-simplify]: Simplify (- 0) into 0 6.322 * [backup-simplify]: Simplify (+ 0 0) into 0 6.322 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 6.323 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 6.324 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.324 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 6.326 * [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 6.326 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.327 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 6.327 * [backup-simplify]: Simplify (- 0) into 0 6.327 * [backup-simplify]: Simplify (+ 0 0) into 0 6.328 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (log (* 2 PI))))) into 0 6.330 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.330 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))))) into 0 6.331 * [backup-simplify]: Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0 6.331 * [taylor]: Taking taylor expansion of 0 in k 6.331 * [backup-simplify]: Simplify 0 into 0 6.331 * [backup-simplify]: Simplify 0 into 0 6.331 * [backup-simplify]: Simplify 0 into 0 6.333 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 6.334 * [backup-simplify]: Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (+ (* 0 0) (* 0 (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) into 0 6.335 * [backup-simplify]: Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) 6.335 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) 6.336 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 6.336 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.340 * [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 6.340 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.341 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 6.342 * [backup-simplify]: Simplify (- 0) into 0 6.342 * [backup-simplify]: Simplify (+ 0 0) into 0 6.342 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 6.343 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 6.345 * [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 6.346 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.352 * [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 6.353 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.354 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 6.354 * [backup-simplify]: Simplify (- 0) into 0 6.355 * [backup-simplify]: Simplify (+ 0 0) into 0 6.356 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log (* 2 PI)))))) into 0 6.359 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 6.360 * [backup-simplify]: Simplify (+ (* (pow (* 2 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 6.362 * [backup-simplify]: Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0 6.362 * [taylor]: Taking taylor expansion of 0 in k 6.362 * [backup-simplify]: Simplify 0 into 0 6.362 * [backup-simplify]: Simplify 0 into 0 6.362 * [backup-simplify]: Simplify 0 into 0 6.362 * [backup-simplify]: Simplify 0 into 0 6.371 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 6.372 * [backup-simplify]: Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 6.373 * [backup-simplify]: Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) 6.373 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) 6.375 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) k)) (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (pow k 3)))))))) 6.376 * [backup-simplify]: Simplify (* (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) (/ (pow (* 2 PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) into (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) 6.376 * [approximate]: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in (n k) around 0 6.376 * [taylor]: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k 6.376 * [taylor]: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) in k 6.376 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 6.376 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in k 6.376 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in k 6.376 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 6.376 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 6.376 * [taylor]: Taking taylor expansion of 1/2 in k 6.376 * [backup-simplify]: Simplify 1/2 into 1/2 6.376 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.376 * [taylor]: Taking taylor expansion of k in k 6.376 * [backup-simplify]: Simplify 0 into 0 6.376 * [backup-simplify]: Simplify 1 into 1 6.376 * [backup-simplify]: Simplify (/ 1 1) into 1 6.376 * [taylor]: Taking taylor expansion of 1/2 in k 6.376 * [backup-simplify]: Simplify 1/2 into 1/2 6.376 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k 6.376 * [taylor]: Taking taylor expansion of (/ -1 n) in k 6.376 * [taylor]: Taking taylor expansion of -1 in k 6.376 * [backup-simplify]: Simplify -1 into -1 6.376 * [taylor]: Taking taylor expansion of n in k 6.376 * [backup-simplify]: Simplify n into n 6.376 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n) 6.376 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n)) 6.377 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 6.377 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 6.377 * [backup-simplify]: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) 6.377 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 6.377 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in k 6.377 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in k 6.377 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in k 6.377 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 6.377 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 6.377 * [taylor]: Taking taylor expansion of 1/2 in k 6.377 * [backup-simplify]: Simplify 1/2 into 1/2 6.377 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.377 * [taylor]: Taking taylor expansion of k in k 6.377 * [backup-simplify]: Simplify 0 into 0 6.377 * [backup-simplify]: Simplify 1 into 1 6.377 * [backup-simplify]: Simplify (/ 1 1) into 1 6.377 * [taylor]: Taking taylor expansion of 1/2 in k 6.377 * [backup-simplify]: Simplify 1/2 into 1/2 6.377 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 6.378 * [taylor]: Taking taylor expansion of (* 2 PI) in k 6.378 * [taylor]: Taking taylor expansion of 2 in k 6.378 * [backup-simplify]: Simplify 2 into 2 6.378 * [taylor]: Taking taylor expansion of PI in k 6.378 * [backup-simplify]: Simplify PI into PI 6.378 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 6.379 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 6.379 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 6.380 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 6.381 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 6.381 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 6.381 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 6.381 * [taylor]: Taking taylor expansion of (/ -1 k) in k 6.382 * [taylor]: Taking taylor expansion of -1 in k 6.382 * [backup-simplify]: Simplify -1 into -1 6.382 * [taylor]: Taking taylor expansion of k in k 6.382 * [backup-simplify]: Simplify 0 into 0 6.382 * [backup-simplify]: Simplify 1 into 1 6.382 * [backup-simplify]: Simplify (/ -1 1) into -1 6.382 * [backup-simplify]: Simplify (sqrt 0) into 0 6.383 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 6.383 * [backup-simplify]: Simplify (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) 6.384 * [backup-simplify]: Simplify (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)))) 6.384 * [taylor]: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in n 6.384 * [taylor]: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) in n 6.384 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 6.384 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 6.384 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 6.384 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 6.384 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 6.384 * [taylor]: Taking taylor expansion of 1/2 in n 6.384 * [backup-simplify]: Simplify 1/2 into 1/2 6.384 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.384 * [taylor]: Taking taylor expansion of k in n 6.384 * [backup-simplify]: Simplify k into k 6.384 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.384 * [taylor]: Taking taylor expansion of 1/2 in n 6.384 * [backup-simplify]: Simplify 1/2 into 1/2 6.384 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 6.384 * [taylor]: Taking taylor expansion of (/ -1 n) in n 6.384 * [taylor]: Taking taylor expansion of -1 in n 6.384 * [backup-simplify]: Simplify -1 into -1 6.384 * [taylor]: Taking taylor expansion of n in n 6.384 * [backup-simplify]: Simplify 0 into 0 6.384 * [backup-simplify]: Simplify 1 into 1 6.385 * [backup-simplify]: Simplify (/ -1 1) into -1 6.385 * [backup-simplify]: Simplify (log -1) into (log -1) 6.385 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 6.385 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 6.385 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 6.386 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 6.386 * [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)))) 6.386 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in n 6.386 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in n 6.386 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in n 6.386 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 6.386 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 6.386 * [taylor]: Taking taylor expansion of 1/2 in n 6.386 * [backup-simplify]: Simplify 1/2 into 1/2 6.386 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.386 * [taylor]: Taking taylor expansion of k in n 6.386 * [backup-simplify]: Simplify k into k 6.386 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.386 * [taylor]: Taking taylor expansion of 1/2 in n 6.386 * [backup-simplify]: Simplify 1/2 into 1/2 6.386 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 6.386 * [taylor]: Taking taylor expansion of (* 2 PI) in n 6.386 * [taylor]: Taking taylor expansion of 2 in n 6.386 * [backup-simplify]: Simplify 2 into 2 6.386 * [taylor]: Taking taylor expansion of PI in n 6.386 * [backup-simplify]: Simplify PI into PI 6.387 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 6.387 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 6.387 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 6.388 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 6.388 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) 6.389 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 6.389 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 6.389 * [taylor]: Taking taylor expansion of (/ -1 k) in n 6.389 * [taylor]: Taking taylor expansion of -1 in n 6.389 * [backup-simplify]: Simplify -1 into -1 6.389 * [taylor]: Taking taylor expansion of k in n 6.389 * [backup-simplify]: Simplify k into k 6.389 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 6.389 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 6.389 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 6.389 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 6.390 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) 6.391 * [backup-simplify]: Simplify (/ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (sqrt (/ -1 k))) into (/ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (sqrt (/ -1 k))) 6.391 * [taylor]: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in n 6.391 * [taylor]: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) in n 6.391 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 6.391 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 6.391 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 6.391 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 6.391 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 6.391 * [taylor]: Taking taylor expansion of 1/2 in n 6.391 * [backup-simplify]: Simplify 1/2 into 1/2 6.391 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.391 * [taylor]: Taking taylor expansion of k in n 6.391 * [backup-simplify]: Simplify k into k 6.391 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.391 * [taylor]: Taking taylor expansion of 1/2 in n 6.391 * [backup-simplify]: Simplify 1/2 into 1/2 6.391 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 6.391 * [taylor]: Taking taylor expansion of (/ -1 n) in n 6.391 * [taylor]: Taking taylor expansion of -1 in n 6.391 * [backup-simplify]: Simplify -1 into -1 6.391 * [taylor]: Taking taylor expansion of n in n 6.391 * [backup-simplify]: Simplify 0 into 0 6.391 * [backup-simplify]: Simplify 1 into 1 6.391 * [backup-simplify]: Simplify (/ -1 1) into -1 6.392 * [backup-simplify]: Simplify (log -1) into (log -1) 6.392 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 6.392 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 6.392 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 6.393 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 6.393 * [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)))) 6.393 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in n 6.393 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in n 6.393 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in n 6.393 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 6.393 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 6.393 * [taylor]: Taking taylor expansion of 1/2 in n 6.393 * [backup-simplify]: Simplify 1/2 into 1/2 6.393 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.393 * [taylor]: Taking taylor expansion of k in n 6.393 * [backup-simplify]: Simplify k into k 6.393 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.393 * [taylor]: Taking taylor expansion of 1/2 in n 6.393 * [backup-simplify]: Simplify 1/2 into 1/2 6.393 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 6.393 * [taylor]: Taking taylor expansion of (* 2 PI) in n 6.393 * [taylor]: Taking taylor expansion of 2 in n 6.393 * [backup-simplify]: Simplify 2 into 2 6.393 * [taylor]: Taking taylor expansion of PI in n 6.393 * [backup-simplify]: Simplify PI into PI 6.394 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 6.394 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 6.394 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 6.394 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 6.395 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) 6.396 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 6.396 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 6.396 * [taylor]: Taking taylor expansion of (/ -1 k) in n 6.396 * [taylor]: Taking taylor expansion of -1 in n 6.396 * [backup-simplify]: Simplify -1 into -1 6.396 * [taylor]: Taking taylor expansion of k in n 6.396 * [backup-simplify]: Simplify k into k 6.396 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 6.396 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 6.396 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 6.396 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 6.397 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) 6.398 * [backup-simplify]: Simplify (/ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (sqrt (/ -1 k))) into (/ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (sqrt (/ -1 k))) 6.398 * [taylor]: Taking taylor expansion of (/ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (sqrt (/ -1 k))) in k 6.398 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) in k 6.398 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in k 6.398 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in k 6.398 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in k 6.398 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 6.398 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 6.398 * [taylor]: Taking taylor expansion of 1/2 in k 6.398 * [backup-simplify]: Simplify 1/2 into 1/2 6.398 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.398 * [taylor]: Taking taylor expansion of k in k 6.398 * [backup-simplify]: Simplify 0 into 0 6.398 * [backup-simplify]: Simplify 1 into 1 6.398 * [backup-simplify]: Simplify (/ 1 1) into 1 6.398 * [taylor]: Taking taylor expansion of 1/2 in k 6.398 * [backup-simplify]: Simplify 1/2 into 1/2 6.398 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 6.398 * [taylor]: Taking taylor expansion of (* 2 PI) in k 6.398 * [taylor]: Taking taylor expansion of 2 in k 6.398 * [backup-simplify]: Simplify 2 into 2 6.398 * [taylor]: Taking taylor expansion of PI in k 6.398 * [backup-simplify]: Simplify PI into PI 6.399 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 6.399 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 6.400 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 6.400 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 6.401 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 6.402 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 6.402 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) in k 6.402 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) in k 6.402 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 6.402 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 6.402 * [taylor]: Taking taylor expansion of 1/2 in k 6.402 * [backup-simplify]: Simplify 1/2 into 1/2 6.402 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.402 * [taylor]: Taking taylor expansion of k in k 6.402 * [backup-simplify]: Simplify 0 into 0 6.402 * [backup-simplify]: Simplify 1 into 1 6.402 * [backup-simplify]: Simplify (/ 1 1) into 1 6.402 * [taylor]: Taking taylor expansion of 1/2 in k 6.402 * [backup-simplify]: Simplify 1/2 into 1/2 6.402 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k 6.402 * [taylor]: Taking taylor expansion of (log -1) in k 6.402 * [taylor]: Taking taylor expansion of -1 in k 6.402 * [backup-simplify]: Simplify -1 into -1 6.403 * [backup-simplify]: Simplify (log -1) into (log -1) 6.403 * [taylor]: Taking taylor expansion of (log n) in k 6.403 * [taylor]: Taking taylor expansion of n in k 6.403 * [backup-simplify]: Simplify n into n 6.403 * [backup-simplify]: Simplify (log n) into (log n) 6.403 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 6.403 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 6.403 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.404 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n)) 6.404 * [backup-simplify]: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n))) 6.404 * [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)))) 6.404 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 6.404 * [taylor]: Taking taylor expansion of (/ -1 k) in k 6.404 * [taylor]: Taking taylor expansion of -1 in k 6.404 * [backup-simplify]: Simplify -1 into -1 6.404 * [taylor]: Taking taylor expansion of k in k 6.404 * [backup-simplify]: Simplify 0 into 0 6.404 * [backup-simplify]: Simplify 1 into 1 6.405 * [backup-simplify]: Simplify (/ -1 1) into -1 6.405 * [backup-simplify]: Simplify (sqrt 0) into 0 6.406 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 6.406 * [backup-simplify]: Simplify (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) into (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) 6.407 * [backup-simplify]: Simplify (/ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) +nan.0) into (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) 6.408 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) into (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) 6.409 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 6.410 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 6.410 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.410 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 6.410 * [backup-simplify]: Simplify (+ 0 0) into 0 6.411 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log (* 2 PI)))) into 0 6.412 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) (+ (* (/ (pow 0 1) 1)))) into 0 6.412 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 6.413 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 6.413 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.414 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 6.414 * [backup-simplify]: Simplify (+ 0 0) into 0 6.414 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 6.415 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -1) (log n)))) into 0 6.416 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 6.416 * [backup-simplify]: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 0) (* 0 (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 6.417 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 6.417 * [taylor]: Taking taylor expansion of 0 in k 6.417 * [backup-simplify]: Simplify 0 into 0 6.417 * [backup-simplify]: Simplify 0 into 0 6.418 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) into 0 6.418 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 6.420 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 6.421 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))))) 6.422 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))))) into (- (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))))) 6.423 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 6.425 * [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 6.425 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.426 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 6.426 * [backup-simplify]: Simplify (+ 0 0) into 0 6.426 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (log (* 2 PI))))) into 0 6.428 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.429 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.430 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0 6.430 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.431 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 6.431 * [backup-simplify]: Simplify (+ 0 0) into 0 6.432 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 6.432 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0 6.433 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.434 * [backup-simplify]: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 0) (+ (* 0 0) (* 0 (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 6.434 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.435 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 6.436 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 6.436 * [taylor]: Taking taylor expansion of 0 in k 6.436 * [backup-simplify]: Simplify 0 into 0 6.436 * [backup-simplify]: Simplify 0 into 0 6.436 * [backup-simplify]: Simplify 0 into 0 6.437 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))))) into 0 6.437 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.440 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 6.442 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))))) 6.443 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))))) into (- (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))))) 6.446 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) k)) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (pow k 2))) (- (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))))))))) 6.446 * * * [progress]: simplifying candidates 6.446 * * * * [progress]: [ 1 / 231 ] simplifiying candidate # 6.446 * * * * [progress]: [ 2 / 231 ] simplifiying candidate # 6.446 * * * * [progress]: [ 3 / 231 ] simplifiying candidate # 6.446 * * * * [progress]: [ 4 / 231 ] simplifiying candidate # 6.446 * * * * [progress]: [ 5 / 231 ] simplifiying candidate # 6.446 * * * * [progress]: [ 6 / 231 ] simplifiying candidate # 6.446 * * * * [progress]: [ 7 / 231 ] simplifiying candidate # 6.446 * * * * [progress]: [ 8 / 231 ] simplifiying candidate # 6.447 * * * * [progress]: [ 9 / 231 ] simplifiying candidate # 6.447 * * * * [progress]: [ 10 / 231 ] simplifiying candidate # 6.447 * * * * [progress]: [ 11 / 231 ] simplifiying candidate # 6.447 * * * * [progress]: [ 12 / 231 ] simplifiying candidate # 6.447 * * * * [progress]: [ 13 / 231 ] simplifiying candidate # 6.447 * * * * [progress]: [ 14 / 231 ] simplifiying candidate # 6.447 * * * * [progress]: [ 15 / 231 ] 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candidate # 6.447 * * * * [progress]: [ 30 / 231 ] simplifiying candidate # 6.447 * * * * [progress]: [ 31 / 231 ] simplifiying candidate # 6.448 * * * * [progress]: [ 32 / 231 ] simplifiying candidate # 6.448 * * * * [progress]: [ 33 / 231 ] simplifiying candidate # 6.448 * * * * [progress]: [ 34 / 231 ] simplifiying candidate # 6.448 * * * * [progress]: [ 35 / 231 ] simplifiying candidate # 6.448 * * * * [progress]: [ 36 / 231 ] simplifiying candidate # 6.448 * * * * [progress]: [ 37 / 231 ] simplifiying candidate # 6.448 * * * * [progress]: [ 38 / 231 ] simplifiying candidate # 6.448 * * * * [progress]: [ 39 / 231 ] simplifiying candidate # 6.448 * * * * [progress]: [ 40 / 231 ] simplifiying candidate # 6.448 * * * * [progress]: [ 41 / 231 ] simplifiying candidate # 6.448 * * * * [progress]: [ 42 / 231 ] simplifiying candidate # 6.448 * * * * [progress]: [ 43 / 231 ] simplifiying candidate # 6.448 * * * * [progress]: [ 44 / 231 ] simplifiying candidate # 6.448 * * * * [progress]: [ 45 / 231 ] simplifiying candidate # 6.448 * * * * [progress]: [ 46 / 231 ] simplifiying candidate # 6.448 * * * * [progress]: [ 47 / 231 ] simplifiying candidate # 6.448 * * * * [progress]: [ 48 / 231 ] simplifiying candidate #real (real->posit16 (pow (* 2 PI) (- 1/2 (/ k 2))))) (sqrt k))))> 6.448 * * * * [progress]: [ 49 / 231 ] simplifiying candidate # 6.448 * * * * [progress]: [ 50 / 231 ] simplifiying candidate # 6.448 * * * * [progress]: [ 51 / 231 ] simplifiying candidate # 6.448 * * * * [progress]: [ 52 / 231 ] simplifiying candidate # 6.448 * * * * [progress]: [ 53 / 231 ] simplifiying candidate # 6.448 * * * * [progress]: [ 54 / 231 ] simplifiying candidate # 6.448 * * * * [progress]: [ 55 / 231 ] simplifiying candidate # 6.448 * * * * [progress]: [ 56 / 231 ] simplifiying candidate # 6.449 * * * * [progress]: [ 57 / 231 ] simplifiying candidate # 6.449 * * * * [progress]: [ 58 / 231 ] simplifiying candidate # 6.449 * * * * [progress]: [ 59 / 231 ] simplifiying candidate # 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k))))))> 6.451 * * * * [progress]: [ 121 / 231 ] simplifiying candidate # 6.451 * * * * [progress]: [ 122 / 231 ] simplifiying candidate # 6.451 * * * * [progress]: [ 123 / 231 ] simplifiying candidate # 6.452 * * * * [progress]: [ 124 / 231 ] simplifiying candidate # 6.452 * * * * [progress]: [ 125 / 231 ] simplifiying candidate # 6.452 * * * * [progress]: [ 126 / 231 ] simplifiying candidate # 6.452 * * * * [progress]: [ 127 / 231 ] simplifiying candidate # 6.452 * * * * [progress]: [ 128 / 231 ] simplifiying candidate # 6.452 * * * * [progress]: [ 129 / 231 ] simplifiying candidate # 6.452 * * * * [progress]: [ 130 / 231 ] simplifiying candidate # 6.452 * * * * [progress]: [ 131 / 231 ] simplifiying candidate # 6.452 * * * * [progress]: [ 132 / 231 ] simplifiying candidate # 6.452 * * * * [progress]: [ 133 / 231 ] simplifiying candidate # 6.452 * * * * [progress]: [ 134 / 231 ] simplifiying candidate # 6.452 * * * * [progress]: [ 135 / 231 ] simplifiying candidate # 6.452 * * * * 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6.456 * * * * [progress]: [ 213 / 231 ] simplifiying candidate # 6.456 * * * * [progress]: [ 214 / 231 ] simplifiying candidate # 6.456 * * * * [progress]: [ 215 / 231 ] simplifiying candidate # 6.456 * * * * [progress]: [ 216 / 231 ] simplifiying candidate # 6.456 * * * * [progress]: [ 217 / 231 ] simplifiying candidate # 6.456 * * * * [progress]: [ 218 / 231 ] simplifiying candidate #real (real->posit16 (* (pow n (- 1/2 (/ k 2))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))))))> 6.456 * * * * [progress]: [ 219 / 231 ] simplifiying candidate # 6.456 * * * * [progress]: [ 220 / 231 ] simplifiying candidate # 6.456 * * * * [progress]: [ 221 / 231 ] simplifiying candidate # 6.456 * * * * [progress]: [ 222 / 231 ] simplifiying candidate # 6.456 * * * * [progress]: [ 223 / 231 ] simplifiying candidate # 6.456 * * * * [progress]: [ 224 / 231 ] simplifiying candidate # 6.456 * * * * [progress]: [ 225 / 231 ] simplifiying candidate # 6.456 * * * * [progress]: [ 226 / 231 ] simplifiying candidate # 6.456 * * * * [progress]: [ 227 / 231 ] simplifiying candidate # 6.456 * * * * [progress]: [ 228 / 231 ] simplifiying candidate # 6.456 * * * * [progress]: [ 229 / 231 ] simplifiying candidate # 6.456 * * * * [progress]: [ 230 / 231 ] simplifiying candidate # 6.456 * * * * [progress]: [ 231 / 231 ] simplifiying candidate # 6.465 * [simplify]: Simplifying: (* (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 1/2) (pow n (- (/ k 2))) (pow n 1/2) (pow n (- (/ k 2))) (pow (* (cbrt n) (cbrt n)) (- 1/2 (/ k 2))) (pow (cbrt n) (- 1/2 (/ k 2))) (pow (sqrt n) (- 1/2 (/ k 2))) (pow (sqrt n) (- 1/2 (/ k 2))) (pow 1 (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2))) (log (pow n (- 1/2 (/ k 2)))) (exp (pow n (- 1/2 (/ k 2)))) (* (cbrt (pow n (- 1/2 (/ k 2)))) (cbrt (pow n (- 1/2 (/ k 2))))) (cbrt (pow n (- 1/2 (/ k 2)))) (* (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (sqrt (pow n (- 1/2 (/ k 2)))) (sqrt (pow n (- 1/2 (/ k 2)))) (pow n (/ (- 1/2 (/ k 2)) 2)) (pow n (/ (- 1/2 (/ k 2)) 2)) (real->posit16 (pow n (- 1/2 (/ k 2)))) (* (+ (log 2) (log PI)) (- 1/2 (/ k 2))) (* (log (* 2 PI)) (- 1/2 (/ k 2))) (* (log (* 2 PI)) (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (pow (* 2 PI) 1/2) (pow (* 2 PI) (/ k 2)) (pow (* 2 PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* 2 PI) (sqrt (- 1/2 (/ k 2)))) (pow (* 2 PI) 1) (pow (* 2 PI) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* 2 PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (pow (* 2 PI) 1) (pow (* 2 PI) 1/2) (pow (* 2 PI) (- (/ k 2))) (pow (* 2 PI) 1/2) (pow (* 2 PI) (- (/ k 2))) (pow 2 (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2))) (log (pow (* 2 PI) (- 1/2 (/ k 2)))) (exp (pow (* 2 PI) (- 1/2 (/ k 2)))) (* (cbrt (pow (* 2 PI) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 PI) (- 1/2 (/ k 2))))) (cbrt (pow (* 2 PI) (- 1/2 (/ k 2)))) (* (* (pow (* 2 PI) (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2)))) (pow (* 2 PI) (- 1/2 (/ k 2)))) (sqrt (pow (* 2 PI) (- 1/2 (/ k 2)))) (sqrt (pow (* 2 PI) (- 1/2 (/ k 2)))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)) (real->posit16 (pow (* 2 PI) (- 1/2 (/ k 2)))) (- (* (+ (log 2) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k))) (- (* (log (* 2 PI)) (- 1/2 (/ k 2))) (log (sqrt k))) (- (* (log (* 2 PI)) (- 1/2 (/ k 2))) (log (sqrt k))) (- (log (pow (* 2 PI) (- 1/2 (/ k 2)))) (log (sqrt k))) (log (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))) (exp (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))) (/ (* (* (pow (* 2 PI) (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2)))) (pow (* 2 PI) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))) (* (* (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))) (- (pow (* 2 PI) (- 1/2 (/ k 2)))) (- (sqrt k)) (/ (pow (* 2 PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 PI) (- (/ k 2))) (cbrt (sqrt k))) (/ (pow (* 2 PI) 1/2) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* 2 PI) (- (/ k 2))) (sqrt (cbrt k))) (/ (pow (* 2 PI) 1/2) (sqrt (sqrt k))) (/ (pow (* 2 PI) (- (/ k 2))) (sqrt (sqrt k))) (/ (pow (* 2 PI) 1/2) (sqrt 1)) (/ (pow (* 2 PI) (- (/ k 2))) (sqrt k)) (/ (pow (* 2 PI) 1/2) (sqrt (sqrt k))) (/ (pow (* 2 PI) (- (/ k 2))) (sqrt (sqrt k))) (/ (pow (* 2 PI) 1/2) 1) (/ (pow (* 2 PI) (- (/ k 2))) (sqrt k)) (/ (pow (* 2 PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 PI) (- (/ k 2))) (cbrt (sqrt k))) (/ (pow (* 2 PI) 1/2) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* 2 PI) (- (/ k 2))) (sqrt (cbrt k))) (/ (pow (* 2 PI) 1/2) (sqrt (sqrt k))) (/ (pow (* 2 PI) (- (/ k 2))) (sqrt (sqrt k))) (/ (pow (* 2 PI) 1/2) (sqrt 1)) (/ (pow (* 2 PI) (- (/ k 2))) (sqrt k)) (/ (pow (* 2 PI) 1/2) (sqrt (sqrt k))) (/ (pow (* 2 PI) (- (/ k 2))) (sqrt (sqrt k))) (/ (pow (* 2 PI) 1/2) 1) (/ (pow (* 2 PI) (- (/ k 2))) (sqrt k)) (/ (pow 2 (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt 1)) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) (/ (* (cbrt (pow (* 2 PI) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* 2 PI) 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[simplify]: iteration 2: (1053 enodes) 7.463 * * [simplify]: Extracting #0: cost 168 inf + 0 7.464 * * [simplify]: Extracting #1: cost 680 inf + 2 7.468 * * [simplify]: Extracting #2: cost 946 inf + 18335 7.492 * * [simplify]: Extracting #3: cost 908 inf + 131099 7.563 * * [simplify]: Extracting #4: cost 518 inf + 331893 7.634 * * [simplify]: Extracting #5: cost 200 inf + 510195 7.758 * * [simplify]: Extracting #6: cost 79 inf + 588252 7.894 * * [simplify]: Extracting #7: cost 18 inf + 622427 8.025 * * [simplify]: Extracting #8: cost 1 inf + 644165 8.187 * * [simplify]: Extracting #9: cost 0 inf + 645550 8.300 * [simplify]: Simplified to: (* (- 1/2 (/ k 2)) (log n)) (* (- 1/2 (/ k 2)) (log n)) (- 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 (sqrt n) (pow n (- (/ k 2))) (sqrt n) (pow n (- (/ k 2))) (pow (* (cbrt n) (cbrt 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2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) (fabs (cbrt k))) (* (pow n (- 1/2 (/ k 2))) (/ (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (* (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)) (pow n (- 1/2 (/ k 2)))) (* (pow n (- 1/2 (/ k 2))) (/ (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (* (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)) (pow n (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2))) (* (pow (* 2 PI) (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (/ (* (pow (* 2 PI) (- 1/2 (/ k 2))) (pow n (- (/ k 2)))) (sqrt k)) (/ (* (pow (* 2 PI) (- 1/2 (/ k 2))) (pow n (- (/ k 2)))) (sqrt k)) (/ (* (pow (cbrt n) (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2)))) (sqrt k)) (/ (* (pow (* 2 PI) (- 1/2 (/ k 2))) (pow (sqrt n) (- 1/2 (/ k 2)))) (sqrt k)) (/ (* (pow (* 2 PI) (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (sqrt k)) (/ (* (cbrt (pow n (- 1/2 (/ k 2)))) (pow (* 2 PI) (- 1/2 (/ k 2)))) (sqrt k)) (/ (* (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (pow n (- 1/2 (/ k 2))))) (sqrt k)) (/ (* (pow (* 2 PI) (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (sqrt k)) (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (- 1/2 (/ k 2)))) (sqrt k)) (* (pow (* 2 PI) (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (/ (* (sqrt n) (pow (* 2 PI) (- 1/2 (/ k 2)))) (sqrt k)) (real->posit16 (/ (* (pow (* 2 PI) (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (sqrt k))) (+ (* (sqrt n) (* (* (* k (log n)) (* k (log n))) 1/8)) (+ (sqrt n) (* (* (sqrt n) (* k (log n))) -1/2))) (exp (* (- 1/2 (* 1/2 k)) (- (- (log n))))) (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (- (log -1) (log n))))) (+ (- (sqrt (* 2 PI)) (* (sqrt PI) (* (* (* k (sqrt 2)) (log (* 2 PI))) 1/2))) (* 1/8 (* (* (sqrt 2) (* (* (log (* 2 PI)) k) (* (log (* 2 PI)) k))) (sqrt PI)))) (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k))) (+ (- (* (* (sqrt 2) (* k k)) (* (sqrt PI) +nan.0))) (- (* (* +nan.0 (sqrt 2)) (sqrt PI)) (+ (- (* (log (* 2 PI)) (* (* (sqrt 2) (* k k)) (* (sqrt PI) +nan.0))) (* (* +nan.0 (sqrt PI)) (* (* (log (* 2 PI)) (log (* 2 PI))) (* (sqrt 2) (* k k))))) (* +nan.0 (- (* (sqrt 2) (* (sqrt PI) (* k (log (* 2 PI))))) (* (* (sqrt PI) (sqrt 2)) k)))))) (+ (- (/ +nan.0 (/ (* (* k k) k) (pow (* 2 PI) (- 1/2 (* 1/2 k)))))) (* +nan.0 (- (/ (pow (* 2 PI) (- 1/2 (* 1/2 k))) k) (/ (/ (pow (* 2 PI) (- 1/2 (* 1/2 k))) k) k)))) (+ (* (/ (pow (* 2 PI) (- 1/2 (* 1/2 k))) k) (- +nan.0)) (* +nan.0 (- (pow (* 2 PI) (- 1/2 (* 1/2 k))) (/ (/ (pow (* 2 PI) (- 1/2 (* 1/2 k))) k) k)))) (- (+ (- (* (* (sqrt 2) (* k k)) (* (sqrt (* PI n)) +nan.0)) (* (* k (sqrt 2)) (* (sqrt (* PI n)) +nan.0))) (+ (- (* (* (sqrt 2) (* (* (log (* 2 PI)) k) (* (log (* 2 PI)) k))) (* (sqrt (* PI n)) +nan.0)) (* +nan.0 (* (* (* k (log n)) (* k (log n))) (* (sqrt (* PI n)) (sqrt 2))))) (+ (- (* +nan.0 (* (* k (log n)) (* (sqrt (* PI n)) (sqrt 2)))) (* (* +nan.0 (sqrt (* PI n))) (* (* (log n) (* k k)) (sqrt 2)))) (- (* (* (* (log n) (* k k)) (* (sqrt 2) (log (* 2 PI)))) (* (sqrt (* PI n)) +nan.0)) (- (* +nan.0 (* (sqrt (* PI n)) (sqrt 2))) (- (* (sqrt (* PI n)) (* +nan.0 (* (* k (sqrt 2)) (log (* 2 PI))))) (* (* (* k k) (* (sqrt 2) (log (* 2 PI)))) (* (sqrt (* PI n)) +nan.0))))))))) (+ (* (- +nan.0) (* (/ (exp (* (- 1/2 (* 1/2 k)) (- (- (log n))))) k) (pow (* 2 PI) (- 1/2 (* 1/2 k))))) (- (/ (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (- (log n)))))) (/ (* k k) (pow (* 2 PI) (- 1/2 (* 1/2 k))))) (/ (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (- (log n)))))) (/ (* (* k k) k) (pow (* 2 PI) (- 1/2 (* 1/2 k))))))) (+ (- (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (- (log -1) (log n))))) +nan.0) (/ k (pow (* 2 PI) (- 1/2 (* 1/2 k)))))) (* +nan.0 (- (* (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (- (log -1) (log n))))) k) (/ (pow (* 2 PI) (- 1/2 (* 1/2 k))) k)) (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (- (log -1) (log n))))))))) 8.321 * * * [progress]: adding candidates to table 11.307 * * [progress]: iteration 3 / 4 11.307 * * * [progress]: picking best candidate 11.334 * * * * [pick]: Picked # 11.334 * * * [progress]: localizing error 11.399 * * * [progress]: generating rewritten candidates 11.400 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1) 11.411 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 2 1) 11.429 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1) 11.446 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 11.560 * * * [progress]: generating series expansions 11.560 * * * * [progress]: [ 1 / 4 ] generating series at (2 1) 11.561 * [backup-simplify]: Simplify (pow n (- 1/2 (/ k 2))) into (pow n (- 1/2 (* 1/2 k))) 11.561 * [approximate]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in (n k) around 0 11.561 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 11.561 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 11.561 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 11.561 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.561 * [taylor]: Taking taylor expansion of 1/2 in k 11.561 * [backup-simplify]: Simplify 1/2 into 1/2 11.561 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.561 * [taylor]: Taking taylor expansion of 1/2 in k 11.561 * [backup-simplify]: Simplify 1/2 into 1/2 11.561 * [taylor]: Taking taylor expansion of k in k 11.561 * [backup-simplify]: Simplify 0 into 0 11.561 * [backup-simplify]: Simplify 1 into 1 11.561 * [taylor]: Taking taylor expansion of (log n) in k 11.561 * [taylor]: Taking taylor expansion of n in k 11.561 * [backup-simplify]: Simplify n into n 11.561 * [backup-simplify]: Simplify (log n) into (log n) 11.562 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.562 * [backup-simplify]: Simplify (- 0) into 0 11.562 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.562 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 11.562 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 11.562 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 11.562 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 11.562 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 11.562 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 11.562 * [taylor]: Taking taylor expansion of 1/2 in n 11.562 * [backup-simplify]: Simplify 1/2 into 1/2 11.562 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 11.562 * [taylor]: Taking taylor expansion of 1/2 in n 11.562 * [backup-simplify]: Simplify 1/2 into 1/2 11.562 * [taylor]: Taking taylor expansion of k in n 11.562 * [backup-simplify]: Simplify k into k 11.562 * [taylor]: Taking taylor expansion of (log n) in n 11.562 * [taylor]: Taking taylor expansion of n in n 11.562 * [backup-simplify]: Simplify 0 into 0 11.562 * [backup-simplify]: Simplify 1 into 1 11.563 * [backup-simplify]: Simplify (log 1) into 0 11.563 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 11.563 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 11.563 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 11.563 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 11.563 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 11.563 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 11.563 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 11.563 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 11.563 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 11.563 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 11.563 * [taylor]: Taking taylor expansion of 1/2 in n 11.563 * [backup-simplify]: Simplify 1/2 into 1/2 11.563 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 11.563 * [taylor]: Taking taylor expansion of 1/2 in n 11.563 * [backup-simplify]: Simplify 1/2 into 1/2 11.563 * [taylor]: Taking taylor expansion of k in n 11.563 * [backup-simplify]: Simplify k into k 11.563 * [taylor]: Taking taylor expansion of (log n) in n 11.564 * [taylor]: Taking taylor expansion of n in n 11.564 * [backup-simplify]: Simplify 0 into 0 11.564 * [backup-simplify]: Simplify 1 into 1 11.564 * [backup-simplify]: Simplify (log 1) into 0 11.564 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 11.564 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 11.564 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 11.564 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 11.564 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 11.564 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 11.564 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 11.564 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 11.564 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 11.564 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.565 * [taylor]: Taking taylor expansion of 1/2 in k 11.565 * [backup-simplify]: Simplify 1/2 into 1/2 11.565 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.565 * [taylor]: Taking taylor expansion of 1/2 in k 11.565 * [backup-simplify]: Simplify 1/2 into 1/2 11.565 * [taylor]: Taking taylor expansion of k in k 11.565 * [backup-simplify]: Simplify 0 into 0 11.565 * [backup-simplify]: Simplify 1 into 1 11.565 * [taylor]: Taking taylor expansion of (log n) in k 11.565 * [taylor]: Taking taylor expansion of n in k 11.565 * [backup-simplify]: Simplify n into n 11.565 * [backup-simplify]: Simplify (log n) into (log n) 11.565 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.565 * [backup-simplify]: Simplify (- 0) into 0 11.565 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.566 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 11.566 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 11.566 * [backup-simplify]: Simplify (pow n 1/2) into (pow n 1/2) 11.566 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 11.567 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 11.567 * [backup-simplify]: Simplify (- 0) into 0 11.567 * [backup-simplify]: Simplify (+ 0 0) into 0 11.567 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 11.568 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log n))) into 0 11.568 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 11.568 * [taylor]: Taking taylor expansion of 0 in k 11.568 * [backup-simplify]: Simplify 0 into 0 11.568 * [backup-simplify]: Simplify 0 into 0 11.569 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 11.569 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 11.569 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.570 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.570 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log n))) into (- (* 1/2 (log n))) 11.570 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n))) 11.570 * [backup-simplify]: Simplify (* -1/2 (* (sqrt n) (log n))) into (* -1/2 (* (sqrt n) (log n))) 11.572 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 11.573 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 11.573 * [backup-simplify]: Simplify (- 0) into 0 11.573 * [backup-simplify]: Simplify (+ 0 0) into 0 11.574 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 11.574 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0 11.575 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.575 * [taylor]: Taking taylor expansion of 0 in k 11.575 * [backup-simplify]: Simplify 0 into 0 11.575 * [backup-simplify]: Simplify 0 into 0 11.575 * [backup-simplify]: Simplify 0 into 0 11.576 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 11.586 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 11.587 * [backup-simplify]: Simplify (- 0) into 0 11.587 * [backup-simplify]: Simplify (+ 0 0) into 0 11.588 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log n)))) into 0 11.588 * [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))) 11.588 * [backup-simplify]: Simplify (* 1/8 (* (sqrt n) (pow (log n) 2))) into (* 1/8 (* (sqrt n) (pow (log n) 2))) 11.589 * [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)))) 11.589 * [backup-simplify]: Simplify (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 11.589 * [approximate]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 11.589 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 11.589 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in k 11.589 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in k 11.589 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 11.589 * [taylor]: Taking taylor expansion of 1/2 in k 11.589 * [backup-simplify]: Simplify 1/2 into 1/2 11.589 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.589 * [taylor]: Taking taylor expansion of 1/2 in k 11.589 * [backup-simplify]: Simplify 1/2 into 1/2 11.589 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.589 * [taylor]: Taking taylor expansion of k in k 11.589 * [backup-simplify]: Simplify 0 into 0 11.589 * [backup-simplify]: Simplify 1 into 1 11.589 * [backup-simplify]: Simplify (/ 1 1) into 1 11.589 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k 11.589 * [taylor]: Taking taylor expansion of (/ 1 n) in k 11.589 * [taylor]: Taking taylor expansion of n in k 11.589 * [backup-simplify]: Simplify n into n 11.589 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n) 11.589 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n)) 11.590 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.590 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.590 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.590 * [backup-simplify]: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) 11.590 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 11.590 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 11.590 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 11.590 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 11.590 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 11.590 * [taylor]: Taking taylor expansion of 1/2 in n 11.590 * [backup-simplify]: Simplify 1/2 into 1/2 11.590 * [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 (/ 1 n)) in n 11.591 * [taylor]: Taking taylor expansion of (/ 1 n) in n 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 (/ 1 1) into 1 11.591 * [backup-simplify]: Simplify (log 1) into 0 11.591 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.591 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 11.591 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 11.592 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 11.592 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 11.592 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 11.592 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 11.592 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 11.592 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 11.592 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 11.592 * [taylor]: Taking taylor expansion of 1/2 in n 11.592 * [backup-simplify]: Simplify 1/2 into 1/2 11.592 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.592 * [taylor]: Taking taylor expansion of 1/2 in n 11.592 * [backup-simplify]: Simplify 1/2 into 1/2 11.592 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.592 * [taylor]: Taking taylor expansion of k in n 11.592 * [backup-simplify]: Simplify k into k 11.592 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.592 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 11.592 * [taylor]: Taking taylor expansion of (/ 1 n) in n 11.592 * [taylor]: Taking taylor expansion of n in n 11.592 * [backup-simplify]: Simplify 0 into 0 11.592 * [backup-simplify]: Simplify 1 into 1 11.592 * [backup-simplify]: Simplify (/ 1 1) into 1 11.593 * [backup-simplify]: Simplify (log 1) into 0 11.593 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.593 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 11.593 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 11.593 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 11.593 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 11.593 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 11.593 * [taylor]: Taking taylor expansion of (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) in k 11.593 * [taylor]: Taking taylor expansion of (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) in k 11.593 * [taylor]: Taking taylor expansion of -1 in k 11.593 * [backup-simplify]: Simplify -1 into -1 11.593 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log n)) in k 11.593 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 11.593 * [taylor]: Taking taylor expansion of 1/2 in k 11.593 * [backup-simplify]: Simplify 1/2 into 1/2 11.593 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.594 * [taylor]: Taking taylor expansion of 1/2 in k 11.594 * [backup-simplify]: Simplify 1/2 into 1/2 11.594 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.594 * [taylor]: Taking taylor expansion of k in k 11.594 * [backup-simplify]: Simplify 0 into 0 11.594 * [backup-simplify]: Simplify 1 into 1 11.594 * [backup-simplify]: Simplify (/ 1 1) into 1 11.594 * [taylor]: Taking taylor expansion of (log n) in k 11.594 * [taylor]: Taking taylor expansion of n in k 11.594 * [backup-simplify]: Simplify n into n 11.594 * [backup-simplify]: Simplify (log n) into (log n) 11.594 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.594 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.595 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.595 * [backup-simplify]: Simplify (* -1/2 (log n)) into (* -1/2 (log n)) 11.595 * [backup-simplify]: Simplify (* -1 (* -1/2 (log n))) into (* 1/2 (log n)) 11.595 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 11.595 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 11.596 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 11.596 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 11.596 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.597 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 11.597 * [backup-simplify]: Simplify (- 0) into 0 11.597 * [backup-simplify]: Simplify (+ 0 0) into 0 11.597 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 11.598 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 11.598 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 11.598 * [taylor]: Taking taylor expansion of 0 in k 11.598 * [backup-simplify]: Simplify 0 into 0 11.598 * [backup-simplify]: Simplify 0 into 0 11.598 * [backup-simplify]: Simplify 0 into 0 11.599 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.600 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 11.601 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.601 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 11.602 * [backup-simplify]: Simplify (- 0) into 0 11.602 * [backup-simplify]: Simplify (+ 0 0) into 0 11.602 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 11.602 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 11.603 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.603 * [taylor]: Taking taylor expansion of 0 in k 11.603 * [backup-simplify]: Simplify 0 into 0 11.603 * [backup-simplify]: Simplify 0 into 0 11.603 * [backup-simplify]: Simplify 0 into 0 11.603 * [backup-simplify]: Simplify 0 into 0 11.604 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.607 * [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 11.607 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.608 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 11.608 * [backup-simplify]: Simplify (- 0) into 0 11.608 * [backup-simplify]: Simplify (+ 0 0) into 0 11.609 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 11.609 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 11.610 * [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 11.610 * [taylor]: Taking taylor expansion of 0 in k 11.610 * [backup-simplify]: Simplify 0 into 0 11.610 * [backup-simplify]: Simplify 0 into 0 11.611 * [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))))) 11.611 * [backup-simplify]: Simplify (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 11.611 * [approximate]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 11.611 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 11.611 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in k 11.611 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in k 11.611 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 11.611 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.611 * [taylor]: Taking taylor expansion of 1/2 in k 11.611 * [backup-simplify]: Simplify 1/2 into 1/2 11.611 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.611 * [taylor]: Taking taylor expansion of k in k 11.611 * [backup-simplify]: Simplify 0 into 0 11.611 * [backup-simplify]: Simplify 1 into 1 11.611 * [backup-simplify]: Simplify (/ 1 1) into 1 11.611 * [taylor]: Taking taylor expansion of 1/2 in k 11.611 * [backup-simplify]: Simplify 1/2 into 1/2 11.611 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k 11.611 * [taylor]: Taking taylor expansion of (/ -1 n) in k 11.611 * [taylor]: Taking taylor expansion of -1 in k 11.611 * [backup-simplify]: Simplify -1 into -1 11.611 * [taylor]: Taking taylor expansion of n in k 11.611 * [backup-simplify]: Simplify n into n 11.611 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n) 11.611 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n)) 11.612 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.612 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.612 * [backup-simplify]: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) 11.612 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 11.612 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 11.612 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 11.612 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 11.612 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 11.612 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.612 * [taylor]: Taking taylor expansion of 1/2 in n 11.612 * [backup-simplify]: Simplify 1/2 into 1/2 11.612 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.612 * [taylor]: Taking taylor expansion of k in n 11.612 * [backup-simplify]: Simplify k into k 11.612 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.612 * [taylor]: Taking taylor expansion of 1/2 in n 11.612 * [backup-simplify]: Simplify 1/2 into 1/2 11.612 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 11.612 * [taylor]: Taking taylor expansion of (/ -1 n) in n 11.612 * [taylor]: Taking taylor expansion of -1 in n 11.612 * [backup-simplify]: Simplify -1 into -1 11.612 * [taylor]: Taking taylor expansion of n in n 11.612 * [backup-simplify]: Simplify 0 into 0 11.612 * [backup-simplify]: Simplify 1 into 1 11.613 * [backup-simplify]: Simplify (/ -1 1) into -1 11.613 * [backup-simplify]: Simplify (log -1) into (log -1) 11.613 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.613 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 11.614 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 11.614 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 11.614 * [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)))) 11.614 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 11.614 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 11.614 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 11.614 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 11.614 * [taylor]: Taking taylor expansion of (* 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 k) in n 11.614 * [taylor]: Taking taylor expansion of k in n 11.614 * [backup-simplify]: Simplify k into k 11.615 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 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 (log (/ -1 n)) in n 11.615 * [taylor]: Taking taylor expansion of (/ -1 n) in n 11.615 * [taylor]: Taking taylor expansion of -1 in n 11.615 * [backup-simplify]: Simplify -1 into -1 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 (/ -1 1) into -1 11.615 * [backup-simplify]: Simplify (log -1) into (log -1) 11.615 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.615 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 11.616 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 11.616 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 11.616 * [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)))) 11.617 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) in k 11.617 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) in k 11.617 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 11.617 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.617 * [taylor]: Taking taylor expansion of 1/2 in k 11.617 * [backup-simplify]: Simplify 1/2 into 1/2 11.617 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.617 * [taylor]: Taking taylor expansion of k in k 11.617 * [backup-simplify]: Simplify 0 into 0 11.617 * [backup-simplify]: Simplify 1 into 1 11.617 * [backup-simplify]: Simplify (/ 1 1) into 1 11.617 * [taylor]: Taking taylor expansion of 1/2 in k 11.617 * [backup-simplify]: Simplify 1/2 into 1/2 11.617 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k 11.617 * [taylor]: Taking taylor expansion of (log -1) in k 11.617 * [taylor]: Taking taylor expansion of -1 in k 11.617 * [backup-simplify]: Simplify -1 into -1 11.617 * [backup-simplify]: Simplify (log -1) into (log -1) 11.617 * [taylor]: Taking taylor expansion of (log n) in k 11.617 * [taylor]: Taking taylor expansion of n in k 11.617 * [backup-simplify]: Simplify n into n 11.617 * [backup-simplify]: Simplify (log n) into (log n) 11.618 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.618 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.618 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 11.618 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n)) 11.619 * [backup-simplify]: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n))) 11.619 * [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)))) 11.619 * [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)))) 11.620 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 11.621 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 11.621 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.621 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 11.621 * [backup-simplify]: Simplify (+ 0 0) into 0 11.622 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 11.622 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -1) (log n)))) into 0 11.623 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 11.623 * [taylor]: Taking taylor expansion of 0 in k 11.623 * [backup-simplify]: Simplify 0 into 0 11.623 * [backup-simplify]: Simplify 0 into 0 11.623 * [backup-simplify]: Simplify 0 into 0 11.624 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.625 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0 11.625 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.626 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 11.626 * [backup-simplify]: Simplify (+ 0 0) into 0 11.627 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 11.627 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0 11.629 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.629 * [taylor]: Taking taylor expansion of 0 in k 11.629 * [backup-simplify]: Simplify 0 into 0 11.629 * [backup-simplify]: Simplify 0 into 0 11.629 * [backup-simplify]: Simplify 0 into 0 11.629 * [backup-simplify]: Simplify 0 into 0 11.629 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.632 * [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 11.632 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.633 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 11.633 * [backup-simplify]: Simplify (+ 0 0) into 0 11.634 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 11.635 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -1) (log n)))))) into 0 11.636 * [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 11.636 * [taylor]: Taking taylor expansion of 0 in k 11.636 * [backup-simplify]: Simplify 0 into 0 11.636 * [backup-simplify]: Simplify 0 into 0 11.637 * [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))))) 11.637 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 2 1) 11.637 * [backup-simplify]: Simplify (pow (* 2 PI) (- 1/2 (/ k 2))) into (pow (* 2 PI) (- 1/2 (* 1/2 k))) 11.637 * [approximate]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in (k) around 0 11.637 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in k 11.637 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) in k 11.637 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) in k 11.637 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.637 * [taylor]: Taking taylor expansion of 1/2 in k 11.637 * [backup-simplify]: Simplify 1/2 into 1/2 11.637 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.638 * [taylor]: Taking taylor expansion of 1/2 in k 11.638 * [backup-simplify]: Simplify 1/2 into 1/2 11.638 * [taylor]: Taking taylor expansion of k in k 11.638 * [backup-simplify]: Simplify 0 into 0 11.638 * [backup-simplify]: Simplify 1 into 1 11.638 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 11.638 * [taylor]: Taking taylor expansion of (* 2 PI) in k 11.638 * [taylor]: Taking taylor expansion of 2 in k 11.638 * [backup-simplify]: Simplify 2 into 2 11.638 * [taylor]: Taking taylor expansion of PI in k 11.638 * [backup-simplify]: Simplify PI into PI 11.638 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.639 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.639 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.639 * [backup-simplify]: Simplify (- 0) into 0 11.639 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.641 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 11.642 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) 11.642 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in k 11.642 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) in k 11.642 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) in k 11.642 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.642 * [taylor]: Taking taylor expansion of 1/2 in k 11.642 * [backup-simplify]: Simplify 1/2 into 1/2 11.642 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.642 * [taylor]: Taking taylor expansion of 1/2 in k 11.642 * [backup-simplify]: Simplify 1/2 into 1/2 11.642 * [taylor]: Taking taylor expansion of k in k 11.642 * [backup-simplify]: Simplify 0 into 0 11.642 * [backup-simplify]: Simplify 1 into 1 11.642 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 11.642 * [taylor]: Taking taylor expansion of (* 2 PI) in k 11.642 * [taylor]: Taking taylor expansion of 2 in k 11.642 * [backup-simplify]: Simplify 2 into 2 11.642 * [taylor]: Taking taylor expansion of PI in k 11.642 * [backup-simplify]: Simplify PI into PI 11.643 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.643 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.644 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.644 * [backup-simplify]: Simplify (- 0) into 0 11.644 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.645 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 11.647 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) 11.648 * [backup-simplify]: Simplify (pow (* 2 PI) 1/2) into (pow (* 2 PI) 1/2) 11.649 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 11.650 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.650 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 11.650 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.651 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.653 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 PI)))) into (- (* 1/2 (log (* 2 PI)))) 11.660 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) 11.663 * [backup-simplify]: Simplify (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) into (* -1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) 11.664 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 11.666 * [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 11.666 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 11.667 * [backup-simplify]: Simplify (- 0) into 0 11.667 * [backup-simplify]: Simplify (+ 0 0) into 0 11.668 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 PI))))) into 0 11.682 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) 11.685 * [backup-simplify]: Simplify (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) into (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI))) 11.693 * [backup-simplify]: Simplify (+ (* (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) k) (pow (* 2 PI) 1/2))) into (- (+ (* 1/8 (* (* (sqrt 2) (* (pow k 2) (pow (log (* 2 PI)) 2))) (sqrt PI))) (pow (* 2 PI) 1/2)) (* 1/2 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt PI)))) 11.693 * [backup-simplify]: Simplify (pow (* 2 PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 11.694 * [approximate]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in (k) around 0 11.694 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in k 11.694 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in k 11.694 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in k 11.694 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 11.694 * [taylor]: Taking taylor expansion of 1/2 in k 11.694 * [backup-simplify]: Simplify 1/2 into 1/2 11.694 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.694 * [taylor]: Taking taylor expansion of 1/2 in k 11.694 * [backup-simplify]: Simplify 1/2 into 1/2 11.694 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.694 * [taylor]: Taking taylor expansion of k in k 11.694 * [backup-simplify]: Simplify 0 into 0 11.694 * [backup-simplify]: Simplify 1 into 1 11.694 * [backup-simplify]: Simplify (/ 1 1) into 1 11.694 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 11.694 * [taylor]: Taking taylor expansion of (* 2 PI) in k 11.694 * [taylor]: Taking taylor expansion of 2 in k 11.694 * [backup-simplify]: Simplify 2 into 2 11.694 * [taylor]: Taking taylor expansion of PI in k 11.694 * [backup-simplify]: Simplify PI into PI 11.694 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.695 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.695 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.696 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.696 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.697 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) 11.698 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 11.698 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in k 11.698 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in k 11.698 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in k 11.698 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 11.698 * [taylor]: Taking taylor expansion of 1/2 in k 11.698 * [backup-simplify]: Simplify 1/2 into 1/2 11.698 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.698 * [taylor]: Taking taylor expansion of 1/2 in k 11.698 * [backup-simplify]: Simplify 1/2 into 1/2 11.698 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.698 * [taylor]: Taking taylor expansion of k in k 11.698 * [backup-simplify]: Simplify 0 into 0 11.698 * [backup-simplify]: Simplify 1 into 1 11.698 * [backup-simplify]: Simplify (/ 1 1) into 1 11.698 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 11.698 * [taylor]: Taking taylor expansion of (* 2 PI) in k 11.698 * [taylor]: Taking taylor expansion of 2 in k 11.698 * [backup-simplify]: Simplify 2 into 2 11.698 * [taylor]: Taking taylor expansion of PI in k 11.698 * [backup-simplify]: Simplify PI into PI 11.699 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.699 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.700 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.700 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.700 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.701 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) 11.702 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 11.703 * [backup-simplify]: Simplify (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 11.703 * [backup-simplify]: Simplify 0 into 0 11.703 * [backup-simplify]: Simplify 0 into 0 11.703 * [backup-simplify]: Simplify 0 into 0 11.703 * [backup-simplify]: Simplify 0 into 0 11.703 * [backup-simplify]: Simplify 0 into 0 11.703 * [backup-simplify]: Simplify 0 into 0 11.703 * [backup-simplify]: Simplify (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) into (pow (* 2 PI) (- 1/2 (* 1/2 k))) 11.704 * [backup-simplify]: Simplify (pow (* 2 PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 11.704 * [approximate]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in (k) around 0 11.704 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in k 11.704 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in k 11.704 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in k 11.704 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 11.704 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.704 * [taylor]: Taking taylor expansion of 1/2 in k 11.704 * [backup-simplify]: Simplify 1/2 into 1/2 11.704 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.704 * [taylor]: Taking taylor expansion of k in k 11.704 * [backup-simplify]: Simplify 0 into 0 11.704 * [backup-simplify]: Simplify 1 into 1 11.704 * [backup-simplify]: Simplify (/ 1 1) into 1 11.704 * [taylor]: Taking taylor expansion of 1/2 in k 11.704 * [backup-simplify]: Simplify 1/2 into 1/2 11.704 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 11.704 * [taylor]: Taking taylor expansion of (* 2 PI) in k 11.704 * [taylor]: Taking taylor expansion of 2 in k 11.704 * [backup-simplify]: Simplify 2 into 2 11.704 * [taylor]: Taking taylor expansion of PI in k 11.704 * [backup-simplify]: Simplify PI into PI 11.705 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.707 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.707 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.707 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.709 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 11.709 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 11.709 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in k 11.710 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in k 11.710 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in k 11.710 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 11.710 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.710 * [taylor]: Taking taylor expansion of 1/2 in k 11.710 * [backup-simplify]: Simplify 1/2 into 1/2 11.710 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.710 * [taylor]: Taking taylor expansion of k in k 11.710 * [backup-simplify]: Simplify 0 into 0 11.710 * [backup-simplify]: Simplify 1 into 1 11.710 * [backup-simplify]: Simplify (/ 1 1) into 1 11.710 * [taylor]: Taking taylor expansion of 1/2 in k 11.710 * [backup-simplify]: Simplify 1/2 into 1/2 11.710 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 11.710 * [taylor]: Taking taylor expansion of (* 2 PI) in k 11.710 * [taylor]: Taking taylor expansion of 2 in k 11.710 * [backup-simplify]: Simplify 2 into 2 11.710 * [taylor]: Taking taylor expansion of PI in k 11.710 * [backup-simplify]: Simplify PI into PI 11.710 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.711 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.712 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.712 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.713 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 11.714 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 11.714 * [backup-simplify]: Simplify (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 11.714 * [backup-simplify]: Simplify 0 into 0 11.714 * [backup-simplify]: Simplify 0 into 0 11.714 * [backup-simplify]: Simplify 0 into 0 11.714 * [backup-simplify]: Simplify 0 into 0 11.714 * [backup-simplify]: Simplify 0 into 0 11.714 * [backup-simplify]: Simplify 0 into 0 11.715 * [backup-simplify]: Simplify (pow (* 2 PI) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) into (pow (* 2 PI) (- 1/2 (* 1/2 k))) 11.715 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1) 11.715 * [backup-simplify]: Simplify (pow (* 2 PI) (- 1/2 (/ k 2))) into (pow (* 2 PI) (- 1/2 (* 1/2 k))) 11.715 * [approximate]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in (k) around 0 11.715 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in k 11.715 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) in k 11.715 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) in k 11.715 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.715 * [taylor]: Taking taylor expansion of 1/2 in k 11.715 * [backup-simplify]: Simplify 1/2 into 1/2 11.715 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.715 * [taylor]: Taking taylor expansion of 1/2 in k 11.715 * [backup-simplify]: Simplify 1/2 into 1/2 11.715 * [taylor]: Taking taylor expansion of k in k 11.715 * [backup-simplify]: Simplify 0 into 0 11.715 * [backup-simplify]: Simplify 1 into 1 11.715 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 11.715 * [taylor]: Taking taylor expansion of (* 2 PI) in k 11.715 * [taylor]: Taking taylor expansion of 2 in k 11.715 * [backup-simplify]: Simplify 2 into 2 11.715 * [taylor]: Taking taylor expansion of PI in k 11.715 * [backup-simplify]: Simplify PI into PI 11.716 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.716 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.717 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.717 * [backup-simplify]: Simplify (- 0) into 0 11.717 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.718 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 11.720 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) 11.720 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in k 11.720 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) in k 11.720 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) in k 11.720 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.720 * [taylor]: Taking taylor expansion of 1/2 in k 11.720 * [backup-simplify]: Simplify 1/2 into 1/2 11.720 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.720 * [taylor]: Taking taylor expansion of 1/2 in k 11.720 * [backup-simplify]: Simplify 1/2 into 1/2 11.720 * [taylor]: Taking taylor expansion of k in k 11.720 * [backup-simplify]: Simplify 0 into 0 11.720 * [backup-simplify]: Simplify 1 into 1 11.720 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 11.720 * [taylor]: Taking taylor expansion of (* 2 PI) in k 11.720 * [taylor]: Taking taylor expansion of 2 in k 11.720 * [backup-simplify]: Simplify 2 into 2 11.720 * [taylor]: Taking taylor expansion of PI in k 11.720 * [backup-simplify]: Simplify PI into PI 11.720 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.721 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.721 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.722 * [backup-simplify]: Simplify (- 0) into 0 11.722 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.723 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 11.725 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) 11.726 * [backup-simplify]: Simplify (pow (* 2 PI) 1/2) into (pow (* 2 PI) 1/2) 11.726 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 11.727 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.728 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 11.728 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.728 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.730 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 PI)))) into (- (* 1/2 (log (* 2 PI)))) 11.738 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) 11.741 * [backup-simplify]: Simplify (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) into (* -1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) 11.742 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 11.743 * [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 11.744 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 11.744 * [backup-simplify]: Simplify (- 0) into 0 11.745 * [backup-simplify]: Simplify (+ 0 0) into 0 11.745 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 PI))))) into 0 11.754 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) 11.757 * [backup-simplify]: Simplify (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) into (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI))) 11.767 * [backup-simplify]: Simplify (+ (* (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) k) (pow (* 2 PI) 1/2))) into (- (+ (* 1/8 (* (* (sqrt 2) (* (pow k 2) (pow (log (* 2 PI)) 2))) (sqrt PI))) (pow (* 2 PI) 1/2)) (* 1/2 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt PI)))) 11.768 * [backup-simplify]: Simplify (pow (* 2 PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 11.768 * [approximate]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in (k) around 0 11.768 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in k 11.768 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in k 11.768 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in k 11.768 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 11.768 * [taylor]: Taking taylor expansion of 1/2 in k 11.768 * [backup-simplify]: Simplify 1/2 into 1/2 11.768 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.768 * [taylor]: Taking taylor expansion of 1/2 in k 11.768 * [backup-simplify]: Simplify 1/2 into 1/2 11.768 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.768 * [taylor]: Taking taylor expansion of k in k 11.768 * [backup-simplify]: Simplify 0 into 0 11.768 * [backup-simplify]: Simplify 1 into 1 11.768 * [backup-simplify]: Simplify (/ 1 1) into 1 11.768 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 11.768 * [taylor]: Taking taylor expansion of (* 2 PI) in k 11.768 * [taylor]: Taking taylor expansion of 2 in k 11.769 * [backup-simplify]: Simplify 2 into 2 11.769 * [taylor]: Taking taylor expansion of PI in k 11.769 * [backup-simplify]: Simplify PI into PI 11.769 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.770 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.771 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.771 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.771 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.780 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) 11.781 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 11.781 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in k 11.781 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in k 11.781 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in k 11.781 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 11.781 * [taylor]: Taking taylor expansion of 1/2 in k 11.781 * [backup-simplify]: Simplify 1/2 into 1/2 11.781 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.781 * [taylor]: Taking taylor expansion of 1/2 in k 11.781 * [backup-simplify]: Simplify 1/2 into 1/2 11.781 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.781 * [taylor]: Taking taylor expansion of k in k 11.781 * [backup-simplify]: Simplify 0 into 0 11.781 * [backup-simplify]: Simplify 1 into 1 11.782 * [backup-simplify]: Simplify (/ 1 1) into 1 11.782 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 11.782 * [taylor]: Taking taylor expansion of (* 2 PI) in k 11.782 * [taylor]: Taking taylor expansion of 2 in k 11.782 * [backup-simplify]: Simplify 2 into 2 11.782 * [taylor]: Taking taylor expansion of PI in k 11.782 * [backup-simplify]: Simplify PI into PI 11.782 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.783 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.784 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.784 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.785 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.787 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) 11.788 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 11.788 * [backup-simplify]: Simplify (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 11.788 * [backup-simplify]: Simplify 0 into 0 11.788 * [backup-simplify]: Simplify 0 into 0 11.788 * [backup-simplify]: Simplify 0 into 0 11.789 * [backup-simplify]: Simplify 0 into 0 11.789 * [backup-simplify]: Simplify 0 into 0 11.789 * [backup-simplify]: Simplify 0 into 0 11.789 * [backup-simplify]: Simplify (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) into (pow (* 2 PI) (- 1/2 (* 1/2 k))) 11.790 * [backup-simplify]: Simplify (pow (* 2 PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 11.790 * [approximate]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in (k) around 0 11.790 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in k 11.790 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in k 11.790 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in k 11.790 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 11.790 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.790 * [taylor]: Taking taylor expansion of 1/2 in k 11.790 * [backup-simplify]: Simplify 1/2 into 1/2 11.790 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.790 * [taylor]: Taking taylor expansion of k in k 11.790 * [backup-simplify]: Simplify 0 into 0 11.790 * [backup-simplify]: Simplify 1 into 1 11.791 * [backup-simplify]: Simplify (/ 1 1) into 1 11.791 * [taylor]: Taking taylor expansion of 1/2 in k 11.791 * [backup-simplify]: Simplify 1/2 into 1/2 11.791 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 11.791 * [taylor]: Taking taylor expansion of (* 2 PI) in k 11.791 * [taylor]: Taking taylor expansion of 2 in k 11.791 * [backup-simplify]: Simplify 2 into 2 11.791 * [taylor]: Taking taylor expansion of PI in k 11.791 * [backup-simplify]: Simplify PI into PI 11.791 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.793 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.793 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.793 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.795 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 11.797 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 11.797 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in k 11.797 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in k 11.797 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in k 11.797 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 11.797 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.797 * [taylor]: Taking taylor expansion of 1/2 in k 11.797 * [backup-simplify]: Simplify 1/2 into 1/2 11.797 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.797 * [taylor]: Taking taylor expansion of k in k 11.797 * [backup-simplify]: Simplify 0 into 0 11.797 * [backup-simplify]: Simplify 1 into 1 11.797 * [backup-simplify]: Simplify (/ 1 1) into 1 11.797 * [taylor]: Taking taylor expansion of 1/2 in k 11.797 * [backup-simplify]: Simplify 1/2 into 1/2 11.797 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 11.797 * [taylor]: Taking taylor expansion of (* 2 PI) in k 11.797 * [taylor]: Taking taylor expansion of 2 in k 11.797 * [backup-simplify]: Simplify 2 into 2 11.797 * [taylor]: Taking taylor expansion of PI in k 11.797 * [backup-simplify]: Simplify PI into PI 11.798 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.799 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.799 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.800 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.801 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 11.803 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 11.803 * [backup-simplify]: Simplify (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 11.803 * [backup-simplify]: Simplify 0 into 0 11.803 * [backup-simplify]: Simplify 0 into 0 11.803 * [backup-simplify]: Simplify 0 into 0 11.803 * [backup-simplify]: Simplify 0 into 0 11.803 * [backup-simplify]: Simplify 0 into 0 11.803 * [backup-simplify]: Simplify 0 into 0 11.804 * [backup-simplify]: Simplify (pow (* 2 PI) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) into (pow (* 2 PI) (- 1/2 (* 1/2 k))) 11.804 * * * * [progress]: [ 4 / 4 ] generating series at (2) 11.805 * [backup-simplify]: Simplify (* (pow n (- 1/2 (/ k 2))) (/ (sqrt (pow (* 2 PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* 2 PI) (- 1/2 (/ k 2))))))) into (* (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) 11.805 * [approximate]: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in (n k) around 0 11.805 * [taylor]: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k 11.805 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) in k 11.806 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 11.806 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 11.806 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 11.806 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.806 * [taylor]: Taking taylor expansion of 1/2 in k 11.806 * [backup-simplify]: Simplify 1/2 into 1/2 11.806 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.806 * [taylor]: Taking taylor expansion of 1/2 in k 11.806 * [backup-simplify]: Simplify 1/2 into 1/2 11.806 * [taylor]: Taking taylor expansion of k in k 11.806 * [backup-simplify]: Simplify 0 into 0 11.806 * [backup-simplify]: Simplify 1 into 1 11.806 * [taylor]: Taking taylor expansion of (log n) in k 11.806 * [taylor]: Taking taylor expansion of n in k 11.806 * [backup-simplify]: Simplify n into n 11.806 * [backup-simplify]: Simplify (log n) into (log n) 11.806 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.807 * [backup-simplify]: Simplify (- 0) into 0 11.807 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.807 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 11.808 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 11.808 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in k 11.808 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) in k 11.808 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) in k 11.808 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.808 * [taylor]: Taking taylor expansion of 1/2 in k 11.808 * [backup-simplify]: Simplify 1/2 into 1/2 11.808 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.808 * [taylor]: Taking taylor expansion of 1/2 in k 11.808 * [backup-simplify]: Simplify 1/2 into 1/2 11.808 * [taylor]: Taking taylor expansion of k in k 11.808 * [backup-simplify]: Simplify 0 into 0 11.808 * [backup-simplify]: Simplify 1 into 1 11.808 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 11.808 * [taylor]: Taking taylor expansion of (* 2 PI) in k 11.808 * [taylor]: Taking taylor expansion of 2 in k 11.808 * [backup-simplify]: Simplify 2 into 2 11.808 * [taylor]: Taking taylor expansion of PI in k 11.808 * [backup-simplify]: Simplify PI into PI 11.809 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.810 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.810 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.811 * [backup-simplify]: Simplify (- 0) into 0 11.811 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.813 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 11.816 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) 11.817 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.817 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.817 * [taylor]: Taking taylor expansion of k in k 11.817 * [backup-simplify]: Simplify 0 into 0 11.817 * [backup-simplify]: Simplify 1 into 1 11.817 * [backup-simplify]: Simplify (/ 1 1) into 1 11.817 * [backup-simplify]: Simplify (sqrt 0) into 0 11.819 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.819 * [taylor]: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in n 11.819 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) in n 11.819 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 11.819 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 11.819 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 11.819 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 11.819 * [taylor]: Taking taylor expansion of 1/2 in n 11.819 * [backup-simplify]: Simplify 1/2 into 1/2 11.819 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 11.819 * [taylor]: Taking taylor expansion of 1/2 in n 11.819 * [backup-simplify]: Simplify 1/2 into 1/2 11.819 * [taylor]: Taking taylor expansion of k in n 11.819 * [backup-simplify]: Simplify k into k 11.819 * [taylor]: Taking taylor expansion of (log n) in n 11.819 * [taylor]: Taking taylor expansion of n in n 11.820 * [backup-simplify]: Simplify 0 into 0 11.820 * [backup-simplify]: Simplify 1 into 1 11.820 * [backup-simplify]: Simplify (log 1) into 0 11.820 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 11.820 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 11.820 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 11.821 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 11.821 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 11.821 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 11.821 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in n 11.821 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) in n 11.821 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) in n 11.821 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 11.821 * [taylor]: Taking taylor expansion of 1/2 in n 11.821 * [backup-simplify]: Simplify 1/2 into 1/2 11.821 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 11.821 * [taylor]: Taking taylor expansion of 1/2 in n 11.821 * [backup-simplify]: Simplify 1/2 into 1/2 11.821 * [taylor]: Taking taylor expansion of k in n 11.821 * [backup-simplify]: Simplify k into k 11.821 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 11.821 * [taylor]: Taking taylor expansion of (* 2 PI) in n 11.821 * [taylor]: Taking taylor expansion of 2 in n 11.821 * [backup-simplify]: Simplify 2 into 2 11.821 * [taylor]: Taking taylor expansion of PI in n 11.821 * [backup-simplify]: Simplify PI into PI 11.822 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.823 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.823 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 11.823 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 11.823 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 11.824 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) into (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) 11.825 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 k))) 11.825 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 11.825 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.825 * [taylor]: Taking taylor expansion of k in n 11.825 * [backup-simplify]: Simplify k into k 11.825 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.826 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 11.826 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.826 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 11.826 * [taylor]: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in n 11.826 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) in n 11.826 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 11.826 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 11.826 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 11.826 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 11.826 * [taylor]: Taking taylor expansion of 1/2 in n 11.826 * [backup-simplify]: Simplify 1/2 into 1/2 11.826 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 11.826 * [taylor]: Taking taylor expansion of 1/2 in n 11.826 * [backup-simplify]: Simplify 1/2 into 1/2 11.826 * [taylor]: Taking taylor expansion of k in n 11.826 * [backup-simplify]: Simplify k into k 11.826 * [taylor]: Taking taylor expansion of (log n) in n 11.826 * [taylor]: Taking taylor expansion of n in n 11.826 * [backup-simplify]: Simplify 0 into 0 11.826 * [backup-simplify]: Simplify 1 into 1 11.827 * [backup-simplify]: Simplify (log 1) into 0 11.827 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 11.827 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 11.827 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 11.827 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 11.827 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 11.827 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 11.828 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in n 11.828 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) in n 11.828 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) in n 11.828 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 11.828 * [taylor]: Taking taylor expansion of 1/2 in n 11.828 * [backup-simplify]: Simplify 1/2 into 1/2 11.828 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 11.828 * [taylor]: Taking taylor expansion of 1/2 in n 11.828 * [backup-simplify]: Simplify 1/2 into 1/2 11.828 * [taylor]: Taking taylor expansion of k in n 11.828 * [backup-simplify]: Simplify k into k 11.828 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 11.828 * [taylor]: Taking taylor expansion of (* 2 PI) in n 11.828 * [taylor]: Taking taylor expansion of 2 in n 11.828 * [backup-simplify]: Simplify 2 into 2 11.828 * [taylor]: Taking taylor expansion of PI in n 11.828 * [backup-simplify]: Simplify PI into PI 11.829 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.830 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.830 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 11.830 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 11.830 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 11.831 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) into (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) 11.832 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 k))) 11.832 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 11.832 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.832 * [taylor]: Taking taylor expansion of k in n 11.832 * [backup-simplify]: Simplify k into k 11.832 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.833 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 11.833 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.833 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 11.834 * [backup-simplify]: Simplify (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) into (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) 11.834 * [backup-simplify]: Simplify (* (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) into (* (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) 11.834 * [taylor]: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k 11.834 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) in k 11.834 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 11.834 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 11.835 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 11.835 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.835 * [taylor]: Taking taylor expansion of 1/2 in k 11.835 * [backup-simplify]: Simplify 1/2 into 1/2 11.835 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.835 * [taylor]: Taking taylor expansion of 1/2 in k 11.835 * [backup-simplify]: Simplify 1/2 into 1/2 11.835 * [taylor]: Taking taylor expansion of k in k 11.835 * [backup-simplify]: Simplify 0 into 0 11.835 * [backup-simplify]: Simplify 1 into 1 11.835 * [taylor]: Taking taylor expansion of (log n) in k 11.835 * [taylor]: Taking taylor expansion of n in k 11.835 * [backup-simplify]: Simplify n into n 11.835 * [backup-simplify]: Simplify (log n) into (log n) 11.835 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.836 * [backup-simplify]: Simplify (- 0) into 0 11.836 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.836 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 11.836 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 11.836 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in k 11.836 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) in k 11.836 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) in k 11.837 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.837 * [taylor]: Taking taylor expansion of 1/2 in k 11.837 * [backup-simplify]: Simplify 1/2 into 1/2 11.837 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.837 * [taylor]: Taking taylor expansion of 1/2 in k 11.837 * [backup-simplify]: Simplify 1/2 into 1/2 11.837 * [taylor]: Taking taylor expansion of k in k 11.837 * [backup-simplify]: Simplify 0 into 0 11.837 * [backup-simplify]: Simplify 1 into 1 11.837 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 11.837 * [taylor]: Taking taylor expansion of (* 2 PI) in k 11.837 * [taylor]: Taking taylor expansion of 2 in k 11.837 * [backup-simplify]: Simplify 2 into 2 11.837 * [taylor]: Taking taylor expansion of PI in k 11.837 * [backup-simplify]: Simplify PI into PI 11.837 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.839 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.839 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.839 * [backup-simplify]: Simplify (- 0) into 0 11.840 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.842 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 11.845 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) 11.845 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.845 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.845 * [taylor]: Taking taylor expansion of k in k 11.845 * [backup-simplify]: Simplify 0 into 0 11.845 * [backup-simplify]: Simplify 1 into 1 11.845 * [backup-simplify]: Simplify (/ 1 1) into 1 11.846 * [backup-simplify]: Simplify (sqrt 0) into 0 11.847 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.848 * [backup-simplify]: Simplify (* (pow n 1/2) (pow (* 2 PI) 1/2)) into (sqrt (* PI (* n 2))) 11.849 * [backup-simplify]: Simplify (* (sqrt (* PI (* n 2))) 0) into 0 11.849 * [backup-simplify]: Simplify 0 into 0 11.849 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 11.851 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.852 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 11.852 * [backup-simplify]: Simplify (- 0) into 0 11.852 * [backup-simplify]: Simplify (+ 0 0) into 0 11.853 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log (* 2 PI)))) into 0 11.855 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) (+ (* (/ (pow 0 1) 1)))) into 0 11.856 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 11.857 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 11.857 * [backup-simplify]: Simplify (- 0) into 0 11.857 * [backup-simplify]: Simplify (+ 0 0) into 0 11.858 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 11.858 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log n))) into 0 11.859 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 11.860 * [backup-simplify]: Simplify (+ (* (pow n (- 1/2 (* 1/2 k))) 0) (* 0 (pow (* 2 PI) (- 1/2 (* 1/2 k))))) into 0 11.860 * [backup-simplify]: Simplify (+ (* (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) 0) (* 0 (sqrt (/ 1 k)))) into 0 11.860 * [taylor]: Taking taylor expansion of 0 in k 11.860 * [backup-simplify]: Simplify 0 into 0 11.861 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 11.864 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.865 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 11.865 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.865 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.869 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 PI)))) into (- (* 1/2 (log (* 2 PI)))) 11.882 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) 11.883 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 11.884 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 11.884 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.885 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.885 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log n))) into (- (* 1/2 (log n))) 11.885 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n))) 11.891 * [backup-simplify]: Simplify (+ (* (pow n 1/2) (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI))))) (* (* -1/2 (* (sqrt n) (log n))) (pow (* 2 PI) 1/2))) into (- (+ (* 1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))) 11.895 * [backup-simplify]: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (* (- (+ (* 1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 11.895 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 11.895 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.896 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 11.897 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 11.899 * [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 11.899 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 11.900 * [backup-simplify]: Simplify (- 0) into 0 11.900 * [backup-simplify]: Simplify (+ 0 0) into 0 11.901 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (log (* 2 PI))))) into 0 11.902 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.904 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 11.904 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 11.905 * [backup-simplify]: Simplify (- 0) into 0 11.905 * [backup-simplify]: Simplify (+ 0 0) into 0 11.905 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 11.905 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0 11.906 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.907 * [backup-simplify]: Simplify (+ (* (pow n (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (pow (* 2 PI) (- 1/2 (* 1/2 k)))))) into 0 11.908 * [backup-simplify]: Simplify (+ (* (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 11.908 * [taylor]: Taking taylor expansion of 0 in k 11.908 * [backup-simplify]: Simplify 0 into 0 11.908 * [backup-simplify]: Simplify 0 into 0 11.908 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 11.910 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.911 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 11.913 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 11.918 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 11.919 * [backup-simplify]: Simplify (- 0) into 0 11.919 * [backup-simplify]: Simplify (+ 0 0) into 0 11.920 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 PI))))) into 0 11.929 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) 11.930 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 11.930 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 11.931 * [backup-simplify]: Simplify (- 0) into 0 11.931 * [backup-simplify]: Simplify (+ 0 0) into 0 11.931 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log n)))) into 0 11.932 * [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))) 11.942 * [backup-simplify]: Simplify (+ (* (pow n 1/2) (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2)))) (+ (* (* -1/2 (* (sqrt n) (log n))) (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI))))) (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (pow (* 2 PI) 1/2)))) into (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (* 1/4 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))))) 11.951 * [backup-simplify]: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))) +nan.0) (* (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (* 1/4 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))) 11.955 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))) 11.956 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.956 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 11.958 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.965 * [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 11.966 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 11.966 * [backup-simplify]: Simplify (- 0) into 0 11.967 * [backup-simplify]: Simplify (+ 0 0) into 0 11.968 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log (* 2 PI)))))) into 0 11.971 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 11.977 * [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 11.978 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 11.979 * [backup-simplify]: Simplify (- 0) into 0 11.979 * [backup-simplify]: Simplify (+ 0 0) into 0 11.980 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 11.981 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0 11.982 * [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 11.984 * [backup-simplify]: Simplify (+ (* (pow n (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (* 2 PI) (- 1/2 (* 1/2 k))))))) into 0 11.986 * [backup-simplify]: Simplify (+ (* (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0 11.986 * [taylor]: Taking taylor expansion of 0 in k 11.986 * [backup-simplify]: Simplify 0 into 0 11.986 * [backup-simplify]: Simplify 0 into 0 11.986 * [backup-simplify]: Simplify 0 into 0 11.987 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.991 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.992 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.999 * [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 12.000 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 12.000 * [backup-simplify]: Simplify (- 0) into 0 12.001 * [backup-simplify]: Simplify (+ 0 0) into 0 12.002 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 PI)))))) into 0 12.023 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 3))) 12.026 * [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 12.028 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 12.028 * [backup-simplify]: Simplify (- 0) into 0 12.028 * [backup-simplify]: Simplify (+ 0 0) into 0 12.030 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log n))))) into 0 12.031 * [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))) 12.050 * [backup-simplify]: Simplify (+ (* (pow n 1/2) (* -1/48 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 3)))) (+ (* (* -1/2 (* (sqrt n) (log n))) (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2)))) (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI))))) (* (* -1/48 (* (sqrt n) (pow (log n) 3))) (pow (* 2 PI) 1/2))))) into (- (+ (* 1/48 (* (* (sqrt 2) (pow (log n) 3)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (log n) (pow (log (* 2 PI)) 2))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (pow (log n) 2) (log (* 2 PI)))) (sqrt (* n PI)))) (* 1/48 (* (* (sqrt 2) (pow (log (* 2 PI)) 3)) (sqrt (* n PI)))))))) 12.074 * [backup-simplify]: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))) +nan.0) (+ (* (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (* 1/4 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))))) +nan.0) (* (- (+ (* 1/48 (* (* (sqrt 2) (pow (log n) 3)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (log n) (pow (log (* 2 PI)) 2))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (pow (log n) 2) (log (* 2 PI)))) (sqrt (* n PI)))) (* 1/48 (* (* (sqrt 2) (pow (log (* 2 PI)) 3)) (sqrt (* n PI)))))))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI))))))))))))))) 12.081 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI))))))))))))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI))))))))))))))) 12.092 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))) (* k 1)) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (pow k 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) k) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log (* 2 PI)) 2) (* (sqrt 2) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (pow (log n) 2) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) k)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log (* 2 PI)) (* (sqrt 2) (* (log n) (pow k 2)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log (* 2 PI)) (* (sqrt 2) (pow k 2))) (sqrt (* n PI))))))))))))))))))))))) 12.093 * [backup-simplify]: Simplify (* (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) (/ (sqrt (pow (* 2 PI) (- 1/2 (/ (/ 1 k) 2)))) (/ (sqrt (/ 1 k)) (sqrt (pow (* 2 PI) (- 1/2 (/ (/ 1 k) 2))))))) into (* (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) 12.093 * [approximate]: Taking taylor expansion of (* (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in (n k) around 0 12.093 * [taylor]: Taking taylor expansion of (* (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k 12.093 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 12.093 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in k 12.093 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in k 12.093 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in k 12.093 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 12.093 * [taylor]: Taking taylor expansion of 1/2 in k 12.093 * [backup-simplify]: Simplify 1/2 into 1/2 12.093 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 12.093 * [taylor]: Taking taylor expansion of 1/2 in k 12.093 * [backup-simplify]: Simplify 1/2 into 1/2 12.093 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.093 * [taylor]: Taking taylor expansion of k in k 12.093 * [backup-simplify]: Simplify 0 into 0 12.093 * [backup-simplify]: Simplify 1 into 1 12.093 * [backup-simplify]: Simplify (/ 1 1) into 1 12.093 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 12.093 * [taylor]: Taking taylor expansion of (* 2 PI) in k 12.093 * [taylor]: Taking taylor expansion of 2 in k 12.093 * [backup-simplify]: Simplify 2 into 2 12.093 * [taylor]: Taking taylor expansion of PI in k 12.093 * [backup-simplify]: Simplify PI into PI 12.094 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.094 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.095 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.095 * [backup-simplify]: Simplify (- 1/2) into -1/2 12.095 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 12.097 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) 12.098 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 12.098 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 12.098 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in k 12.098 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in k 12.098 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 12.098 * [taylor]: Taking taylor expansion of 1/2 in k 12.098 * [backup-simplify]: Simplify 1/2 into 1/2 12.098 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 12.098 * [taylor]: Taking taylor expansion of 1/2 in k 12.098 * [backup-simplify]: Simplify 1/2 into 1/2 12.098 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.099 * [taylor]: Taking taylor expansion of k in k 12.099 * [backup-simplify]: Simplify 0 into 0 12.099 * [backup-simplify]: Simplify 1 into 1 12.099 * [backup-simplify]: Simplify (/ 1 1) into 1 12.099 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k 12.099 * [taylor]: Taking taylor expansion of (/ 1 n) in k 12.099 * [taylor]: Taking taylor expansion of n in k 12.099 * [backup-simplify]: Simplify n into n 12.099 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n) 12.099 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n)) 12.100 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.100 * [backup-simplify]: Simplify (- 1/2) into -1/2 12.100 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 12.100 * [backup-simplify]: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) 12.101 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 12.101 * [taylor]: Taking taylor expansion of (sqrt k) in k 12.101 * [taylor]: Taking taylor expansion of k in k 12.101 * [backup-simplify]: Simplify 0 into 0 12.101 * [backup-simplify]: Simplify 1 into 1 12.101 * [backup-simplify]: Simplify (sqrt 0) into 0 12.103 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.103 * [taylor]: Taking taylor expansion of (* (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in n 12.103 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 12.103 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in n 12.103 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in n 12.103 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in n 12.103 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 12.103 * [taylor]: Taking taylor expansion of 1/2 in n 12.103 * [backup-simplify]: Simplify 1/2 into 1/2 12.103 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.103 * [taylor]: Taking taylor expansion of 1/2 in n 12.103 * [backup-simplify]: Simplify 1/2 into 1/2 12.103 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.103 * [taylor]: Taking taylor expansion of k in n 12.103 * [backup-simplify]: Simplify k into k 12.103 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.103 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 12.103 * [taylor]: Taking taylor expansion of (* 2 PI) in n 12.103 * [taylor]: Taking taylor expansion of 2 in n 12.103 * [backup-simplify]: Simplify 2 into 2 12.103 * [taylor]: Taking taylor expansion of PI in n 12.103 * [backup-simplify]: Simplify PI into PI 12.104 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.105 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.105 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.105 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 12.105 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 12.106 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) into (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) 12.107 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 12.107 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 12.107 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 12.107 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 12.107 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 12.107 * [taylor]: Taking taylor expansion of 1/2 in n 12.107 * [backup-simplify]: Simplify 1/2 into 1/2 12.107 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.107 * [taylor]: Taking taylor expansion of 1/2 in n 12.107 * [backup-simplify]: Simplify 1/2 into 1/2 12.107 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.107 * [taylor]: Taking taylor expansion of k in n 12.108 * [backup-simplify]: Simplify k into k 12.108 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.108 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 12.108 * [taylor]: Taking taylor expansion of (/ 1 n) in n 12.108 * [taylor]: Taking taylor expansion of n in n 12.108 * [backup-simplify]: Simplify 0 into 0 12.108 * [backup-simplify]: Simplify 1 into 1 12.108 * [backup-simplify]: Simplify (/ 1 1) into 1 12.108 * [backup-simplify]: Simplify (log 1) into 0 12.108 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.109 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 12.109 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 12.109 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 12.109 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 12.109 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 12.109 * [taylor]: Taking taylor expansion of (sqrt k) in n 12.109 * [taylor]: Taking taylor expansion of k in n 12.110 * [backup-simplify]: Simplify k into k 12.110 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 12.110 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 12.110 * [taylor]: Taking taylor expansion of (* (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in n 12.110 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 12.110 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in n 12.110 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in n 12.110 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in n 12.110 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 12.110 * [taylor]: Taking taylor expansion of 1/2 in n 12.110 * [backup-simplify]: Simplify 1/2 into 1/2 12.110 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.110 * [taylor]: Taking taylor expansion of 1/2 in n 12.110 * [backup-simplify]: Simplify 1/2 into 1/2 12.110 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.110 * [taylor]: Taking taylor expansion of k in n 12.110 * [backup-simplify]: Simplify k into k 12.110 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.110 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 12.110 * [taylor]: Taking taylor expansion of (* 2 PI) in n 12.110 * [taylor]: Taking taylor expansion of 2 in n 12.110 * [backup-simplify]: Simplify 2 into 2 12.110 * [taylor]: Taking taylor expansion of PI in n 12.110 * [backup-simplify]: Simplify PI into PI 12.111 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.112 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.112 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.112 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 12.112 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 12.113 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) into (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) 12.114 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 12.114 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 12.114 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 12.114 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 12.114 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 12.114 * [taylor]: Taking taylor expansion of 1/2 in n 12.114 * [backup-simplify]: Simplify 1/2 into 1/2 12.114 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.115 * [taylor]: Taking taylor expansion of 1/2 in n 12.115 * [backup-simplify]: Simplify 1/2 into 1/2 12.115 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.115 * [taylor]: Taking taylor expansion of k in n 12.115 * [backup-simplify]: Simplify k into k 12.115 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.115 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 12.115 * [taylor]: Taking taylor expansion of (/ 1 n) in n 12.115 * [taylor]: Taking taylor expansion of n in n 12.115 * [backup-simplify]: Simplify 0 into 0 12.115 * [backup-simplify]: Simplify 1 into 1 12.115 * [backup-simplify]: Simplify (/ 1 1) into 1 12.116 * [backup-simplify]: Simplify (log 1) into 0 12.116 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.116 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 12.116 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 12.116 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 12.116 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 12.117 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 12.117 * [taylor]: Taking taylor expansion of (sqrt k) in n 12.117 * [taylor]: Taking taylor expansion of k in n 12.117 * [backup-simplify]: Simplify k into k 12.117 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 12.117 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 12.118 * [backup-simplify]: Simplify (* (pow (* 2 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 (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) 12.118 * [backup-simplify]: Simplify (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) into (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) 12.118 * [taylor]: Taking taylor expansion of (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k 12.118 * [taylor]: Taking taylor expansion of (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) in k 12.119 * [taylor]: Taking taylor expansion of (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) in k 12.119 * [taylor]: Taking taylor expansion of (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) in k 12.119 * [taylor]: Taking taylor expansion of -1 in k 12.119 * [backup-simplify]: Simplify -1 into -1 12.119 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log n)) in k 12.119 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 12.119 * [taylor]: Taking taylor expansion of 1/2 in k 12.119 * [backup-simplify]: Simplify 1/2 into 1/2 12.119 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 12.119 * [taylor]: Taking taylor expansion of 1/2 in k 12.119 * [backup-simplify]: Simplify 1/2 into 1/2 12.119 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.119 * [taylor]: Taking taylor expansion of k in k 12.119 * [backup-simplify]: Simplify 0 into 0 12.119 * [backup-simplify]: Simplify 1 into 1 12.119 * [backup-simplify]: Simplify (/ 1 1) into 1 12.119 * [taylor]: Taking taylor expansion of (log n) in k 12.119 * [taylor]: Taking taylor expansion of n in k 12.119 * [backup-simplify]: Simplify n into n 12.119 * [backup-simplify]: Simplify (log n) into (log n) 12.120 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.120 * [backup-simplify]: Simplify (- 1/2) into -1/2 12.121 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 12.121 * [backup-simplify]: Simplify (* -1/2 (log n)) into (* -1/2 (log n)) 12.121 * [backup-simplify]: Simplify (* -1 (* -1/2 (log n))) into (* 1/2 (log n)) 12.121 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 12.121 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in k 12.121 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in k 12.121 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in k 12.121 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 12.121 * [taylor]: Taking taylor expansion of 1/2 in k 12.121 * [backup-simplify]: Simplify 1/2 into 1/2 12.121 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 12.121 * [taylor]: Taking taylor expansion of 1/2 in k 12.121 * [backup-simplify]: Simplify 1/2 into 1/2 12.121 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.121 * [taylor]: Taking taylor expansion of k in k 12.121 * [backup-simplify]: Simplify 0 into 0 12.121 * [backup-simplify]: Simplify 1 into 1 12.122 * [backup-simplify]: Simplify (/ 1 1) into 1 12.122 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 12.122 * [taylor]: Taking taylor expansion of (* 2 PI) in k 12.122 * [taylor]: Taking taylor expansion of 2 in k 12.122 * [backup-simplify]: Simplify 2 into 2 12.122 * [taylor]: Taking taylor expansion of PI in k 12.122 * [backup-simplify]: Simplify PI into PI 12.122 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.124 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.124 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.124 * [backup-simplify]: Simplify (- 1/2) into -1/2 12.125 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 12.126 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) 12.128 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 12.128 * [taylor]: Taking taylor expansion of (sqrt k) in k 12.128 * [taylor]: Taking taylor expansion of k in k 12.128 * [backup-simplify]: Simplify 0 into 0 12.128 * [backup-simplify]: Simplify 1 into 1 12.128 * [backup-simplify]: Simplify (sqrt 0) into 0 12.130 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.130 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) 12.131 * [backup-simplify]: Simplify (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 12.131 * [backup-simplify]: Simplify 0 into 0 12.132 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 12.133 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 12.133 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.134 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 12.134 * [backup-simplify]: Simplify (- 0) into 0 12.135 * [backup-simplify]: Simplify (+ 0 0) into 0 12.135 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 12.135 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 12.136 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 12.137 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 12.139 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 12.139 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.139 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 12.140 * [backup-simplify]: Simplify (- 0) into 0 12.140 * [backup-simplify]: Simplify (+ 0 0) into 0 12.141 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (log (* 2 PI)))) into 0 12.143 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) (+ (* (/ (pow 0 1) 1)))) into 0 12.144 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))))) into 0 12.145 * [backup-simplify]: Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (sqrt k))) into 0 12.145 * [taylor]: Taking taylor expansion of 0 in k 12.145 * [backup-simplify]: Simplify 0 into 0 12.145 * [backup-simplify]: Simplify 0 into 0 12.146 * [backup-simplify]: Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (* 0 (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))) into 0 12.147 * [backup-simplify]: Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) 12.148 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) 12.149 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 12.150 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.153 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 12.153 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.154 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 12.154 * [backup-simplify]: Simplify (- 0) into 0 12.154 * [backup-simplify]: Simplify (+ 0 0) into 0 12.155 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 12.155 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 12.157 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.158 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 12.161 * [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 12.162 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.163 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 12.163 * [backup-simplify]: Simplify (- 0) into 0 12.163 * [backup-simplify]: Simplify (+ 0 0) into 0 12.164 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (log (* 2 PI))))) into 0 12.165 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.166 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))))) into 0 12.167 * [backup-simplify]: Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0 12.167 * [taylor]: Taking taylor expansion of 0 in k 12.167 * [backup-simplify]: Simplify 0 into 0 12.167 * [backup-simplify]: Simplify 0 into 0 12.167 * [backup-simplify]: Simplify 0 into 0 12.169 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.169 * [backup-simplify]: Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (+ (* 0 0) (* 0 (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) into 0 12.170 * [backup-simplify]: Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) 12.171 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) 12.171 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 12.172 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.179 * [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 12.180 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.181 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 12.181 * [backup-simplify]: Simplify (- 0) into 0 12.181 * [backup-simplify]: Simplify (+ 0 0) into 0 12.181 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 12.182 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 12.183 * [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 12.184 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.187 * [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 12.188 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.188 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 12.189 * [backup-simplify]: Simplify (- 0) into 0 12.189 * [backup-simplify]: Simplify (+ 0 0) into 0 12.190 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log (* 2 PI)))))) into 0 12.192 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 12.193 * [backup-simplify]: Simplify (+ (* (pow (* 2 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 12.195 * [backup-simplify]: Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0 12.195 * [taylor]: Taking taylor expansion of 0 in k 12.195 * [backup-simplify]: Simplify 0 into 0 12.195 * [backup-simplify]: Simplify 0 into 0 12.195 * [backup-simplify]: Simplify 0 into 0 12.195 * [backup-simplify]: Simplify 0 into 0 12.200 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.202 * [backup-simplify]: Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 12.203 * [backup-simplify]: Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) 12.204 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) 12.208 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) k)) (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (pow k 3)))))))) 12.210 * [backup-simplify]: Simplify (* (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) (/ (sqrt (pow (* 2 PI) (- 1/2 (/ (/ 1 (- k)) 2)))) (/ (sqrt (/ 1 (- k))) (sqrt (pow (* 2 PI) (- 1/2 (/ (/ 1 (- k)) 2))))))) into (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) 12.210 * [approximate]: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in (n k) around 0 12.210 * [taylor]: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k 12.210 * [taylor]: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) in k 12.210 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 12.210 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in k 12.210 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in k 12.210 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 12.210 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 12.210 * [taylor]: Taking taylor expansion of 1/2 in k 12.210 * [backup-simplify]: Simplify 1/2 into 1/2 12.210 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.210 * [taylor]: Taking taylor expansion of k in k 12.210 * [backup-simplify]: Simplify 0 into 0 12.210 * [backup-simplify]: Simplify 1 into 1 12.210 * [backup-simplify]: Simplify (/ 1 1) into 1 12.211 * [taylor]: Taking taylor expansion of 1/2 in k 12.211 * [backup-simplify]: Simplify 1/2 into 1/2 12.211 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k 12.211 * [taylor]: Taking taylor expansion of (/ -1 n) in k 12.211 * [taylor]: Taking taylor expansion of -1 in k 12.211 * [backup-simplify]: Simplify -1 into -1 12.211 * [taylor]: Taking taylor expansion of n in k 12.211 * [backup-simplify]: Simplify n into n 12.211 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n) 12.211 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n)) 12.211 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.212 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 12.212 * [backup-simplify]: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) 12.212 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 12.212 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in k 12.212 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in k 12.212 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in k 12.212 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 12.212 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 12.212 * [taylor]: Taking taylor expansion of 1/2 in k 12.212 * [backup-simplify]: Simplify 1/2 into 1/2 12.212 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.212 * [taylor]: Taking taylor expansion of k in k 12.212 * [backup-simplify]: Simplify 0 into 0 12.212 * [backup-simplify]: Simplify 1 into 1 12.213 * [backup-simplify]: Simplify (/ 1 1) into 1 12.213 * [taylor]: Taking taylor expansion of 1/2 in k 12.213 * [backup-simplify]: Simplify 1/2 into 1/2 12.213 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 12.213 * [taylor]: Taking taylor expansion of (* 2 PI) in k 12.213 * [taylor]: Taking taylor expansion of 2 in k 12.213 * [backup-simplify]: Simplify 2 into 2 12.213 * [taylor]: Taking taylor expansion of PI in k 12.213 * [backup-simplify]: Simplify PI into PI 12.214 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.215 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.215 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.216 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 12.218 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 12.219 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 12.219 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.219 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.219 * [taylor]: Taking taylor expansion of -1 in k 12.219 * [backup-simplify]: Simplify -1 into -1 12.219 * [taylor]: Taking taylor expansion of k in k 12.219 * [backup-simplify]: Simplify 0 into 0 12.219 * [backup-simplify]: Simplify 1 into 1 12.220 * [backup-simplify]: Simplify (/ -1 1) into -1 12.220 * [backup-simplify]: Simplify (sqrt 0) into 0 12.221 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.222 * [backup-simplify]: Simplify (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) 12.223 * [backup-simplify]: Simplify (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)))) 12.223 * [taylor]: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in n 12.223 * [taylor]: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) in n 12.223 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 12.223 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 12.223 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 12.223 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 12.223 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.223 * [taylor]: Taking taylor expansion of 1/2 in n 12.223 * [backup-simplify]: Simplify 1/2 into 1/2 12.223 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.224 * [taylor]: Taking taylor expansion of k in n 12.224 * [backup-simplify]: Simplify k into k 12.224 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.224 * [taylor]: Taking taylor expansion of 1/2 in n 12.224 * [backup-simplify]: Simplify 1/2 into 1/2 12.224 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 12.224 * [taylor]: Taking taylor expansion of (/ -1 n) in n 12.224 * [taylor]: Taking taylor expansion of -1 in n 12.224 * [backup-simplify]: Simplify -1 into -1 12.224 * [taylor]: Taking taylor expansion of n in n 12.224 * [backup-simplify]: Simplify 0 into 0 12.224 * [backup-simplify]: Simplify 1 into 1 12.224 * [backup-simplify]: Simplify (/ -1 1) into -1 12.225 * [backup-simplify]: Simplify (log -1) into (log -1) 12.225 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.225 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 12.226 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 12.226 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 12.227 * [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)))) 12.227 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in n 12.227 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in n 12.227 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in n 12.227 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 12.227 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.227 * [taylor]: Taking taylor expansion of 1/2 in n 12.227 * [backup-simplify]: Simplify 1/2 into 1/2 12.227 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.227 * [taylor]: Taking taylor expansion of k in n 12.227 * [backup-simplify]: Simplify k into k 12.227 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.227 * [taylor]: Taking taylor expansion of 1/2 in n 12.227 * [backup-simplify]: Simplify 1/2 into 1/2 12.227 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 12.227 * [taylor]: Taking taylor expansion of (* 2 PI) in n 12.227 * [taylor]: Taking taylor expansion of 2 in n 12.227 * [backup-simplify]: Simplify 2 into 2 12.228 * [taylor]: Taking taylor expansion of PI in n 12.228 * [backup-simplify]: Simplify PI into PI 12.228 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.229 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.229 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.229 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 12.231 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) 12.232 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 12.232 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 12.232 * [taylor]: Taking taylor expansion of (/ -1 k) in n 12.232 * [taylor]: Taking taylor expansion of -1 in n 12.232 * [backup-simplify]: Simplify -1 into -1 12.232 * [taylor]: Taking taylor expansion of k in n 12.232 * [backup-simplify]: Simplify k into k 12.232 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 12.232 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 12.232 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 12.232 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 12.234 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) 12.235 * [backup-simplify]: Simplify (/ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (sqrt (/ -1 k))) into (/ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (sqrt (/ -1 k))) 12.235 * [taylor]: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in n 12.235 * [taylor]: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) in n 12.235 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 12.235 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 12.235 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 12.235 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 12.235 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.236 * [taylor]: Taking taylor expansion of 1/2 in n 12.236 * [backup-simplify]: Simplify 1/2 into 1/2 12.236 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.236 * [taylor]: Taking taylor expansion of k in n 12.236 * [backup-simplify]: Simplify k into k 12.236 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.236 * [taylor]: Taking taylor expansion of 1/2 in n 12.236 * [backup-simplify]: Simplify 1/2 into 1/2 12.236 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 12.236 * [taylor]: Taking taylor expansion of (/ -1 n) in n 12.236 * [taylor]: Taking taylor expansion of -1 in n 12.236 * [backup-simplify]: Simplify -1 into -1 12.236 * [taylor]: Taking taylor expansion of n in n 12.236 * [backup-simplify]: Simplify 0 into 0 12.236 * [backup-simplify]: Simplify 1 into 1 12.236 * [backup-simplify]: Simplify (/ -1 1) into -1 12.237 * [backup-simplify]: Simplify (log -1) into (log -1) 12.237 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.237 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 12.238 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 12.238 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 12.239 * [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)))) 12.239 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in n 12.239 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in n 12.239 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in n 12.239 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 12.239 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.239 * [taylor]: Taking taylor expansion of 1/2 in n 12.239 * [backup-simplify]: Simplify 1/2 into 1/2 12.239 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.239 * [taylor]: Taking taylor expansion of k in n 12.239 * [backup-simplify]: Simplify k into k 12.240 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.240 * [taylor]: Taking taylor expansion of 1/2 in n 12.240 * [backup-simplify]: Simplify 1/2 into 1/2 12.240 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 12.240 * [taylor]: Taking taylor expansion of (* 2 PI) in n 12.240 * [taylor]: Taking taylor expansion of 2 in n 12.240 * [backup-simplify]: Simplify 2 into 2 12.240 * [taylor]: Taking taylor expansion of PI in n 12.240 * [backup-simplify]: Simplify PI into PI 12.240 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.242 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.242 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.242 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 12.243 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) 12.244 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 12.245 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 12.245 * [taylor]: Taking taylor expansion of (/ -1 k) in n 12.245 * [taylor]: Taking taylor expansion of -1 in n 12.245 * [backup-simplify]: Simplify -1 into -1 12.245 * [taylor]: Taking taylor expansion of k in n 12.245 * [backup-simplify]: Simplify k into k 12.245 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 12.245 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 12.245 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 12.245 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 12.246 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) 12.248 * [backup-simplify]: Simplify (/ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (sqrt (/ -1 k))) into (/ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (sqrt (/ -1 k))) 12.248 * [taylor]: Taking taylor expansion of (/ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (sqrt (/ -1 k))) in k 12.248 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) in k 12.248 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in k 12.249 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in k 12.249 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in k 12.249 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 12.249 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 12.249 * [taylor]: Taking taylor expansion of 1/2 in k 12.249 * [backup-simplify]: Simplify 1/2 into 1/2 12.249 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.249 * [taylor]: Taking taylor expansion of k in k 12.249 * [backup-simplify]: Simplify 0 into 0 12.249 * [backup-simplify]: Simplify 1 into 1 12.249 * [backup-simplify]: Simplify (/ 1 1) into 1 12.249 * [taylor]: Taking taylor expansion of 1/2 in k 12.249 * [backup-simplify]: Simplify 1/2 into 1/2 12.249 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 12.249 * [taylor]: Taking taylor expansion of (* 2 PI) in k 12.249 * [taylor]: Taking taylor expansion of 2 in k 12.250 * [backup-simplify]: Simplify 2 into 2 12.250 * [taylor]: Taking taylor expansion of PI in k 12.250 * [backup-simplify]: Simplify PI into PI 12.250 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.251 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.252 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.252 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 12.254 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 12.256 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 12.256 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) in k 12.256 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) in k 12.256 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 12.256 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 12.256 * [taylor]: Taking taylor expansion of 1/2 in k 12.256 * [backup-simplify]: Simplify 1/2 into 1/2 12.256 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.256 * [taylor]: Taking taylor expansion of k in k 12.256 * [backup-simplify]: Simplify 0 into 0 12.256 * [backup-simplify]: Simplify 1 into 1 12.256 * [backup-simplify]: Simplify (/ 1 1) into 1 12.256 * [taylor]: Taking taylor expansion of 1/2 in k 12.256 * [backup-simplify]: Simplify 1/2 into 1/2 12.256 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k 12.256 * [taylor]: Taking taylor expansion of (log -1) in k 12.256 * [taylor]: Taking taylor expansion of -1 in k 12.257 * [backup-simplify]: Simplify -1 into -1 12.257 * [backup-simplify]: Simplify (log -1) into (log -1) 12.257 * [taylor]: Taking taylor expansion of (log n) in k 12.257 * [taylor]: Taking taylor expansion of n in k 12.257 * [backup-simplify]: Simplify n into n 12.257 * [backup-simplify]: Simplify (log n) into (log n) 12.257 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.258 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 12.258 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.259 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n)) 12.259 * [backup-simplify]: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n))) 12.260 * [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)))) 12.260 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.260 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.260 * [taylor]: Taking taylor expansion of -1 in k 12.260 * [backup-simplify]: Simplify -1 into -1 12.260 * [taylor]: Taking taylor expansion of k in k 12.260 * [backup-simplify]: Simplify 0 into 0 12.260 * [backup-simplify]: Simplify 1 into 1 12.260 * [backup-simplify]: Simplify (/ -1 1) into -1 12.261 * [backup-simplify]: Simplify (sqrt 0) into 0 12.262 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.264 * [backup-simplify]: Simplify (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) into (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) 12.265 * [backup-simplify]: Simplify (/ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) +nan.0) into (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) 12.266 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) into (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) 12.267 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 12.269 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 12.269 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.270 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 12.270 * [backup-simplify]: Simplify (+ 0 0) into 0 12.271 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log (* 2 PI)))) into 0 12.273 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) (+ (* (/ (pow 0 1) 1)))) into 0 12.274 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 12.276 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 12.276 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.276 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 12.277 * [backup-simplify]: Simplify (+ 0 0) into 0 12.278 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 12.278 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -1) (log n)))) into 0 12.279 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 12.280 * [backup-simplify]: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 0) (* 0 (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 12.282 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 12.282 * [taylor]: Taking taylor expansion of 0 in k 12.282 * [backup-simplify]: Simplify 0 into 0 12.282 * [backup-simplify]: Simplify 0 into 0 12.283 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) into 0 12.284 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 12.287 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.288 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))))) 12.289 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))))) into (- (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))))) 12.290 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 12.292 * [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 12.292 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.293 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 12.293 * [backup-simplify]: Simplify (+ 0 0) into 0 12.294 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (log (* 2 PI))))) into 0 12.295 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.296 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.298 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0 12.298 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.298 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 12.299 * [backup-simplify]: Simplify (+ 0 0) into 0 12.300 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 12.300 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0 12.301 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.302 * [backup-simplify]: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 0) (+ (* 0 0) (* 0 (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 12.302 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.303 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 12.304 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 12.304 * [taylor]: Taking taylor expansion of 0 in k 12.304 * [backup-simplify]: Simplify 0 into 0 12.304 * [backup-simplify]: Simplify 0 into 0 12.304 * [backup-simplify]: Simplify 0 into 0 12.305 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))))) into 0 12.305 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.313 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.315 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))))) 12.316 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))))) into (- (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))))) 12.320 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) k)) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (pow k 2))) (- (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))))))))) 12.320 * * * [progress]: simplifying candidates 12.321 * * * * [progress]: [ 1 / 838 ] simplifiying candidate # 12.321 * * * * [progress]: [ 2 / 838 ] simplifiying candidate # 12.321 * * * * [progress]: [ 3 / 838 ] simplifiying candidate # 12.321 * * * * [progress]: [ 4 / 838 ] simplifiying candidate # 12.321 * * * * [progress]: [ 5 / 838 ] simplifiying candidate # 12.321 * * * * [progress]: [ 6 / 838 ] simplifiying candidate # 12.321 * * * * [progress]: [ 7 / 838 ] simplifiying candidate # 12.321 * * * * [progress]: [ 8 / 838 ] simplifiying candidate # 12.321 * * * * [progress]: [ 9 / 838 ] simplifiying candidate # 12.321 * * * * [progress]: [ 10 / 838 ] simplifiying candidate # 12.321 * * * * [progress]: [ 11 / 838 ] simplifiying candidate # 12.321 * * * * [progress]: [ 12 / 838 ] simplifiying candidate # 12.321 * * * * [progress]: [ 13 / 838 ] simplifiying candidate # 12.322 * * * * [progress]: [ 14 / 838 ] simplifiying candidate # 12.322 * * * * [progress]: [ 15 / 838 ] simplifiying candidate # 12.322 * * * * [progress]: [ 16 / 838 ] simplifiying candidate # 12.322 * * * * [progress]: [ 17 / 838 ] simplifiying candidate # 12.322 * * * * [progress]: [ 18 / 838 ] simplifiying candidate # 12.322 * * * * [progress]: [ 19 / 838 ] simplifiying candidate # 12.322 * * * * [progress]: [ 20 / 838 ] simplifiying candidate # 12.322 * * * * [progress]: [ 21 / 838 ] simplifiying candidate # 12.322 * * * * [progress]: [ 22 / 838 ] simplifiying candidate # 12.322 * * * * [progress]: [ 23 / 838 ] simplifiying candidate # 12.322 * * * * [progress]: [ 24 / 838 ] simplifiying candidate #real (real->posit16 (pow n (- 1/2 (/ k 2))))) (/ (sqrt (pow (* 2 PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* 2 PI) (- 1/2 (/ k 2))))))))> 12.322 * * * * [progress]: [ 25 / 838 ] simplifiying candidate # 12.322 * * * * [progress]: [ 26 / 838 ] simplifiying candidate # 12.322 * * * * [progress]: [ 27 / 838 ] simplifiying candidate # 12.323 * * * * [progress]: [ 28 / 838 ] simplifiying candidate # 12.323 * * * * [progress]: [ 29 / 838 ] simplifiying candidate # 12.323 * * * * [progress]: [ 30 / 838 ] simplifiying candidate # 12.323 * * * * [progress]: [ 31 / 838 ] simplifiying candidate # 12.323 * * * * [progress]: [ 32 / 838 ] simplifiying candidate # 12.323 * * * * [progress]: [ 33 / 838 ] simplifiying candidate # 12.323 * * * * [progress]: [ 34 / 838 ] simplifiying candidate # 12.323 * * * * [progress]: [ 35 / 838 ] simplifiying candidate # 12.323 * * * * [progress]: [ 36 / 838 ] simplifiying candidate # 12.323 * * * * [progress]: [ 37 / 838 ] simplifiying candidate # 12.323 * * * * [progress]: [ 38 / 838 ] simplifiying candidate # 12.323 * * * * [progress]: [ 39 / 838 ] simplifiying candidate # 12.323 * * * * [progress]: [ 40 / 838 ] simplifiying candidate # 12.324 * * * * [progress]: [ 41 / 838 ] simplifiying candidate # 12.324 * * * * [progress]: [ 42 / 838 ] simplifiying candidate # 12.324 * * * * [progress]: [ 43 / 838 ] simplifiying candidate # 12.325 * * * * [progress]: [ 44 / 838 ] simplifiying candidate # 12.325 * * * * [progress]: [ 45 / 838 ] simplifiying candidate # 12.325 * * * * [progress]: [ 46 / 838 ] simplifiying candidate # 12.325 * * * * [progress]: [ 47 / 838 ] simplifiying candidate # 12.325 * * * * [progress]: [ 48 / 838 ] simplifiying candidate #real (real->posit16 (pow (* 2 PI) (- 1/2 (/ k 2))))))))))> 12.325 * * * * [progress]: [ 49 / 838 ] simplifiying candidate # 12.325 * * * * [progress]: [ 50 / 838 ] simplifiying candidate # 12.325 * * * * [progress]: [ 51 / 838 ] simplifiying candidate # 12.325 * * * * [progress]: [ 52 / 838 ] simplifiying candidate # 12.325 * * * * [progress]: [ 53 / 838 ] simplifiying candidate # 12.325 * * * * [progress]: [ 54 / 838 ] simplifiying candidate # 12.325 * * * * [progress]: [ 55 / 838 ] simplifiying candidate # 12.325 * * * * [progress]: [ 56 / 838 ] simplifiying candidate # 12.326 * * * * [progress]: [ 57 / 838 ] simplifiying candidate # 12.326 * * * * [progress]: [ 58 / 838 ] simplifiying candidate # 12.326 * * * * [progress]: [ 59 / 838 ] simplifiying candidate # 12.326 * * * * [progress]: [ 60 / 838 ] simplifiying candidate # 12.326 * * * * [progress]: [ 61 / 838 ] simplifiying candidate # 12.326 * * * * [progress]: [ 62 / 838 ] simplifiying candidate # 12.326 * * * * [progress]: [ 63 / 838 ] simplifiying candidate # 12.326 * * * * [progress]: [ 64 / 838 ] simplifiying candidate # 12.326 * * * * [progress]: [ 65 / 838 ] simplifiying candidate # 12.326 * * * * [progress]: [ 66 / 838 ] simplifiying candidate # 12.326 * * * * [progress]: [ 67 / 838 ] simplifiying candidate # 12.326 * * * * [progress]: [ 68 / 838 ] simplifiying candidate # 12.327 * * * * [progress]: [ 69 / 838 ] simplifiying candidate # 12.327 * * * * [progress]: [ 70 / 838 ] simplifiying candidate # 12.327 * * * * [progress]: [ 71 / 838 ] simplifiying candidate # 12.327 * * * * [progress]: [ 72 / 838 ] simplifiying candidate #real (real->posit16 (pow (* 2 PI) (- 1/2 (/ k 2)))))) (/ (sqrt k) (sqrt (pow (* 2 PI) (- 1/2 (/ k 2))))))))> 12.327 * * * * [progress]: [ 73 / 838 ] simplifiying candidate # 12.327 * * * * [progress]: [ 74 / 838 ] simplifiying candidate # 12.327 * * * * [progress]: [ 75 / 838 ] simplifiying candidate # 12.327 * * * * [progress]: [ 76 / 838 ] simplifiying candidate # 12.327 * * * * [progress]: [ 77 / 838 ] simplifiying candidate # 12.327 * * * * [progress]: [ 78 / 838 ] simplifiying candidate # 12.327 * * * * [progress]: [ 79 / 838 ] simplifiying candidate # 12.327 * * * * [progress]: [ 80 / 838 ] simplifiying candidate # 12.327 * * * * [progress]: [ 81 / 838 ] simplifiying candidate # 12.328 * * * * [progress]: [ 82 / 838 ] simplifiying candidate # 12.328 * * * * [progress]: [ 83 / 838 ] simplifiying candidate # 12.328 * * * * [progress]: [ 84 / 838 ] simplifiying candidate # 12.328 * * * * [progress]: [ 85 / 838 ] simplifiying candidate # 12.328 * * * * [progress]: [ 86 / 838 ] simplifiying candidate # 12.328 * * * * [progress]: [ 87 / 838 ] simplifiying candidate # 12.328 * * * * [progress]: [ 88 / 838 ] simplifiying candidate # 12.328 * * * * [progress]: [ 89 / 838 ] simplifiying candidate # 12.328 * * * * [progress]: [ 90 / 838 ] simplifiying candidate # 12.328 * * * * [progress]: [ 91 / 838 ] simplifiying candidate # 12.328 * * * * [progress]: [ 92 / 838 ] simplifiying candidate # 12.328 * * * * [progress]: [ 93 / 838 ] simplifiying candidate # 12.329 * * * * [progress]: [ 94 / 838 ] simplifiying candidate # 12.329 * * * * [progress]: [ 95 / 838 ] simplifiying candidate # 12.329 * * * * [progress]: [ 96 / 838 ] simplifiying candidate # 12.329 * * * * [progress]: [ 97 / 838 ] simplifiying candidate # 12.329 * * * * [progress]: [ 98 / 838 ] simplifiying candidate # 12.329 * * * * [progress]: [ 99 / 838 ] simplifiying candidate # 12.329 * * * * [progress]: [ 100 / 838 ] simplifiying candidate # 12.329 * * * * [progress]: [ 101 / 838 ] simplifiying candidate # 12.329 * * * * [progress]: [ 102 / 838 ] simplifiying candidate # 12.329 * * * * [progress]: [ 103 / 838 ] simplifiying candidate # 12.329 * * * * [progress]: [ 104 / 838 ] simplifiying candidate # 12.330 * * * * [progress]: [ 105 / 838 ] simplifiying candidate # 12.330 * * * * [progress]: [ 106 / 838 ] simplifiying candidate # 12.330 * * * * [progress]: [ 107 / 838 ] simplifiying candidate # 12.330 * * * * [progress]: [ 108 / 838 ] simplifiying candidate # 12.330 * * * * [progress]: [ 109 / 838 ] simplifiying candidate # 12.330 * * * * [progress]: [ 110 / 838 ] simplifiying candidate # 12.330 * * * * [progress]: [ 111 / 838 ] simplifiying candidate # 12.330 * * * * [progress]: [ 112 / 838 ] simplifiying candidate # 12.330 * * * * [progress]: [ 113 / 838 ] simplifiying candidate # 12.330 * * * * [progress]: [ 114 / 838 ] simplifiying candidate # 12.331 * * * * [progress]: [ 115 / 838 ] simplifiying candidate # 12.331 * * * * [progress]: [ 116 / 838 ] simplifiying candidate # 12.331 * * * * [progress]: [ 117 / 838 ] simplifiying candidate # 12.331 * * * * [progress]: [ 118 / 838 ] simplifiying candidate # 12.331 * * * * [progress]: [ 119 / 838 ] simplifiying candidate # 12.331 * * * * [progress]: [ 120 / 838 ] simplifiying candidate # 12.331 * * * * [progress]: [ 121 / 838 ] simplifiying candidate # 12.331 * * * * [progress]: [ 122 / 838 ] simplifiying candidate # 12.331 * * * * [progress]: [ 123 / 838 ] simplifiying candidate # 12.331 * * * * [progress]: [ 124 / 838 ] simplifiying candidate # 12.331 * * * * [progress]: [ 125 / 838 ] simplifiying candidate # 12.332 * * * * [progress]: [ 126 / 838 ] simplifiying candidate # 12.332 * * * * [progress]: [ 127 / 838 ] simplifiying candidate 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#12: cost 31 inf + 928548 16.095 * * [simplify]: Extracting #13: cost 19 inf + 936114 16.255 * * [simplify]: Extracting #14: cost 14 inf + 942959 16.422 * * [simplify]: Extracting #15: cost 6 inf + 955879 16.565 * * [simplify]: Extracting #16: cost 1 inf + 965684 16.703 * * [simplify]: Extracting #17: cost 0 inf + 967309 16.888 * * [simplify]: Extracting #18: cost 0 inf + 967189 17.081 * [simplify]: Simplified to: (* (- 1/2 (/ k 2)) (log n)) (* (- 1/2 (/ k 2)) (log n)) (- 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 (sqrt n) (pow n (- (/ k 2))) (sqrt n) (pow n (- (/ k 2))) (pow (* (cbrt n) (cbrt n)) (- 1/2 (/ k 2))) (pow (cbrt n) (- 1/2 (/ k 2))) (pow (sqrt n) (- 1/2 (/ k 2))) (pow (sqrt n) (- 1/2 (/ k 2))) 1 (pow n (- 1/2 (/ k 2))) (* (- 1/2 (/ k 2)) (log n)) (exp (pow n (- 1/2 (/ k 2)))) (* (cbrt (pow n (- 1/2 (/ k 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2)))))) (/ (* (pow n (- 1/2 (/ k 2))) (sqrt (sqrt (pow (* 2 PI) (- 1/2 (/ k 2)))))) (/ 1 (sqrt (sqrt (pow (* 2 PI) (- 1/2 (/ k 2))))))) (* (pow n (- 1/2 (/ k 2))) (sqrt (sqrt (pow (* 2 PI) (- 1/2 (/ k 2)))))) (* (pow n (- 1/2 (/ k 2))) (sqrt (sqrt (pow (* 2 PI) (- 1/2 (/ k 2)))))) (* (/ (sqrt (sqrt (pow (* 2 PI) (- 1/2 (/ k 2))))) (sqrt k)) (pow n (- 1/2 (/ k 2)))) (* (pow n (- 1/2 (/ k 2))) (/ (sqrt (sqrt (pow (* 2 PI) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (sqrt (* 2 PI)))))) (* (pow n (- 1/2 (/ k 2))) (/ (/ 1 (cbrt (/ (sqrt k) (sqrt (pow (* 2 PI) (- 1/2 (/ k 2))))))) (cbrt (/ (sqrt k) (sqrt (pow (* 2 PI) (- 1/2 (/ k 2)))))))) (/ (* (pow n (- 1/2 (/ k 2))) 1) (sqrt (/ (sqrt k) (sqrt (pow (* 2 PI) (- 1/2 (/ k 2))))))) (/ (* (pow n (- 1/2 (/ k 2))) 1) (* (/ (cbrt (sqrt k)) (cbrt (sqrt (pow (* 2 PI) (- 1/2 (/ k 2)))))) (/ (cbrt (sqrt k)) (cbrt (sqrt (pow (* 2 PI) (- 1/2 (/ k 2)))))))) (/ (* (pow n (- 1/2 (/ k 2))) 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt (* 2 PI))))) (/ (* 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PI) (* (sqrt 2) (* k (log (* 2 PI))))) 1/2)) (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k))) (- (- (* +nan.0 (* (sqrt (* PI n)) (* (* k k) (sqrt 2)))) (- (* +nan.0 (* (* k (sqrt 2)) (sqrt (* PI n)))) (- (* (* (* (* (* (log (* 2 PI)) (log (* 2 PI))) (sqrt 2)) (* k k)) (sqrt (* PI n))) +nan.0) (- (* (* (sqrt 2) (* (* (* k k) (* (log n) (log n))) (sqrt (* PI n)))) +nan.0) (- (* (* +nan.0 (* (* k (log n)) (sqrt 2))) (sqrt (* PI n))) (- (* (* +nan.0 (* (* (sqrt 2) (log n)) (* k k))) (sqrt (* PI n))) (- (* (* +nan.0 (* (log (* 2 PI)) (* (* (sqrt 2) (log n)) (* k k)))) (sqrt (* PI n))) (- (* (* +nan.0 (sqrt 2)) (sqrt (* PI n))) (- (* +nan.0 (* (sqrt (* PI n)) (* (sqrt 2) (* k (log (* 2 PI)))))) (* +nan.0 (* (log (* 2 PI)) (* (sqrt (* PI n)) (* (* k k) (sqrt 2))))))))))))))) (- (- (* (/ (* (exp (- (* (- (log n)) (- 1/2 (* 1/2 k))))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) k) +nan.0) (- (* (/ (* (exp (- (* (- (log n)) (- 1/2 (* 1/2 k))))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (* k k)) +nan.0) (/ (* +nan.0 (* (exp (- (* (- (log n)) (- 1/2 (* 1/2 k))))) (pow (* 2 PI) (- 1/2 (* 1/2 k))))) (* k (* k k)))))) (- (- (* +nan.0 (/ (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (exp (* (- (log -1) (log (/ -1 n))) (- 1/2 (* 1/2 k))))) k)) (- (* +nan.0 (/ (exp (* (- (log -1) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (/ (* k k) (pow (* 2 PI) (- 1/2 (* 1/2 k)))))) (* +nan.0 (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (exp (* (- (log -1) (log (/ -1 n))) (- 1/2 (* 1/2 k))))))))) 17.200 * * * [progress]: adding candidates to table 32.544 * * [progress]: iteration 4 / 4 32.544 * * * [progress]: picking best candidate 32.572 * * * * [pick]: Picked # 32.572 * * * [progress]: localizing error 32.637 * * * [progress]: generating rewritten candidates 32.637 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1 2) 32.650 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 2 1) 32.660 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1) 32.671 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 32.810 * * * [progress]: generating series expansions 32.810 * * * * [progress]: [ 1 / 4 ] generating series at (2 1 2) 32.810 * [backup-simplify]: Simplify (pow n (- 1/2 (/ k 2))) into (pow n (- 1/2 (* 1/2 k))) 32.810 * [approximate]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in (n k) around 0 32.811 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 32.811 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 32.811 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 32.811 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 32.811 * [taylor]: Taking taylor expansion of 1/2 in k 32.811 * [backup-simplify]: Simplify 1/2 into 1/2 32.811 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 32.811 * [taylor]: Taking taylor expansion of 1/2 in k 32.811 * [backup-simplify]: Simplify 1/2 into 1/2 32.811 * [taylor]: Taking taylor expansion of k in k 32.811 * [backup-simplify]: Simplify 0 into 0 32.811 * [backup-simplify]: Simplify 1 into 1 32.811 * [taylor]: Taking taylor expansion of (log n) in k 32.811 * [taylor]: Taking taylor expansion of n in k 32.811 * [backup-simplify]: Simplify n into n 32.811 * [backup-simplify]: Simplify (log n) into (log n) 32.811 * [backup-simplify]: Simplify (* 1/2 0) into 0 32.812 * [backup-simplify]: Simplify (- 0) into 0 32.812 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 32.812 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 32.812 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 32.812 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 32.812 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 32.812 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 32.812 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 32.812 * [taylor]: Taking taylor expansion of 1/2 in n 32.812 * [backup-simplify]: Simplify 1/2 into 1/2 32.812 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 32.812 * [taylor]: Taking taylor expansion of 1/2 in n 32.812 * [backup-simplify]: Simplify 1/2 into 1/2 32.812 * [taylor]: Taking taylor expansion of k in n 32.812 * [backup-simplify]: Simplify k into k 32.812 * [taylor]: Taking taylor expansion of (log n) in n 32.812 * [taylor]: Taking taylor expansion of n in n 32.812 * [backup-simplify]: Simplify 0 into 0 32.812 * [backup-simplify]: Simplify 1 into 1 32.813 * [backup-simplify]: Simplify (log 1) into 0 32.813 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 32.813 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 32.813 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 32.813 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 32.813 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 32.813 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 32.813 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 32.813 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 32.813 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 32.813 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 32.813 * [taylor]: Taking taylor expansion of 1/2 in n 32.813 * [backup-simplify]: Simplify 1/2 into 1/2 32.813 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 32.813 * [taylor]: Taking taylor expansion of 1/2 in n 32.814 * [backup-simplify]: Simplify 1/2 into 1/2 32.814 * [taylor]: Taking taylor expansion of k in n 32.814 * [backup-simplify]: Simplify k into k 32.814 * [taylor]: Taking taylor expansion of (log n) in n 32.814 * [taylor]: Taking taylor expansion of n in n 32.814 * [backup-simplify]: Simplify 0 into 0 32.814 * [backup-simplify]: Simplify 1 into 1 32.814 * [backup-simplify]: Simplify (log 1) into 0 32.814 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 32.814 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 32.814 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 32.814 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 32.814 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 32.814 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 32.815 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 32.815 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 32.815 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 32.815 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 32.815 * [taylor]: Taking taylor expansion of 1/2 in k 32.815 * [backup-simplify]: Simplify 1/2 into 1/2 32.815 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 32.815 * [taylor]: Taking taylor expansion of 1/2 in k 32.815 * [backup-simplify]: Simplify 1/2 into 1/2 32.815 * [taylor]: Taking taylor expansion of k in k 32.815 * [backup-simplify]: Simplify 0 into 0 32.815 * [backup-simplify]: Simplify 1 into 1 32.815 * [taylor]: Taking taylor expansion of (log n) in k 32.815 * [taylor]: Taking taylor expansion of n in k 32.815 * [backup-simplify]: Simplify n into n 32.815 * [backup-simplify]: Simplify (log n) into (log n) 32.815 * [backup-simplify]: Simplify (* 1/2 0) into 0 32.815 * [backup-simplify]: Simplify (- 0) into 0 32.816 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 32.816 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 32.816 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 32.816 * [backup-simplify]: Simplify (pow n 1/2) into (pow n 1/2) 32.817 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 32.817 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 32.817 * [backup-simplify]: Simplify (- 0) into 0 32.817 * [backup-simplify]: Simplify (+ 0 0) into 0 32.818 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 32.818 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log n))) into 0 32.818 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 32.818 * [taylor]: Taking taylor expansion of 0 in k 32.818 * [backup-simplify]: Simplify 0 into 0 32.818 * [backup-simplify]: Simplify 0 into 0 32.819 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 32.819 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 32.819 * [backup-simplify]: Simplify (- 1/2) into -1/2 32.820 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 32.820 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log n))) into (- (* 1/2 (log n))) 32.820 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n))) 32.820 * [backup-simplify]: Simplify (* -1/2 (* (sqrt n) (log n))) into (* -1/2 (* (sqrt n) (log n))) 32.822 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 32.822 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 32.823 * [backup-simplify]: Simplify (- 0) into 0 32.823 * [backup-simplify]: Simplify (+ 0 0) into 0 32.823 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 32.824 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0 32.824 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 32.824 * [taylor]: Taking taylor expansion of 0 in k 32.824 * [backup-simplify]: Simplify 0 into 0 32.824 * [backup-simplify]: Simplify 0 into 0 32.824 * [backup-simplify]: Simplify 0 into 0 32.825 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 32.826 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 32.826 * [backup-simplify]: Simplify (- 0) into 0 32.827 * [backup-simplify]: Simplify (+ 0 0) into 0 32.827 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log n)))) into 0 32.828 * [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))) 32.828 * [backup-simplify]: Simplify (* 1/8 (* (sqrt n) (pow (log n) 2))) into (* 1/8 (* (sqrt n) (pow (log n) 2))) 32.828 * [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)))) 32.828 * [backup-simplify]: Simplify (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 32.828 * [approximate]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 32.828 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 32.828 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in k 32.828 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in k 32.828 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 32.828 * [taylor]: Taking taylor expansion of 1/2 in k 32.828 * [backup-simplify]: Simplify 1/2 into 1/2 32.828 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 32.828 * [taylor]: Taking taylor expansion of 1/2 in k 32.828 * [backup-simplify]: Simplify 1/2 into 1/2 32.828 * [taylor]: Taking taylor expansion of (/ 1 k) in k 32.828 * [taylor]: Taking taylor expansion of k in k 32.829 * [backup-simplify]: Simplify 0 into 0 32.829 * [backup-simplify]: Simplify 1 into 1 32.829 * [backup-simplify]: Simplify (/ 1 1) into 1 32.829 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k 32.829 * [taylor]: Taking taylor expansion of (/ 1 n) in k 32.829 * [taylor]: Taking taylor expansion of n in k 32.829 * [backup-simplify]: Simplify n into n 32.829 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n) 32.829 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n)) 32.829 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 32.829 * [backup-simplify]: Simplify (- 1/2) into -1/2 32.830 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 32.830 * [backup-simplify]: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) 32.830 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 32.830 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 32.830 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 32.830 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 32.830 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 32.830 * [taylor]: Taking taylor expansion of 1/2 in n 32.830 * [backup-simplify]: Simplify 1/2 into 1/2 32.830 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 32.830 * [taylor]: Taking taylor expansion of 1/2 in n 32.830 * [backup-simplify]: Simplify 1/2 into 1/2 32.830 * [taylor]: Taking taylor expansion of (/ 1 k) in n 32.830 * [taylor]: Taking taylor expansion of k in n 32.830 * [backup-simplify]: Simplify k into k 32.830 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 32.830 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 32.830 * [taylor]: Taking taylor expansion of (/ 1 n) in n 32.830 * [taylor]: Taking taylor expansion of n in n 32.830 * [backup-simplify]: Simplify 0 into 0 32.830 * [backup-simplify]: Simplify 1 into 1 32.830 * [backup-simplify]: Simplify (/ 1 1) into 1 32.831 * [backup-simplify]: Simplify (log 1) into 0 32.831 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 32.831 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 32.831 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 32.831 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 32.831 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 32.831 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 32.831 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 32.831 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 32.831 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 32.831 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 32.831 * [taylor]: Taking taylor expansion of 1/2 in n 32.831 * [backup-simplify]: Simplify 1/2 into 1/2 32.831 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 32.832 * [taylor]: Taking taylor expansion of 1/2 in n 32.832 * [backup-simplify]: Simplify 1/2 into 1/2 32.832 * [taylor]: Taking taylor expansion of (/ 1 k) in n 32.832 * [taylor]: Taking taylor expansion of k in n 32.832 * [backup-simplify]: Simplify k into k 32.832 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 32.832 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 32.832 * [taylor]: Taking taylor expansion of (/ 1 n) in n 32.832 * [taylor]: Taking taylor expansion of n in n 32.832 * [backup-simplify]: Simplify 0 into 0 32.832 * [backup-simplify]: Simplify 1 into 1 32.832 * [backup-simplify]: Simplify (/ 1 1) into 1 32.832 * [backup-simplify]: Simplify (log 1) into 0 32.832 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 32.832 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 32.832 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 32.833 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 32.833 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 32.833 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 32.833 * [taylor]: Taking taylor expansion of (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) in k 32.833 * [taylor]: Taking taylor expansion of (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) in k 32.833 * [taylor]: Taking taylor expansion of -1 in k 32.833 * [backup-simplify]: Simplify -1 into -1 32.833 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log n)) in k 32.833 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 32.833 * [taylor]: Taking taylor expansion of 1/2 in k 32.833 * [backup-simplify]: Simplify 1/2 into 1/2 32.833 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 32.833 * [taylor]: Taking taylor expansion of 1/2 in k 32.833 * [backup-simplify]: Simplify 1/2 into 1/2 32.833 * [taylor]: Taking taylor expansion of (/ 1 k) in k 32.833 * [taylor]: Taking taylor expansion of k in k 32.833 * [backup-simplify]: Simplify 0 into 0 32.833 * [backup-simplify]: Simplify 1 into 1 32.833 * [backup-simplify]: Simplify (/ 1 1) into 1 32.833 * [taylor]: Taking taylor expansion of (log n) in k 32.833 * [taylor]: Taking taylor expansion of n in k 32.833 * [backup-simplify]: Simplify n into n 32.833 * [backup-simplify]: Simplify (log n) into (log n) 32.834 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 32.834 * [backup-simplify]: Simplify (- 1/2) into -1/2 32.834 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 32.834 * [backup-simplify]: Simplify (* -1/2 (log n)) into (* -1/2 (log n)) 32.834 * [backup-simplify]: Simplify (* -1 (* -1/2 (log n))) into (* 1/2 (log n)) 32.834 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 32.835 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 32.835 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 32.837 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 32.837 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 32.837 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 32.838 * [backup-simplify]: Simplify (- 0) into 0 32.838 * [backup-simplify]: Simplify (+ 0 0) into 0 32.838 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 32.838 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 32.839 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 32.839 * [taylor]: Taking taylor expansion of 0 in k 32.839 * [backup-simplify]: Simplify 0 into 0 32.839 * [backup-simplify]: Simplify 0 into 0 32.840 * [backup-simplify]: Simplify 0 into 0 32.840 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 32.843 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 32.843 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 32.844 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 32.845 * [backup-simplify]: Simplify (- 0) into 0 32.845 * [backup-simplify]: Simplify (+ 0 0) into 0 32.845 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 32.846 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 32.847 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 32.847 * [taylor]: Taking taylor expansion of 0 in k 32.847 * [backup-simplify]: Simplify 0 into 0 32.847 * [backup-simplify]: Simplify 0 into 0 32.848 * [backup-simplify]: Simplify 0 into 0 32.848 * [backup-simplify]: Simplify 0 into 0 32.849 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 32.854 * [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 32.854 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 32.855 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 32.856 * [backup-simplify]: Simplify (- 0) into 0 32.856 * [backup-simplify]: Simplify (+ 0 0) into 0 32.857 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 32.857 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 32.859 * [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 32.859 * [taylor]: Taking taylor expansion of 0 in k 32.859 * [backup-simplify]: Simplify 0 into 0 32.859 * [backup-simplify]: Simplify 0 into 0 32.859 * [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))))) 32.860 * [backup-simplify]: Simplify (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 32.860 * [approximate]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 32.860 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 32.860 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in k 32.860 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in k 32.860 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 32.860 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 32.860 * [taylor]: Taking taylor expansion of 1/2 in k 32.860 * [backup-simplify]: Simplify 1/2 into 1/2 32.860 * [taylor]: Taking taylor expansion of (/ 1 k) in k 32.860 * [taylor]: Taking taylor expansion of k in k 32.860 * [backup-simplify]: Simplify 0 into 0 32.860 * [backup-simplify]: Simplify 1 into 1 32.860 * [backup-simplify]: Simplify (/ 1 1) into 1 32.860 * [taylor]: Taking taylor expansion of 1/2 in k 32.860 * [backup-simplify]: Simplify 1/2 into 1/2 32.861 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k 32.861 * [taylor]: Taking taylor expansion of (/ -1 n) in k 32.861 * [taylor]: Taking taylor expansion of -1 in k 32.861 * [backup-simplify]: Simplify -1 into -1 32.861 * [taylor]: Taking taylor expansion of n in k 32.861 * [backup-simplify]: Simplify n into n 32.861 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n) 32.861 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n)) 32.861 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 32.862 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 32.862 * [backup-simplify]: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) 32.862 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 32.862 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 32.862 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 32.862 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 32.862 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 32.862 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 32.862 * [taylor]: Taking taylor expansion of 1/2 in n 32.862 * [backup-simplify]: Simplify 1/2 into 1/2 32.862 * [taylor]: Taking taylor expansion of (/ 1 k) in n 32.862 * [taylor]: Taking taylor expansion of k in n 32.862 * [backup-simplify]: Simplify k into k 32.862 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 32.862 * [taylor]: Taking taylor expansion of 1/2 in n 32.862 * [backup-simplify]: Simplify 1/2 into 1/2 32.862 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 32.862 * [taylor]: Taking taylor expansion of (/ -1 n) in n 32.862 * [taylor]: Taking taylor expansion of -1 in n 32.862 * [backup-simplify]: Simplify -1 into -1 32.862 * [taylor]: Taking taylor expansion of n in n 32.862 * [backup-simplify]: Simplify 0 into 0 32.862 * [backup-simplify]: Simplify 1 into 1 32.863 * [backup-simplify]: Simplify (/ -1 1) into -1 32.863 * [backup-simplify]: Simplify (log -1) into (log -1) 32.863 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 32.863 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 32.864 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 32.865 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 32.865 * [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)))) 32.866 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 32.866 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 32.866 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 32.866 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 32.866 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 32.866 * [taylor]: Taking taylor expansion of 1/2 in n 32.866 * [backup-simplify]: Simplify 1/2 into 1/2 32.866 * [taylor]: Taking taylor expansion of (/ 1 k) in n 32.866 * [taylor]: Taking taylor expansion of k in n 32.866 * [backup-simplify]: Simplify k into k 32.866 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 32.866 * [taylor]: Taking taylor expansion of 1/2 in n 32.866 * [backup-simplify]: Simplify 1/2 into 1/2 32.866 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 32.866 * [taylor]: Taking taylor expansion of (/ -1 n) in n 32.866 * [taylor]: Taking taylor expansion of -1 in n 32.866 * [backup-simplify]: Simplify -1 into -1 32.866 * [taylor]: Taking taylor expansion of n in n 32.866 * [backup-simplify]: Simplify 0 into 0 32.866 * [backup-simplify]: Simplify 1 into 1 32.866 * [backup-simplify]: Simplify (/ -1 1) into -1 32.867 * [backup-simplify]: Simplify (log -1) into (log -1) 32.867 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 32.867 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 32.868 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 32.868 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 32.869 * [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)))) 32.869 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) in k 32.869 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) in k 32.869 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 32.869 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 32.869 * [taylor]: Taking taylor expansion of 1/2 in k 32.869 * [backup-simplify]: Simplify 1/2 into 1/2 32.869 * [taylor]: Taking taylor expansion of (/ 1 k) in k 32.869 * [taylor]: Taking taylor expansion of k in k 32.869 * [backup-simplify]: Simplify 0 into 0 32.869 * [backup-simplify]: Simplify 1 into 1 32.869 * [backup-simplify]: Simplify (/ 1 1) into 1 32.869 * [taylor]: Taking taylor expansion of 1/2 in k 32.870 * [backup-simplify]: Simplify 1/2 into 1/2 32.870 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k 32.870 * [taylor]: Taking taylor expansion of (log -1) in k 32.870 * [taylor]: Taking taylor expansion of -1 in k 32.870 * [backup-simplify]: Simplify -1 into -1 32.870 * [backup-simplify]: Simplify (log -1) into (log -1) 32.870 * [taylor]: Taking taylor expansion of (log n) in k 32.870 * [taylor]: Taking taylor expansion of n in k 32.870 * [backup-simplify]: Simplify n into n 32.870 * [backup-simplify]: Simplify (log n) into (log n) 32.871 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 32.871 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 32.871 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 32.871 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n)) 32.872 * [backup-simplify]: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n))) 32.872 * [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)))) 32.873 * [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)))) 32.874 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 32.875 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 32.875 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 32.876 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 32.876 * [backup-simplify]: Simplify (+ 0 0) into 0 32.877 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 32.877 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -1) (log n)))) into 0 32.879 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 32.879 * [taylor]: Taking taylor expansion of 0 in k 32.879 * [backup-simplify]: Simplify 0 into 0 32.879 * [backup-simplify]: Simplify 0 into 0 32.879 * [backup-simplify]: Simplify 0 into 0 32.880 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 32.883 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0 32.883 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 32.884 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 32.884 * [backup-simplify]: Simplify (+ 0 0) into 0 32.885 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 32.886 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0 32.888 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 32.888 * [taylor]: Taking taylor expansion of 0 in k 32.888 * [backup-simplify]: Simplify 0 into 0 32.888 * [backup-simplify]: Simplify 0 into 0 32.888 * [backup-simplify]: Simplify 0 into 0 32.888 * [backup-simplify]: Simplify 0 into 0 32.889 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 32.895 * [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 32.895 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 32.896 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 32.897 * [backup-simplify]: Simplify (+ 0 0) into 0 32.898 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 32.899 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -1) (log n)))))) into 0 32.901 * [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 32.902 * [taylor]: Taking taylor expansion of 0 in k 32.902 * [backup-simplify]: Simplify 0 into 0 32.902 * [backup-simplify]: Simplify 0 into 0 32.902 * [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))))) 32.902 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 2 1) 32.903 * [backup-simplify]: Simplify (pow (* 2 PI) (- 1/2 (/ k 2))) into (pow (* 2 PI) (- 1/2 (* 1/2 k))) 32.903 * [approximate]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in (k) around 0 32.903 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in k 32.903 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) in k 32.903 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) in k 32.903 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 32.903 * [taylor]: Taking taylor expansion of 1/2 in k 32.903 * [backup-simplify]: Simplify 1/2 into 1/2 32.903 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 32.903 * [taylor]: Taking taylor expansion of 1/2 in k 32.903 * [backup-simplify]: Simplify 1/2 into 1/2 32.903 * [taylor]: Taking taylor expansion of k in k 32.903 * [backup-simplify]: Simplify 0 into 0 32.903 * [backup-simplify]: Simplify 1 into 1 32.903 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 32.903 * [taylor]: Taking taylor expansion of (* 2 PI) in k 32.903 * [taylor]: Taking taylor expansion of 2 in k 32.903 * [backup-simplify]: Simplify 2 into 2 32.903 * [taylor]: Taking taylor expansion of PI in k 32.903 * [backup-simplify]: Simplify PI into PI 32.904 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 32.904 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 32.905 * [backup-simplify]: Simplify (* 1/2 0) into 0 32.905 * [backup-simplify]: Simplify (- 0) into 0 32.905 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 32.906 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 32.908 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) 32.908 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in k 32.908 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) in k 32.908 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) in k 32.908 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 32.908 * [taylor]: Taking taylor expansion of 1/2 in k 32.908 * [backup-simplify]: Simplify 1/2 into 1/2 32.908 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 32.908 * [taylor]: Taking taylor expansion of 1/2 in k 32.908 * [backup-simplify]: Simplify 1/2 into 1/2 32.908 * [taylor]: Taking taylor expansion of k in k 32.908 * [backup-simplify]: Simplify 0 into 0 32.908 * [backup-simplify]: Simplify 1 into 1 32.908 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 32.908 * [taylor]: Taking taylor expansion of (* 2 PI) in k 32.908 * [taylor]: Taking taylor expansion of 2 in k 32.908 * [backup-simplify]: Simplify 2 into 2 32.908 * [taylor]: Taking taylor expansion of PI in k 32.908 * [backup-simplify]: Simplify PI into PI 32.908 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 32.909 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 32.909 * [backup-simplify]: Simplify (* 1/2 0) into 0 32.910 * [backup-simplify]: Simplify (- 0) into 0 32.910 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 32.911 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 32.913 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) 32.913 * [backup-simplify]: Simplify (pow (* 2 PI) 1/2) into (pow (* 2 PI) 1/2) 32.914 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 32.915 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 32.916 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 32.916 * [backup-simplify]: Simplify (- 1/2) into -1/2 32.916 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 32.918 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 PI)))) into (- (* 1/2 (log (* 2 PI)))) 32.931 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) 32.934 * [backup-simplify]: Simplify (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) into (* -1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) 32.935 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 32.937 * [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 32.937 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 32.938 * [backup-simplify]: Simplify (- 0) into 0 32.938 * [backup-simplify]: Simplify (+ 0 0) into 0 32.939 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 PI))))) into 0 32.947 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) 32.950 * [backup-simplify]: Simplify (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) into (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI))) 32.958 * [backup-simplify]: Simplify (+ (* (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) k) (pow (* 2 PI) 1/2))) into (- (+ (* 1/8 (* (* (sqrt 2) (* (pow k 2) (pow (log (* 2 PI)) 2))) (sqrt PI))) (pow (* 2 PI) 1/2)) (* 1/2 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt PI)))) 32.959 * [backup-simplify]: Simplify (pow (* 2 PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 32.959 * [approximate]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in (k) around 0 32.959 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in k 32.959 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in k 32.959 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in k 32.959 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 32.959 * [taylor]: Taking taylor expansion of 1/2 in k 32.959 * [backup-simplify]: Simplify 1/2 into 1/2 32.959 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 32.959 * [taylor]: Taking taylor expansion of 1/2 in k 32.959 * [backup-simplify]: Simplify 1/2 into 1/2 32.959 * [taylor]: Taking taylor expansion of (/ 1 k) in k 32.959 * [taylor]: Taking taylor expansion of k in k 32.959 * [backup-simplify]: Simplify 0 into 0 32.959 * [backup-simplify]: Simplify 1 into 1 32.959 * [backup-simplify]: Simplify (/ 1 1) into 1 32.959 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 32.959 * [taylor]: Taking taylor expansion of (* 2 PI) in k 32.959 * [taylor]: Taking taylor expansion of 2 in k 32.960 * [backup-simplify]: Simplify 2 into 2 32.960 * [taylor]: Taking taylor expansion of PI in k 32.960 * [backup-simplify]: Simplify PI into PI 32.960 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 32.960 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 32.961 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 32.961 * [backup-simplify]: Simplify (- 1/2) into -1/2 32.961 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 32.962 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) 32.963 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 32.963 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in k 32.963 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in k 32.963 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in k 32.963 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 32.963 * [taylor]: Taking taylor expansion of 1/2 in k 32.963 * [backup-simplify]: Simplify 1/2 into 1/2 32.963 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 32.963 * [taylor]: Taking taylor expansion of 1/2 in k 32.963 * [backup-simplify]: Simplify 1/2 into 1/2 32.963 * [taylor]: Taking taylor expansion of (/ 1 k) in k 32.963 * [taylor]: Taking taylor expansion of k in k 32.963 * [backup-simplify]: Simplify 0 into 0 32.963 * [backup-simplify]: Simplify 1 into 1 32.964 * [backup-simplify]: Simplify (/ 1 1) into 1 32.964 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 32.964 * [taylor]: Taking taylor expansion of (* 2 PI) in k 32.964 * [taylor]: Taking taylor expansion of 2 in k 32.964 * [backup-simplify]: Simplify 2 into 2 32.964 * [taylor]: Taking taylor expansion of PI in k 32.964 * [backup-simplify]: Simplify PI into PI 32.964 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 32.965 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 32.965 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 32.965 * [backup-simplify]: Simplify (- 1/2) into -1/2 32.966 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 32.967 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) 32.967 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 32.968 * [backup-simplify]: Simplify (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 32.968 * [backup-simplify]: Simplify 0 into 0 32.968 * [backup-simplify]: Simplify 0 into 0 32.968 * [backup-simplify]: Simplify 0 into 0 32.968 * [backup-simplify]: Simplify 0 into 0 32.968 * [backup-simplify]: Simplify 0 into 0 32.968 * [backup-simplify]: Simplify 0 into 0 32.968 * [backup-simplify]: Simplify (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) into (pow (* 2 PI) (- 1/2 (* 1/2 k))) 32.969 * [backup-simplify]: Simplify (pow (* 2 PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 32.969 * [approximate]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in (k) around 0 32.969 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in k 32.969 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in k 32.969 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in k 32.969 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 32.969 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 32.969 * [taylor]: Taking taylor expansion of 1/2 in k 32.969 * [backup-simplify]: Simplify 1/2 into 1/2 32.969 * [taylor]: Taking taylor expansion of (/ 1 k) in k 32.969 * [taylor]: Taking taylor expansion of k in k 32.969 * [backup-simplify]: Simplify 0 into 0 32.969 * [backup-simplify]: Simplify 1 into 1 32.969 * [backup-simplify]: Simplify (/ 1 1) into 1 32.969 * [taylor]: Taking taylor expansion of 1/2 in k 32.969 * [backup-simplify]: Simplify 1/2 into 1/2 32.969 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 32.969 * [taylor]: Taking taylor expansion of (* 2 PI) in k 32.969 * [taylor]: Taking taylor expansion of 2 in k 32.969 * [backup-simplify]: Simplify 2 into 2 32.969 * [taylor]: Taking taylor expansion of PI in k 32.969 * [backup-simplify]: Simplify PI into PI 32.970 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 32.970 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 32.971 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 32.971 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 32.972 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 32.973 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 32.973 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in k 32.973 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in k 32.973 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in k 32.973 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 32.973 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 32.973 * [taylor]: Taking taylor expansion of 1/2 in k 32.973 * [backup-simplify]: Simplify 1/2 into 1/2 32.973 * [taylor]: Taking taylor expansion of (/ 1 k) in k 32.973 * [taylor]: Taking taylor expansion of k in k 32.973 * [backup-simplify]: Simplify 0 into 0 32.973 * [backup-simplify]: Simplify 1 into 1 32.973 * [backup-simplify]: Simplify (/ 1 1) into 1 32.973 * [taylor]: Taking taylor expansion of 1/2 in k 32.973 * [backup-simplify]: Simplify 1/2 into 1/2 32.973 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 32.973 * [taylor]: Taking taylor expansion of (* 2 PI) in k 32.973 * [taylor]: Taking taylor expansion of 2 in k 32.973 * [backup-simplify]: Simplify 2 into 2 32.973 * [taylor]: Taking taylor expansion of PI in k 32.973 * [backup-simplify]: Simplify PI into PI 32.974 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 32.974 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 32.974 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 32.975 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 32.977 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 32.978 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 32.979 * [backup-simplify]: Simplify (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 32.979 * [backup-simplify]: Simplify 0 into 0 32.979 * [backup-simplify]: Simplify 0 into 0 32.979 * [backup-simplify]: Simplify 0 into 0 32.979 * [backup-simplify]: Simplify 0 into 0 32.979 * [backup-simplify]: Simplify 0 into 0 32.979 * [backup-simplify]: Simplify 0 into 0 32.979 * [backup-simplify]: Simplify (pow (* 2 PI) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) into (pow (* 2 PI) (- 1/2 (* 1/2 k))) 32.979 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1) 32.980 * [backup-simplify]: Simplify (pow PI (- 1/2 (/ k 2))) into (pow PI (- 1/2 (* 1/2 k))) 32.980 * [approximate]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in (k) around 0 32.980 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 32.980 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 32.980 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 32.980 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 32.980 * [taylor]: Taking taylor expansion of 1/2 in k 32.980 * [backup-simplify]: Simplify 1/2 into 1/2 32.980 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 32.980 * [taylor]: Taking taylor expansion of 1/2 in k 32.980 * [backup-simplify]: Simplify 1/2 into 1/2 32.980 * [taylor]: Taking taylor expansion of k in k 32.980 * [backup-simplify]: Simplify 0 into 0 32.980 * [backup-simplify]: Simplify 1 into 1 32.980 * [taylor]: Taking taylor expansion of (log PI) in k 32.980 * [taylor]: Taking taylor expansion of PI in k 32.980 * [backup-simplify]: Simplify PI into PI 32.980 * [backup-simplify]: Simplify (log PI) into (log PI) 32.981 * [backup-simplify]: Simplify (* 1/2 0) into 0 32.981 * [backup-simplify]: Simplify (- 0) into 0 32.982 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 32.983 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 32.984 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 32.984 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 32.984 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 32.984 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 32.984 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 32.984 * [taylor]: Taking taylor expansion of 1/2 in k 32.984 * [backup-simplify]: Simplify 1/2 into 1/2 32.984 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 32.984 * [taylor]: Taking taylor expansion of 1/2 in k 32.984 * [backup-simplify]: Simplify 1/2 into 1/2 32.984 * [taylor]: Taking taylor expansion of k in k 32.984 * [backup-simplify]: Simplify 0 into 0 32.984 * [backup-simplify]: Simplify 1 into 1 32.984 * [taylor]: Taking taylor expansion of (log PI) in k 32.984 * [taylor]: Taking taylor expansion of PI in k 32.984 * [backup-simplify]: Simplify PI into PI 32.985 * [backup-simplify]: Simplify (log PI) into (log PI) 32.985 * [backup-simplify]: Simplify (* 1/2 0) into 0 32.986 * [backup-simplify]: Simplify (- 0) into 0 32.986 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 32.987 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 32.989 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 32.989 * [backup-simplify]: Simplify (pow PI 1/2) into (pow PI 1/2) 32.991 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 32.991 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 32.992 * [backup-simplify]: Simplify (- 1/2) into -1/2 32.992 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 32.994 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 33.003 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 33.004 * [backup-simplify]: Simplify (* -1/2 (* (log PI) (sqrt PI))) into (* -1/2 (* (log PI) (sqrt PI))) 33.006 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 33.007 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 33.007 * [backup-simplify]: Simplify (- 0) into 0 33.007 * [backup-simplify]: Simplify (+ 0 0) into 0 33.008 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 33.015 * [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))) 33.017 * [backup-simplify]: Simplify (* 1/8 (* (pow (log PI) 2) (sqrt PI))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 33.021 * [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)))) 33.022 * [backup-simplify]: Simplify (pow PI (- 1/2 (/ (/ 1 k) 2))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 33.022 * [approximate]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in (k) around 0 33.022 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 33.022 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 33.022 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 33.022 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 33.022 * [taylor]: Taking taylor expansion of 1/2 in k 33.022 * [backup-simplify]: Simplify 1/2 into 1/2 33.022 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 33.022 * [taylor]: Taking taylor expansion of 1/2 in k 33.022 * [backup-simplify]: Simplify 1/2 into 1/2 33.022 * [taylor]: Taking taylor expansion of (/ 1 k) in k 33.022 * [taylor]: Taking taylor expansion of k in k 33.022 * [backup-simplify]: Simplify 0 into 0 33.022 * [backup-simplify]: Simplify 1 into 1 33.022 * [backup-simplify]: Simplify (/ 1 1) into 1 33.022 * [taylor]: Taking taylor expansion of (log PI) in k 33.022 * [taylor]: Taking taylor expansion of PI in k 33.022 * [backup-simplify]: Simplify PI into PI 33.022 * [backup-simplify]: Simplify (log PI) into (log PI) 33.023 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 33.023 * [backup-simplify]: Simplify (- 1/2) into -1/2 33.023 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 33.024 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 33.024 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 33.024 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 33.024 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 33.024 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 33.024 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 33.024 * [taylor]: Taking taylor expansion of 1/2 in k 33.024 * [backup-simplify]: Simplify 1/2 into 1/2 33.024 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 33.024 * [taylor]: Taking taylor expansion of 1/2 in k 33.024 * [backup-simplify]: Simplify 1/2 into 1/2 33.024 * [taylor]: Taking taylor expansion of (/ 1 k) in k 33.024 * [taylor]: Taking taylor expansion of k in k 33.024 * [backup-simplify]: Simplify 0 into 0 33.025 * [backup-simplify]: Simplify 1 into 1 33.030 * [backup-simplify]: Simplify (/ 1 1) into 1 33.031 * [taylor]: Taking taylor expansion of (log PI) in k 33.031 * [taylor]: Taking taylor expansion of PI in k 33.031 * [backup-simplify]: Simplify PI into PI 33.031 * [backup-simplify]: Simplify (log PI) into (log PI) 33.032 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 33.032 * [backup-simplify]: Simplify (- 1/2) into -1/2 33.032 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 33.033 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 33.033 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 33.033 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 k)))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 33.033 * [backup-simplify]: Simplify 0 into 0 33.033 * [backup-simplify]: Simplify 0 into 0 33.033 * [backup-simplify]: Simplify 0 into 0 33.033 * [backup-simplify]: Simplify 0 into 0 33.033 * [backup-simplify]: Simplify 0 into 0 33.033 * [backup-simplify]: Simplify 0 into 0 33.033 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) into (pow PI (- 1/2 (* 1/2 k))) 33.034 * [backup-simplify]: Simplify (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 33.034 * [approximate]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in (k) around 0 33.034 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 33.034 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 33.034 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 33.034 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 33.034 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 33.034 * [taylor]: Taking taylor expansion of 1/2 in k 33.034 * [backup-simplify]: Simplify 1/2 into 1/2 33.034 * [taylor]: Taking taylor expansion of (/ 1 k) in k 33.034 * [taylor]: Taking taylor expansion of k in k 33.034 * [backup-simplify]: Simplify 0 into 0 33.034 * [backup-simplify]: Simplify 1 into 1 33.034 * [backup-simplify]: Simplify (/ 1 1) into 1 33.034 * [taylor]: Taking taylor expansion of 1/2 in k 33.034 * [backup-simplify]: Simplify 1/2 into 1/2 33.034 * [taylor]: Taking taylor expansion of (log PI) in k 33.034 * [taylor]: Taking taylor expansion of PI in k 33.034 * [backup-simplify]: Simplify PI into PI 33.035 * [backup-simplify]: Simplify (log PI) into (log PI) 33.035 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 33.036 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 33.037 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 33.037 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 33.037 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 33.037 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 33.037 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 33.037 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 33.037 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 33.037 * [taylor]: Taking taylor expansion of 1/2 in k 33.037 * [backup-simplify]: Simplify 1/2 into 1/2 33.037 * [taylor]: Taking taylor expansion of (/ 1 k) in k 33.037 * [taylor]: Taking taylor expansion of k in k 33.037 * [backup-simplify]: Simplify 0 into 0 33.037 * [backup-simplify]: Simplify 1 into 1 33.038 * [backup-simplify]: Simplify (/ 1 1) into 1 33.038 * [taylor]: Taking taylor expansion of 1/2 in k 33.038 * [backup-simplify]: Simplify 1/2 into 1/2 33.038 * [taylor]: Taking taylor expansion of (log PI) in k 33.038 * [taylor]: Taking taylor expansion of PI in k 33.038 * [backup-simplify]: Simplify PI into PI 33.038 * [backup-simplify]: Simplify (log PI) into (log PI) 33.038 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 33.039 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 33.039 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 33.040 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 33.040 * [backup-simplify]: Simplify (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 33.040 * [backup-simplify]: Simplify 0 into 0 33.040 * [backup-simplify]: Simplify 0 into 0 33.040 * [backup-simplify]: Simplify 0 into 0 33.040 * [backup-simplify]: Simplify 0 into 0 33.040 * [backup-simplify]: Simplify 0 into 0 33.040 * [backup-simplify]: Simplify 0 into 0 33.040 * [backup-simplify]: Simplify (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) into (pow PI (- 1/2 (* 1/2 k))) 33.040 * * * * [progress]: [ 4 / 4 ] generating series at (2) 33.041 * [backup-simplify]: Simplify (* (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* 2 PI) (- 1/2 (/ k 2))))))) into (* (pow n (- 1/2 (* 1/2 k))) (sqrt (/ (* (pow 2 (- 1/2 (* 1/2 k))) (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) k))) 33.041 * [approximate]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (sqrt (/ (* (pow 2 (- 1/2 (* 1/2 k))) (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) k))) in (k n) around 0 33.041 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (sqrt (/ (* (pow 2 (- 1/2 (* 1/2 k))) (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) k))) in n 33.041 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 33.041 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 33.041 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 33.041 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 33.041 * [taylor]: Taking taylor expansion of 1/2 in n 33.041 * [backup-simplify]: Simplify 1/2 into 1/2 33.041 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 33.041 * [taylor]: Taking taylor expansion of 1/2 in n 33.041 * [backup-simplify]: Simplify 1/2 into 1/2 33.041 * [taylor]: Taking taylor expansion of k in n 33.041 * [backup-simplify]: Simplify k into k 33.041 * [taylor]: Taking taylor expansion of (log n) in n 33.041 * [taylor]: Taking taylor expansion of n in n 33.041 * [backup-simplify]: Simplify 0 into 0 33.041 * [backup-simplify]: Simplify 1 into 1 33.041 * [backup-simplify]: Simplify (log 1) into 0 33.041 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 33.041 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 33.041 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 33.042 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 33.042 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 33.042 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 33.042 * [taylor]: Taking taylor expansion of (sqrt (/ (* (pow 2 (- 1/2 (* 1/2 k))) (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) k)) in n 33.042 * [taylor]: Taking taylor expansion of (/ (* (pow 2 (- 1/2 (* 1/2 k))) (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) k) in n 33.042 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 k))) (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) in n 33.042 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in n 33.042 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in n 33.042 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in n 33.042 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 33.042 * [taylor]: Taking taylor expansion of 1/2 in n 33.042 * [backup-simplify]: Simplify 1/2 into 1/2 33.042 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 33.042 * [taylor]: Taking taylor expansion of 1/2 in n 33.042 * [backup-simplify]: Simplify 1/2 into 1/2 33.042 * [taylor]: Taking taylor expansion of k in n 33.042 * [backup-simplify]: Simplify k into k 33.042 * [taylor]: Taking taylor expansion of (log 2) in n 33.042 * [taylor]: Taking taylor expansion of 2 in n 33.042 * [backup-simplify]: Simplify 2 into 2 33.042 * [backup-simplify]: Simplify (log 2) into (log 2) 33.042 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 33.042 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 33.042 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 33.043 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log 2)) into (* (log 2) (- 1/2 (* 1/2 k))) 33.043 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 k)))) into (exp (* (log 2) (- 1/2 (* 1/2 k)))) 33.043 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in n 33.043 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in n 33.043 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) in n 33.043 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) in n 33.043 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 33.043 * [taylor]: Taking taylor expansion of 1/2 in n 33.043 * [backup-simplify]: Simplify 1/2 into 1/2 33.043 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 33.043 * [taylor]: Taking taylor expansion of 1/2 in n 33.043 * [backup-simplify]: Simplify 1/2 into 1/2 33.043 * [taylor]: Taking taylor expansion of k in n 33.043 * [backup-simplify]: Simplify k into k 33.043 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 33.043 * [taylor]: Taking taylor expansion of (* 2 PI) in n 33.043 * [taylor]: Taking taylor expansion of 2 in n 33.043 * [backup-simplify]: Simplify 2 into 2 33.043 * [taylor]: Taking taylor expansion of PI in n 33.043 * [backup-simplify]: Simplify PI into PI 33.044 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 33.044 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 33.044 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 33.044 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 33.044 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 33.045 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) into (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) 33.046 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 k))) 33.046 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in n 33.046 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in n 33.046 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in n 33.046 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 33.046 * [taylor]: Taking taylor expansion of 1/2 in n 33.046 * [backup-simplify]: Simplify 1/2 into 1/2 33.046 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 33.046 * [taylor]: Taking taylor expansion of 1/2 in n 33.046 * [backup-simplify]: Simplify 1/2 into 1/2 33.046 * [taylor]: Taking taylor expansion of k in n 33.046 * [backup-simplify]: Simplify k into k 33.046 * [taylor]: Taking taylor expansion of (log PI) in n 33.046 * [taylor]: Taking taylor expansion of PI in n 33.046 * [backup-simplify]: Simplify PI into PI 33.046 * [backup-simplify]: Simplify (log PI) into (log PI) 33.046 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 33.046 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 33.046 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 33.047 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log PI)) into (* (- 1/2 (* 1/2 k)) (log PI)) 33.047 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log PI))) into (pow PI (- 1/2 (* 1/2 k))) 33.047 * [taylor]: Taking taylor expansion of k in n 33.047 * [backup-simplify]: Simplify k into k 33.048 * [backup-simplify]: Simplify (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) into (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) 33.048 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) into (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) 33.049 * [backup-simplify]: Simplify (/ (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) k) into (/ (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) k) 33.050 * [backup-simplify]: Simplify (sqrt (/ (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) k)) into (sqrt (/ (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) k)) 33.051 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 33.051 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 33.051 * [backup-simplify]: Simplify (- 0) into 0 33.052 * [backup-simplify]: Simplify (+ 0 0) into 0 33.052 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log PI))) into 0 33.053 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 33.053 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 33.054 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 33.055 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 33.055 * [backup-simplify]: Simplify (- 0) into 0 33.055 * [backup-simplify]: Simplify (+ 0 0) into 0 33.056 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log (* 2 PI)))) into 0 33.057 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) (+ (* (/ (pow 0 1) 1)))) into 0 33.057 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) 0) (* 0 (pow PI (- 1/2 (* 1/2 k))))) into 0 33.058 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 33.058 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 33.059 * [backup-simplify]: Simplify (- 0) into 0 33.059 * [backup-simplify]: Simplify (+ 0 0) into 0 33.059 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log 2))) into 0 33.060 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 33.061 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) 0) (* 0 (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))))) into 0 33.061 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) k) (/ 0 k)))) into 0 33.062 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) k)))) into 0 33.062 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (sqrt (/ (* (pow 2 (- 1/2 (* 1/2 k))) (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) k))) in k 33.062 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 33.062 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 33.062 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 33.062 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 33.062 * [taylor]: Taking taylor expansion of 1/2 in k 33.062 * [backup-simplify]: Simplify 1/2 into 1/2 33.062 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 33.062 * [taylor]: Taking taylor expansion of 1/2 in k 33.062 * [backup-simplify]: Simplify 1/2 into 1/2 33.062 * [taylor]: Taking taylor expansion of k in k 33.062 * [backup-simplify]: Simplify 0 into 0 33.062 * [backup-simplify]: Simplify 1 into 1 33.062 * [taylor]: Taking taylor expansion of (log n) in k 33.062 * [taylor]: Taking taylor expansion of n in k 33.063 * [backup-simplify]: Simplify n into n 33.063 * [backup-simplify]: Simplify (log n) into (log n) 33.063 * [backup-simplify]: Simplify (* 1/2 0) into 0 33.063 * [backup-simplify]: Simplify (- 0) into 0 33.064 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 33.064 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 33.064 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 33.064 * [taylor]: Taking taylor expansion of (sqrt (/ (* (pow 2 (- 1/2 (* 1/2 k))) (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) k)) in k 33.064 * [taylor]: Taking taylor expansion of (/ (* (pow 2 (- 1/2 (* 1/2 k))) (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) k) in k 33.064 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 k))) (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) in k 33.064 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in k 33.064 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in k 33.064 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in k 33.064 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 33.064 * [taylor]: Taking taylor expansion of 1/2 in k 33.064 * [backup-simplify]: Simplify 1/2 into 1/2 33.064 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 33.064 * [taylor]: Taking taylor expansion of 1/2 in k 33.064 * [backup-simplify]: Simplify 1/2 into 1/2 33.064 * [taylor]: Taking taylor expansion of k in k 33.064 * [backup-simplify]: Simplify 0 into 0 33.064 * [backup-simplify]: Simplify 1 into 1 33.064 * [taylor]: Taking taylor expansion of (log 2) in k 33.064 * [taylor]: Taking taylor expansion of 2 in k 33.064 * [backup-simplify]: Simplify 2 into 2 33.065 * [backup-simplify]: Simplify (log 2) into (log 2) 33.065 * [backup-simplify]: Simplify (* 1/2 0) into 0 33.066 * [backup-simplify]: Simplify (- 0) into 0 33.066 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 33.067 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 33.069 * [backup-simplify]: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2) 33.069 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in k 33.069 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in k 33.069 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) in k 33.069 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) in k 33.069 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 33.069 * [taylor]: Taking taylor expansion of 1/2 in k 33.069 * [backup-simplify]: Simplify 1/2 into 1/2 33.069 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 33.069 * [taylor]: Taking taylor expansion of 1/2 in k 33.069 * [backup-simplify]: Simplify 1/2 into 1/2 33.069 * [taylor]: Taking taylor expansion of k in k 33.069 * [backup-simplify]: Simplify 0 into 0 33.069 * [backup-simplify]: Simplify 1 into 1 33.069 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 33.069 * [taylor]: Taking taylor expansion of (* 2 PI) in k 33.069 * [taylor]: Taking taylor expansion of 2 in k 33.069 * [backup-simplify]: Simplify 2 into 2 33.069 * [taylor]: Taking taylor expansion of PI in k 33.069 * [backup-simplify]: Simplify PI into PI 33.070 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 33.071 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 33.071 * [backup-simplify]: Simplify (* 1/2 0) into 0 33.072 * [backup-simplify]: Simplify (- 0) into 0 33.072 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 33.074 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 33.076 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) 33.077 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 33.077 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 33.077 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 33.077 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 33.077 * [taylor]: Taking taylor expansion of 1/2 in k 33.077 * [backup-simplify]: Simplify 1/2 into 1/2 33.077 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 33.077 * [taylor]: Taking taylor expansion of 1/2 in k 33.077 * [backup-simplify]: Simplify 1/2 into 1/2 33.077 * [taylor]: Taking taylor expansion of k in k 33.077 * [backup-simplify]: Simplify 0 into 0 33.077 * [backup-simplify]: Simplify 1 into 1 33.077 * [taylor]: Taking taylor expansion of (log PI) in k 33.077 * [taylor]: Taking taylor expansion of PI in k 33.077 * [backup-simplify]: Simplify PI into PI 33.077 * [backup-simplify]: Simplify (log PI) into (log PI) 33.078 * [backup-simplify]: Simplify (* 1/2 0) into 0 33.078 * [backup-simplify]: Simplify (- 0) into 0 33.078 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 33.079 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 33.081 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 33.081 * [taylor]: Taking taylor expansion of k in k 33.081 * [backup-simplify]: Simplify 0 into 0 33.081 * [backup-simplify]: Simplify 1 into 1 33.083 * [backup-simplify]: Simplify (* (pow (* 2 PI) 1/2) (pow PI 1/2)) into (* PI (sqrt 2)) 33.085 * [backup-simplify]: Simplify (* (pow 2 1/2) (* PI (sqrt 2))) into (* (* PI (sqrt 2)) (sqrt 2)) 33.086 * [backup-simplify]: Simplify (/ (* (* PI (sqrt 2)) (sqrt 2)) 1) into (* (pow (sqrt 2) 2) PI) 33.087 * [backup-simplify]: Simplify (sqrt 0) into 0 33.089 * [backup-simplify]: Simplify (/ (* (pow (sqrt 2) 2) PI) (* 2 (sqrt 0))) into (* +nan.0 (* (pow (sqrt 2) 2) PI)) 33.089 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (sqrt (/ (* (pow 2 (- 1/2 (* 1/2 k))) (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) k))) in k 33.089 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 33.089 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 33.089 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 33.089 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 33.089 * [taylor]: Taking taylor expansion of 1/2 in k 33.089 * [backup-simplify]: Simplify 1/2 into 1/2 33.089 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 33.089 * [taylor]: Taking taylor expansion of 1/2 in k 33.089 * [backup-simplify]: Simplify 1/2 into 1/2 33.089 * [taylor]: Taking taylor expansion of k in k 33.089 * [backup-simplify]: Simplify 0 into 0 33.089 * [backup-simplify]: Simplify 1 into 1 33.089 * [taylor]: Taking taylor expansion of (log n) in k 33.089 * [taylor]: Taking taylor expansion of n in k 33.089 * [backup-simplify]: Simplify n into n 33.089 * [backup-simplify]: Simplify (log n) into (log n) 33.089 * [backup-simplify]: Simplify (* 1/2 0) into 0 33.090 * [backup-simplify]: Simplify (- 0) into 0 33.090 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 33.090 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 33.090 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 33.090 * [taylor]: Taking taylor expansion of (sqrt (/ (* (pow 2 (- 1/2 (* 1/2 k))) (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) k)) in k 33.090 * [taylor]: Taking taylor expansion of (/ (* (pow 2 (- 1/2 (* 1/2 k))) (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) k) in k 33.090 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 k))) (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) in k 33.090 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in k 33.090 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in k 33.090 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in k 33.090 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 33.090 * [taylor]: Taking taylor expansion of 1/2 in k 33.090 * [backup-simplify]: Simplify 1/2 into 1/2 33.090 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 33.090 * [taylor]: Taking taylor expansion of 1/2 in k 33.090 * [backup-simplify]: Simplify 1/2 into 1/2 33.090 * [taylor]: Taking taylor expansion of k in k 33.090 * [backup-simplify]: Simplify 0 into 0 33.090 * [backup-simplify]: Simplify 1 into 1 33.090 * [taylor]: Taking taylor expansion of (log 2) in k 33.090 * [taylor]: Taking taylor expansion of 2 in k 33.090 * [backup-simplify]: Simplify 2 into 2 33.090 * [backup-simplify]: Simplify (log 2) into (log 2) 33.091 * [backup-simplify]: Simplify (* 1/2 0) into 0 33.091 * [backup-simplify]: Simplify (- 0) into 0 33.091 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 33.092 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 33.093 * [backup-simplify]: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2) 33.093 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in k 33.093 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in k 33.093 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) in k 33.093 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) in k 33.093 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 33.093 * [taylor]: Taking taylor expansion of 1/2 in k 33.093 * [backup-simplify]: Simplify 1/2 into 1/2 33.093 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 33.093 * [taylor]: Taking taylor expansion of 1/2 in k 33.093 * [backup-simplify]: Simplify 1/2 into 1/2 33.093 * [taylor]: Taking taylor expansion of k in k 33.093 * [backup-simplify]: Simplify 0 into 0 33.093 * [backup-simplify]: Simplify 1 into 1 33.093 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 33.093 * [taylor]: Taking taylor expansion of (* 2 PI) in k 33.093 * [taylor]: Taking taylor expansion of 2 in k 33.093 * [backup-simplify]: Simplify 2 into 2 33.093 * [taylor]: Taking taylor expansion of PI in k 33.093 * [backup-simplify]: Simplify PI into PI 33.093 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 33.094 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 33.094 * [backup-simplify]: Simplify (* 1/2 0) into 0 33.095 * [backup-simplify]: Simplify (- 0) into 0 33.095 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 33.096 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 33.097 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) 33.097 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 33.098 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 33.098 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 33.098 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 33.098 * [taylor]: Taking taylor expansion of 1/2 in k 33.098 * [backup-simplify]: Simplify 1/2 into 1/2 33.098 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 33.098 * [taylor]: Taking taylor expansion of 1/2 in k 33.098 * [backup-simplify]: Simplify 1/2 into 1/2 33.098 * [taylor]: Taking taylor expansion of k in k 33.098 * [backup-simplify]: Simplify 0 into 0 33.098 * [backup-simplify]: Simplify 1 into 1 33.098 * [taylor]: Taking taylor expansion of (log PI) in k 33.098 * [taylor]: Taking taylor expansion of PI in k 33.098 * [backup-simplify]: Simplify PI into PI 33.098 * [backup-simplify]: Simplify (log PI) into (log PI) 33.098 * [backup-simplify]: Simplify (* 1/2 0) into 0 33.099 * [backup-simplify]: Simplify (- 0) into 0 33.099 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 33.099 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 33.100 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 33.100 * [taylor]: Taking taylor expansion of k in k 33.101 * [backup-simplify]: Simplify 0 into 0 33.101 * [backup-simplify]: Simplify 1 into 1 33.102 * [backup-simplify]: Simplify (* (pow (* 2 PI) 1/2) (pow PI 1/2)) into (* PI (sqrt 2)) 33.104 * [backup-simplify]: Simplify (* (pow 2 1/2) (* PI (sqrt 2))) into (* (* PI (sqrt 2)) (sqrt 2)) 33.105 * [backup-simplify]: Simplify (/ (* (* PI (sqrt 2)) (sqrt 2)) 1) into (* (pow (sqrt 2) 2) PI) 33.106 * [backup-simplify]: Simplify (sqrt 0) into 0 33.107 * [backup-simplify]: Simplify (/ (* (pow (sqrt 2) 2) PI) (* 2 (sqrt 0))) into (* +nan.0 (* (pow (sqrt 2) 2) PI)) 33.108 * [backup-simplify]: Simplify (* (pow n 1/2) 0) into 0 33.108 * [taylor]: Taking taylor expansion of 0 in n 33.108 * [backup-simplify]: Simplify 0 into 0 33.108 * [backup-simplify]: Simplify 0 into 0 33.108 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 33.109 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 33.109 * [backup-simplify]: Simplify (- 1/2) into -1/2 33.109 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 33.109 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log n))) into (- (* 1/2 (log n))) 33.110 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n))) 33.111 * [backup-simplify]: Simplify (+ (* (pow n 1/2) (* +nan.0 (* (pow (sqrt 2) 2) PI))) (* (* -1/2 (* (sqrt n) (log n))) 0)) into (- (* +nan.0 (* (* (pow (sqrt 2) 2) PI) (sqrt n)))) 33.111 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (pow (sqrt 2) 2) PI) (sqrt n)))) in n 33.111 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (pow (sqrt 2) 2) PI) (sqrt n))) in n 33.111 * [taylor]: Taking taylor expansion of +nan.0 in n 33.111 * [backup-simplify]: Simplify +nan.0 into +nan.0 33.111 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 2) 2) PI) (sqrt n)) in n 33.111 * [taylor]: Taking taylor expansion of (* (pow (sqrt 2) 2) PI) in n 33.111 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 2) in n 33.111 * [taylor]: Taking taylor expansion of (sqrt 2) in n 33.111 * [taylor]: Taking taylor expansion of 2 in n 33.111 * [backup-simplify]: Simplify 2 into 2 33.112 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 33.112 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 33.112 * [taylor]: Taking taylor expansion of PI in n 33.112 * [backup-simplify]: Simplify PI into PI 33.112 * [taylor]: Taking taylor expansion of (sqrt n) in n 33.112 * [taylor]: Taking taylor expansion of n in n 33.112 * [backup-simplify]: Simplify 0 into 0 33.112 * [backup-simplify]: Simplify 1 into 1 33.112 * [backup-simplify]: Simplify (sqrt 0) into 0 33.113 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 33.114 * [backup-simplify]: Simplify (* (sqrt 2) (sqrt 2)) into (pow (sqrt 2) 2) 33.115 * [backup-simplify]: Simplify (* (pow (sqrt 2) 2) PI) into (* (pow (sqrt 2) 2) PI) 33.115 * [backup-simplify]: Simplify (* (* (pow (sqrt 2) 2) PI) 0) into 0 33.116 * [backup-simplify]: Simplify (* +nan.0 0) into 0 33.116 * [backup-simplify]: Simplify (- 0) into 0 33.116 * [backup-simplify]: Simplify 0 into 0 33.116 * [backup-simplify]: Simplify 0 into 0 33.117 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 33.117 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 33.118 * [backup-simplify]: Simplify (- 1/2) into -1/2 33.118 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 33.119 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 33.125 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 33.125 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 33.127 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 33.127 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 33.127 * [backup-simplify]: Simplify (- 1/2) into -1/2 33.133 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 33.135 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 PI)))) into (- (* 1/2 (log (* 2 PI)))) 33.143 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) 33.152 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) 1/2) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) (pow PI 1/2))) into (- (+ (* 1/2 (* (sqrt 2) (* (log PI) PI))) (* 1/2 (* (sqrt 2) (* PI (log (* 2 PI))))))) 33.153 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 33.153 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 33.154 * [backup-simplify]: Simplify (- 1/2) into -1/2 33.154 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 33.155 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log 2))) into (- (* 1/2 (log 2))) 33.160 * [backup-simplify]: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 1) 1)))) into (* -1/2 (* (log 2) (sqrt 2))) 33.176 * [backup-simplify]: Simplify (+ (* (pow 2 1/2) (- (+ (* 1/2 (* (sqrt 2) (* (log PI) PI))) (* 1/2 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (* (* -1/2 (* (log 2) (sqrt 2))) (* PI (sqrt 2)))) into (- (+ (* 1/2 (* (log 2) (* (pow (sqrt 2) 2) PI))) (+ (* 1/2 (* (pow (sqrt 2) 2) (* (log PI) PI))) (* 1/2 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))))))) 33.205 * [backup-simplify]: Simplify (- (/ (- (+ (* 1/2 (* (log 2) (* (pow (sqrt 2) 2) PI))) (+ (* 1/2 (* (pow (sqrt 2) 2) (* (log PI) PI))) (* 1/2 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))))))) 1) (+ (* (* (pow (sqrt 2) 2) PI) (/ 0 1)))) into (- (+ (* 1/2 (* (log 2) (* (pow (sqrt 2) 2) PI))) (+ (* 1/2 (* (pow (sqrt 2) 2) (* (log PI) PI))) (* 1/2 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))))))) 33.252 * [backup-simplify]: Simplify (/ (- (- (+ (* 1/2 (* (log 2) (* (pow (sqrt 2) 2) PI))) (+ (* 1/2 (* (pow (sqrt 2) 2) (* (log PI) PI))) (* 1/2 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))))))) (pow (* +nan.0 (* (pow (sqrt 2) 2) PI)) 2) (+)) (* 2 0)) into (* +nan.0 (+ (* 1/2 (* (log 2) (* (pow (sqrt 2) 2) PI))) (- (+ (* 1/2 (* (pow (sqrt 2) 2) (* (log PI) PI))) (* 1/2 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))))) (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2)))))) 33.254 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 33.255 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 33.255 * [backup-simplify]: Simplify (- 0) into 0 33.255 * [backup-simplify]: Simplify (+ 0 0) into 0 33.256 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log n)))) into 0 33.257 * [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))) 33.278 * [backup-simplify]: Simplify (+ (* (pow n 1/2) (* +nan.0 (+ (* 1/2 (* (log 2) (* (pow (sqrt 2) 2) PI))) (- (+ (* 1/2 (* (pow (sqrt 2) 2) (* (log PI) PI))) (* 1/2 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))))) (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2))))))) (+ (* (* -1/2 (* (sqrt n) (log n))) (* +nan.0 (* (pow (sqrt 2) 2) PI))) (* (* 1/8 (* (sqrt n) (pow (log n) 2))) 0))) into (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (pow PI 2)) (sqrt n))) (- (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))) (sqrt n)))))))))))) 33.278 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (pow PI 2)) (sqrt n))) (- (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))) (sqrt n)))))))))))) in n 33.278 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (pow PI 2)) (sqrt n))) (- (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))) (sqrt n))))))))))) in n 33.278 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) PI)) (sqrt n))) in n 33.278 * [taylor]: Taking taylor expansion of +nan.0 in n 33.278 * [backup-simplify]: Simplify +nan.0 into +nan.0 33.278 * [taylor]: Taking taylor expansion of (* (* (log 2) (* (pow (sqrt 2) 2) PI)) (sqrt n)) in n 33.278 * [taylor]: Taking taylor expansion of (* (log 2) (* (pow (sqrt 2) 2) PI)) in n 33.278 * [taylor]: Taking taylor expansion of (log 2) in n 33.278 * [taylor]: Taking taylor expansion of 2 in n 33.278 * [backup-simplify]: Simplify 2 into 2 33.279 * [backup-simplify]: Simplify (log 2) into (log 2) 33.279 * [taylor]: Taking taylor expansion of (* (pow (sqrt 2) 2) PI) in n 33.279 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 2) in n 33.279 * [taylor]: Taking taylor expansion of (sqrt 2) in n 33.279 * [taylor]: Taking taylor expansion of 2 in n 33.279 * [backup-simplify]: Simplify 2 into 2 33.279 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 33.279 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 33.279 * [taylor]: Taking taylor expansion of PI in n 33.279 * [backup-simplify]: Simplify PI into PI 33.280 * [taylor]: Taking taylor expansion of (sqrt n) in n 33.280 * [taylor]: Taking taylor expansion of n in n 33.280 * [backup-simplify]: Simplify 0 into 0 33.280 * [backup-simplify]: Simplify 1 into 1 33.280 * [backup-simplify]: Simplify (sqrt 0) into 0 33.281 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 33.281 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (pow PI 2)) (sqrt n))) (- (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))) (sqrt n)))))))))) in n 33.281 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (pow PI 2)) (sqrt n))) (- (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))) (sqrt n))))))))) in n 33.281 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (log n))) (sqrt n))) in n 33.281 * [taylor]: Taking taylor expansion of +nan.0 in n 33.281 * [backup-simplify]: Simplify +nan.0 into +nan.0 33.281 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 2) 2) (* PI (log n))) (sqrt n)) in n 33.281 * [taylor]: Taking taylor expansion of (* (pow (sqrt 2) 2) (* PI (log n))) in n 33.281 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 2) in n 33.281 * [taylor]: Taking taylor expansion of (sqrt 2) in n 33.281 * [taylor]: Taking taylor expansion of 2 in n 33.281 * [backup-simplify]: Simplify 2 into 2 33.281 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 33.282 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 33.282 * [taylor]: Taking taylor expansion of (* PI (log n)) in n 33.282 * [taylor]: Taking taylor expansion of PI in n 33.282 * [backup-simplify]: Simplify PI into PI 33.282 * [taylor]: Taking taylor expansion of (log n) in n 33.282 * [taylor]: Taking taylor expansion of n in n 33.282 * [backup-simplify]: Simplify 0 into 0 33.282 * [backup-simplify]: Simplify 1 into 1 33.282 * [backup-simplify]: Simplify (log 1) into 0 33.282 * [taylor]: Taking taylor expansion of (sqrt n) in n 33.282 * [taylor]: Taking taylor expansion of n in n 33.282 * [backup-simplify]: Simplify 0 into 0 33.282 * [backup-simplify]: Simplify 1 into 1 33.282 * [backup-simplify]: Simplify (sqrt 0) into 0 33.283 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 33.283 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (pow PI 2)) (sqrt n))) (- (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))) (sqrt n)))))))) in n 33.283 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (pow PI 2)) (sqrt n))) (- (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))) (sqrt n))))))) in n 33.283 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) PI)) (sqrt n))) in n 33.283 * [taylor]: Taking taylor expansion of +nan.0 in n 33.283 * [backup-simplify]: Simplify +nan.0 into +nan.0 33.283 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 2) 2) (* (log PI) PI)) (sqrt n)) in n 33.283 * [taylor]: Taking taylor expansion of (* (pow (sqrt 2) 2) (* (log PI) PI)) in n 33.283 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 2) in n 33.283 * [taylor]: Taking taylor expansion of (sqrt 2) in n 33.283 * [taylor]: Taking taylor expansion of 2 in n 33.283 * [backup-simplify]: Simplify 2 into 2 33.283 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 33.284 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 33.284 * [taylor]: Taking taylor expansion of (* (log PI) PI) in n 33.284 * [taylor]: Taking taylor expansion of (log PI) in n 33.284 * [taylor]: Taking taylor expansion of PI in n 33.284 * [backup-simplify]: Simplify PI into PI 33.284 * [backup-simplify]: Simplify (log PI) into (log PI) 33.284 * [taylor]: Taking taylor expansion of PI in n 33.284 * [backup-simplify]: Simplify PI into PI 33.284 * [taylor]: Taking taylor expansion of (sqrt n) in n 33.284 * [taylor]: Taking taylor expansion of n in n 33.284 * [backup-simplify]: Simplify 0 into 0 33.284 * [backup-simplify]: Simplify 1 into 1 33.285 * [backup-simplify]: Simplify (sqrt 0) into 0 33.285 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 33.285 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (pow PI 2)) (sqrt n))) (- (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))) (sqrt n)))))) in n 33.285 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (pow PI 2)) (sqrt n))) (- (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))) (sqrt n))))) in n 33.285 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (pow (sqrt 2) 4) (pow PI 2)) (sqrt n))) in n 33.285 * [taylor]: Taking taylor expansion of +nan.0 in n 33.285 * [backup-simplify]: Simplify +nan.0 into +nan.0 33.285 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 2) 4) (pow PI 2)) (sqrt n)) in n 33.285 * [taylor]: Taking taylor expansion of (* (pow (sqrt 2) 4) (pow PI 2)) in n 33.286 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 4) in n 33.286 * [taylor]: Taking taylor expansion of (sqrt 2) in n 33.286 * [taylor]: Taking taylor expansion of 2 in n 33.286 * [backup-simplify]: Simplify 2 into 2 33.286 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 33.286 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 33.286 * [taylor]: Taking taylor expansion of (pow PI 2) in n 33.286 * [taylor]: Taking taylor expansion of PI in n 33.286 * [backup-simplify]: Simplify PI into PI 33.286 * [taylor]: Taking taylor expansion of (sqrt n) in n 33.286 * [taylor]: Taking taylor expansion of n in n 33.286 * [backup-simplify]: Simplify 0 into 0 33.286 * [backup-simplify]: Simplify 1 into 1 33.287 * [backup-simplify]: Simplify (sqrt 0) into 0 33.287 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 33.287 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))) (sqrt n)))) in n 33.287 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))) (sqrt n))) in n 33.287 * [taylor]: Taking taylor expansion of +nan.0 in n 33.287 * [backup-simplify]: Simplify +nan.0 into +nan.0 33.288 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))) (sqrt n)) in n 33.288 * [taylor]: Taking taylor expansion of (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))) in n 33.288 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 2) in n 33.288 * [taylor]: Taking taylor expansion of (sqrt 2) in n 33.288 * [taylor]: Taking taylor expansion of 2 in n 33.288 * [backup-simplify]: Simplify 2 into 2 33.288 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 33.288 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 33.288 * [taylor]: Taking taylor expansion of (* PI (log (* 2 PI))) in n 33.288 * [taylor]: Taking taylor expansion of PI in n 33.288 * [backup-simplify]: Simplify PI into PI 33.288 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 33.288 * [taylor]: Taking taylor expansion of (* 2 PI) in n 33.288 * [taylor]: Taking taylor expansion of 2 in n 33.288 * [backup-simplify]: Simplify 2 into 2 33.288 * [taylor]: Taking taylor expansion of PI in n 33.288 * [backup-simplify]: Simplify PI into PI 33.289 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 33.289 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 33.289 * [taylor]: Taking taylor expansion of (sqrt n) in n 33.289 * [taylor]: Taking taylor expansion of n in n 33.289 * [backup-simplify]: Simplify 0 into 0 33.289 * [backup-simplify]: Simplify 1 into 1 33.290 * [backup-simplify]: Simplify (sqrt 0) into 0 33.290 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 33.291 * [backup-simplify]: Simplify (* (sqrt 2) (sqrt 2)) into (pow (sqrt 2) 2) 33.292 * [backup-simplify]: Simplify (* (pow (sqrt 2) 2) PI) into (* (pow (sqrt 2) 2) PI) 33.294 * [backup-simplify]: Simplify (* (log 2) (* (pow (sqrt 2) 2) PI)) into (* (log 2) (* (pow (sqrt 2) 2) PI)) 33.295 * [backup-simplify]: Simplify (* (* (log 2) (* (pow (sqrt 2) 2) PI)) 0) into 0 33.295 * [backup-simplify]: Simplify (* +nan.0 0) into 0 33.296 * [backup-simplify]: Simplify (* (sqrt 2) (sqrt 2)) into (pow (sqrt 2) 2) 33.296 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 33.296 * [backup-simplify]: Simplify (* PI (log n)) into (* PI (log n)) 33.297 * [backup-simplify]: Simplify (* (pow (sqrt 2) 2) (* PI (log n))) into (* (pow (sqrt 2) 2) (* PI (log n))) 33.297 * [backup-simplify]: Simplify (* (* (pow (sqrt 2) 2) (* PI (log n))) 0) into 0 33.298 * [backup-simplify]: Simplify (* +nan.0 0) into 0 33.299 * [backup-simplify]: Simplify (* (sqrt 2) (sqrt 2)) into (pow (sqrt 2) 2) 33.299 * [backup-simplify]: Simplify (* (log PI) PI) into (* (log PI) PI) 33.302 * [backup-simplify]: Simplify (* (pow (sqrt 2) 2) (* (log PI) PI)) into (* (pow (sqrt 2) 2) (* (log PI) PI)) 33.304 * [backup-simplify]: Simplify (* (* (pow (sqrt 2) 2) (* (log PI) PI)) 0) into 0 33.304 * [backup-simplify]: Simplify (* +nan.0 0) into 0 33.305 * [backup-simplify]: Simplify (* (sqrt 2) (sqrt 2)) into (pow (sqrt 2) 2) 33.308 * [backup-simplify]: Simplify (* (pow (sqrt 2) 2) (pow (sqrt 2) 2)) into (pow (sqrt 2) 4) 33.308 * [backup-simplify]: Simplify (* PI PI) into (pow PI 2) 33.310 * [backup-simplify]: Simplify (* (pow (sqrt 2) 4) (pow PI 2)) into (* (pow (sqrt 2) 4) (pow PI 2)) 33.311 * [backup-simplify]: Simplify (* (* (pow (sqrt 2) 4) (pow PI 2)) 0) into 0 33.312 * [backup-simplify]: Simplify (* +nan.0 0) into 0 33.313 * [backup-simplify]: Simplify (* (sqrt 2) (sqrt 2)) into (pow (sqrt 2) 2) 33.315 * [backup-simplify]: Simplify (* PI (log (* 2 PI))) into (* PI (log (* 2 PI))) 33.318 * [backup-simplify]: Simplify (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))) into (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))) 33.320 * [backup-simplify]: Simplify (* (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))) 0) into 0 33.321 * [backup-simplify]: Simplify (* +nan.0 0) into 0 33.321 * [backup-simplify]: Simplify (- 0) into 0 33.321 * [backup-simplify]: Simplify (+ 0 0) into 0 33.322 * [backup-simplify]: Simplify (- 0) into 0 33.322 * [backup-simplify]: Simplify (+ 0 0) into 0 33.322 * [backup-simplify]: Simplify (- 0) into 0 33.323 * [backup-simplify]: Simplify (+ 0 0) into 0 33.323 * [backup-simplify]: Simplify (- 0) into 0 33.323 * [backup-simplify]: Simplify (+ 0 0) into 0 33.324 * [backup-simplify]: Simplify (- 0) into 0 33.324 * [backup-simplify]: Simplify 0 into 0 33.325 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (sqrt 2))) into 0 33.326 * [backup-simplify]: Simplify (+ (* (pow (sqrt 2) 2) 0) (* 0 PI)) into 0 33.330 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 2) 2) PI) +nan.0) (* 0 0)) into (- (* +nan.0 (* (pow (sqrt 2) 2) PI))) 33.337 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (pow (sqrt 2) 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (pow (sqrt 2) 2) PI))) 33.342 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (pow (sqrt 2) 2) PI)))) into (- (* +nan.0 (* (pow (sqrt 2) 2) PI))) 33.346 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 2) 2) PI))) into (- (* +nan.0 (* (pow (sqrt 2) 2) PI))) 33.346 * [backup-simplify]: Simplify 0 into 0 33.349 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 33.350 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 33.350 * [backup-simplify]: Simplify (- 0) into 0 33.351 * [backup-simplify]: Simplify (+ 0 0) into 0 33.352 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 33.366 * [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))) 33.367 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 33.369 * [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 33.369 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 33.369 * [backup-simplify]: Simplify (- 0) into 0 33.370 * [backup-simplify]: Simplify (+ 0 0) into 0 33.371 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 PI))))) into 0 33.379 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) 33.400 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) 1/2) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) (pow PI 1/2)))) into (+ (* 1/8 (* (sqrt 2) (* (pow (log PI) 2) PI))) (+ (* 1/4 (* (sqrt 2) (* (log PI) (* PI (log (* 2 PI)))))) (* 1/8 (* (sqrt 2) (* PI (pow (log (* 2 PI)) 2)))))) 33.403 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 33.404 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 33.405 * [backup-simplify]: Simplify (- 0) into 0 33.405 * [backup-simplify]: Simplify (+ 0 0) into 0 33.406 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log 2)))) into 0 33.416 * [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))) 33.494 * [backup-simplify]: Simplify (+ (* (pow 2 1/2) (+ (* 1/8 (* (sqrt 2) (* (pow (log PI) 2) PI))) (+ (* 1/4 (* (sqrt 2) (* (log PI) (* PI (log (* 2 PI)))))) (* 1/8 (* (sqrt 2) (* PI (pow (log (* 2 PI)) 2))))))) (+ (* (* -1/2 (* (log 2) (sqrt 2))) (- (+ (* 1/2 (* (sqrt 2) (* (log PI) PI))) (* 1/2 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (* (* 1/8 (* (pow (log 2) 2) (sqrt 2))) (* PI (sqrt 2))))) into (+ (* 1/4 (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI)))) (+ (* 1/8 (* (pow (log 2) 2) (* (pow (sqrt 2) 2) PI))) (+ (* 1/4 (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI)))))) (+ (* 1/4 (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))))) (+ (* 1/8 (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI))) (* 1/8 (* (pow (sqrt 2) 2) (* PI (pow (log (* 2 PI)) 2))))))))) 33.567 * [backup-simplify]: Simplify (- (/ (+ (* 1/4 (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI)))) (+ (* 1/8 (* (pow (log 2) 2) (* (pow (sqrt 2) 2) PI))) (+ (* 1/4 (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI)))))) (+ (* 1/4 (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))))) (+ (* 1/8 (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI))) (* 1/8 (* (pow (sqrt 2) 2) (* PI (pow (log (* 2 PI)) 2))))))))) 1) (+ (* (* (pow (sqrt 2) 2) PI) (/ 0 1)) (* (- (+ (* 1/2 (* (log 2) (* (pow (sqrt 2) 2) PI))) (+ (* 1/2 (* (pow (sqrt 2) 2) (* (log PI) PI))) (* 1/2 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))))))) (/ 0 1)))) into (+ (* 1/8 (* (pow (log 2) 2) (* (pow (sqrt 2) 2) PI))) (+ (* 1/4 (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))))) (+ (* 1/8 (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI))) (+ (* 1/8 (* (pow (sqrt 2) 2) (* PI (pow (log (* 2 PI)) 2)))) (+ (* 1/4 (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI)))) (* 1/4 (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI))))))))))) 33.694 * [backup-simplify]: Simplify (/ (- (+ (* 1/8 (* (pow (log 2) 2) (* (pow (sqrt 2) 2) PI))) (+ (* 1/4 (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))))) (+ (* 1/8 (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI))) (+ (* 1/8 (* (pow (sqrt 2) 2) (* PI (pow (log (* 2 PI)) 2)))) (+ (* 1/4 (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI)))) (* 1/4 (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI))))))))))) (+ (* 2 (* (* +nan.0 (* (pow (sqrt 2) 2) PI)) (* +nan.0 (+ (* 1/2 (* (log 2) (* (pow (sqrt 2) 2) PI))) (- (+ (* 1/2 (* (pow (sqrt 2) 2) (* (log PI) PI))) (* 1/2 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))))) (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2)))))))))) (* 2 0)) into (* +nan.0 (- (+ (* 1/8 (* (pow (log 2) 2) (* (pow (sqrt 2) 2) PI))) (+ (* 1/4 (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))))) (+ (* 1/8 (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI))) (+ (* 1/8 (* (pow (sqrt 2) 2) (* PI (pow (log (* 2 PI)) 2)))) (+ (* 1/4 (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI)))) (* 1/4 (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI))))))))))) (+ (* +nan.0 (* (log 2) (* (pow (sqrt 2) 4) (pow PI 2)))) (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (* (log PI) (pow PI 2)))) (- (+ (* +nan.0 (* (pow (sqrt 2) 6) (pow PI 3))) (- (* +nan.0 (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI))))))))))))) 33.697 * [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 33.698 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 33.698 * [backup-simplify]: Simplify (- 0) into 0 33.699 * [backup-simplify]: Simplify (+ 0 0) into 0 33.700 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log n))))) into 0 33.701 * [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))) 33.894 * [backup-simplify]: Simplify (+ (* (pow n 1/2) (* +nan.0 (- (+ (* 1/8 (* (pow (log 2) 2) (* (pow (sqrt 2) 2) PI))) (+ (* 1/4 (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))))) (+ (* 1/8 (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI))) (+ (* 1/8 (* (pow (sqrt 2) 2) (* PI (pow (log (* 2 PI)) 2)))) (+ (* 1/4 (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI)))) (* 1/4 (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI))))))))))) (+ (* +nan.0 (* (log 2) (* (pow (sqrt 2) 4) (pow PI 2)))) (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (* (log PI) (pow PI 2)))) (- (+ (* +nan.0 (* (pow (sqrt 2) 6) (pow PI 3))) (- (* +nan.0 (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))))))))))))) (+ (* (* -1/2 (* (sqrt n) (log n))) (* +nan.0 (+ (* 1/2 (* (log 2) (* (pow (sqrt 2) 2) PI))) (- (+ (* 1/2 (* (pow (sqrt 2) 2) (* (log PI) PI))) (* 1/2 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))))) (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2))))))) (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (* +nan.0 (* (pow (sqrt 2) 2) PI))) (* (* -1/48 (* (sqrt n) (pow (log n) 3))) 0)))) into (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 4) (pow PI 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (* (pow (sqrt 2) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (log PI) (pow PI 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 6) (pow PI 3)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log (* 2 PI)) 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log n) 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n)))))))))))))))))))))))))))))))) 33.894 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 4) (pow PI 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (* (pow (sqrt 2) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (log PI) (pow PI 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 6) (pow PI 3)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log (* 2 PI)) 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log n) 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n)))))))))))))))))))))))))))))))) in n 33.894 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 4) (pow PI 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (* (pow (sqrt 2) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (log PI) (pow PI 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 6) (pow PI 3)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log (* 2 PI)) 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log n) 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n))))))))))))))))))))))))))))))) in n 33.894 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 4) (pow PI 2))) (sqrt n))) in n 33.894 * [taylor]: Taking taylor expansion of +nan.0 in n 33.894 * [backup-simplify]: Simplify +nan.0 into +nan.0 33.894 * [taylor]: Taking taylor expansion of (* (* (log 2) (* (pow (sqrt 2) 4) (pow PI 2))) (sqrt n)) in n 33.894 * [taylor]: Taking taylor expansion of (* (log 2) (* (pow (sqrt 2) 4) (pow PI 2))) in n 33.894 * [taylor]: Taking taylor expansion of (log 2) in n 33.894 * [taylor]: Taking taylor expansion of 2 in n 33.894 * [backup-simplify]: Simplify 2 into 2 33.895 * [backup-simplify]: Simplify (log 2) into (log 2) 33.895 * [taylor]: Taking taylor expansion of (* (pow (sqrt 2) 4) (pow PI 2)) in n 33.895 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 4) in n 33.895 * [taylor]: Taking taylor expansion of (sqrt 2) in n 33.895 * [taylor]: Taking taylor expansion of 2 in n 33.895 * [backup-simplify]: Simplify 2 into 2 33.895 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 33.895 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 33.895 * [taylor]: Taking taylor expansion of (pow PI 2) in n 33.895 * [taylor]: Taking taylor expansion of PI in n 33.895 * [backup-simplify]: Simplify PI into PI 33.895 * [taylor]: Taking taylor expansion of (sqrt n) in n 33.895 * [taylor]: Taking taylor expansion of n in n 33.895 * [backup-simplify]: Simplify 0 into 0 33.895 * [backup-simplify]: Simplify 1 into 1 33.896 * [backup-simplify]: Simplify (sqrt 0) into 0 33.897 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 33.897 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (pow (log 2) 2) (* (pow (sqrt 2) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (log PI) (pow PI 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 6) (pow PI 3)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log (* 2 PI)) 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log n) 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n)))))))))))))))))))))))))))))) in n 33.897 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (pow (log 2) 2) (* (pow (sqrt 2) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (log PI) (pow PI 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 6) (pow PI 3)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log (* 2 PI)) 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log n) 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n))))))))))))))))))))))))))))) in n 33.897 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (pow (log 2) 2) (* (pow (sqrt 2) 2) PI)) (sqrt n))) in n 33.897 * [taylor]: Taking taylor expansion of +nan.0 in n 33.897 * [backup-simplify]: Simplify +nan.0 into +nan.0 33.897 * [taylor]: Taking taylor expansion of (* (* (pow (log 2) 2) (* (pow (sqrt 2) 2) PI)) (sqrt n)) in n 33.897 * [taylor]: Taking taylor expansion of (* (pow (log 2) 2) (* (pow (sqrt 2) 2) PI)) in n 33.897 * [taylor]: Taking taylor expansion of (pow (log 2) 2) in n 33.897 * [taylor]: Taking taylor expansion of (log 2) in n 33.897 * [taylor]: Taking taylor expansion of 2 in n 33.897 * [backup-simplify]: Simplify 2 into 2 33.897 * [backup-simplify]: Simplify (log 2) into (log 2) 33.897 * [taylor]: Taking taylor expansion of (* (pow (sqrt 2) 2) PI) in n 33.897 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 2) in n 33.897 * [taylor]: Taking taylor expansion of (sqrt 2) in n 33.897 * [taylor]: Taking taylor expansion of 2 in n 33.897 * [backup-simplify]: Simplify 2 into 2 33.897 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 33.898 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 33.898 * [taylor]: Taking taylor expansion of PI in n 33.898 * [backup-simplify]: Simplify PI into PI 33.898 * [taylor]: Taking taylor expansion of (sqrt n) in n 33.898 * [taylor]: Taking taylor expansion of n in n 33.898 * [backup-simplify]: Simplify 0 into 0 33.898 * [backup-simplify]: Simplify 1 into 1 33.898 * [backup-simplify]: Simplify (sqrt 0) into 0 33.899 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 33.899 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (log PI) (pow PI 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 6) (pow PI 3)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log (* 2 PI)) 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log n) 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n)))))))))))))))))))))))))))) in n 33.899 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (log PI) (pow PI 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 6) (pow PI 3)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log (* 2 PI)) 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log n) 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n))))))))))))))))))))))))))) in n 33.899 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (pow (sqrt 2) 4) (* (log PI) (pow PI 2))) (sqrt n))) in n 33.899 * [taylor]: Taking taylor expansion of +nan.0 in n 33.899 * [backup-simplify]: Simplify +nan.0 into +nan.0 33.899 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 2) 4) (* (log PI) (pow PI 2))) (sqrt n)) in n 33.899 * [taylor]: Taking taylor expansion of (* (pow (sqrt 2) 4) (* (log PI) (pow PI 2))) in n 33.899 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 4) in n 33.899 * [taylor]: Taking taylor expansion of (sqrt 2) in n 33.899 * [taylor]: Taking taylor expansion of 2 in n 33.899 * [backup-simplify]: Simplify 2 into 2 33.900 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 33.900 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 33.900 * [taylor]: Taking taylor expansion of (* (log PI) (pow PI 2)) in n 33.900 * [taylor]: Taking taylor expansion of (log PI) in n 33.900 * [taylor]: Taking taylor expansion of PI in n 33.900 * [backup-simplify]: Simplify PI into PI 33.900 * [backup-simplify]: Simplify (log PI) into (log PI) 33.900 * [taylor]: Taking taylor expansion of (pow PI 2) in n 33.900 * [taylor]: Taking taylor expansion of PI in n 33.900 * [backup-simplify]: Simplify PI into PI 33.900 * [taylor]: Taking taylor expansion of (sqrt n) in n 33.900 * [taylor]: Taking taylor expansion of n in n 33.900 * [backup-simplify]: Simplify 0 into 0 33.900 * [backup-simplify]: Simplify 1 into 1 33.901 * [backup-simplify]: Simplify (sqrt 0) into 0 33.901 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 33.901 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (pow (sqrt 2) 6) (pow PI 3)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log (* 2 PI)) 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log n) 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n)))))))))))))))))))))))))) in n 33.902 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (pow (sqrt 2) 6) (pow PI 3)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log (* 2 PI)) 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log n) 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n))))))))))))))))))))))))) in n 33.902 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (pow (sqrt 2) 6) (pow PI 3)) (sqrt n))) in n 33.902 * [taylor]: Taking taylor expansion of +nan.0 in n 33.902 * [backup-simplify]: Simplify +nan.0 into +nan.0 33.902 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 2) 6) (pow PI 3)) (sqrt n)) in n 33.902 * [taylor]: Taking taylor expansion of (* (pow (sqrt 2) 6) (pow PI 3)) in n 33.902 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 6) in n 33.902 * [taylor]: Taking taylor expansion of (sqrt 2) in n 33.902 * [taylor]: Taking taylor expansion of 2 in n 33.902 * [backup-simplify]: Simplify 2 into 2 33.902 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 33.902 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 33.902 * [taylor]: Taking taylor expansion of (pow PI 3) in n 33.902 * [taylor]: Taking taylor expansion of PI in n 33.902 * [backup-simplify]: Simplify PI into PI 33.902 * [taylor]: Taking taylor expansion of (sqrt n) in n 33.902 * [taylor]: Taking taylor expansion of n in n 33.902 * [backup-simplify]: Simplify 0 into 0 33.902 * [backup-simplify]: Simplify 1 into 1 33.903 * [backup-simplify]: Simplify (sqrt 0) into 0 33.904 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 33.904 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log (* 2 PI)) 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log n) 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n)))))))))))))))))))))))) in n 33.904 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log (* 2 PI)) 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log n) 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n))))))))))))))))))))))) in n 33.904 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log (* 2 PI)) 2))) (sqrt n))) in n 33.904 * [taylor]: Taking taylor expansion of +nan.0 in n 33.904 * [backup-simplify]: Simplify +nan.0 into +nan.0 33.904 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 2) 2) (* PI (pow (log (* 2 PI)) 2))) (sqrt n)) in n 33.904 * [taylor]: Taking taylor expansion of (* (pow (sqrt 2) 2) (* PI (pow (log (* 2 PI)) 2))) in n 33.904 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 2) in n 33.904 * [taylor]: Taking taylor expansion of (sqrt 2) in n 33.904 * [taylor]: Taking taylor expansion of 2 in n 33.904 * [backup-simplify]: Simplify 2 into 2 33.904 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 33.904 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 33.904 * [taylor]: Taking taylor expansion of (* PI (pow (log (* 2 PI)) 2)) in n 33.904 * [taylor]: Taking taylor expansion of PI in n 33.905 * [backup-simplify]: Simplify PI into PI 33.905 * [taylor]: Taking taylor expansion of (pow (log (* 2 PI)) 2) in n 33.905 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 33.905 * [taylor]: Taking taylor expansion of (* 2 PI) in n 33.905 * [taylor]: Taking taylor expansion of 2 in n 33.905 * [backup-simplify]: Simplify 2 into 2 33.905 * [taylor]: Taking taylor expansion of PI in n 33.905 * [backup-simplify]: Simplify PI into PI 33.905 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 33.906 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 33.906 * [taylor]: Taking taylor expansion of (sqrt n) in n 33.906 * [taylor]: Taking taylor expansion of n in n 33.906 * [backup-simplify]: Simplify 0 into 0 33.906 * [backup-simplify]: Simplify 1 into 1 33.906 * [backup-simplify]: Simplify (sqrt 0) into 0 33.907 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 33.907 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log n) 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n)))))))))))))))))))))) in n 33.907 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log n) 2))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n))))))))))))))))))))) in n 33.907 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (pow (log n) 2))) (sqrt n))) in n 33.907 * [taylor]: Taking taylor expansion of +nan.0 in n 33.907 * [backup-simplify]: Simplify +nan.0 into +nan.0 33.907 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 2) 2) (* PI (pow (log n) 2))) (sqrt n)) in n 33.907 * [taylor]: Taking taylor expansion of (* (pow (sqrt 2) 2) (* PI (pow (log n) 2))) in n 33.907 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 2) in n 33.907 * [taylor]: Taking taylor expansion of (sqrt 2) in n 33.907 * [taylor]: Taking taylor expansion of 2 in n 33.907 * [backup-simplify]: Simplify 2 into 2 33.907 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 33.908 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 33.908 * [taylor]: Taking taylor expansion of (* PI (pow (log n) 2)) in n 33.908 * [taylor]: Taking taylor expansion of PI in n 33.908 * [backup-simplify]: Simplify PI into PI 33.908 * [taylor]: Taking taylor expansion of (pow (log n) 2) in n 33.908 * [taylor]: Taking taylor expansion of (log n) in n 33.908 * [taylor]: Taking taylor expansion of n in n 33.908 * [backup-simplify]: Simplify 0 into 0 33.908 * [backup-simplify]: Simplify 1 into 1 33.908 * [backup-simplify]: Simplify (log 1) into 0 33.908 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 33.908 * [taylor]: Taking taylor expansion of (sqrt n) in n 33.908 * [taylor]: Taking taylor expansion of n in n 33.908 * [backup-simplify]: Simplify 0 into 0 33.908 * [backup-simplify]: Simplify 1 into 1 33.909 * [backup-simplify]: Simplify (sqrt 0) into 0 33.909 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 33.909 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n)))))))))))))))))))) in n 33.909 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n))))))))))))))))))) in n 33.910 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI))))) (sqrt n))) in n 33.910 * [taylor]: Taking taylor expansion of +nan.0 in n 33.910 * [backup-simplify]: Simplify +nan.0 into +nan.0 33.910 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI))))) (sqrt n)) in n 33.910 * [taylor]: Taking taylor expansion of (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI))))) in n 33.910 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 2) in n 33.910 * [taylor]: Taking taylor expansion of (sqrt 2) in n 33.910 * [taylor]: Taking taylor expansion of 2 in n 33.910 * [backup-simplify]: Simplify 2 into 2 33.910 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 33.910 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 33.910 * [taylor]: Taking taylor expansion of (* (log PI) (* PI (log (* 2 PI)))) in n 33.910 * [taylor]: Taking taylor expansion of (log PI) in n 33.910 * [taylor]: Taking taylor expansion of PI in n 33.910 * [backup-simplify]: Simplify PI into PI 33.911 * [backup-simplify]: Simplify (log PI) into (log PI) 33.911 * [taylor]: Taking taylor expansion of (* PI (log (* 2 PI))) in n 33.911 * [taylor]: Taking taylor expansion of PI in n 33.911 * [backup-simplify]: Simplify PI into PI 33.911 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 33.911 * [taylor]: Taking taylor expansion of (* 2 PI) in n 33.911 * [taylor]: Taking taylor expansion of 2 in n 33.911 * [backup-simplify]: Simplify 2 into 2 33.911 * [taylor]: Taking taylor expansion of PI in n 33.911 * [backup-simplify]: Simplify PI into PI 33.911 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 33.912 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 33.912 * [taylor]: Taking taylor expansion of (sqrt n) in n 33.912 * [taylor]: Taking taylor expansion of n in n 33.912 * [backup-simplify]: Simplify 0 into 0 33.912 * [backup-simplify]: Simplify 1 into 1 33.912 * [backup-simplify]: Simplify (sqrt 0) into 0 33.913 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 33.913 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n)))))))))))))))))) in n 33.914 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n))))))))))))))))) in n 33.914 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) (sqrt n))) in n 33.914 * [taylor]: Taking taylor expansion of +nan.0 in n 33.914 * [backup-simplify]: Simplify +nan.0 into +nan.0 33.914 * [taylor]: Taking taylor expansion of (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) (sqrt n)) in n 33.914 * [taylor]: Taking taylor expansion of (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) in n 33.914 * [taylor]: Taking taylor expansion of (log 2) in n 33.914 * [taylor]: Taking taylor expansion of 2 in n 33.914 * [backup-simplify]: Simplify 2 into 2 33.914 * [backup-simplify]: Simplify (log 2) into (log 2) 33.914 * [taylor]: Taking taylor expansion of (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))) in n 33.914 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 2) in n 33.914 * [taylor]: Taking taylor expansion of (sqrt 2) in n 33.914 * [taylor]: Taking taylor expansion of 2 in n 33.914 * [backup-simplify]: Simplify 2 into 2 33.915 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 33.915 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 33.915 * [taylor]: Taking taylor expansion of (* PI (log (* 2 PI))) in n 33.915 * [taylor]: Taking taylor expansion of PI in n 33.915 * [backup-simplify]: Simplify PI into PI 33.915 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 33.915 * [taylor]: Taking taylor expansion of (* 2 PI) in n 33.915 * [taylor]: Taking taylor expansion of 2 in n 33.915 * [backup-simplify]: Simplify 2 into 2 33.915 * [taylor]: Taking taylor expansion of PI in n 33.915 * [backup-simplify]: Simplify PI into PI 33.915 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 33.916 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 33.916 * [taylor]: Taking taylor expansion of (sqrt n) in n 33.916 * [taylor]: Taking taylor expansion of n in n 33.916 * [backup-simplify]: Simplify 0 into 0 33.916 * [backup-simplify]: Simplify 1 into 1 33.916 * [backup-simplify]: Simplify (sqrt 0) into 0 33.917 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 33.917 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n)))))))))))))))) in n 33.917 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n))))))))))))))) in n 33.917 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI))) (sqrt n))) in n 33.917 * [taylor]: Taking taylor expansion of +nan.0 in n 33.917 * [backup-simplify]: Simplify +nan.0 into +nan.0 33.917 * [taylor]: Taking taylor expansion of (* (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI))) (sqrt n)) in n 33.917 * [taylor]: Taking taylor expansion of (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI))) in n 33.917 * [taylor]: Taking taylor expansion of (log 2) in n 33.917 * [taylor]: Taking taylor expansion of 2 in n 33.917 * [backup-simplify]: Simplify 2 into 2 33.918 * [backup-simplify]: Simplify (log 2) into (log 2) 33.918 * [taylor]: Taking taylor expansion of (* (pow (sqrt 2) 2) (* (log PI) PI)) in n 33.918 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 2) in n 33.918 * [taylor]: Taking taylor expansion of (sqrt 2) in n 33.918 * [taylor]: Taking taylor expansion of 2 in n 33.918 * [backup-simplify]: Simplify 2 into 2 33.918 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 33.918 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 33.918 * [taylor]: Taking taylor expansion of (* (log PI) PI) in n 33.918 * [taylor]: Taking taylor expansion of (log PI) in n 33.918 * [taylor]: Taking taylor expansion of PI in n 33.919 * [backup-simplify]: Simplify PI into PI 33.919 * [backup-simplify]: Simplify (log PI) into (log PI) 33.919 * [taylor]: Taking taylor expansion of PI in n 33.919 * [backup-simplify]: Simplify PI into PI 33.919 * [taylor]: Taking taylor expansion of (sqrt n) in n 33.919 * [taylor]: Taking taylor expansion of n in n 33.919 * [backup-simplify]: Simplify 0 into 0 33.919 * [backup-simplify]: Simplify 1 into 1 33.919 * [backup-simplify]: Simplify (sqrt 0) into 0 33.920 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 33.920 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n)))))))))))))) in n 33.920 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n))))))))))))) in n 33.920 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) (sqrt n))) in n 33.920 * [taylor]: Taking taylor expansion of +nan.0 in n 33.920 * [backup-simplify]: Simplify +nan.0 into +nan.0 33.920 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) (sqrt n)) in n 33.920 * [taylor]: Taking taylor expansion of (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) in n 33.920 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 4) in n 33.920 * [taylor]: Taking taylor expansion of (sqrt 2) in n 33.920 * [taylor]: Taking taylor expansion of 2 in n 33.920 * [backup-simplify]: Simplify 2 into 2 33.920 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 33.921 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 33.921 * [taylor]: Taking taylor expansion of (* (pow PI 2) (log n)) in n 33.921 * [taylor]: Taking taylor expansion of (pow PI 2) in n 33.921 * [taylor]: Taking taylor expansion of PI in n 33.921 * [backup-simplify]: Simplify PI into PI 33.921 * [taylor]: Taking taylor expansion of (log n) in n 33.921 * [taylor]: Taking taylor expansion of n in n 33.921 * [backup-simplify]: Simplify 0 into 0 33.921 * [backup-simplify]: Simplify 1 into 1 33.921 * [backup-simplify]: Simplify (log 1) into 0 33.921 * [taylor]: Taking taylor expansion of (sqrt n) in n 33.921 * [taylor]: Taking taylor expansion of n in n 33.921 * [backup-simplify]: Simplify 0 into 0 33.921 * [backup-simplify]: Simplify 1 into 1 33.921 * [backup-simplify]: Simplify (sqrt 0) into 0 33.922 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 33.922 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n)))))))))))) in n 33.922 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n))))))))))) in n 33.922 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) (sqrt n))) in n 33.922 * [taylor]: Taking taylor expansion of +nan.0 in n 33.922 * [backup-simplify]: Simplify +nan.0 into +nan.0 33.922 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) (sqrt n)) in n 33.922 * [taylor]: Taking taylor expansion of (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) in n 33.922 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 4) in n 33.922 * [taylor]: Taking taylor expansion of (sqrt 2) in n 33.923 * [taylor]: Taking taylor expansion of 2 in n 33.923 * [backup-simplify]: Simplify 2 into 2 33.923 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 33.923 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 33.924 * [taylor]: Taking taylor expansion of (* (pow PI 2) (log (* 2 PI))) in n 33.924 * [taylor]: Taking taylor expansion of (pow PI 2) in n 33.924 * [taylor]: Taking taylor expansion of PI in n 33.924 * [backup-simplify]: Simplify PI into PI 33.924 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 33.924 * [taylor]: Taking taylor expansion of (* 2 PI) in n 33.924 * [taylor]: Taking taylor expansion of 2 in n 33.924 * [backup-simplify]: Simplify 2 into 2 33.924 * [taylor]: Taking taylor expansion of PI in n 33.924 * [backup-simplify]: Simplify PI into PI 33.924 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 33.925 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 33.925 * [taylor]: Taking taylor expansion of (sqrt n) in n 33.925 * [taylor]: Taking taylor expansion of n in n 33.925 * [backup-simplify]: Simplify 0 into 0 33.925 * [backup-simplify]: Simplify 1 into 1 33.926 * [backup-simplify]: Simplify (sqrt 0) into 0 33.927 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 33.927 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n)))))))))) in n 33.927 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n))))))))) in n 33.927 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n))) in n 33.927 * [taylor]: Taking taylor expansion of +nan.0 in n 33.927 * [backup-simplify]: Simplify +nan.0 into +nan.0 33.927 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) (sqrt n)) in n 33.927 * [taylor]: Taking taylor expansion of (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) in n 33.927 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 2) in n 33.927 * [taylor]: Taking taylor expansion of (sqrt 2) in n 33.927 * [taylor]: Taking taylor expansion of 2 in n 33.927 * [backup-simplify]: Simplify 2 into 2 33.928 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 33.928 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 33.928 * [taylor]: Taking taylor expansion of (* (pow (log PI) 2) PI) in n 33.928 * [taylor]: Taking taylor expansion of (pow (log PI) 2) in n 33.928 * [taylor]: Taking taylor expansion of (log PI) in n 33.928 * [taylor]: Taking taylor expansion of PI in n 33.928 * [backup-simplify]: Simplify PI into PI 33.929 * [backup-simplify]: Simplify (log PI) into (log PI) 33.929 * [taylor]: Taking taylor expansion of PI in n 33.929 * [backup-simplify]: Simplify PI into PI 33.929 * [taylor]: Taking taylor expansion of (sqrt n) in n 33.929 * [taylor]: Taking taylor expansion of n in n 33.929 * [backup-simplify]: Simplify 0 into 0 33.929 * [backup-simplify]: Simplify 1 into 1 33.929 * [backup-simplify]: Simplify (sqrt 0) into 0 33.931 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 33.931 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n)))))))) in n 33.931 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n))))))) in n 33.931 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n))) in n 33.931 * [taylor]: Taking taylor expansion of +nan.0 in n 33.931 * [backup-simplify]: Simplify +nan.0 into +nan.0 33.931 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) (sqrt n)) in n 33.931 * [taylor]: Taking taylor expansion of (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) in n 33.931 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 2) in n 33.931 * [taylor]: Taking taylor expansion of (sqrt 2) in n 33.931 * [taylor]: Taking taylor expansion of 2 in n 33.931 * [backup-simplify]: Simplify 2 into 2 33.931 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 33.932 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 33.932 * [taylor]: Taking taylor expansion of (* PI (* (log n) (log (* 2 PI)))) in n 33.932 * [taylor]: Taking taylor expansion of PI in n 33.932 * [backup-simplify]: Simplify PI into PI 33.932 * [taylor]: Taking taylor expansion of (* (log n) (log (* 2 PI))) in n 33.932 * [taylor]: Taking taylor expansion of (log n) in n 33.932 * [taylor]: Taking taylor expansion of n in n 33.932 * [backup-simplify]: Simplify 0 into 0 33.932 * [backup-simplify]: Simplify 1 into 1 33.933 * [backup-simplify]: Simplify (log 1) into 0 33.933 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 33.933 * [taylor]: Taking taylor expansion of (* 2 PI) in n 33.933 * [taylor]: Taking taylor expansion of 2 in n 33.933 * [backup-simplify]: Simplify 2 into 2 33.933 * [taylor]: Taking taylor expansion of PI in n 33.933 * [backup-simplify]: Simplify PI into PI 33.933 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 33.934 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 33.934 * [taylor]: Taking taylor expansion of (sqrt n) in n 33.934 * [taylor]: Taking taylor expansion of n in n 33.934 * [backup-simplify]: Simplify 0 into 0 33.934 * [backup-simplify]: Simplify 1 into 1 33.935 * [backup-simplify]: Simplify (sqrt 0) into 0 33.936 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 33.936 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n)))))) in n 33.936 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n))))) in n 33.936 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n))) in n 33.936 * [taylor]: Taking taylor expansion of +nan.0 in n 33.936 * [backup-simplify]: Simplify +nan.0 into +nan.0 33.936 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) (sqrt n)) in n 33.936 * [taylor]: Taking taylor expansion of (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) in n 33.936 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 2) in n 33.936 * [taylor]: Taking taylor expansion of (sqrt 2) in n 33.936 * [taylor]: Taking taylor expansion of 2 in n 33.936 * [backup-simplify]: Simplify 2 into 2 33.937 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 33.937 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 33.937 * [taylor]: Taking taylor expansion of (* (log PI) (* PI (log n))) in n 33.937 * [taylor]: Taking taylor expansion of (log PI) in n 33.938 * [taylor]: Taking taylor expansion of PI in n 33.938 * [backup-simplify]: Simplify PI into PI 33.938 * [backup-simplify]: Simplify (log PI) into (log PI) 33.938 * [taylor]: Taking taylor expansion of (* PI (log n)) in n 33.938 * [taylor]: Taking taylor expansion of PI in n 33.938 * [backup-simplify]: Simplify PI into PI 33.938 * [taylor]: Taking taylor expansion of (log n) in n 33.938 * [taylor]: Taking taylor expansion of n in n 33.938 * [backup-simplify]: Simplify 0 into 0 33.938 * [backup-simplify]: Simplify 1 into 1 33.938 * [backup-simplify]: Simplify (log 1) into 0 33.939 * [taylor]: Taking taylor expansion of (sqrt n) in n 33.939 * [taylor]: Taking taylor expansion of n in n 33.939 * [backup-simplify]: Simplify 0 into 0 33.939 * [backup-simplify]: Simplify 1 into 1 33.939 * [backup-simplify]: Simplify (sqrt 0) into 0 33.940 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 33.940 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n)))) in n 33.940 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n))) in n 33.940 * [taylor]: Taking taylor expansion of +nan.0 in n 33.940 * [backup-simplify]: Simplify +nan.0 into +nan.0 33.940 * [taylor]: Taking taylor expansion of (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) (sqrt n)) in n 33.940 * [taylor]: Taking taylor expansion of (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) in n 33.940 * [taylor]: Taking taylor expansion of (log 2) in n 33.941 * [taylor]: Taking taylor expansion of 2 in n 33.941 * [backup-simplify]: Simplify 2 into 2 33.941 * [backup-simplify]: Simplify (log 2) into (log 2) 33.941 * [taylor]: Taking taylor expansion of (* (pow (sqrt 2) 2) (* PI (log n))) in n 33.941 * [taylor]: Taking taylor expansion of (pow (sqrt 2) 2) in n 33.941 * [taylor]: Taking taylor expansion of (sqrt 2) in n 33.941 * [taylor]: Taking taylor expansion of 2 in n 33.941 * [backup-simplify]: Simplify 2 into 2 33.941 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 33.942 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 33.942 * [taylor]: Taking taylor expansion of (* PI (log n)) in n 33.942 * [taylor]: Taking taylor expansion of PI in n 33.942 * [backup-simplify]: Simplify PI into PI 33.942 * [taylor]: Taking taylor expansion of (log n) in n 33.942 * [taylor]: Taking taylor expansion of n in n 33.942 * [backup-simplify]: Simplify 0 into 0 33.942 * [backup-simplify]: Simplify 1 into 1 33.943 * [backup-simplify]: Simplify (log 1) into 0 33.943 * [taylor]: Taking taylor expansion of (sqrt n) in n 33.943 * [taylor]: Taking taylor expansion of n in n 33.943 * [backup-simplify]: Simplify 0 into 0 33.943 * [backup-simplify]: Simplify 1 into 1 33.943 * [backup-simplify]: Simplify (sqrt 0) into 0 33.944 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 33.946 * [backup-simplify]: Simplify (* (sqrt 2) (sqrt 2)) into (pow (sqrt 2) 2) 33.948 * [backup-simplify]: Simplify (* (pow (sqrt 2) 2) (pow (sqrt 2) 2)) into (pow (sqrt 2) 4) 33.949 * [backup-simplify]: Simplify (* PI PI) into (pow PI 2) 33.951 * [backup-simplify]: Simplify (* (pow (sqrt 2) 4) (pow PI 2)) into (* (pow (sqrt 2) 4) (pow PI 2)) 33.954 * [backup-simplify]: Simplify (* (log 2) (* (pow (sqrt 2) 4) (pow PI 2))) into (* (log 2) (* (pow (sqrt 2) 4) (pow PI 2))) 33.956 * [backup-simplify]: Simplify (* (* (log 2) (* (pow (sqrt 2) 4) (pow PI 2))) 0) into 0 33.956 * [backup-simplify]: Simplify (* +nan.0 0) into 0 33.958 * [backup-simplify]: Simplify (* (log 2) (log 2)) into (pow (log 2) 2) 33.959 * [backup-simplify]: Simplify (* (sqrt 2) (sqrt 2)) into (pow (sqrt 2) 2) 33.960 * [backup-simplify]: Simplify (* (pow (sqrt 2) 2) PI) into (* (pow (sqrt 2) 2) PI) 33.963 * [backup-simplify]: Simplify (* (pow (log 2) 2) (* (pow (sqrt 2) 2) PI)) into (* (pow (log 2) 2) (* (pow (sqrt 2) 2) PI)) 33.965 * [backup-simplify]: Simplify (* (* (pow (log 2) 2) (* (pow (sqrt 2) 2) PI)) 0) into 0 33.972 * [backup-simplify]: Simplify (* +nan.0 0) into 0 33.974 * [backup-simplify]: Simplify (* (sqrt 2) (sqrt 2)) into (pow (sqrt 2) 2) 33.976 * [backup-simplify]: Simplify (* (pow (sqrt 2) 2) (pow (sqrt 2) 2)) into (pow (sqrt 2) 4) 33.977 * [backup-simplify]: Simplify (* PI PI) into (pow PI 2) 33.978 * [backup-simplify]: Simplify (* (log PI) (pow PI 2)) into (* (log PI) (pow PI 2)) 33.982 * [backup-simplify]: Simplify (* (pow (sqrt 2) 4) (* (log PI) (pow PI 2))) into (* (pow (sqrt 2) 4) (* (log PI) (pow PI 2))) 33.983 * [backup-simplify]: Simplify (* (* (pow (sqrt 2) 4) (* (log PI) (pow PI 2))) 0) into 0 33.984 * [backup-simplify]: Simplify (* +nan.0 0) into 0 33.985 * [backup-simplify]: Simplify (* (sqrt 2) (sqrt 2)) into (pow (sqrt 2) 2) 33.987 * [backup-simplify]: Simplify (* (sqrt 2) (pow (sqrt 2) 2)) into (pow (sqrt 2) 3) 33.989 * [backup-simplify]: Simplify (* (pow (sqrt 2) 3) (pow (sqrt 2) 3)) into (pow (sqrt 2) 6) 33.989 * [backup-simplify]: Simplify (* PI PI) into (pow PI 2) 33.990 * [backup-simplify]: Simplify (* PI (pow PI 2)) into (pow PI 3) 33.993 * [backup-simplify]: Simplify (* (pow (sqrt 2) 6) (pow PI 3)) into (* (pow (sqrt 2) 6) (pow PI 3)) 33.994 * [backup-simplify]: Simplify (* (* (pow (sqrt 2) 6) (pow PI 3)) 0) into 0 33.994 * [backup-simplify]: Simplify (* +nan.0 0) into 0 33.996 * [backup-simplify]: Simplify (* (sqrt 2) (sqrt 2)) into (pow (sqrt 2) 2) 33.999 * [backup-simplify]: Simplify (* (log (* 2 PI)) (log (* 2 PI))) into (pow (log (* 2 PI)) 2) 34.001 * [backup-simplify]: Simplify (* PI (pow (log (* 2 PI)) 2)) into (* PI (pow (log (* 2 PI)) 2)) 34.006 * [backup-simplify]: Simplify (* (pow (sqrt 2) 2) (* PI (pow (log (* 2 PI)) 2))) into (* (pow (sqrt 2) 2) (* PI (pow (log (* 2 PI)) 2))) 34.007 * [backup-simplify]: Simplify (* (* (pow (sqrt 2) 2) (* PI (pow (log (* 2 PI)) 2))) 0) into 0 34.007 * [backup-simplify]: Simplify (* +nan.0 0) into 0 34.008 * [backup-simplify]: Simplify (* (sqrt 2) (sqrt 2)) into (pow (sqrt 2) 2) 34.008 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 34.009 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 34.009 * [backup-simplify]: Simplify (* (log n) (log n)) into (pow (log n) 2) 34.009 * [backup-simplify]: Simplify (* PI (pow (log n) 2)) into (* PI (pow (log n) 2)) 34.010 * [backup-simplify]: Simplify (* (pow (sqrt 2) 2) (* PI (pow (log n) 2))) into (* (pow (sqrt 2) 2) (* PI (pow (log n) 2))) 34.010 * [backup-simplify]: Simplify (* (* (pow (sqrt 2) 2) (* PI (pow (log n) 2))) 0) into 0 34.010 * [backup-simplify]: Simplify (* +nan.0 0) into 0 34.011 * [backup-simplify]: Simplify (* (sqrt 2) (sqrt 2)) into (pow (sqrt 2) 2) 34.012 * [backup-simplify]: Simplify (* PI (log (* 2 PI))) into (* PI (log (* 2 PI))) 34.014 * [backup-simplify]: Simplify (* (log PI) (* PI (log (* 2 PI)))) into (* (log PI) (* PI (log (* 2 PI)))) 34.018 * [backup-simplify]: Simplify (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI))))) into (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI))))) 34.019 * [backup-simplify]: Simplify (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log (* 2 PI))))) 0) into 0 34.019 * [backup-simplify]: Simplify (* +nan.0 0) into 0 34.020 * [backup-simplify]: Simplify (* (sqrt 2) (sqrt 2)) into (pow (sqrt 2) 2) 34.021 * [backup-simplify]: Simplify (* PI (log (* 2 PI))) into (* PI (log (* 2 PI))) 34.023 * [backup-simplify]: Simplify (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))) into (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))) 34.027 * [backup-simplify]: Simplify (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) into (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) 34.028 * [backup-simplify]: Simplify (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) 0) into 0 34.028 * [backup-simplify]: Simplify (* +nan.0 0) into 0 34.029 * [backup-simplify]: Simplify (* (sqrt 2) (sqrt 2)) into (pow (sqrt 2) 2) 34.029 * [backup-simplify]: Simplify (* (log PI) PI) into (* (log PI) PI) 34.031 * [backup-simplify]: Simplify (* (pow (sqrt 2) 2) (* (log PI) PI)) into (* (pow (sqrt 2) 2) (* (log PI) PI)) 34.034 * [backup-simplify]: Simplify (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI))) into (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI))) 34.035 * [backup-simplify]: Simplify (* (* (log 2) (* (pow (sqrt 2) 2) (* (log PI) PI))) 0) into 0 34.035 * [backup-simplify]: Simplify (* +nan.0 0) into 0 34.036 * [backup-simplify]: Simplify (* (sqrt 2) (sqrt 2)) into (pow (sqrt 2) 2) 34.037 * [backup-simplify]: Simplify (* (pow (sqrt 2) 2) (pow (sqrt 2) 2)) into (pow (sqrt 2) 4) 34.037 * [backup-simplify]: Simplify (* PI PI) into (pow PI 2) 34.038 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 34.038 * [backup-simplify]: Simplify (* (pow PI 2) (log n)) into (* (pow PI 2) (log n)) 34.039 * [backup-simplify]: Simplify (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) into (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) 34.040 * [backup-simplify]: Simplify (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log n))) 0) into 0 34.040 * [backup-simplify]: Simplify (* +nan.0 0) into 0 34.041 * [backup-simplify]: Simplify (* (sqrt 2) (sqrt 2)) into (pow (sqrt 2) 2) 34.042 * [backup-simplify]: Simplify (* (pow (sqrt 2) 2) (pow (sqrt 2) 2)) into (pow (sqrt 2) 4) 34.042 * [backup-simplify]: Simplify (* PI PI) into (pow PI 2) 34.044 * [backup-simplify]: Simplify (* (pow PI 2) (log (* 2 PI))) into (* (pow PI 2) (log (* 2 PI))) 34.047 * [backup-simplify]: Simplify (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) into (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) 34.048 * [backup-simplify]: Simplify (* (* (pow (sqrt 2) 4) (* (pow PI 2) (log (* 2 PI)))) 0) into 0 34.048 * [backup-simplify]: Simplify (* +nan.0 0) into 0 34.049 * [backup-simplify]: Simplify (* (sqrt 2) (sqrt 2)) into (pow (sqrt 2) 2) 34.050 * [backup-simplify]: Simplify (* (log PI) (log PI)) into (pow (log PI) 2) 34.051 * [backup-simplify]: Simplify (* (pow (log PI) 2) PI) into (* (pow (log PI) 2) PI) 34.053 * [backup-simplify]: Simplify (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) into (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) 34.054 * [backup-simplify]: Simplify (* (* (pow (sqrt 2) 2) (* (pow (log PI) 2) PI)) 0) into 0 34.054 * [backup-simplify]: Simplify (* +nan.0 0) into 0 34.055 * [backup-simplify]: Simplify (* (sqrt 2) (sqrt 2)) into (pow (sqrt 2) 2) 34.056 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 34.057 * [backup-simplify]: Simplify (* (log n) (log (* 2 PI))) into (* (log n) (log (* 2 PI))) 34.058 * [backup-simplify]: Simplify (* PI (* (log n) (log (* 2 PI)))) into (* PI (* (log n) (log (* 2 PI)))) 34.060 * [backup-simplify]: Simplify (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) into (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) 34.062 * [backup-simplify]: Simplify (* (* (pow (sqrt 2) 2) (* PI (* (log n) (log (* 2 PI))))) 0) into 0 34.062 * [backup-simplify]: Simplify (* +nan.0 0) into 0 34.063 * [backup-simplify]: Simplify (* (sqrt 2) (sqrt 2)) into (pow (sqrt 2) 2) 34.064 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 34.064 * [backup-simplify]: Simplify (* PI (log n)) into (* PI (log n)) 34.064 * [backup-simplify]: Simplify (* (log PI) (* PI (log n))) into (* (log PI) (* PI (log n))) 34.065 * [backup-simplify]: Simplify (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) into (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) 34.067 * [backup-simplify]: Simplify (* (* (pow (sqrt 2) 2) (* (log PI) (* PI (log n)))) 0) into 0 34.067 * [backup-simplify]: Simplify (* +nan.0 0) into 0 34.068 * [backup-simplify]: Simplify (* (sqrt 2) (sqrt 2)) into (pow (sqrt 2) 2) 34.069 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 34.069 * [backup-simplify]: Simplify (* PI (log n)) into (* PI (log n)) 34.070 * [backup-simplify]: Simplify (* (pow (sqrt 2) 2) (* PI (log n))) into (* (pow (sqrt 2) 2) (* PI (log n))) 34.071 * [backup-simplify]: Simplify (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) into (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) 34.072 * [backup-simplify]: Simplify (* (* (log 2) (* (pow (sqrt 2) 2) (* PI (log n)))) 0) into 0 34.072 * [backup-simplify]: Simplify (* +nan.0 0) into 0 34.072 * [backup-simplify]: Simplify (- 0) into 0 34.072 * [backup-simplify]: Simplify (+ 0 0) into 0 34.073 * [backup-simplify]: Simplify (- 0) into 0 34.073 * [backup-simplify]: Simplify (+ 0 0) into 0 34.073 * [backup-simplify]: Simplify (- 0) into 0 34.073 * [backup-simplify]: Simplify (+ 0 0) into 0 34.074 * [backup-simplify]: Simplify (- 0) into 0 34.074 * [backup-simplify]: Simplify (+ 0 0) into 0 34.074 * [backup-simplify]: Simplify (- 0) into 0 34.075 * [backup-simplify]: Simplify (+ 0 0) into 0 34.075 * [backup-simplify]: Simplify (- 0) into 0 34.075 * [backup-simplify]: Simplify (+ 0 0) into 0 34.075 * [backup-simplify]: Simplify (- 0) into 0 34.076 * [backup-simplify]: Simplify (+ 0 0) into 0 34.076 * [backup-simplify]: Simplify (- 0) into 0 34.076 * [backup-simplify]: Simplify (+ 0 0) into 0 34.076 * [backup-simplify]: Simplify (- 0) into 0 34.076 * [backup-simplify]: Simplify (+ 0 0) into 0 34.077 * [backup-simplify]: Simplify (- 0) into 0 34.077 * [backup-simplify]: Simplify (+ 0 0) into 0 34.077 * [backup-simplify]: Simplify (- 0) into 0 34.082 * [backup-simplify]: Simplify (+ 0 0) into 0 34.083 * [backup-simplify]: Simplify (- 0) into 0 34.083 * [backup-simplify]: Simplify (+ 0 0) into 0 34.084 * [backup-simplify]: Simplify (- 0) into 0 34.084 * [backup-simplify]: Simplify (+ 0 0) into 0 34.084 * [backup-simplify]: Simplify (- 0) into 0 34.084 * [backup-simplify]: Simplify (+ 0 0) into 0 34.085 * [backup-simplify]: Simplify (- 0) into 0 34.085 * [backup-simplify]: Simplify 0 into 0 34.085 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (sqrt 2))) into 0 34.086 * [backup-simplify]: Simplify (+ (* (pow (sqrt 2) 2) 0) (* 0 PI)) into 0 34.087 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 34.088 * [backup-simplify]: Simplify (+ (* (log 2) 0) (* 0 (* (pow (sqrt 2) 2) PI))) into 0 34.091 * [backup-simplify]: Simplify (+ (* (* (log 2) (* (pow (sqrt 2) 2) PI)) +nan.0) (* 0 0)) into (- (* +nan.0 (* (log 2) (* (pow (sqrt 2) 2) PI)))) 34.097 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (log 2) (* (pow (sqrt 2) 2) PI))))) (* 0 0)) into (- (* +nan.0 (* (log 2) (* (pow (sqrt 2) 2) PI)))) 34.098 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 34.098 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 34.098 * [backup-simplify]: Simplify (+ (* PI 0) (* 0 (log n))) into 0 34.099 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (sqrt 2))) into 0 34.100 * [backup-simplify]: Simplify (+ (* (pow (sqrt 2) 2) 0) (* 0 (* PI (log n)))) into 0 34.101 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 2) 2) (* PI (log n))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log n))))) 34.103 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log n)))))) (* 0 0)) into (- (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log n))))) 34.104 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 34.105 * [backup-simplify]: Simplify (+ (* (log PI) 0) (* 0 PI)) into 0 34.106 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (sqrt 2))) into 0 34.107 * [backup-simplify]: Simplify (+ (* (pow (sqrt 2) 2) 0) (* 0 (* (log PI) PI))) into 0 34.114 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 2) 2) (* (log PI) PI)) +nan.0) (* 0 0)) into (- (* +nan.0 (* (pow (sqrt 2) 2) (* (log PI) PI)))) 34.123 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (pow (sqrt 2) 2) (* (log PI) PI))))) (* 0 0)) into (- (* +nan.0 (* (pow (sqrt 2) 2) (* (log PI) PI)))) 34.124 * [backup-simplify]: Simplify (+ (* PI 0) (* 0 PI)) into 0 34.124 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (sqrt 2))) into 0 34.125 * [backup-simplify]: Simplify (+ (* (pow (sqrt 2) 2) 0) (* 0 (pow (sqrt 2) 2))) into 0 34.126 * [backup-simplify]: Simplify (+ (* (pow (sqrt 2) 4) 0) (* 0 (pow PI 2))) into 0 34.129 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 2) 4) (pow PI 2)) +nan.0) (* 0 0)) into (- (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2)))) 34.134 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2))))) (* 0 0)) into (- (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2)))) 34.134 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 34.136 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 34.136 * [backup-simplify]: Simplify (+ (* PI 0) (* 0 (log (* 2 PI)))) into 0 34.137 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (sqrt 2))) into 0 34.138 * [backup-simplify]: Simplify (+ (* (pow (sqrt 2) 2) 0) (* 0 (* PI (log (* 2 PI))))) into 0 34.142 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))))) 34.149 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))))) (* 0 0)) into (- (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))))) 34.154 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))))) into (- (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))))) 34.163 * [backup-simplify]: Simplify (+ (- (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2)))) (- (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))))) into (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2))) (- (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))))))) 34.180 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2))) (- (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2))) (- (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))))))) 34.214 * [backup-simplify]: Simplify (+ (- (* +nan.0 (* (pow (sqrt 2) 2) (* (log PI) PI)))) (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2))) (- (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2))) (- (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))))))))) 34.235 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2))) (- (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2))) (- (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))))))))) 34.252 * [backup-simplify]: Simplify (+ (- (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log n))))) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2))) (- (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log n)))) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2))) (- (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))))))))))) 34.271 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log n)))) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2))) (- (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))))))))))) into (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log n)))) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2))) (- (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI)))))))))))) 34.315 * [backup-simplify]: Simplify (+ (- (* +nan.0 (* (log 2) (* (pow (sqrt 2) 2) PI)))) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log n)))) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2))) (- (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))))))))))) into (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (pow (sqrt 2) 2) PI))) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) (- (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2)))))))))))) 34.367 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (pow (sqrt 2) 2) PI))) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) (- (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2))))))))))))) into (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (pow (sqrt 2) 2) PI))) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) (- (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2)))))))))))) 34.416 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (pow (sqrt 2) 2) PI))) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) (- (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2)))))))))))) into (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (pow (sqrt 2) 2) PI))) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) (- (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2)))))))))))) 34.420 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 34.421 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 34.422 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (* 0 (sqrt 2)))) into 0 34.423 * [backup-simplify]: Simplify (+ (* (pow (sqrt 2) 2) 0) (+ (* 0 0) (* 0 PI))) into 0 34.428 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 2) 2) PI) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (pow (sqrt 2) 2) PI))) 34.436 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (pow (sqrt 2) 2) PI)))) (+ (* 0 (- (* +nan.0 (* (pow (sqrt 2) 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (pow (sqrt 2) 2) PI))) 34.440 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (pow (sqrt 2) 2) PI)))) into (- (* +nan.0 (* (pow (sqrt 2) 2) PI))) 34.444 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 2) 2) PI))) into (- (* +nan.0 (* (pow (sqrt 2) 2) PI))) 34.508 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (pow (sqrt 2) 2) PI))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (pow (sqrt 2) 2) PI))) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* PI (log (* 2 PI))))) (- (* +nan.0 (* (pow (sqrt 2) 4) (pow PI 2)))))))))))) (* n k)) (* (- (* +nan.0 (* (pow (sqrt 2) 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (log 2) (* (pow (sqrt 2) 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (pow (sqrt 2) 4) (* n (* (pow PI 2) k)))) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* n (* PI (* (log PI) k))))) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* n PI))) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* n (* PI (* (log n) k))))) (- (+ (* +nan.0 (* (pow (sqrt 2) 2) (* (pow n 2) PI))) (- (* +nan.0 (* (log (* 2 PI)) (* (pow (sqrt 2) 2) (* n (* PI k)))))))))))))))))) 34.508 * [backup-simplify]: Simplify (* (* (sqrt (pow 2 (- 1/2 (/ (/ 1 k) 2)))) (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2)))) (/ (sqrt (pow PI (- 1/2 (/ (/ 1 k) 2)))) (/ (sqrt (/ 1 k)) (sqrt (pow (* 2 PI) (- 1/2 (/ (/ 1 k) 2))))))) into (* (sqrt (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) 34.509 * [approximate]: Taking taylor expansion of (* (sqrt (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in (k n) around 0 34.509 * [taylor]: Taking taylor expansion of (* (sqrt (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 34.509 * [taylor]: Taking taylor expansion of (sqrt (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k)))) in n 34.509 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k))) in n 34.509 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in n 34.509 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in n 34.509 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in n 34.509 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 34.509 * [taylor]: Taking taylor expansion of 1/2 in n 34.509 * [backup-simplify]: Simplify 1/2 into 1/2 34.509 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.509 * [taylor]: Taking taylor expansion of 1/2 in n 34.509 * [backup-simplify]: Simplify 1/2 into 1/2 34.509 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.509 * [taylor]: Taking taylor expansion of k in n 34.509 * [backup-simplify]: Simplify k into k 34.509 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.509 * [taylor]: Taking taylor expansion of (log 2) in n 34.509 * [taylor]: Taking taylor expansion of 2 in n 34.509 * [backup-simplify]: Simplify 2 into 2 34.509 * [backup-simplify]: Simplify (log 2) into (log 2) 34.509 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.509 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 34.509 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 34.510 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 34.510 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 34.510 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k)) in n 34.510 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 34.510 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 34.510 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 34.510 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 34.510 * [taylor]: Taking taylor expansion of 1/2 in n 34.510 * [backup-simplify]: Simplify 1/2 into 1/2 34.510 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.510 * [taylor]: Taking taylor expansion of 1/2 in n 34.510 * [backup-simplify]: Simplify 1/2 into 1/2 34.510 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.510 * [taylor]: Taking taylor expansion of k in n 34.510 * [backup-simplify]: Simplify k into k 34.510 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.510 * [taylor]: Taking taylor expansion of (log PI) in n 34.510 * [taylor]: Taking taylor expansion of PI in n 34.510 * [backup-simplify]: Simplify PI into PI 34.511 * [backup-simplify]: Simplify (log PI) into (log PI) 34.511 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.511 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 34.511 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 34.511 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 34.511 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 34.511 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k) in n 34.511 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in n 34.511 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in n 34.511 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in n 34.511 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 34.511 * [taylor]: Taking taylor expansion of 1/2 in n 34.512 * [backup-simplify]: Simplify 1/2 into 1/2 34.512 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.512 * [taylor]: Taking taylor expansion of 1/2 in n 34.512 * [backup-simplify]: Simplify 1/2 into 1/2 34.512 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.512 * [taylor]: Taking taylor expansion of k in n 34.512 * [backup-simplify]: Simplify k into k 34.512 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.512 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 34.512 * [taylor]: Taking taylor expansion of (* 2 PI) in n 34.512 * [taylor]: Taking taylor expansion of 2 in n 34.512 * [backup-simplify]: Simplify 2 into 2 34.512 * [taylor]: Taking taylor expansion of PI in n 34.512 * [backup-simplify]: Simplify PI into PI 34.512 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 34.513 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 34.513 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.513 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 34.513 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 34.514 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) into (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) 34.514 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 34.514 * [taylor]: Taking taylor expansion of k in n 34.514 * [backup-simplify]: Simplify k into k 34.515 * [backup-simplify]: Simplify (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k) into (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k) 34.515 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k)) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k)) 34.516 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k))) 34.517 * [backup-simplify]: Simplify (sqrt (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k)))) into (sqrt (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k)))) 34.518 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 34.519 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 34.519 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 34.519 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 34.519 * [backup-simplify]: Simplify (- 0) into 0 34.520 * [backup-simplify]: Simplify (+ 0 0) into 0 34.520 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (log (* 2 PI)))) into 0 34.521 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) (+ (* (/ (pow 0 1) 1)))) into 0 34.522 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 k)) into 0 34.523 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 34.523 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 34.523 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 34.523 * [backup-simplify]: Simplify (- 0) into 0 34.524 * [backup-simplify]: Simplify (+ 0 0) into 0 34.524 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (log PI))) into 0 34.525 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 34.526 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k))) into 0 34.526 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 34.527 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 34.527 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 34.527 * [backup-simplify]: Simplify (- 0) into 0 34.527 * [backup-simplify]: Simplify (+ 0 0) into 0 34.528 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (log 2))) into 0 34.528 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 34.529 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k)))) into 0 34.530 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k)))))) into 0 34.530 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 34.530 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 34.530 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 34.530 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 34.530 * [taylor]: Taking taylor expansion of 1/2 in n 34.530 * [backup-simplify]: Simplify 1/2 into 1/2 34.530 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.530 * [taylor]: Taking taylor expansion of 1/2 in n 34.530 * [backup-simplify]: Simplify 1/2 into 1/2 34.530 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.530 * [taylor]: Taking taylor expansion of k in n 34.530 * [backup-simplify]: Simplify k into k 34.530 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.530 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 34.530 * [taylor]: Taking taylor expansion of (/ 1 n) in n 34.530 * [taylor]: Taking taylor expansion of n in n 34.530 * [backup-simplify]: Simplify 0 into 0 34.530 * [backup-simplify]: Simplify 1 into 1 34.531 * [backup-simplify]: Simplify (/ 1 1) into 1 34.531 * [backup-simplify]: Simplify (log 1) into 0 34.531 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.531 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 34.531 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 34.532 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 34.532 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 34.532 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 34.532 * [taylor]: Taking taylor expansion of (* (sqrt (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 34.532 * [taylor]: Taking taylor expansion of (sqrt (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k)))) in k 34.532 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k))) in k 34.532 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in k 34.532 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in k 34.532 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in k 34.532 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 34.532 * [taylor]: Taking taylor expansion of 1/2 in k 34.532 * [backup-simplify]: Simplify 1/2 into 1/2 34.532 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 34.532 * [taylor]: Taking taylor expansion of 1/2 in k 34.532 * [backup-simplify]: Simplify 1/2 into 1/2 34.532 * [taylor]: Taking taylor expansion of (/ 1 k) in k 34.532 * [taylor]: Taking taylor expansion of k in k 34.532 * [backup-simplify]: Simplify 0 into 0 34.532 * [backup-simplify]: Simplify 1 into 1 34.533 * [backup-simplify]: Simplify (/ 1 1) into 1 34.533 * [taylor]: Taking taylor expansion of (log 2) in k 34.533 * [taylor]: Taking taylor expansion of 2 in k 34.533 * [backup-simplify]: Simplify 2 into 2 34.533 * [backup-simplify]: Simplify (log 2) into (log 2) 34.534 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 34.534 * [backup-simplify]: Simplify (- 1/2) into -1/2 34.534 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 34.535 * [backup-simplify]: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2)) 34.536 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 34.536 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k)) in k 34.536 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 34.536 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 34.536 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 34.536 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 34.536 * [taylor]: Taking taylor expansion of 1/2 in k 34.536 * [backup-simplify]: Simplify 1/2 into 1/2 34.536 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 34.536 * [taylor]: Taking taylor expansion of 1/2 in k 34.536 * [backup-simplify]: Simplify 1/2 into 1/2 34.536 * [taylor]: Taking taylor expansion of (/ 1 k) in k 34.536 * [taylor]: Taking taylor expansion of k in k 34.536 * [backup-simplify]: Simplify 0 into 0 34.536 * [backup-simplify]: Simplify 1 into 1 34.537 * [backup-simplify]: Simplify (/ 1 1) into 1 34.537 * [taylor]: Taking taylor expansion of (log PI) in k 34.537 * [taylor]: Taking taylor expansion of PI in k 34.537 * [backup-simplify]: Simplify PI into PI 34.537 * [backup-simplify]: Simplify (log PI) into (log PI) 34.538 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 34.538 * [backup-simplify]: Simplify (- 1/2) into -1/2 34.538 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 34.539 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 34.540 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 34.540 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k) in k 34.540 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in k 34.540 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in k 34.540 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in k 34.540 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 34.540 * [taylor]: Taking taylor expansion of 1/2 in k 34.540 * [backup-simplify]: Simplify 1/2 into 1/2 34.540 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 34.540 * [taylor]: Taking taylor expansion of 1/2 in k 34.540 * [backup-simplify]: Simplify 1/2 into 1/2 34.540 * [taylor]: Taking taylor expansion of (/ 1 k) in k 34.540 * [taylor]: Taking taylor expansion of k in k 34.540 * [backup-simplify]: Simplify 0 into 0 34.540 * [backup-simplify]: Simplify 1 into 1 34.540 * [backup-simplify]: Simplify (/ 1 1) into 1 34.540 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 34.540 * [taylor]: Taking taylor expansion of (* 2 PI) in k 34.540 * [taylor]: Taking taylor expansion of 2 in k 34.541 * [backup-simplify]: Simplify 2 into 2 34.541 * [taylor]: Taking taylor expansion of PI in k 34.541 * [backup-simplify]: Simplify PI into PI 34.541 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 34.542 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 34.542 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 34.543 * [backup-simplify]: Simplify (- 1/2) into -1/2 34.543 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 34.545 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) 34.546 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 34.546 * [taylor]: Taking taylor expansion of k in k 34.546 * [backup-simplify]: Simplify 0 into 0 34.546 * [backup-simplify]: Simplify 1 into 1 34.547 * [backup-simplify]: Simplify (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 0) into 0 34.547 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) into 0 34.547 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 34.548 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 1) (* 0 0)) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 34.549 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) (* 0 0)) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) 34.551 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 0)) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))) 34.551 * [backup-simplify]: Simplify (sqrt 0) into 0 34.553 * [backup-simplify]: Simplify (/ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))) (* 2 (sqrt 0))) into (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) 34.553 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 34.553 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in k 34.553 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in k 34.553 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 34.553 * [taylor]: Taking taylor expansion of 1/2 in k 34.553 * [backup-simplify]: Simplify 1/2 into 1/2 34.553 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 34.553 * [taylor]: Taking taylor expansion of 1/2 in k 34.553 * [backup-simplify]: Simplify 1/2 into 1/2 34.553 * [taylor]: Taking taylor expansion of (/ 1 k) in k 34.553 * [taylor]: Taking taylor expansion of k in k 34.553 * [backup-simplify]: Simplify 0 into 0 34.553 * [backup-simplify]: Simplify 1 into 1 34.554 * [backup-simplify]: Simplify (/ 1 1) into 1 34.554 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k 34.554 * [taylor]: Taking taylor expansion of (/ 1 n) in k 34.554 * [taylor]: Taking taylor expansion of n in k 34.554 * [backup-simplify]: Simplify n into n 34.554 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n) 34.554 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n)) 34.554 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 34.555 * [backup-simplify]: Simplify (- 1/2) into -1/2 34.555 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 34.555 * [backup-simplify]: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) 34.555 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 34.555 * [taylor]: Taking taylor expansion of (* (sqrt (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 34.555 * [taylor]: Taking taylor expansion of (sqrt (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k)))) in k 34.555 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k))) in k 34.555 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in k 34.555 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in k 34.555 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in k 34.556 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 34.556 * [taylor]: Taking taylor expansion of 1/2 in k 34.556 * [backup-simplify]: Simplify 1/2 into 1/2 34.556 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 34.556 * [taylor]: Taking taylor expansion of 1/2 in k 34.556 * [backup-simplify]: Simplify 1/2 into 1/2 34.556 * [taylor]: Taking taylor expansion of (/ 1 k) in k 34.556 * [taylor]: Taking taylor expansion of k in k 34.556 * [backup-simplify]: Simplify 0 into 0 34.556 * [backup-simplify]: Simplify 1 into 1 34.556 * [backup-simplify]: Simplify (/ 1 1) into 1 34.556 * [taylor]: Taking taylor expansion of (log 2) in k 34.556 * [taylor]: Taking taylor expansion of 2 in k 34.556 * [backup-simplify]: Simplify 2 into 2 34.557 * [backup-simplify]: Simplify (log 2) into (log 2) 34.557 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 34.558 * [backup-simplify]: Simplify (- 1/2) into -1/2 34.558 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 34.559 * [backup-simplify]: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2)) 34.559 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 34.559 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k)) in k 34.559 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 34.559 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 34.559 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 34.559 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 34.559 * [taylor]: Taking taylor expansion of 1/2 in k 34.559 * [backup-simplify]: Simplify 1/2 into 1/2 34.559 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 34.559 * [taylor]: Taking taylor expansion of 1/2 in k 34.560 * [backup-simplify]: Simplify 1/2 into 1/2 34.560 * [taylor]: Taking taylor expansion of (/ 1 k) in k 34.560 * [taylor]: Taking taylor expansion of k in k 34.560 * [backup-simplify]: Simplify 0 into 0 34.560 * [backup-simplify]: Simplify 1 into 1 34.560 * [backup-simplify]: Simplify (/ 1 1) into 1 34.560 * [taylor]: Taking taylor expansion of (log PI) in k 34.560 * [taylor]: Taking taylor expansion of PI in k 34.560 * [backup-simplify]: Simplify PI into PI 34.560 * [backup-simplify]: Simplify (log PI) into (log PI) 34.561 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 34.561 * [backup-simplify]: Simplify (- 1/2) into -1/2 34.562 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 34.562 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 34.563 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 34.563 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) k) in k 34.563 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in k 34.563 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in k 34.563 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in k 34.563 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 34.563 * [taylor]: Taking taylor expansion of 1/2 in k 34.563 * [backup-simplify]: Simplify 1/2 into 1/2 34.563 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 34.563 * [taylor]: Taking taylor expansion of 1/2 in k 34.563 * [backup-simplify]: Simplify 1/2 into 1/2 34.563 * [taylor]: Taking taylor expansion of (/ 1 k) in k 34.563 * [taylor]: Taking taylor expansion of k in k 34.563 * [backup-simplify]: Simplify 0 into 0 34.563 * [backup-simplify]: Simplify 1 into 1 34.564 * [backup-simplify]: Simplify (/ 1 1) into 1 34.564 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 34.564 * [taylor]: Taking taylor expansion of (* 2 PI) in k 34.564 * [taylor]: Taking taylor expansion of 2 in k 34.564 * [backup-simplify]: Simplify 2 into 2 34.564 * [taylor]: Taking taylor expansion of PI in k 34.564 * [backup-simplify]: Simplify PI into PI 34.564 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 34.566 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 34.566 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 34.566 * [backup-simplify]: Simplify (- 1/2) into -1/2 34.567 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 34.568 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) 34.569 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 34.570 * [taylor]: Taking taylor expansion of k in k 34.570 * [backup-simplify]: Simplify 0 into 0 34.570 * [backup-simplify]: Simplify 1 into 1 34.570 * [backup-simplify]: Simplify (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 0) into 0 34.570 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) into 0 34.571 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 34.571 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 1) (* 0 0)) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 34.572 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) (* 0 0)) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) 34.573 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 0)) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))) 34.573 * [backup-simplify]: Simplify (sqrt 0) into 0 34.574 * [backup-simplify]: Simplify (/ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))) (* 2 (sqrt 0))) into (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) 34.574 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 34.574 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in k 34.574 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in k 34.574 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 34.574 * [taylor]: Taking taylor expansion of 1/2 in k 34.574 * [backup-simplify]: Simplify 1/2 into 1/2 34.574 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 34.574 * [taylor]: Taking taylor expansion of 1/2 in k 34.574 * [backup-simplify]: Simplify 1/2 into 1/2 34.574 * [taylor]: Taking taylor expansion of (/ 1 k) in k 34.574 * [taylor]: Taking taylor expansion of k in k 34.574 * [backup-simplify]: Simplify 0 into 0 34.574 * [backup-simplify]: Simplify 1 into 1 34.575 * [backup-simplify]: Simplify (/ 1 1) into 1 34.575 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k 34.575 * [taylor]: Taking taylor expansion of (/ 1 n) in k 34.575 * [taylor]: Taking taylor expansion of n in k 34.575 * [backup-simplify]: Simplify n into n 34.575 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n) 34.575 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n)) 34.575 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 34.575 * [backup-simplify]: Simplify (- 1/2) into -1/2 34.576 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 34.576 * [backup-simplify]: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) 34.576 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 34.576 * [backup-simplify]: Simplify (* 0 (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) into 0 34.576 * [taylor]: Taking taylor expansion of 0 in n 34.576 * [backup-simplify]: Simplify 0 into 0 34.576 * [backup-simplify]: Simplify 0 into 0 34.577 * [backup-simplify]: Simplify (+ (* 0 0) (* (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))))) 34.577 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))))) in n 34.577 * [taylor]: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) in n 34.577 * [taylor]: Taking taylor expansion of +nan.0 in n 34.577 * [backup-simplify]: Simplify +nan.0 into +nan.0 34.577 * [taylor]: Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 34.577 * [taylor]: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n 34.577 * [taylor]: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n 34.577 * [taylor]: Taking taylor expansion of (log 2) in n 34.577 * [taylor]: Taking taylor expansion of 2 in n 34.577 * [backup-simplify]: Simplify 2 into 2 34.578 * [backup-simplify]: Simplify (log 2) into (log 2) 34.578 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 34.578 * [taylor]: Taking taylor expansion of 1/2 in n 34.578 * [backup-simplify]: Simplify 1/2 into 1/2 34.578 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.578 * [taylor]: Taking taylor expansion of 1/2 in n 34.578 * [backup-simplify]: Simplify 1/2 into 1/2 34.578 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.578 * [taylor]: Taking taylor expansion of k in n 34.578 * [backup-simplify]: Simplify k into k 34.578 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.578 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.578 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 34.578 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 34.579 * [backup-simplify]: Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 34.579 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 34.579 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 34.579 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 34.579 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 34.579 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 34.579 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 34.579 * [taylor]: Taking taylor expansion of 1/2 in n 34.579 * [backup-simplify]: Simplify 1/2 into 1/2 34.579 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.579 * [taylor]: Taking taylor expansion of 1/2 in n 34.579 * [backup-simplify]: Simplify 1/2 into 1/2 34.579 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.579 * [taylor]: Taking taylor expansion of k in n 34.579 * [backup-simplify]: Simplify k into k 34.579 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.579 * [taylor]: Taking taylor expansion of (log PI) in n 34.579 * [taylor]: Taking taylor expansion of PI in n 34.579 * [backup-simplify]: Simplify PI into PI 34.580 * [backup-simplify]: Simplify (log PI) into (log PI) 34.580 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.580 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 34.580 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 34.580 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 34.580 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 34.580 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 34.580 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in n 34.580 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in n 34.581 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in n 34.581 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 34.581 * [taylor]: Taking taylor expansion of 1/2 in n 34.581 * [backup-simplify]: Simplify 1/2 into 1/2 34.581 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.581 * [taylor]: Taking taylor expansion of 1/2 in n 34.581 * [backup-simplify]: Simplify 1/2 into 1/2 34.581 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.581 * [taylor]: Taking taylor expansion of k in n 34.581 * [backup-simplify]: Simplify k into k 34.581 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.581 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 34.581 * [taylor]: Taking taylor expansion of (* 2 PI) in n 34.581 * [taylor]: Taking taylor expansion of 2 in n 34.581 * [backup-simplify]: Simplify 2 into 2 34.581 * [taylor]: Taking taylor expansion of PI in n 34.581 * [backup-simplify]: Simplify PI into PI 34.581 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 34.582 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 34.582 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.582 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 34.582 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 34.583 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) into (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) 34.583 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 34.583 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 34.583 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 34.583 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 34.583 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 34.583 * [taylor]: Taking taylor expansion of 1/2 in n 34.583 * [backup-simplify]: Simplify 1/2 into 1/2 34.583 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.583 * [taylor]: Taking taylor expansion of 1/2 in n 34.584 * [backup-simplify]: Simplify 1/2 into 1/2 34.584 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.584 * [taylor]: Taking taylor expansion of k in n 34.584 * [backup-simplify]: Simplify k into k 34.584 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.584 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 34.584 * [taylor]: Taking taylor expansion of (/ 1 n) in n 34.584 * [taylor]: Taking taylor expansion of n in n 34.584 * [backup-simplify]: Simplify 0 into 0 34.584 * [backup-simplify]: Simplify 1 into 1 34.584 * [backup-simplify]: Simplify (/ 1 1) into 1 34.584 * [backup-simplify]: Simplify (log 1) into 0 34.584 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.584 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 34.584 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 34.590 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 34.590 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 34.590 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 34.591 * [backup-simplify]: Simplify (* (pow (* 2 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 (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) 34.591 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))) 34.592 * [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)))) (pow (* 2 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)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) 34.593 * [backup-simplify]: Simplify (* +nan.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)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))))) into (* +nan.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)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))))) 34.594 * [backup-simplify]: Simplify (- (* +nan.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)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))))) into (- (* +nan.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)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))))) 34.595 * [backup-simplify]: Simplify (- (* +nan.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)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))))) into (- (* +nan.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)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))))) 34.595 * [backup-simplify]: Simplify 0 into 0 34.596 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 1) (* 0 0))) into 0 34.596 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) (* 0 0))) into 0 34.597 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 0))) into 0 34.599 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) 2) (+)) (* 2 0)) into (* +nan.0 (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 2) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 2) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2)))) 34.602 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) 0) (* (* +nan.0 (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 2) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 2) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 2) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 2) (* (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))))) 34.602 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 2) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 2) (* (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))))) in n 34.602 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 2) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 2) (* (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) in n 34.602 * [taylor]: Taking taylor expansion of +nan.0 in n 34.602 * [backup-simplify]: Simplify +nan.0 into +nan.0 34.602 * [taylor]: Taking taylor expansion of (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 2) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 2) (* (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 34.602 * [taylor]: Taking taylor expansion of (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 2) in n 34.602 * [taylor]: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n 34.602 * [taylor]: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n 34.602 * [taylor]: Taking taylor expansion of (log 2) in n 34.602 * [taylor]: Taking taylor expansion of 2 in n 34.602 * [backup-simplify]: Simplify 2 into 2 34.603 * [backup-simplify]: Simplify (log 2) into (log 2) 34.603 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 34.603 * [taylor]: Taking taylor expansion of 1/2 in n 34.603 * [backup-simplify]: Simplify 1/2 into 1/2 34.603 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.603 * [taylor]: Taking taylor expansion of 1/2 in n 34.603 * [backup-simplify]: Simplify 1/2 into 1/2 34.603 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.603 * [taylor]: Taking taylor expansion of k in n 34.603 * [backup-simplify]: Simplify k into k 34.603 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.603 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.603 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 34.603 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 34.604 * [backup-simplify]: Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 34.604 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 34.604 * [taylor]: Taking taylor expansion of (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 2) (* (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 34.604 * [taylor]: Taking taylor expansion of (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 2) in n 34.604 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 34.604 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 34.604 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 34.604 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 34.604 * [taylor]: Taking taylor expansion of 1/2 in n 34.604 * [backup-simplify]: Simplify 1/2 into 1/2 34.604 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.604 * [taylor]: Taking taylor expansion of 1/2 in n 34.605 * [backup-simplify]: Simplify 1/2 into 1/2 34.605 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.605 * [taylor]: Taking taylor expansion of k in n 34.605 * [backup-simplify]: Simplify k into k 34.605 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.605 * [taylor]: Taking taylor expansion of (log PI) in n 34.605 * [taylor]: Taking taylor expansion of PI in n 34.605 * [backup-simplify]: Simplify PI into PI 34.605 * [backup-simplify]: Simplify (log PI) into (log PI) 34.605 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.605 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 34.605 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 34.606 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 34.606 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 34.607 * [taylor]: Taking taylor expansion of (* (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 34.607 * [taylor]: Taking taylor expansion of (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2) in n 34.607 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in n 34.607 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in n 34.607 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in n 34.607 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 34.607 * [taylor]: Taking taylor expansion of 1/2 in n 34.607 * [backup-simplify]: Simplify 1/2 into 1/2 34.607 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.607 * [taylor]: Taking taylor expansion of 1/2 in n 34.607 * [backup-simplify]: Simplify 1/2 into 1/2 34.607 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.607 * [taylor]: Taking taylor expansion of k in n 34.607 * [backup-simplify]: Simplify k into k 34.607 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.607 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 34.607 * [taylor]: Taking taylor expansion of (* 2 PI) in n 34.607 * [taylor]: Taking taylor expansion of 2 in n 34.607 * [backup-simplify]: Simplify 2 into 2 34.607 * [taylor]: Taking taylor expansion of PI in n 34.607 * [backup-simplify]: Simplify PI into PI 34.608 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 34.609 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 34.609 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.609 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 34.609 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 34.611 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) into (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) 34.611 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 34.611 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 34.612 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 34.612 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 34.612 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 34.612 * [taylor]: Taking taylor expansion of 1/2 in n 34.612 * [backup-simplify]: Simplify 1/2 into 1/2 34.612 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.612 * [taylor]: Taking taylor expansion of 1/2 in n 34.612 * [backup-simplify]: Simplify 1/2 into 1/2 34.612 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.612 * [taylor]: Taking taylor expansion of k in n 34.612 * [backup-simplify]: Simplify k into k 34.612 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.612 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 34.612 * [taylor]: Taking taylor expansion of (/ 1 n) in n 34.612 * [taylor]: Taking taylor expansion of n in n 34.612 * [backup-simplify]: Simplify 0 into 0 34.612 * [backup-simplify]: Simplify 1 into 1 34.612 * [backup-simplify]: Simplify (/ 1 1) into 1 34.612 * [backup-simplify]: Simplify (log 1) into 0 34.612 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.612 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 34.612 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 34.613 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 34.613 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 34.613 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 34.614 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))) into (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 2) 34.614 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) into (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 2) 34.614 * [backup-simplify]: Simplify (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) into (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2) 34.615 * [backup-simplify]: Simplify (* (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2) (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2)) 34.615 * [backup-simplify]: Simplify (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 2) (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 2) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2))) 34.616 * [backup-simplify]: Simplify (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 2) (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 2) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2)))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 2) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 2) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2)))) 34.617 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 2) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 2) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2))))) into (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 2) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 2) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2))))) 34.618 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 2) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 2) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2)))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 2) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 2) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2)))))) 34.620 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 2) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 2) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2)))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 2) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 2) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2)))))) 34.620 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 34.621 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 34.621 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 34.621 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 34.622 * [backup-simplify]: Simplify (- 0) into 0 34.622 * [backup-simplify]: Simplify (+ 0 0) into 0 34.622 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 34.622 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 34.623 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 34.623 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 34.624 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 34.624 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 34.625 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 34.625 * [backup-simplify]: Simplify (- 0) into 0 34.625 * [backup-simplify]: Simplify (+ 0 0) into 0 34.626 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (log (* 2 PI)))) into 0 34.627 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) (+ (* (/ (pow 0 1) 1)))) into 0 34.627 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))))) into 0 34.628 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 34.629 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 34.629 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 34.629 * [backup-simplify]: Simplify (- 0) into 0 34.629 * [backup-simplify]: Simplify (+ 0 0) into 0 34.630 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (log PI))) into 0 34.631 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 34.632 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) into 0 34.632 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 34.632 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 34.632 * [backup-simplify]: Simplify (- 0) into 0 34.633 * [backup-simplify]: Simplify (+ 0 0) into 0 34.633 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 34.634 * [backup-simplify]: Simplify (+ (* (log 2) 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0 34.635 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 34.635 * [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)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 34.637 * [backup-simplify]: Simplify (+ (* +nan.0 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)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))))) into 0 34.637 * [backup-simplify]: Simplify (- 0) into 0 34.637 * [backup-simplify]: Simplify 0 into 0 34.637 * [backup-simplify]: Simplify 0 into 0 34.638 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 34.639 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) (* 0 0)))) into 0 34.640 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (+ (* 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 0)))) into 0 34.643 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) (* +nan.0 (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 2) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 2) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2)))))))) (* 2 0)) into (* +nan.0 (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 3) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 3) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 3)))) 34.648 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))))) 0) (+ (* (* +nan.0 (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 2) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 2) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2)))) 0) (* (* +nan.0 (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 3) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 3) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 3)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 3) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 3) (* (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 3) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))))) 34.648 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 3) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 3) (* (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 3) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))))) in n 34.648 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 3) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 3) (* (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 3) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) in n 34.648 * [taylor]: Taking taylor expansion of +nan.0 in n 34.648 * [backup-simplify]: Simplify +nan.0 into +nan.0 34.648 * [taylor]: Taking taylor expansion of (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 3) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 3) (* (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 3) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 34.648 * [taylor]: Taking taylor expansion of (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 3) in n 34.648 * [taylor]: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n 34.648 * [taylor]: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n 34.648 * [taylor]: Taking taylor expansion of (log 2) in n 34.648 * [taylor]: Taking taylor expansion of 2 in n 34.648 * [backup-simplify]: Simplify 2 into 2 34.649 * [backup-simplify]: Simplify (log 2) into (log 2) 34.649 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 34.649 * [taylor]: Taking taylor expansion of 1/2 in n 34.649 * [backup-simplify]: Simplify 1/2 into 1/2 34.649 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.649 * [taylor]: Taking taylor expansion of 1/2 in n 34.649 * [backup-simplify]: Simplify 1/2 into 1/2 34.649 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.649 * [taylor]: Taking taylor expansion of k in n 34.649 * [backup-simplify]: Simplify k into k 34.649 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.649 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.649 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 34.649 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 34.650 * [backup-simplify]: Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 34.650 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 34.651 * [taylor]: Taking taylor expansion of (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 3) (* (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 3) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 34.651 * [taylor]: Taking taylor expansion of (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 3) in n 34.651 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 34.651 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 34.651 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 34.651 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 34.651 * [taylor]: Taking taylor expansion of 1/2 in n 34.651 * [backup-simplify]: Simplify 1/2 into 1/2 34.651 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.651 * [taylor]: Taking taylor expansion of 1/2 in n 34.651 * [backup-simplify]: Simplify 1/2 into 1/2 34.651 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.651 * [taylor]: Taking taylor expansion of k in n 34.651 * [backup-simplify]: Simplify k into k 34.651 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.651 * [taylor]: Taking taylor expansion of (log PI) in n 34.651 * [taylor]: Taking taylor expansion of PI in n 34.651 * [backup-simplify]: Simplify PI into PI 34.652 * [backup-simplify]: Simplify (log PI) into (log PI) 34.652 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.652 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 34.652 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 34.653 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 34.653 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 34.653 * [taylor]: Taking taylor expansion of (* (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 3) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 34.653 * [taylor]: Taking taylor expansion of (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 3) in n 34.653 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in n 34.653 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in n 34.653 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in n 34.653 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 34.653 * [taylor]: Taking taylor expansion of 1/2 in n 34.653 * [backup-simplify]: Simplify 1/2 into 1/2 34.653 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.653 * [taylor]: Taking taylor expansion of 1/2 in n 34.653 * [backup-simplify]: Simplify 1/2 into 1/2 34.653 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.653 * [taylor]: Taking taylor expansion of k in n 34.653 * [backup-simplify]: Simplify k into k 34.654 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.654 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 34.654 * [taylor]: Taking taylor expansion of (* 2 PI) in n 34.654 * [taylor]: Taking taylor expansion of 2 in n 34.654 * [backup-simplify]: Simplify 2 into 2 34.654 * [taylor]: Taking taylor expansion of PI in n 34.654 * [backup-simplify]: Simplify PI into PI 34.654 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 34.655 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 34.655 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.655 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 34.655 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 34.656 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) into (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) 34.657 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 34.657 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 34.657 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 34.657 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 34.657 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 34.657 * [taylor]: Taking taylor expansion of 1/2 in n 34.657 * [backup-simplify]: Simplify 1/2 into 1/2 34.657 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.657 * [taylor]: Taking taylor expansion of 1/2 in n 34.657 * [backup-simplify]: Simplify 1/2 into 1/2 34.657 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.657 * [taylor]: Taking taylor expansion of k in n 34.657 * [backup-simplify]: Simplify k into k 34.657 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.657 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 34.657 * [taylor]: Taking taylor expansion of (/ 1 n) in n 34.657 * [taylor]: Taking taylor expansion of n in n 34.657 * [backup-simplify]: Simplify 0 into 0 34.657 * [backup-simplify]: Simplify 1 into 1 34.657 * [backup-simplify]: Simplify (/ 1 1) into 1 34.658 * [backup-simplify]: Simplify (log 1) into 0 34.658 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.658 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 34.658 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 34.658 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 34.658 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 34.658 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 34.659 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))) into (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 2) 34.660 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 2)) into (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 3) 34.660 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) into (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 2) 34.660 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 2)) into (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 3) 34.661 * [backup-simplify]: Simplify (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))) into (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2) 34.661 * [backup-simplify]: Simplify (* (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 2)) into (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 3) 34.662 * [backup-simplify]: Simplify (* (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 3) (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 3)) 34.662 * [backup-simplify]: Simplify (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 3) (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 3))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 3) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 3))) 34.663 * [backup-simplify]: Simplify (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 3) (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 3) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 3)))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 3) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 3) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 3)))) 34.664 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 3) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 3) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 3))))) into (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 3) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 3) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 3))))) 34.665 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 3) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 3) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 3)))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 3) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 3) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 3)))))) 34.666 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 3) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 3) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 3)))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 3) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 3) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) 3)))))) 34.671 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) 3) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) 3) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) 3)))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (* (pow (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) 2) (* (pow (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) 2) (pow (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) 2)))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (* (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 (* 2 PI) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) k)) (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (pow (pow (* 2 PI) (- 1/2 (* 1/2 k))) 3) (* (pow (exp (* (log 2) (- 1/2 (* 1/2 k)))) 3) (pow (pow PI (- 1/2 (* 1/2 k))) 3)))) (pow k 3))) (- (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (pow (pow (* 2 PI) (- 1/2 (* 1/2 k))) 2) (* (pow (exp (* (log 2) (- 1/2 (* 1/2 k)))) 2) (pow (pow PI (- 1/2 (* 1/2 k))) 2)))) (pow k 2)))))))) 34.672 * [backup-simplify]: Simplify (* (* (sqrt (pow 2 (- 1/2 (/ (/ 1 (- k)) 2)))) (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2)))) (/ (sqrt (pow PI (- 1/2 (/ (/ 1 (- k)) 2)))) (/ (sqrt (/ 1 (- k))) (sqrt (pow (* 2 PI) (- 1/2 (/ (/ 1 (- k)) 2))))))) into (* (/ (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) (sqrt (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 34.672 * [approximate]: Taking taylor expansion of (* (/ (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) (sqrt (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) in (k n) around 0 34.672 * [taylor]: Taking taylor expansion of (* (/ (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) (sqrt (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 34.672 * [taylor]: Taking taylor expansion of (/ (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 34.672 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 34.672 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 34.672 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 34.672 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 34.672 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.672 * [taylor]: Taking taylor expansion of 1/2 in n 34.672 * [backup-simplify]: Simplify 1/2 into 1/2 34.672 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.672 * [taylor]: Taking taylor expansion of k in n 34.672 * [backup-simplify]: Simplify k into k 34.672 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.672 * [taylor]: Taking taylor expansion of 1/2 in n 34.672 * [backup-simplify]: Simplify 1/2 into 1/2 34.672 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 34.672 * [taylor]: Taking taylor expansion of (/ -1 n) in n 34.672 * [taylor]: Taking taylor expansion of -1 in n 34.672 * [backup-simplify]: Simplify -1 into -1 34.672 * [taylor]: Taking taylor expansion of n in n 34.672 * [backup-simplify]: Simplify 0 into 0 34.672 * [backup-simplify]: Simplify 1 into 1 34.672 * [backup-simplify]: Simplify (/ -1 1) into -1 34.673 * [backup-simplify]: Simplify (log -1) into (log -1) 34.673 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.673 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 34.673 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 34.673 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 34.674 * [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)))) 34.674 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 34.674 * [taylor]: Taking taylor expansion of (/ -1 k) in n 34.674 * [taylor]: Taking taylor expansion of -1 in n 34.674 * [backup-simplify]: Simplify -1 into -1 34.674 * [taylor]: Taking taylor expansion of k in n 34.674 * [backup-simplify]: Simplify k into k 34.674 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 34.674 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 34.674 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 34.674 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 34.675 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (/ -1 k))) 34.675 * [taylor]: Taking taylor expansion of (sqrt (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 34.675 * [taylor]: Taking taylor expansion of (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 34.675 * [taylor]: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in n 34.675 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in n 34.675 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in n 34.675 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 34.675 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.675 * [taylor]: Taking taylor expansion of 1/2 in n 34.675 * [backup-simplify]: Simplify 1/2 into 1/2 34.675 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.675 * [taylor]: Taking taylor expansion of k in n 34.675 * [backup-simplify]: Simplify k into k 34.675 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.675 * [taylor]: Taking taylor expansion of 1/2 in n 34.675 * [backup-simplify]: Simplify 1/2 into 1/2 34.675 * [taylor]: Taking taylor expansion of (log 2) in n 34.675 * [taylor]: Taking taylor expansion of 2 in n 34.675 * [backup-simplify]: Simplify 2 into 2 34.675 * [backup-simplify]: Simplify (log 2) into (log 2) 34.676 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.676 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 34.676 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 34.676 * [backup-simplify]: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 34.676 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 34.676 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in n 34.676 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in n 34.676 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in n 34.676 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 34.676 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.676 * [taylor]: Taking taylor expansion of 1/2 in n 34.676 * [backup-simplify]: Simplify 1/2 into 1/2 34.676 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.676 * [taylor]: Taking taylor expansion of k in n 34.676 * [backup-simplify]: Simplify k into k 34.676 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.676 * [taylor]: Taking taylor expansion of 1/2 in n 34.676 * [backup-simplify]: Simplify 1/2 into 1/2 34.677 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 34.677 * [taylor]: Taking taylor expansion of (* 2 PI) in n 34.677 * [taylor]: Taking taylor expansion of 2 in n 34.677 * [backup-simplify]: Simplify 2 into 2 34.677 * [taylor]: Taking taylor expansion of PI in n 34.677 * [backup-simplify]: Simplify PI into PI 34.677 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 34.678 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 34.678 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.678 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 34.678 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) 34.679 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 34.679 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 34.679 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 34.679 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 34.679 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 34.679 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.679 * [taylor]: Taking taylor expansion of 1/2 in n 34.679 * [backup-simplify]: Simplify 1/2 into 1/2 34.679 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.679 * [taylor]: Taking taylor expansion of k in n 34.679 * [backup-simplify]: Simplify k into k 34.679 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.679 * [taylor]: Taking taylor expansion of 1/2 in n 34.679 * [backup-simplify]: Simplify 1/2 into 1/2 34.679 * [taylor]: Taking taylor expansion of (log PI) in n 34.679 * [taylor]: Taking taylor expansion of PI in n 34.679 * [backup-simplify]: Simplify PI into PI 34.680 * [backup-simplify]: Simplify (log PI) into (log PI) 34.680 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.680 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 34.680 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 34.680 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 34.681 * [backup-simplify]: Simplify (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 34.682 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 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 (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 34.682 * [backup-simplify]: Simplify (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 34.683 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 34.683 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 34.684 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 34.684 * [backup-simplify]: Simplify (+ 0 0) into 0 34.684 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log PI))) into 0 34.685 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 34.686 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 34.693 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 34.693 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 34.694 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 34.694 * [backup-simplify]: Simplify (+ 0 0) into 0 34.695 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log (* 2 PI)))) into 0 34.697 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) (+ (* (/ (pow 0 1) 1)))) into 0 34.698 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 34.699 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 34.699 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 34.700 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 34.700 * [backup-simplify]: Simplify (+ 0 0) into 0 34.701 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log 2))) into 0 34.702 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (+ (* (/ (pow 0 1) 1)))) into 0 34.704 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 0) (* 0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 34.705 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) into 0 34.705 * [taylor]: Taking taylor expansion of (* (/ (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) (sqrt (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) in k 34.705 * [taylor]: Taking taylor expansion of (/ (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 34.705 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 34.705 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in k 34.705 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in k 34.705 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 34.705 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 34.705 * [taylor]: Taking taylor expansion of 1/2 in k 34.705 * [backup-simplify]: Simplify 1/2 into 1/2 34.705 * [taylor]: Taking taylor expansion of (/ 1 k) in k 34.705 * [taylor]: Taking taylor expansion of k in k 34.705 * [backup-simplify]: Simplify 0 into 0 34.705 * [backup-simplify]: Simplify 1 into 1 34.706 * [backup-simplify]: Simplify (/ 1 1) into 1 34.706 * [taylor]: Taking taylor expansion of 1/2 in k 34.706 * [backup-simplify]: Simplify 1/2 into 1/2 34.706 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k 34.706 * [taylor]: Taking taylor expansion of (/ -1 n) in k 34.706 * [taylor]: Taking taylor expansion of -1 in k 34.706 * [backup-simplify]: Simplify -1 into -1 34.706 * [taylor]: Taking taylor expansion of n in k 34.706 * [backup-simplify]: Simplify n into n 34.706 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n) 34.706 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n)) 34.707 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 34.707 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 34.707 * [backup-simplify]: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) 34.707 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 34.707 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 34.707 * [taylor]: Taking taylor expansion of (/ -1 k) in k 34.707 * [taylor]: Taking taylor expansion of -1 in k 34.707 * [backup-simplify]: Simplify -1 into -1 34.707 * [taylor]: Taking taylor expansion of k in k 34.707 * [backup-simplify]: Simplify 0 into 0 34.707 * [backup-simplify]: Simplify 1 into 1 34.708 * [backup-simplify]: Simplify (/ -1 1) into -1 34.708 * [backup-simplify]: Simplify (sqrt 0) into 0 34.710 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 34.710 * [backup-simplify]: Simplify (/ (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2))) 34.710 * [taylor]: Taking taylor expansion of (sqrt (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in k 34.710 * [taylor]: Taking taylor expansion of (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in k 34.710 * [taylor]: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in k 34.710 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in k 34.710 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in k 34.710 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 34.710 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 34.710 * [taylor]: Taking taylor expansion of 1/2 in k 34.710 * [backup-simplify]: Simplify 1/2 into 1/2 34.710 * [taylor]: Taking taylor expansion of (/ 1 k) in k 34.710 * [taylor]: Taking taylor expansion of k in k 34.710 * [backup-simplify]: Simplify 0 into 0 34.710 * [backup-simplify]: Simplify 1 into 1 34.711 * [backup-simplify]: Simplify (/ 1 1) into 1 34.711 * [taylor]: Taking taylor expansion of 1/2 in k 34.711 * [backup-simplify]: Simplify 1/2 into 1/2 34.711 * [taylor]: Taking taylor expansion of (log 2) in k 34.711 * [taylor]: Taking taylor expansion of 2 in k 34.711 * [backup-simplify]: Simplify 2 into 2 34.711 * [backup-simplify]: Simplify (log 2) into (log 2) 34.712 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 34.712 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 34.713 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 34.714 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 34.714 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 34.714 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in k 34.714 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in k 34.714 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in k 34.714 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 34.714 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 34.714 * [taylor]: Taking taylor expansion of 1/2 in k 34.714 * [backup-simplify]: Simplify 1/2 into 1/2 34.714 * [taylor]: Taking taylor expansion of (/ 1 k) in k 34.714 * [taylor]: Taking taylor expansion of k in k 34.714 * [backup-simplify]: Simplify 0 into 0 34.714 * [backup-simplify]: Simplify 1 into 1 34.715 * [backup-simplify]: Simplify (/ 1 1) into 1 34.715 * [taylor]: Taking taylor expansion of 1/2 in k 34.715 * [backup-simplify]: Simplify 1/2 into 1/2 34.715 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 34.715 * [taylor]: Taking taylor expansion of (* 2 PI) in k 34.715 * [taylor]: Taking taylor expansion of 2 in k 34.715 * [backup-simplify]: Simplify 2 into 2 34.715 * [taylor]: Taking taylor expansion of PI in k 34.715 * [backup-simplify]: Simplify PI into PI 34.715 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 34.716 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 34.717 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 34.717 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 34.719 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 34.721 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 34.721 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 34.721 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 34.721 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 34.721 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 34.721 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 34.721 * [taylor]: Taking taylor expansion of 1/2 in k 34.721 * [backup-simplify]: Simplify 1/2 into 1/2 34.721 * [taylor]: Taking taylor expansion of (/ 1 k) in k 34.721 * [taylor]: Taking taylor expansion of k in k 34.721 * [backup-simplify]: Simplify 0 into 0 34.721 * [backup-simplify]: Simplify 1 into 1 34.721 * [backup-simplify]: Simplify (/ 1 1) into 1 34.721 * [taylor]: Taking taylor expansion of 1/2 in k 34.721 * [backup-simplify]: Simplify 1/2 into 1/2 34.721 * [taylor]: Taking taylor expansion of (log PI) in k 34.721 * [taylor]: Taking taylor expansion of PI in k 34.721 * [backup-simplify]: Simplify PI into PI 34.722 * [backup-simplify]: Simplify (log PI) into (log PI) 34.722 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 34.723 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 34.724 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 34.724 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 34.725 * [backup-simplify]: Simplify (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 34.726 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 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 (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 34.727 * [backup-simplify]: Simplify (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 34.728 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 34.729 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 0) (* 0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 34.730 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) into 0 34.731 * [taylor]: Taking taylor expansion of (* (/ (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) (sqrt (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) in k 34.731 * [taylor]: Taking taylor expansion of (/ (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 34.731 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 34.731 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in k 34.731 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in k 34.731 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 34.731 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 34.731 * [taylor]: Taking taylor expansion of 1/2 in k 34.731 * [backup-simplify]: Simplify 1/2 into 1/2 34.731 * [taylor]: Taking taylor expansion of (/ 1 k) in k 34.731 * [taylor]: Taking taylor expansion of k in k 34.731 * [backup-simplify]: Simplify 0 into 0 34.731 * [backup-simplify]: Simplify 1 into 1 34.731 * [backup-simplify]: Simplify (/ 1 1) into 1 34.731 * [taylor]: Taking taylor expansion of 1/2 in k 34.731 * [backup-simplify]: Simplify 1/2 into 1/2 34.731 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k 34.731 * [taylor]: Taking taylor expansion of (/ -1 n) in k 34.731 * [taylor]: Taking taylor expansion of -1 in k 34.731 * [backup-simplify]: Simplify -1 into -1 34.731 * [taylor]: Taking taylor expansion of n in k 34.731 * [backup-simplify]: Simplify n into n 34.732 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n) 34.732 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n)) 34.732 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 34.733 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 34.733 * [backup-simplify]: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) 34.733 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 34.733 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 34.733 * [taylor]: Taking taylor expansion of (/ -1 k) in k 34.733 * [taylor]: Taking taylor expansion of -1 in k 34.733 * [backup-simplify]: Simplify -1 into -1 34.733 * [taylor]: Taking taylor expansion of k in k 34.733 * [backup-simplify]: Simplify 0 into 0 34.733 * [backup-simplify]: Simplify 1 into 1 34.733 * [backup-simplify]: Simplify (/ -1 1) into -1 34.734 * [backup-simplify]: Simplify (sqrt 0) into 0 34.735 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 34.735 * [backup-simplify]: Simplify (/ (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2))) 34.735 * [taylor]: Taking taylor expansion of (sqrt (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in k 34.736 * [taylor]: Taking taylor expansion of (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in k 34.736 * [taylor]: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in k 34.736 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in k 34.736 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in k 34.736 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 34.736 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 34.736 * [taylor]: Taking taylor expansion of 1/2 in k 34.736 * [backup-simplify]: Simplify 1/2 into 1/2 34.736 * [taylor]: Taking taylor expansion of (/ 1 k) in k 34.736 * [taylor]: Taking taylor expansion of k in k 34.736 * [backup-simplify]: Simplify 0 into 0 34.736 * [backup-simplify]: Simplify 1 into 1 34.736 * [backup-simplify]: Simplify (/ 1 1) into 1 34.736 * [taylor]: Taking taylor expansion of 1/2 in k 34.736 * [backup-simplify]: Simplify 1/2 into 1/2 34.736 * [taylor]: Taking taylor expansion of (log 2) in k 34.736 * [taylor]: Taking taylor expansion of 2 in k 34.736 * [backup-simplify]: Simplify 2 into 2 34.737 * [backup-simplify]: Simplify (log 2) into (log 2) 34.737 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 34.738 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 34.738 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 34.739 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 34.739 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 34.739 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in k 34.739 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in k 34.739 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in k 34.739 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 34.739 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 34.739 * [taylor]: Taking taylor expansion of 1/2 in k 34.739 * [backup-simplify]: Simplify 1/2 into 1/2 34.739 * [taylor]: Taking taylor expansion of (/ 1 k) in k 34.739 * [taylor]: Taking taylor expansion of k in k 34.739 * [backup-simplify]: Simplify 0 into 0 34.739 * [backup-simplify]: Simplify 1 into 1 34.740 * [backup-simplify]: Simplify (/ 1 1) into 1 34.740 * [taylor]: Taking taylor expansion of 1/2 in k 34.740 * [backup-simplify]: Simplify 1/2 into 1/2 34.740 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 34.740 * [taylor]: Taking taylor expansion of (* 2 PI) in k 34.740 * [taylor]: Taking taylor expansion of 2 in k 34.740 * [backup-simplify]: Simplify 2 into 2 34.740 * [taylor]: Taking taylor expansion of PI in k 34.740 * [backup-simplify]: Simplify PI into PI 34.740 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 34.741 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 34.742 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 34.742 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 34.744 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) 34.745 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 34.745 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 34.745 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 34.745 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 34.745 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 34.745 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 34.745 * [taylor]: Taking taylor expansion of 1/2 in k 34.745 * [backup-simplify]: Simplify 1/2 into 1/2 34.745 * [taylor]: Taking taylor expansion of (/ 1 k) in k 34.746 * [taylor]: Taking taylor expansion of k in k 34.746 * [backup-simplify]: Simplify 0 into 0 34.746 * [backup-simplify]: Simplify 1 into 1 34.746 * [backup-simplify]: Simplify (/ 1 1) into 1 34.746 * [taylor]: Taking taylor expansion of 1/2 in k 34.746 * [backup-simplify]: Simplify 1/2 into 1/2 34.746 * [taylor]: Taking taylor expansion of (log PI) in k 34.746 * [taylor]: Taking taylor expansion of PI in k 34.746 * [backup-simplify]: Simplify PI into PI 34.747 * [backup-simplify]: Simplify (log PI) into (log PI) 34.747 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 34.748 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 34.749 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 34.749 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 34.750 * [backup-simplify]: Simplify (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 34.751 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 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 (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 34.752 * [backup-simplify]: Simplify (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 34.753 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 34.754 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 0) (* 0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 34.756 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) into 0 34.757 * [backup-simplify]: Simplify (* (* +nan.0 (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into (* +nan.0 (* (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)))) 34.757 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 34.757 * [taylor]: Taking taylor expansion of +nan.0 in n 34.757 * [backup-simplify]: Simplify +nan.0 into +nan.0 34.757 * [taylor]: Taking taylor expansion of (* (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2))) in n 34.757 * [taylor]: Taking taylor expansion of (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 34.757 * [taylor]: Taking taylor expansion of (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 34.757 * [taylor]: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n 34.757 * [taylor]: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n 34.757 * [taylor]: Taking taylor expansion of (log 2) in n 34.757 * [taylor]: Taking taylor expansion of 2 in n 34.757 * [backup-simplify]: Simplify 2 into 2 34.758 * [backup-simplify]: Simplify (log 2) into (log 2) 34.758 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 34.758 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.758 * [taylor]: Taking taylor expansion of 1/2 in n 34.758 * [backup-simplify]: Simplify 1/2 into 1/2 34.758 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.758 * [taylor]: Taking taylor expansion of k in n 34.758 * [backup-simplify]: Simplify k into k 34.758 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.758 * [taylor]: Taking taylor expansion of 1/2 in n 34.758 * [backup-simplify]: Simplify 1/2 into 1/2 34.758 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.758 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 34.759 * [backup-simplify]: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 34.759 * [backup-simplify]: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 34.759 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 34.759 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in n 34.759 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in n 34.759 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in n 34.759 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 34.760 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.760 * [taylor]: Taking taylor expansion of 1/2 in n 34.760 * [backup-simplify]: Simplify 1/2 into 1/2 34.760 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.760 * [taylor]: Taking taylor expansion of k in n 34.760 * [backup-simplify]: Simplify k into k 34.760 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.760 * [taylor]: Taking taylor expansion of 1/2 in n 34.760 * [backup-simplify]: Simplify 1/2 into 1/2 34.760 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 34.760 * [taylor]: Taking taylor expansion of (* 2 PI) in n 34.760 * [taylor]: Taking taylor expansion of 2 in n 34.760 * [backup-simplify]: Simplify 2 into 2 34.760 * [taylor]: Taking taylor expansion of PI in n 34.760 * [backup-simplify]: Simplify PI into PI 34.760 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 34.761 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 34.762 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.762 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 34.763 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) 34.764 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 34.764 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 34.764 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 34.764 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 34.764 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 34.764 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.764 * [taylor]: Taking taylor expansion of 1/2 in n 34.764 * [backup-simplify]: Simplify 1/2 into 1/2 34.764 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.764 * [taylor]: Taking taylor expansion of k in n 34.764 * [backup-simplify]: Simplify k into k 34.764 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.764 * [taylor]: Taking taylor expansion of 1/2 in n 34.765 * [backup-simplify]: Simplify 1/2 into 1/2 34.765 * [taylor]: Taking taylor expansion of (log PI) in n 34.765 * [taylor]: Taking taylor expansion of PI in n 34.765 * [backup-simplify]: Simplify PI into PI 34.765 * [backup-simplify]: Simplify (log PI) into (log PI) 34.765 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.765 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 34.766 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 34.766 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 34.767 * [backup-simplify]: Simplify (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 34.768 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 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 (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 34.770 * [backup-simplify]: Simplify (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 34.771 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 34.772 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 34.772 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 34.773 * [backup-simplify]: Simplify (+ 0 0) into 0 34.773 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log PI))) into 0 34.775 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 34.776 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 34.778 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 34.779 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 34.779 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 34.780 * [backup-simplify]: Simplify (+ 0 0) into 0 34.781 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log (* 2 PI)))) into 0 34.783 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) (+ (* (/ (pow 0 1) 1)))) into 0 34.783 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 34.783 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 34.784 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 34.784 * [backup-simplify]: Simplify (+ 0 0) into 0 34.785 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 34.785 * [backup-simplify]: Simplify (+ (* (log 2) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 34.786 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (+ (* (/ (pow 0 1) 1)))) into 0 34.787 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 0) (* 0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 34.787 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) into 0 34.787 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 34.787 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 34.787 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 34.787 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 34.787 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.787 * [taylor]: Taking taylor expansion of 1/2 in n 34.787 * [backup-simplify]: Simplify 1/2 into 1/2 34.787 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.788 * [taylor]: Taking taylor expansion of k in n 34.788 * [backup-simplify]: Simplify k into k 34.788 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.788 * [taylor]: Taking taylor expansion of 1/2 in n 34.788 * [backup-simplify]: Simplify 1/2 into 1/2 34.788 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 34.788 * [taylor]: Taking taylor expansion of (/ -1 n) in n 34.788 * [taylor]: Taking taylor expansion of -1 in n 34.788 * [backup-simplify]: Simplify -1 into -1 34.788 * [taylor]: Taking taylor expansion of n in n 34.788 * [backup-simplify]: Simplify 0 into 0 34.788 * [backup-simplify]: Simplify 1 into 1 34.788 * [backup-simplify]: Simplify (/ -1 1) into -1 34.788 * [backup-simplify]: Simplify (log -1) into (log -1) 34.788 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.788 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 34.789 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 34.789 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 34.790 * [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)))) 34.791 * [backup-simplify]: Simplify (* (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 34.792 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) 34.793 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) 34.793 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 34.795 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 34.796 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)))) 34.797 * [backup-simplify]: Simplify (+ (* (* +nan.0 (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2))) 0) (* (- (* +nan.0 (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (* (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2))))) 34.797 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 34.797 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 34.797 * [taylor]: Taking taylor expansion of +nan.0 in n 34.797 * [backup-simplify]: Simplify +nan.0 into +nan.0 34.797 * [taylor]: Taking taylor expansion of (* (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2))) in n 34.797 * [taylor]: Taking taylor expansion of (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 34.797 * [taylor]: Taking taylor expansion of (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 34.797 * [taylor]: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n 34.797 * [taylor]: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n 34.797 * [taylor]: Taking taylor expansion of (log 2) in n 34.797 * [taylor]: Taking taylor expansion of 2 in n 34.797 * [backup-simplify]: Simplify 2 into 2 34.797 * [backup-simplify]: Simplify (log 2) into (log 2) 34.797 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 34.797 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.797 * [taylor]: Taking taylor expansion of 1/2 in n 34.797 * [backup-simplify]: Simplify 1/2 into 1/2 34.797 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.798 * [taylor]: Taking taylor expansion of k in n 34.798 * [backup-simplify]: Simplify k into k 34.798 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.798 * [taylor]: Taking taylor expansion of 1/2 in n 34.798 * [backup-simplify]: Simplify 1/2 into 1/2 34.798 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.798 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 34.798 * [backup-simplify]: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 34.798 * [backup-simplify]: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 34.798 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 34.798 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in n 34.798 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in n 34.798 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in n 34.798 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 34.798 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.798 * [taylor]: Taking taylor expansion of 1/2 in n 34.798 * [backup-simplify]: Simplify 1/2 into 1/2 34.798 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.798 * [taylor]: Taking taylor expansion of k in n 34.798 * [backup-simplify]: Simplify k into k 34.799 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.799 * [taylor]: Taking taylor expansion of 1/2 in n 34.799 * [backup-simplify]: Simplify 1/2 into 1/2 34.799 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 34.799 * [taylor]: Taking taylor expansion of (* 2 PI) in n 34.799 * [taylor]: Taking taylor expansion of 2 in n 34.799 * [backup-simplify]: Simplify 2 into 2 34.799 * [taylor]: Taking taylor expansion of PI in n 34.799 * [backup-simplify]: Simplify PI into PI 34.799 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 34.800 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 34.800 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.800 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 34.801 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) 34.801 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 34.801 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 34.801 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 34.801 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 34.802 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 34.802 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.802 * [taylor]: Taking taylor expansion of 1/2 in n 34.802 * [backup-simplify]: Simplify 1/2 into 1/2 34.802 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.802 * [taylor]: Taking taylor expansion of k in n 34.802 * [backup-simplify]: Simplify k into k 34.802 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.802 * [taylor]: Taking taylor expansion of 1/2 in n 34.802 * [backup-simplify]: Simplify 1/2 into 1/2 34.802 * [taylor]: Taking taylor expansion of (log PI) in n 34.802 * [taylor]: Taking taylor expansion of PI in n 34.802 * [backup-simplify]: Simplify PI into PI 34.802 * [backup-simplify]: Simplify (log PI) into (log PI) 34.802 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.802 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 34.802 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 34.803 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 34.803 * [backup-simplify]: Simplify (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 34.804 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 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 (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 34.805 * [backup-simplify]: Simplify (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 34.806 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 34.806 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 34.806 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 34.806 * [backup-simplify]: Simplify (+ 0 0) into 0 34.807 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log PI))) into 0 34.808 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 34.808 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 34.809 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 34.809 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 34.810 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 34.810 * [backup-simplify]: Simplify (+ 0 0) into 0 34.810 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log (* 2 PI)))) into 0 34.811 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) (+ (* (/ (pow 0 1) 1)))) into 0 34.812 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 34.812 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 34.812 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 34.813 * [backup-simplify]: Simplify (+ 0 0) into 0 34.813 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 34.814 * [backup-simplify]: Simplify (+ (* (log 2) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 34.815 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (+ (* (/ (pow 0 1) 1)))) into 0 34.815 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 0) (* 0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 34.816 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) into 0 34.816 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 34.816 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 34.816 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 34.816 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 34.816 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.816 * [taylor]: Taking taylor expansion of 1/2 in n 34.816 * [backup-simplify]: Simplify 1/2 into 1/2 34.816 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.816 * [taylor]: Taking taylor expansion of k in n 34.816 * [backup-simplify]: Simplify k into k 34.816 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.816 * [taylor]: Taking taylor expansion of 1/2 in n 34.816 * [backup-simplify]: Simplify 1/2 into 1/2 34.816 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 34.816 * [taylor]: Taking taylor expansion of (/ -1 n) in n 34.816 * [taylor]: Taking taylor expansion of -1 in n 34.816 * [backup-simplify]: Simplify -1 into -1 34.816 * [taylor]: Taking taylor expansion of n in n 34.816 * [backup-simplify]: Simplify 0 into 0 34.816 * [backup-simplify]: Simplify 1 into 1 34.821 * [backup-simplify]: Simplify (/ -1 1) into -1 34.822 * [backup-simplify]: Simplify (log -1) into (log -1) 34.822 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.822 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 34.823 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 34.823 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 34.823 * [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)))) 34.825 * [backup-simplify]: Simplify (* (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 34.827 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) 34.829 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))))) 34.831 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))))) 34.832 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 34.833 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 34.833 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 34.834 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 34.834 * [backup-simplify]: Simplify (+ 0 0) into 0 34.835 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 34.835 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -1) (log n)))) into 0 34.837 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 34.838 * [backup-simplify]: Simplify (+ (* (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) into 0 34.841 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))))) into 0 34.841 * [backup-simplify]: Simplify 0 into 0 34.842 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 34.843 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 0) (+ (* 0 0) (* 0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into 0 34.845 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) into 0 34.847 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 34.849 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 34.850 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)))) 34.852 * [backup-simplify]: Simplify (+ (* (* +nan.0 (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2))) 0) (+ (* (- (* +nan.0 (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)))) 0) (* (- (* +nan.0 (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))))) into (- (* +nan.0 (* (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2))))) 34.852 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 34.852 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 34.852 * [taylor]: Taking taylor expansion of +nan.0 in n 34.852 * [backup-simplify]: Simplify +nan.0 into +nan.0 34.852 * [taylor]: Taking taylor expansion of (* (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2))) in n 34.852 * [taylor]: Taking taylor expansion of (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 34.852 * [taylor]: Taking taylor expansion of (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 34.852 * [taylor]: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n 34.852 * [taylor]: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n 34.852 * [taylor]: Taking taylor expansion of (log 2) in n 34.852 * [taylor]: Taking taylor expansion of 2 in n 34.852 * [backup-simplify]: Simplify 2 into 2 34.852 * [backup-simplify]: Simplify (log 2) into (log 2) 34.852 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 34.852 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.852 * [taylor]: Taking taylor expansion of 1/2 in n 34.852 * [backup-simplify]: Simplify 1/2 into 1/2 34.852 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.852 * [taylor]: Taking taylor expansion of k in n 34.852 * [backup-simplify]: Simplify k into k 34.852 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.852 * [taylor]: Taking taylor expansion of 1/2 in n 34.852 * [backup-simplify]: Simplify 1/2 into 1/2 34.852 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.852 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 34.853 * [backup-simplify]: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 34.853 * [backup-simplify]: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 34.853 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 34.853 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in n 34.853 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in n 34.853 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in n 34.853 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 34.853 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.853 * [taylor]: Taking taylor expansion of 1/2 in n 34.853 * [backup-simplify]: Simplify 1/2 into 1/2 34.853 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.853 * [taylor]: Taking taylor expansion of k in n 34.853 * [backup-simplify]: Simplify k into k 34.853 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.853 * [taylor]: Taking taylor expansion of 1/2 in n 34.853 * [backup-simplify]: Simplify 1/2 into 1/2 34.853 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n 34.853 * [taylor]: Taking taylor expansion of (* 2 PI) in n 34.853 * [taylor]: Taking taylor expansion of 2 in n 34.853 * [backup-simplify]: Simplify 2 into 2 34.853 * [taylor]: Taking taylor expansion of PI in n 34.853 * [backup-simplify]: Simplify PI into PI 34.854 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 34.854 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 34.854 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.854 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 34.855 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) 34.856 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 34.856 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 34.856 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 34.856 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 34.856 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 34.856 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.856 * [taylor]: Taking taylor expansion of 1/2 in n 34.856 * [backup-simplify]: Simplify 1/2 into 1/2 34.856 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.856 * [taylor]: Taking taylor expansion of k in n 34.856 * [backup-simplify]: Simplify k into k 34.856 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.856 * [taylor]: Taking taylor expansion of 1/2 in n 34.856 * [backup-simplify]: Simplify 1/2 into 1/2 34.856 * [taylor]: Taking taylor expansion of (log PI) in n 34.856 * [taylor]: Taking taylor expansion of PI in n 34.856 * [backup-simplify]: Simplify PI into PI 34.857 * [backup-simplify]: Simplify (log PI) into (log PI) 34.857 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.857 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 34.857 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 34.857 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 34.858 * [backup-simplify]: Simplify (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 34.859 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 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 (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 34.859 * [backup-simplify]: Simplify (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 34.860 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 34.860 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 34.861 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 34.861 * [backup-simplify]: Simplify (+ 0 0) into 0 34.861 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log PI))) into 0 34.862 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 34.863 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 34.864 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 34.864 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 34.864 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 34.864 * [backup-simplify]: Simplify (+ 0 0) into 0 34.865 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log (* 2 PI)))) into 0 34.866 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) (+ (* (/ (pow 0 1) 1)))) into 0 34.867 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 34.867 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 34.867 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 34.867 * [backup-simplify]: Simplify (+ 0 0) into 0 34.868 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 34.869 * [backup-simplify]: Simplify (+ (* (log 2) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 34.869 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (+ (* (/ (pow 0 1) 1)))) into 0 34.870 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 0) (* 0 (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 34.871 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) into 0 34.871 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 34.871 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 34.871 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 34.871 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 34.871 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 34.871 * [taylor]: Taking taylor expansion of 1/2 in n 34.871 * [backup-simplify]: Simplify 1/2 into 1/2 34.871 * [taylor]: Taking taylor expansion of (/ 1 k) in n 34.871 * [taylor]: Taking taylor expansion of k in n 34.871 * [backup-simplify]: Simplify k into k 34.871 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 34.871 * [taylor]: Taking taylor expansion of 1/2 in n 34.871 * [backup-simplify]: Simplify 1/2 into 1/2 34.871 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 34.871 * [taylor]: Taking taylor expansion of (/ -1 n) in n 34.871 * [taylor]: Taking taylor expansion of -1 in n 34.871 * [backup-simplify]: Simplify -1 into -1 34.871 * [taylor]: Taking taylor expansion of n in n 34.871 * [backup-simplify]: Simplify 0 into 0 34.871 * [backup-simplify]: Simplify 1 into 1 34.871 * [backup-simplify]: Simplify (/ -1 1) into -1 34.872 * [backup-simplify]: Simplify (log -1) into (log -1) 34.872 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 34.872 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 34.872 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 34.873 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 34.873 * [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)))) 34.874 * [backup-simplify]: Simplify (* (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 34.876 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) 34.877 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))))) 34.878 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))))) 34.882 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (sqrt (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (* (pow (* 2 PI) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))))))) into (- (+ (* +nan.0 (* (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow k 2)) (sqrt (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (* (pow PI (- 1/2 (* 1/2 k))) (exp (* (log 2) (- 1/2 (* 1/2 k))))))))) (- (+ (* +nan.0 (* (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) k) (sqrt (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (* (pow PI (- 1/2 (* 1/2 k))) (exp (* (log 2) (- 1/2 (* 1/2 k))))))))) (- (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (sqrt (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))))))))))) 34.882 * * * [progress]: simplifying candidates 34.882 * * * * [progress]: [ 1 / 905 ] simplifiying candidate # 34.882 * * * * [progress]: [ 2 / 905 ] simplifiying candidate # 34.882 * * * * [progress]: [ 3 / 905 ] simplifiying candidate # 34.882 * * * * [progress]: [ 4 / 905 ] simplifiying candidate # 34.882 * * * * [progress]: [ 5 / 905 ] simplifiying candidate # 34.883 * * * * [progress]: [ 6 / 905 ] simplifiying candidate # 34.883 * * * * [progress]: [ 7 / 905 ] simplifiying candidate # 34.883 * * * * [progress]: [ 8 / 905 ] simplifiying candidate # 34.883 * * * * [progress]: [ 9 / 905 ] simplifiying candidate # 34.883 * * * * [progress]: [ 10 / 905 ] simplifiying candidate # 34.883 * * * * [progress]: [ 11 / 905 ] simplifiying candidate # 34.883 * * * * [progress]: [ 12 / 905 ] simplifiying candidate # 34.883 * * * * [progress]: [ 13 / 905 ] simplifiying candidate # 34.883 * * * * [progress]: [ 14 / 905 ] simplifiying candidate # 34.883 * * * * [progress]: [ 15 / 905 ] simplifiying candidate # 34.883 * * * * [progress]: [ 16 / 905 ] simplifiying candidate # 34.883 * * * * [progress]: [ 17 / 905 ] simplifiying candidate # 34.883 * * * * [progress]: [ 18 / 905 ] simplifiying candidate # 34.883 * * * * [progress]: [ 19 / 905 ] simplifiying candidate # 34.883 * * * * [progress]: [ 20 / 905 ] simplifiying candidate # 34.883 * * * * [progress]: [ 21 / 905 ] simplifiying candidate # 34.883 * * * * [progress]: [ 22 / 905 ] simplifiying candidate # 34.883 * * * * [progress]: [ 23 / 905 ] simplifiying candidate # 34.883 * * * * [progress]: [ 24 / 905 ] simplifiying candidate #real (real->posit16 (pow n (- 1/2 (/ k 2)))))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* 2 PI) (- 1/2 (/ k 2))))))))> 34.883 * * * * [progress]: [ 25 / 905 ] simplifiying candidate # 34.884 * * * * [progress]: [ 26 / 905 ] simplifiying candidate # 34.884 * * * * [progress]: [ 27 / 905 ] simplifiying candidate # 34.884 * * * * [progress]: [ 28 / 905 ] simplifiying candidate # 34.884 * * * * [progress]: [ 29 / 905 ] simplifiying candidate # 34.884 * * * * [progress]: [ 30 / 905 ] simplifiying candidate # 34.884 * * * * [progress]: [ 31 / 905 ] simplifiying candidate # 34.884 * * * * [progress]: [ 32 / 905 ] simplifiying candidate # 34.884 * * * * [progress]: [ 33 / 905 ] simplifiying candidate # 34.884 * * * * [progress]: [ 34 / 905 ] simplifiying candidate # 34.884 * * * * [progress]: [ 35 / 905 ] simplifiying candidate # 34.884 * * * * [progress]: [ 36 / 905 ] simplifiying candidate # 34.884 * * * * [progress]: [ 37 / 905 ] simplifiying candidate # 34.884 * * * * [progress]: [ 38 / 905 ] simplifiying candidate # 34.884 * * * * [progress]: [ 39 / 905 ] simplifiying candidate # 34.884 * * * * [progress]: [ 40 / 905 ] simplifiying candidate # 34.884 * * * * [progress]: [ 41 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34.885 * * * * [progress]: [ 56 / 905 ] simplifiying candidate # 34.885 * * * * [progress]: [ 57 / 905 ] simplifiying candidate # 34.885 * * * * [progress]: [ 58 / 905 ] simplifiying candidate # 34.885 * * * * [progress]: [ 59 / 905 ] simplifiying candidate # 34.885 * * * * [progress]: [ 60 / 905 ] simplifiying candidate # 34.885 * * * * [progress]: [ 61 / 905 ] simplifiying candidate # 34.885 * * * * [progress]: [ 62 / 905 ] simplifiying candidate # 34.885 * * * * [progress]: [ 63 / 905 ] simplifiying candidate # 34.885 * * * * [progress]: [ 64 / 905 ] simplifiying candidate # 34.885 * * * * [progress]: [ 65 / 905 ] simplifiying candidate # 34.885 * * * * [progress]: [ 66 / 905 ] simplifiying candidate # 34.885 * * * * [progress]: [ 67 / 905 ] simplifiying candidate # 34.885 * * * * [progress]: [ 68 / 905 ] simplifiying candidate # 34.886 * * * * [progress]: [ 69 / 905 ] simplifiying candidate # 34.886 * * * * [progress]: [ 70 / 905 ] simplifiying candidate # 34.886 * * * * [progress]: [ 71 / 905 ] simplifiying candidate # 34.886 * * * * [progress]: [ 72 / 905 ] simplifiying candidate #real (real->posit16 (pow PI (- 1/2 (/ k 2)))))) (/ (sqrt k) (sqrt (pow (* 2 PI) (- 1/2 (/ k 2))))))))> 34.886 * * * * [progress]: [ 73 / 905 ] simplifiying candidate # 34.886 * * * * [progress]: [ 74 / 905 ] simplifiying candidate # 34.886 * * * * [progress]: [ 75 / 905 ] simplifiying candidate # 34.886 * * * * [progress]: [ 76 / 905 ] simplifiying candidate # 34.886 * * * * [progress]: [ 77 / 905 ] simplifiying candidate # 34.886 * * * * [progress]: [ 78 / 905 ] simplifiying candidate # 34.886 * * * * [progress]: [ 79 / 905 ] simplifiying candidate # 34.886 * * * * [progress]: [ 80 / 905 ] simplifiying candidate # 34.886 * * * * [progress]: [ 81 / 905 ] simplifiying candidate # 34.886 * * * * [progress]: [ 82 / 905 ] simplifiying candidate # 34.886 * * * * [progress]: [ 83 / 905 ] simplifiying candidate # 34.886 * * * * [progress]: [ 84 / 905 ] simplifiying candidate # 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[progress]: [ 880 / 905 ] simplifiying candidate # 34.953 * * * * [progress]: [ 881 / 905 ] simplifiying candidate # 34.953 * * * * [progress]: [ 882 / 905 ] simplifiying candidate # 34.953 * * * * [progress]: [ 883 / 905 ] simplifiying candidate # 34.953 * * * * [progress]: [ 884 / 905 ] simplifiying candidate # 34.953 * * * * [progress]: [ 885 / 905 ] simplifiying candidate # 34.953 * * * * [progress]: [ 886 / 905 ] simplifiying candidate # 34.953 * * * * [progress]: [ 887 / 905 ] simplifiying candidate # 34.953 * * * * [progress]: [ 888 / 905 ] simplifiying candidate # 34.953 * * * * [progress]: [ 889 / 905 ] simplifiying candidate # 34.953 * * * * [progress]: [ 890 / 905 ] simplifiying candidate # 34.954 * * * * [progress]: [ 891 / 905 ] simplifiying candidate # 34.954 * * * * [progress]: [ 892 / 905 ] simplifiying candidate #real (real->posit16 (* (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* 2 PI) (- 1/2 (/ k 2))))))))))> 34.954 * * * * [progress]: [ 893 / 905 ] simplifiying candidate # 34.954 * * * * [progress]: [ 894 / 905 ] simplifiying candidate # 34.954 * * * * [progress]: [ 895 / 905 ] simplifiying candidate # 34.954 * * * * [progress]: [ 896 / 905 ] simplifiying candidate # 34.954 * * * * [progress]: [ 897 / 905 ] simplifiying candidate # 34.954 * * * * [progress]: [ 898 / 905 ] simplifiying candidate # 34.954 * * * * [progress]: [ 899 / 905 ] simplifiying candidate # 34.954 * * * * [progress]: [ 900 / 905 ] simplifiying candidate # 34.954 * * * * [progress]: [ 901 / 905 ] simplifiying candidate # 34.954 * * * * [progress]: [ 902 / 905 ] simplifiying candidate # 34.954 * * * * [progress]: [ 903 / 905 ] simplifiying candidate # 34.954 * * * * [progress]: [ 904 / 905 ] simplifiying candidate # 34.955 * * * * [progress]: [ 905 / 905 ] simplifiying candidate # 34.988 * [simplify]: Simplifying: (* (log n) (- 1/2 (/ k 2))) (* (log n) (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (pow n 1/2) 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2 PI) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))))))))))) 35.021 * * [simplify]: iteration 1: (1288 enodes) 42.350 * * [simplify]: Extracting #0: cost 391 inf + 0 42.355 * * [simplify]: Extracting #1: cost 1637 inf + 3 42.364 * * [simplify]: Extracting #2: cost 2074 inf + 757 42.373 * * [simplify]: Extracting #3: cost 2083 inf + 4367 42.396 * * [simplify]: Extracting #4: cost 2035 inf + 19685 42.440 * * [simplify]: Extracting #5: cost 1662 inf + 183421 42.535 * * [simplify]: Extracting #6: cost 803 inf + 879573 42.783 * * [simplify]: Extracting #7: cost 167 inf + 1497233 43.029 * * [simplify]: Extracting #8: cost 71 inf + 1608559 43.231 * * [simplify]: Extracting #9: cost 50 inf + 1625487 43.493 * * [simplify]: Extracting #10: cost 29 inf + 1640193 43.760 * * [simplify]: Extracting #11: cost 13 inf + 1661612 43.973 * * [simplify]: Extracting #12: cost 6 inf + 1670979 44.235 * * [simplify]: Extracting #13: cost 1 inf + 1679117 44.520 * * [simplify]: Extracting #14: cost 0 inf + 1680613 44.805 * * [simplify]: Extracting #15: cost 0 inf + 1680493 45.061 * [simplify]: Simplified to: (* (- 1/2 (/ k 2)) (log n)) (* (- 1/2 (/ k 2)) (log n)) (- 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 (sqrt n) (pow n (- (/ k 2))) (sqrt n) (pow n (- (/ k 2))) (pow (* (cbrt n) (cbrt n)) (- 1/2 (/ k 2))) (pow (cbrt n) (- 1/2 (/ k 2))) (pow (sqrt n) (- 1/2 (/ k 2))) (pow (sqrt n) (- 1/2 (/ k 2))) 1 (pow n (- 1/2 (/ k 2))) (* (- 1/2 (/ k 2)) (log n)) (exp (pow n (- 1/2 (/ k 2)))) (* (cbrt (pow n (- 1/2 (/ k 2)))) (cbrt (pow n (- 1/2 (/ k 2))))) (cbrt (pow n (- 1/2 (/ k 2)))) (* (pow n (* 2 (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (sqrt (pow n (- 1/2 (/ k 2)))) (sqrt (pow n (- 1/2 (/ k 2)))) (pow n (- 1/4 (/ (/ k 2) 2))) (pow n (- 1/4 (/ (/ k 2) 2))) (real->posit16 (pow n (- 1/2 (/ k 2)))) (* (log (* 2 PI)) (- 1/2 (/ 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(exp (* (- 1/2 (* 1/2 k)) (- (log -1) (- (log -1) (log n))))) k)) (sqrt (* (* (pow PI (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (exp (* (- 1/2 (* 1/2 k)) (log 2)))))) (* (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (- (log -1) (log n)))))) (sqrt (* (* (pow PI (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (exp (* (- 1/2 (* 1/2 k)) (log 2))))))))) 45.244 * * * [progress]: adding candidates to table 65.995 * [progress]: [Phase 3 of 3] Extracting. 65.995 * * [regime]: Finding splitpoints for: (# # # # #) 65.998 * * * [regime-changes]: Trying 2 branch expressions: (n k) 65.998 * * * * [regimes]: Trying to branch on n from (# # # # #) 66.086 * * * * [regimes]: Trying to branch on k from (# # # # #) 66.151 * * * [regime]: Found split indices: #