52.581 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.133 * * * [progress]: [2/2] Setting up program. 0.138 * [progress]: [Phase 2 of 3] Improving. 0.138 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.138 * * [simplify]: iteration 0: 13 enodes 0.141 * * [simplify]: iteration 1: 29 enodes 0.146 * * [simplify]: iteration 2: 59 enodes 0.184 * * [simplify]: iteration 3: 120 enodes 0.229 * * [simplify]: iteration 4: 328 enodes 0.450 * * [simplify]: iteration 5: 1551 enodes 1.118 * * [simplify]: iteration complete: 5000 enodes 1.118 * * [simplify]: Extracting #0: cost 1 inf + 0 1.118 * * [simplify]: Extracting #1: cost 126 inf + 0 1.123 * * [simplify]: Extracting #2: cost 1587 inf + 1 1.133 * * [simplify]: Extracting #3: cost 2139 inf + 128 1.147 * * [simplify]: Extracting #4: cost 2273 inf + 2329 1.173 * * [simplify]: Extracting #5: cost 1683 inf + 209087 1.356 * * [simplify]: Extracting #6: cost 131 inf + 1062869 1.569 * * [simplify]: Extracting #7: cost 0 inf + 1169132 1.762 * [simplify]: Simplified to: (* (/ 1.0 (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) 1.764 * * [progress]: iteration 1 / 4 1.764 * * * [progress]: picking best candidate 1.773 * * * * [pick]: Picked # 1.773 * * * [progress]: localizing error 1.801 * * * [progress]: generating rewritten candidates 1.801 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 1.820 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 1.838 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 1.846 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 1.911 * * * [progress]: generating series expansions 1.911 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 1.912 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 1.912 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 1.912 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.912 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.912 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.912 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.912 * [taylor]: Taking taylor expansion of 0.5 in k 1.912 * [backup-simplify]: Simplify 0.5 into 0.5 1.912 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.912 * [taylor]: Taking taylor expansion of 1.0 in k 1.912 * [backup-simplify]: Simplify 1.0 into 1.0 1.912 * [taylor]: Taking taylor expansion of k in k 1.912 * [backup-simplify]: Simplify 0 into 0 1.912 * [backup-simplify]: Simplify 1 into 1 1.912 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.912 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.912 * [taylor]: Taking taylor expansion of 2.0 in k 1.912 * [backup-simplify]: Simplify 2.0 into 2.0 1.912 * [taylor]: Taking taylor expansion of (* n PI) in k 1.912 * [taylor]: Taking taylor expansion of n in k 1.912 * [backup-simplify]: Simplify n into n 1.912 * [taylor]: Taking taylor expansion of PI in k 1.912 * [backup-simplify]: Simplify PI into PI 1.913 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.913 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.913 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.913 * [backup-simplify]: Simplify (- 0) into 0 1.914 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.914 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 1.914 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 1.915 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 1.915 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.915 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.915 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.915 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.915 * [taylor]: Taking taylor expansion of 0.5 in n 1.915 * [backup-simplify]: Simplify 0.5 into 0.5 1.915 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.915 * [taylor]: Taking taylor expansion of 1.0 in n 1.915 * [backup-simplify]: Simplify 1.0 into 1.0 1.915 * [taylor]: Taking taylor expansion of k in n 1.915 * [backup-simplify]: Simplify k into k 1.915 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.915 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.915 * [taylor]: Taking taylor expansion of 2.0 in n 1.915 * [backup-simplify]: Simplify 2.0 into 2.0 1.915 * [taylor]: Taking taylor expansion of (* n PI) in n 1.915 * [taylor]: Taking taylor expansion of n in n 1.915 * [backup-simplify]: Simplify 0 into 0 1.915 * [backup-simplify]: Simplify 1 into 1 1.915 * [taylor]: Taking taylor expansion of PI in n 1.915 * [backup-simplify]: Simplify PI into PI 1.916 * [backup-simplify]: Simplify (* 0 PI) into 0 1.916 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.918 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.919 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.921 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.921 * [backup-simplify]: Simplify (- k) into (- k) 1.921 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.921 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.922 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.923 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.925 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.925 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.925 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.925 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.925 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.925 * [taylor]: Taking taylor expansion of 0.5 in n 1.925 * [backup-simplify]: Simplify 0.5 into 0.5 1.925 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.925 * [taylor]: Taking taylor expansion of 1.0 in n 1.925 * [backup-simplify]: Simplify 1.0 into 1.0 1.925 * [taylor]: Taking taylor expansion of k in n 1.925 * [backup-simplify]: Simplify k into k 1.925 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.925 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.925 * [taylor]: Taking taylor expansion of 2.0 in n 1.925 * [backup-simplify]: Simplify 2.0 into 2.0 1.925 * [taylor]: Taking taylor expansion of (* n PI) in n 1.925 * [taylor]: Taking taylor expansion of n in n 1.925 * [backup-simplify]: Simplify 0 into 0 1.925 * [backup-simplify]: Simplify 1 into 1 1.925 * [taylor]: Taking taylor expansion of PI in n 1.925 * [backup-simplify]: Simplify PI into PI 1.926 * [backup-simplify]: Simplify (* 0 PI) into 0 1.926 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.927 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.929 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.930 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.930 * [backup-simplify]: Simplify (- k) into (- k) 1.930 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.930 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.932 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.933 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.934 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.934 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.934 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.935 * [taylor]: Taking taylor expansion of 0.5 in k 1.935 * [backup-simplify]: Simplify 0.5 into 0.5 1.935 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.935 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.935 * [taylor]: Taking taylor expansion of 1.0 in k 1.935 * [backup-simplify]: Simplify 1.0 into 1.0 1.935 * [taylor]: Taking taylor expansion of k in k 1.935 * [backup-simplify]: Simplify 0 into 0 1.935 * [backup-simplify]: Simplify 1 into 1 1.935 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.935 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.935 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.935 * [taylor]: Taking taylor expansion of 2.0 in k 1.935 * [backup-simplify]: Simplify 2.0 into 2.0 1.935 * [taylor]: Taking taylor expansion of PI in k 1.935 * [backup-simplify]: Simplify PI into PI 1.935 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.937 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.937 * [taylor]: Taking taylor expansion of (log n) in k 1.937 * [taylor]: Taking taylor expansion of n in k 1.937 * [backup-simplify]: Simplify n into n 1.937 * [backup-simplify]: Simplify (log n) into (log n) 1.937 * [backup-simplify]: Simplify (- 0) into 0 1.938 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.939 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 1.940 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 1.941 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 1.942 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.943 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.945 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.946 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.947 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.948 * [backup-simplify]: Simplify (- 0) into 0 1.948 * [backup-simplify]: Simplify (+ 0 0) into 0 1.949 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 1.950 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.952 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 1.954 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.954 * [taylor]: Taking taylor expansion of 0 in k 1.954 * [backup-simplify]: Simplify 0 into 0 1.954 * [backup-simplify]: Simplify 0 into 0 1.955 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.957 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.958 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.958 * [backup-simplify]: Simplify (+ 0 0) into 0 1.959 * [backup-simplify]: Simplify (- 1) into -1 1.959 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.961 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 1.963 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1.967 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 1.970 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 1.971 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.972 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.980 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 1.980 * [backup-simplify]: Simplify (- 0) into 0 1.981 * [backup-simplify]: Simplify (+ 0 0) into 0 1.982 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 1.983 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.985 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.987 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.987 * [taylor]: Taking taylor expansion of 0 in k 1.987 * [backup-simplify]: Simplify 0 into 0 1.987 * [backup-simplify]: Simplify 0 into 0 1.987 * [backup-simplify]: Simplify 0 into 0 1.988 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.992 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 1.994 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.994 * [backup-simplify]: Simplify (+ 0 0) into 0 1.995 * [backup-simplify]: Simplify (- 0) into 0 1.995 * [backup-simplify]: Simplify (+ 0 0) into 0 1.997 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.000 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.004 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 2.009 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 2.020 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))) 2.021 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 2.021 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 2.021 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.021 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.021 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.021 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.021 * [taylor]: Taking taylor expansion of 0.5 in k 2.021 * [backup-simplify]: Simplify 0.5 into 0.5 2.021 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.021 * [taylor]: Taking taylor expansion of 1.0 in k 2.022 * [backup-simplify]: Simplify 1.0 into 1.0 2.022 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.022 * [taylor]: Taking taylor expansion of k in k 2.022 * [backup-simplify]: Simplify 0 into 0 2.022 * [backup-simplify]: Simplify 1 into 1 2.022 * [backup-simplify]: Simplify (/ 1 1) into 1 2.022 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.022 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.022 * [taylor]: Taking taylor expansion of 2.0 in k 2.022 * [backup-simplify]: Simplify 2.0 into 2.0 2.022 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.022 * [taylor]: Taking taylor expansion of PI in k 2.022 * [backup-simplify]: Simplify PI into PI 2.022 * [taylor]: Taking taylor expansion of n in k 2.022 * [backup-simplify]: Simplify n into n 2.022 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.023 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.023 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.023 * [backup-simplify]: Simplify (- 1) into -1 2.023 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.024 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.024 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.024 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 2.024 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.024 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.024 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.025 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.025 * [taylor]: Taking taylor expansion of 0.5 in n 2.025 * [backup-simplify]: Simplify 0.5 into 0.5 2.025 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.025 * [taylor]: Taking taylor expansion of 1.0 in n 2.025 * [backup-simplify]: Simplify 1.0 into 1.0 2.025 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.025 * [taylor]: Taking taylor expansion of k in n 2.025 * [backup-simplify]: Simplify k into k 2.025 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.025 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.025 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.025 * [taylor]: Taking taylor expansion of 2.0 in n 2.025 * [backup-simplify]: Simplify 2.0 into 2.0 2.025 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.025 * [taylor]: Taking taylor expansion of PI in n 2.025 * [backup-simplify]: Simplify PI into PI 2.025 * [taylor]: Taking taylor expansion of n in n 2.025 * [backup-simplify]: Simplify 0 into 0 2.025 * [backup-simplify]: Simplify 1 into 1 2.026 * [backup-simplify]: Simplify (/ PI 1) into PI 2.026 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.027 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.027 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.027 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.027 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.029 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.030 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 2.032 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 2.032 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.032 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.032 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.032 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.032 * [taylor]: Taking taylor expansion of 0.5 in n 2.032 * [backup-simplify]: Simplify 0.5 into 0.5 2.032 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.032 * [taylor]: Taking taylor expansion of 1.0 in n 2.032 * [backup-simplify]: Simplify 1.0 into 1.0 2.032 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.032 * [taylor]: Taking taylor expansion of k in n 2.032 * [backup-simplify]: Simplify k into k 2.032 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.032 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.032 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.032 * [taylor]: Taking taylor expansion of 2.0 in n 2.032 * [backup-simplify]: Simplify 2.0 into 2.0 2.032 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.032 * [taylor]: Taking taylor expansion of PI in n 2.032 * [backup-simplify]: Simplify PI into PI 2.032 * [taylor]: Taking taylor expansion of n in n 2.032 * [backup-simplify]: Simplify 0 into 0 2.032 * [backup-simplify]: Simplify 1 into 1 2.033 * [backup-simplify]: Simplify (/ PI 1) into PI 2.033 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.034 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.035 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.035 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.035 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.036 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.037 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 2.039 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 2.039 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 2.039 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 2.039 * [taylor]: Taking taylor expansion of 0.5 in k 2.039 * [backup-simplify]: Simplify 0.5 into 0.5 2.039 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 2.039 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.039 * [taylor]: Taking taylor expansion of 1.0 in k 2.039 * [backup-simplify]: Simplify 1.0 into 1.0 2.039 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.039 * [taylor]: Taking taylor expansion of k in k 2.039 * [backup-simplify]: Simplify 0 into 0 2.039 * [backup-simplify]: Simplify 1 into 1 2.039 * [backup-simplify]: Simplify (/ 1 1) into 1 2.039 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.039 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.040 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.040 * [taylor]: Taking taylor expansion of 2.0 in k 2.040 * [backup-simplify]: Simplify 2.0 into 2.0 2.040 * [taylor]: Taking taylor expansion of PI in k 2.040 * [backup-simplify]: Simplify PI into PI 2.040 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.041 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.041 * [taylor]: Taking taylor expansion of (log n) in k 2.041 * [taylor]: Taking taylor expansion of n in k 2.041 * [backup-simplify]: Simplify n into n 2.041 * [backup-simplify]: Simplify (log n) into (log n) 2.042 * [backup-simplify]: Simplify (- 1) into -1 2.042 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.042 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.043 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.045 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.046 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 2.047 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 2.048 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 2.049 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.050 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.052 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.052 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.052 * [backup-simplify]: Simplify (- 0) into 0 2.053 * [backup-simplify]: Simplify (+ 0 0) into 0 2.053 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.055 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.056 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.058 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.058 * [taylor]: Taking taylor expansion of 0 in k 2.058 * [backup-simplify]: Simplify 0 into 0 2.058 * [backup-simplify]: Simplify 0 into 0 2.058 * [backup-simplify]: Simplify 0 into 0 2.059 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.060 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.064 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.065 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.065 * [backup-simplify]: Simplify (- 0) into 0 2.065 * [backup-simplify]: Simplify (+ 0 0) into 0 2.066 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.068 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.069 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.072 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.072 * [taylor]: Taking taylor expansion of 0 in k 2.072 * [backup-simplify]: Simplify 0 into 0 2.072 * [backup-simplify]: Simplify 0 into 0 2.072 * [backup-simplify]: Simplify 0 into 0 2.072 * [backup-simplify]: Simplify 0 into 0 2.073 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.075 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.081 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 2.081 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.081 * [backup-simplify]: Simplify (- 0) into 0 2.082 * [backup-simplify]: Simplify (+ 0 0) into 0 2.083 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.084 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.086 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.089 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.089 * [taylor]: Taking taylor expansion of 0 in k 2.089 * [backup-simplify]: Simplify 0 into 0 2.089 * [backup-simplify]: Simplify 0 into 0 2.091 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) 2.091 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 2.091 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 2.091 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.092 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.092 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.092 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.092 * [taylor]: Taking taylor expansion of 0.5 in k 2.092 * [backup-simplify]: Simplify 0.5 into 0.5 2.092 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.092 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.092 * [taylor]: Taking taylor expansion of k in k 2.092 * [backup-simplify]: Simplify 0 into 0 2.092 * [backup-simplify]: Simplify 1 into 1 2.092 * [backup-simplify]: Simplify (/ 1 1) into 1 2.092 * [taylor]: Taking taylor expansion of 1.0 in k 2.092 * [backup-simplify]: Simplify 1.0 into 1.0 2.092 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.092 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.092 * [taylor]: Taking taylor expansion of -2.0 in k 2.092 * [backup-simplify]: Simplify -2.0 into -2.0 2.092 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.092 * [taylor]: Taking taylor expansion of PI in k 2.092 * [backup-simplify]: Simplify PI into PI 2.092 * [taylor]: Taking taylor expansion of n in k 2.093 * [backup-simplify]: Simplify n into n 2.093 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.093 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.093 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.093 * [backup-simplify]: Simplify (+ 1 0) into 1 2.094 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.094 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.094 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) 2.094 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.094 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.094 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.094 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.094 * [taylor]: Taking taylor expansion of 0.5 in n 2.094 * [backup-simplify]: Simplify 0.5 into 0.5 2.094 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.094 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.094 * [taylor]: Taking taylor expansion of k in n 2.094 * [backup-simplify]: Simplify k into k 2.094 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.094 * [taylor]: Taking taylor expansion of 1.0 in n 2.095 * [backup-simplify]: Simplify 1.0 into 1.0 2.095 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.095 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.095 * [taylor]: Taking taylor expansion of -2.0 in n 2.095 * [backup-simplify]: Simplify -2.0 into -2.0 2.095 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.095 * [taylor]: Taking taylor expansion of PI in n 2.095 * [backup-simplify]: Simplify PI into PI 2.095 * [taylor]: Taking taylor expansion of n in n 2.095 * [backup-simplify]: Simplify 0 into 0 2.095 * [backup-simplify]: Simplify 1 into 1 2.095 * [backup-simplify]: Simplify (/ PI 1) into PI 2.096 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.097 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.097 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.097 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.099 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.100 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 2.100 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 2.100 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.100 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.101 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.101 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.101 * [taylor]: Taking taylor expansion of 0.5 in n 2.101 * [backup-simplify]: Simplify 0.5 into 0.5 2.101 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.101 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.101 * [taylor]: Taking taylor expansion of k in n 2.101 * [backup-simplify]: Simplify k into k 2.101 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.101 * [taylor]: Taking taylor expansion of 1.0 in n 2.101 * [backup-simplify]: Simplify 1.0 into 1.0 2.101 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.101 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.101 * [taylor]: Taking taylor expansion of -2.0 in n 2.101 * [backup-simplify]: Simplify -2.0 into -2.0 2.101 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.101 * [taylor]: Taking taylor expansion of PI in n 2.101 * [backup-simplify]: Simplify PI into PI 2.101 * [taylor]: Taking taylor expansion of n in n 2.101 * [backup-simplify]: Simplify 0 into 0 2.101 * [backup-simplify]: Simplify 1 into 1 2.101 * [backup-simplify]: Simplify (/ PI 1) into PI 2.101 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.102 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.102 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.102 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.103 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.104 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 2.105 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 2.105 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 2.105 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 2.105 * [taylor]: Taking taylor expansion of 0.5 in k 2.105 * [backup-simplify]: Simplify 0.5 into 0.5 2.105 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 2.105 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.105 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.105 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.105 * [taylor]: Taking taylor expansion of -2.0 in k 2.105 * [backup-simplify]: Simplify -2.0 into -2.0 2.105 * [taylor]: Taking taylor expansion of PI in k 2.105 * [backup-simplify]: Simplify PI into PI 2.105 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.106 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.106 * [taylor]: Taking taylor expansion of (log n) in k 2.106 * [taylor]: Taking taylor expansion of n in k 2.106 * [backup-simplify]: Simplify n into n 2.106 * [backup-simplify]: Simplify (log n) into (log n) 2.106 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.106 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.106 * [taylor]: Taking taylor expansion of k in k 2.106 * [backup-simplify]: Simplify 0 into 0 2.106 * [backup-simplify]: Simplify 1 into 1 2.106 * [backup-simplify]: Simplify (/ 1 1) into 1 2.106 * [taylor]: Taking taylor expansion of 1.0 in k 2.106 * [backup-simplify]: Simplify 1.0 into 1.0 2.106 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.107 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.107 * [backup-simplify]: Simplify (+ 1 0) into 1 2.108 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 2.109 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 2.109 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 2.110 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 2.111 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.111 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.112 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.113 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.113 * [backup-simplify]: Simplify (+ 0 0) into 0 2.113 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.114 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.115 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.116 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.116 * [taylor]: Taking taylor expansion of 0 in k 2.116 * [backup-simplify]: Simplify 0 into 0 2.116 * [backup-simplify]: Simplify 0 into 0 2.116 * [backup-simplify]: Simplify 0 into 0 2.119 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.120 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.121 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 2.122 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.122 * [backup-simplify]: Simplify (+ 0 0) into 0 2.123 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.124 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.125 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.126 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.126 * [taylor]: Taking taylor expansion of 0 in k 2.126 * [backup-simplify]: Simplify 0 into 0 2.126 * [backup-simplify]: Simplify 0 into 0 2.126 * [backup-simplify]: Simplify 0 into 0 2.126 * [backup-simplify]: Simplify 0 into 0 2.127 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.128 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.134 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 2.135 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.135 * [backup-simplify]: Simplify (+ 0 0) into 0 2.137 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.138 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.140 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.143 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.143 * [taylor]: Taking taylor expansion of 0 in k 2.143 * [backup-simplify]: Simplify 0 into 0 2.143 * [backup-simplify]: Simplify 0 into 0 2.145 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 2.145 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 2.145 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.145 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 2.145 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.146 * [taylor]: Taking taylor expansion of 2.0 in n 2.146 * [backup-simplify]: Simplify 2.0 into 2.0 2.146 * [taylor]: Taking taylor expansion of (* n PI) in n 2.146 * [taylor]: Taking taylor expansion of n in n 2.146 * [backup-simplify]: Simplify 0 into 0 2.146 * [backup-simplify]: Simplify 1 into 1 2.146 * [taylor]: Taking taylor expansion of PI in n 2.146 * [backup-simplify]: Simplify PI into PI 2.146 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.146 * [taylor]: Taking taylor expansion of 2.0 in n 2.146 * [backup-simplify]: Simplify 2.0 into 2.0 2.146 * [taylor]: Taking taylor expansion of (* n PI) in n 2.146 * [taylor]: Taking taylor expansion of n in n 2.146 * [backup-simplify]: Simplify 0 into 0 2.146 * [backup-simplify]: Simplify 1 into 1 2.146 * [taylor]: Taking taylor expansion of PI in n 2.146 * [backup-simplify]: Simplify PI into PI 2.147 * [backup-simplify]: Simplify (* 0 PI) into 0 2.147 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.147 * [backup-simplify]: Simplify 0 into 0 2.149 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.150 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.151 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.152 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.153 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.153 * [backup-simplify]: Simplify 0 into 0 2.154 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.156 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.156 * [backup-simplify]: Simplify 0 into 0 2.157 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.159 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.159 * [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) (+ (* 0 PI) (* 0 0)))))) into 0 2.162 * [backup-simplify]: Simplify 0 into 0 2.164 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 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 PI) (* 0 0))))))) into 0 2.166 * [backup-simplify]: Simplify 0 into 0 2.168 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.170 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.170 * [backup-simplify]: Simplify 0 into 0 2.171 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.172 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 2.172 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 2.172 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.172 * [taylor]: Taking taylor expansion of 2.0 in n 2.172 * [backup-simplify]: Simplify 2.0 into 2.0 2.172 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.172 * [taylor]: Taking taylor expansion of PI in n 2.172 * [backup-simplify]: Simplify PI into PI 2.172 * [taylor]: Taking taylor expansion of n in n 2.172 * [backup-simplify]: Simplify 0 into 0 2.172 * [backup-simplify]: Simplify 1 into 1 2.172 * [backup-simplify]: Simplify (/ PI 1) into PI 2.172 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.172 * [taylor]: Taking taylor expansion of 2.0 in n 2.172 * [backup-simplify]: Simplify 2.0 into 2.0 2.172 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.172 * [taylor]: Taking taylor expansion of PI in n 2.173 * [backup-simplify]: Simplify PI into PI 2.173 * [taylor]: Taking taylor expansion of n in n 2.173 * [backup-simplify]: Simplify 0 into 0 2.173 * [backup-simplify]: Simplify 1 into 1 2.173 * [backup-simplify]: Simplify (/ PI 1) into PI 2.174 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.174 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.175 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.176 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.176 * [backup-simplify]: Simplify 0 into 0 2.177 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.178 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.178 * [backup-simplify]: Simplify 0 into 0 2.179 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.180 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.180 * [backup-simplify]: Simplify 0 into 0 2.181 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.183 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.183 * [backup-simplify]: Simplify 0 into 0 2.184 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.186 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.186 * [backup-simplify]: Simplify 0 into 0 2.187 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.188 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.188 * [backup-simplify]: Simplify 0 into 0 2.189 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 2.189 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 2.189 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 2.189 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.189 * [taylor]: Taking taylor expansion of -2.0 in n 2.189 * [backup-simplify]: Simplify -2.0 into -2.0 2.189 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.189 * [taylor]: Taking taylor expansion of PI in n 2.189 * [backup-simplify]: Simplify PI into PI 2.189 * [taylor]: Taking taylor expansion of n in n 2.189 * [backup-simplify]: Simplify 0 into 0 2.189 * [backup-simplify]: Simplify 1 into 1 2.189 * [backup-simplify]: Simplify (/ PI 1) into PI 2.189 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.189 * [taylor]: Taking taylor expansion of -2.0 in n 2.189 * [backup-simplify]: Simplify -2.0 into -2.0 2.189 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.189 * [taylor]: Taking taylor expansion of PI in n 2.190 * [backup-simplify]: Simplify PI into PI 2.190 * [taylor]: Taking taylor expansion of n in n 2.190 * [backup-simplify]: Simplify 0 into 0 2.190 * [backup-simplify]: Simplify 1 into 1 2.190 * [backup-simplify]: Simplify (/ PI 1) into PI 2.190 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.191 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.191 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.191 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.192 * [backup-simplify]: Simplify 0 into 0 2.192 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.193 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.193 * [backup-simplify]: Simplify 0 into 0 2.193 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.194 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.194 * [backup-simplify]: Simplify 0 into 0 2.195 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.196 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.196 * [backup-simplify]: Simplify 0 into 0 2.196 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.197 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.197 * [backup-simplify]: Simplify 0 into 0 2.198 * [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 2.199 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.199 * [backup-simplify]: Simplify 0 into 0 2.199 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 2.199 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 2.199 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 2.199 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 2.199 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 2.199 * [taylor]: Taking taylor expansion of 1.0 in k 2.199 * [backup-simplify]: Simplify 1.0 into 1.0 2.200 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.200 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.200 * [taylor]: Taking taylor expansion of k in k 2.200 * [backup-simplify]: Simplify 0 into 0 2.200 * [backup-simplify]: Simplify 1 into 1 2.200 * [backup-simplify]: Simplify (/ 1 1) into 1 2.200 * [backup-simplify]: Simplify (sqrt 0) into 0 2.201 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.201 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 2.201 * [taylor]: Taking taylor expansion of 1.0 in k 2.201 * [backup-simplify]: Simplify 1.0 into 1.0 2.201 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.201 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.201 * [taylor]: Taking taylor expansion of k in k 2.201 * [backup-simplify]: Simplify 0 into 0 2.201 * [backup-simplify]: Simplify 1 into 1 2.201 * [backup-simplify]: Simplify (/ 1 1) into 1 2.202 * [backup-simplify]: Simplify (sqrt 0) into 0 2.202 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.203 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.203 * [backup-simplify]: Simplify 0 into 0 2.204 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 2.204 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.205 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.207 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.208 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 2.208 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.208 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.211 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.212 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 2.213 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.214 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 2.214 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 2.214 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 2.214 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 2.214 * [taylor]: Taking taylor expansion of 1.0 in k 2.214 * [backup-simplify]: Simplify 1.0 into 1.0 2.214 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.214 * [taylor]: Taking taylor expansion of k in k 2.214 * [backup-simplify]: Simplify 0 into 0 2.214 * [backup-simplify]: Simplify 1 into 1 2.214 * [backup-simplify]: Simplify (sqrt 0) into 0 2.215 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.215 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 2.215 * [taylor]: Taking taylor expansion of 1.0 in k 2.215 * [backup-simplify]: Simplify 1.0 into 1.0 2.215 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.215 * [taylor]: Taking taylor expansion of k in k 2.215 * [backup-simplify]: Simplify 0 into 0 2.215 * [backup-simplify]: Simplify 1 into 1 2.215 * [backup-simplify]: Simplify (sqrt 0) into 0 2.216 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.216 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.216 * [backup-simplify]: Simplify 0 into 0 2.217 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 2.217 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.219 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.220 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 2.221 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.223 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.224 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 2.225 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.226 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 2.226 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 2.226 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 2.226 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 2.226 * [taylor]: Taking taylor expansion of 1.0 in k 2.226 * [backup-simplify]: Simplify 1.0 into 1.0 2.226 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.226 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.226 * [taylor]: Taking taylor expansion of -1 in k 2.226 * [backup-simplify]: Simplify -1 into -1 2.226 * [taylor]: Taking taylor expansion of k in k 2.226 * [backup-simplify]: Simplify 0 into 0 2.226 * [backup-simplify]: Simplify 1 into 1 2.226 * [backup-simplify]: Simplify (/ -1 1) into -1 2.226 * [backup-simplify]: Simplify (sqrt 0) into 0 2.227 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.227 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 2.227 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 2.227 * [taylor]: Taking taylor expansion of 1.0 in k 2.227 * [backup-simplify]: Simplify 1.0 into 1.0 2.227 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.228 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.228 * [taylor]: Taking taylor expansion of -1 in k 2.228 * [backup-simplify]: Simplify -1 into -1 2.228 * [taylor]: Taking taylor expansion of k in k 2.228 * [backup-simplify]: Simplify 0 into 0 2.228 * [backup-simplify]: Simplify 1 into 1 2.228 * [backup-simplify]: Simplify (/ -1 1) into -1 2.228 * [backup-simplify]: Simplify (sqrt 0) into 0 2.229 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.229 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 2.229 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.230 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.234 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.235 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 2.236 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.236 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.239 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.241 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 2.241 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.242 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 2.242 * * * * [progress]: [ 4 / 4 ] generating series at (2) 2.243 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) 2.243 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in (k n) around 0 2.243 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n 2.243 * [taylor]: Taking taylor expansion of 1.0 in n 2.243 * [backup-simplify]: Simplify 1.0 into 1.0 2.243 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 2.243 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.243 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.243 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.243 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.243 * [taylor]: Taking taylor expansion of 0.5 in n 2.243 * [backup-simplify]: Simplify 0.5 into 0.5 2.243 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.243 * [taylor]: Taking taylor expansion of 1.0 in n 2.243 * [backup-simplify]: Simplify 1.0 into 1.0 2.243 * [taylor]: Taking taylor expansion of k in n 2.243 * [backup-simplify]: Simplify k into k 2.243 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.243 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.243 * [taylor]: Taking taylor expansion of 2.0 in n 2.243 * [backup-simplify]: Simplify 2.0 into 2.0 2.243 * [taylor]: Taking taylor expansion of (* n PI) in n 2.243 * [taylor]: Taking taylor expansion of n in n 2.243 * [backup-simplify]: Simplify 0 into 0 2.243 * [backup-simplify]: Simplify 1 into 1 2.243 * [taylor]: Taking taylor expansion of PI in n 2.243 * [backup-simplify]: Simplify PI into PI 2.243 * [backup-simplify]: Simplify (* 0 PI) into 0 2.244 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.245 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.246 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.247 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.247 * [backup-simplify]: Simplify (- k) into (- k) 2.247 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.247 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.248 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.248 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.249 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.249 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.249 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.249 * [taylor]: Taking taylor expansion of k in n 2.249 * [backup-simplify]: Simplify k into k 2.249 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.249 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 2.249 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.249 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 2.249 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 2.249 * [taylor]: Taking taylor expansion of 1.0 in k 2.249 * [backup-simplify]: Simplify 1.0 into 1.0 2.249 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 2.250 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.250 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.250 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.250 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.250 * [taylor]: Taking taylor expansion of 0.5 in k 2.250 * [backup-simplify]: Simplify 0.5 into 0.5 2.250 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.250 * [taylor]: Taking taylor expansion of 1.0 in k 2.250 * [backup-simplify]: Simplify 1.0 into 1.0 2.250 * [taylor]: Taking taylor expansion of k in k 2.250 * [backup-simplify]: Simplify 0 into 0 2.250 * [backup-simplify]: Simplify 1 into 1 2.250 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.250 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.250 * [taylor]: Taking taylor expansion of 2.0 in k 2.250 * [backup-simplify]: Simplify 2.0 into 2.0 2.250 * [taylor]: Taking taylor expansion of (* n PI) in k 2.250 * [taylor]: Taking taylor expansion of n in k 2.250 * [backup-simplify]: Simplify n into n 2.250 * [taylor]: Taking taylor expansion of PI in k 2.250 * [backup-simplify]: Simplify PI into PI 2.250 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.250 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.250 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.250 * [backup-simplify]: Simplify (- 0) into 0 2.251 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.251 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.251 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.251 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.251 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.251 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.251 * [taylor]: Taking taylor expansion of k in k 2.251 * [backup-simplify]: Simplify 0 into 0 2.251 * [backup-simplify]: Simplify 1 into 1 2.251 * [backup-simplify]: Simplify (/ 1 1) into 1 2.252 * [backup-simplify]: Simplify (sqrt 0) into 0 2.253 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.253 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 2.253 * [taylor]: Taking taylor expansion of 1.0 in k 2.253 * [backup-simplify]: Simplify 1.0 into 1.0 2.253 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 2.253 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.253 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.253 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.253 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.253 * [taylor]: Taking taylor expansion of 0.5 in k 2.253 * [backup-simplify]: Simplify 0.5 into 0.5 2.253 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.253 * [taylor]: Taking taylor expansion of 1.0 in k 2.253 * [backup-simplify]: Simplify 1.0 into 1.0 2.253 * [taylor]: Taking taylor expansion of k in k 2.253 * [backup-simplify]: Simplify 0 into 0 2.253 * [backup-simplify]: Simplify 1 into 1 2.253 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.253 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.253 * [taylor]: Taking taylor expansion of 2.0 in k 2.253 * [backup-simplify]: Simplify 2.0 into 2.0 2.253 * [taylor]: Taking taylor expansion of (* n PI) in k 2.253 * [taylor]: Taking taylor expansion of n in k 2.253 * [backup-simplify]: Simplify n into n 2.253 * [taylor]: Taking taylor expansion of PI in k 2.253 * [backup-simplify]: Simplify PI into PI 2.253 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.253 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.253 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.254 * [backup-simplify]: Simplify (- 0) into 0 2.254 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.254 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.255 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.255 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.255 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.255 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.255 * [taylor]: Taking taylor expansion of k in k 2.255 * [backup-simplify]: Simplify 0 into 0 2.255 * [backup-simplify]: Simplify 1 into 1 2.255 * [backup-simplify]: Simplify (/ 1 1) into 1 2.255 * [backup-simplify]: Simplify (sqrt 0) into 0 2.256 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.257 * [backup-simplify]: Simplify (* (pow (* 2.0 (* n PI)) 0.5) 0) into 0 2.257 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.257 * [taylor]: Taking taylor expansion of 0 in n 2.257 * [backup-simplify]: Simplify 0 into 0 2.257 * [backup-simplify]: Simplify 0 into 0 2.258 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 2.258 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 2.259 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 2.260 * [backup-simplify]: Simplify (- 1) into -1 2.260 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.262 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 2.263 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 2.263 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1)))) into (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) 2.265 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) +nan.0) (* (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) 0)) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 2.267 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 2.267 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n 2.267 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 2.267 * [taylor]: Taking taylor expansion of +nan.0 in n 2.267 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.267 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 2.267 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.267 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.267 * [taylor]: Taking taylor expansion of 0.5 in n 2.267 * [backup-simplify]: Simplify 0.5 into 0.5 2.267 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.267 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.267 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.267 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.267 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.267 * [taylor]: Taking taylor expansion of 1.0 in n 2.267 * [backup-simplify]: Simplify 1.0 into 1.0 2.267 * [taylor]: Taking taylor expansion of (log PI) in n 2.267 * [taylor]: Taking taylor expansion of PI in n 2.268 * [backup-simplify]: Simplify PI into PI 2.268 * [backup-simplify]: Simplify (log PI) into (log PI) 2.269 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.270 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.270 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.270 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.270 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.270 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.270 * [taylor]: Taking taylor expansion of 1.0 in n 2.270 * [backup-simplify]: Simplify 1.0 into 1.0 2.270 * [taylor]: Taking taylor expansion of (log n) in n 2.270 * [taylor]: Taking taylor expansion of n in n 2.270 * [backup-simplify]: Simplify 0 into 0 2.270 * [backup-simplify]: Simplify 1 into 1 2.270 * [backup-simplify]: Simplify (log 1) into 0 2.270 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.270 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.270 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.270 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.271 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.271 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.271 * [taylor]: Taking taylor expansion of 1.0 in n 2.271 * [backup-simplify]: Simplify 1.0 into 1.0 2.271 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.271 * [taylor]: Taking taylor expansion of 2.0 in n 2.271 * [backup-simplify]: Simplify 2.0 into 2.0 2.271 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.271 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.272 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.273 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 2.274 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 2.274 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 2.275 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 2.276 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 2.277 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 2.278 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 2.279 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 2.279 * [backup-simplify]: Simplify 0 into 0 2.279 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.281 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.282 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 2.282 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 2.283 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 2) into 0 2.284 * [backup-simplify]: Simplify (- 0) into 0 2.284 * [backup-simplify]: Simplify (+ 0 0) into 0 2.285 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 2.285 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 2.286 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) 2.288 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) +nan.0) (+ (* (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) +nan.0) (* (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))) 2.291 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) 2.291 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) in n 2.291 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) in n 2.291 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 2.291 * [taylor]: Taking taylor expansion of +nan.0 in n 2.291 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.291 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 2.291 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 2.291 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.291 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.291 * [taylor]: Taking taylor expansion of 0.5 in n 2.292 * [backup-simplify]: Simplify 0.5 into 0.5 2.292 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.292 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.292 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.292 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.292 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.292 * [taylor]: Taking taylor expansion of 1.0 in n 2.292 * [backup-simplify]: Simplify 1.0 into 1.0 2.292 * [taylor]: Taking taylor expansion of (log PI) in n 2.292 * [taylor]: Taking taylor expansion of PI in n 2.292 * [backup-simplify]: Simplify PI into PI 2.292 * [backup-simplify]: Simplify (log PI) into (log PI) 2.293 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.294 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.294 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.294 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.294 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.294 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.294 * [taylor]: Taking taylor expansion of 1.0 in n 2.294 * [backup-simplify]: Simplify 1.0 into 1.0 2.294 * [taylor]: Taking taylor expansion of (log n) in n 2.294 * [taylor]: Taking taylor expansion of n in n 2.294 * [backup-simplify]: Simplify 0 into 0 2.294 * [backup-simplify]: Simplify 1 into 1 2.294 * [backup-simplify]: Simplify (log 1) into 0 2.294 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.294 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.294 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.294 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.294 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.294 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.294 * [taylor]: Taking taylor expansion of 1.0 in n 2.294 * [backup-simplify]: Simplify 1.0 into 1.0 2.295 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.295 * [taylor]: Taking taylor expansion of 2.0 in n 2.295 * [backup-simplify]: Simplify 2.0 into 2.0 2.295 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.296 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.296 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.297 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 2.298 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 2.298 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 2.299 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 2.301 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 2.301 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.301 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.301 * [taylor]: Taking taylor expansion of 2.0 in n 2.301 * [backup-simplify]: Simplify 2.0 into 2.0 2.301 * [taylor]: Taking taylor expansion of (* n PI) in n 2.301 * [taylor]: Taking taylor expansion of n in n 2.301 * [backup-simplify]: Simplify 0 into 0 2.301 * [backup-simplify]: Simplify 1 into 1 2.301 * [taylor]: Taking taylor expansion of PI in n 2.301 * [backup-simplify]: Simplify PI into PI 2.301 * [backup-simplify]: Simplify (* 0 PI) into 0 2.302 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.303 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.305 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.306 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.306 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n 2.306 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 2.306 * [taylor]: Taking taylor expansion of +nan.0 in n 2.306 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.306 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 2.306 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.307 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.307 * [taylor]: Taking taylor expansion of 0.5 in n 2.307 * [backup-simplify]: Simplify 0.5 into 0.5 2.307 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.307 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.307 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.307 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.307 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.307 * [taylor]: Taking taylor expansion of 1.0 in n 2.307 * [backup-simplify]: Simplify 1.0 into 1.0 2.307 * [taylor]: Taking taylor expansion of (log PI) in n 2.307 * [taylor]: Taking taylor expansion of PI in n 2.307 * [backup-simplify]: Simplify PI into PI 2.307 * [backup-simplify]: Simplify (log PI) into (log PI) 2.308 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.310 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.310 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.310 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.310 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.310 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.310 * [taylor]: Taking taylor expansion of 1.0 in n 2.310 * [backup-simplify]: Simplify 1.0 into 1.0 2.310 * [taylor]: Taking taylor expansion of (log n) in n 2.310 * [taylor]: Taking taylor expansion of n in n 2.310 * [backup-simplify]: Simplify 0 into 0 2.310 * [backup-simplify]: Simplify 1 into 1 2.311 * [backup-simplify]: Simplify (log 1) into 0 2.311 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.311 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.311 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.311 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.311 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.311 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.311 * [taylor]: Taking taylor expansion of 1.0 in n 2.311 * [backup-simplify]: Simplify 1.0 into 1.0 2.311 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.311 * [taylor]: Taking taylor expansion of 2.0 in n 2.312 * [backup-simplify]: Simplify 2.0 into 2.0 2.312 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.313 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.314 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.315 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 2.316 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 2.318 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 2.319 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 2.321 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 2.322 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.325 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n))) 2.327 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) into (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) 2.329 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 2.330 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 2.334 * [backup-simplify]: Simplify (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))) 2.340 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI))))))))) 2.346 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI))))))))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))) 2.348 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 2.349 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 2.351 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 2.356 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.357 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.357 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 2.358 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.359 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 2.361 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 2.361 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 2.363 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 2.364 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 2.366 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1)))) 1) into 0 2.367 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)))) into 0 2.368 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.369 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5))) into 0 2.370 * [backup-simplify]: Simplify (- 0) into 0 2.370 * [backup-simplify]: Simplify 0 into 0 2.370 * [backup-simplify]: Simplify 0 into 0 2.370 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.373 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.373 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.374 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 2.376 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 6) into 0 2.376 * [backup-simplify]: Simplify (- 0) into 0 2.376 * [backup-simplify]: Simplify (+ 0 0) into 0 2.377 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 2.378 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 2.379 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 3) 6)) (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 3))) 2.382 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) +nan.0) (+ (* (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) +nan.0) (+ (* (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) +nan.0) (* (* -0.020833333333333332 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 2.389 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))) (+ (* 0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 2.389 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) in n 2.389 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))) in n 2.389 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 2.389 * [taylor]: Taking taylor expansion of +nan.0 in n 2.389 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.389 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 2.389 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 2.389 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.389 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.389 * [taylor]: Taking taylor expansion of 0.5 in n 2.389 * [backup-simplify]: Simplify 0.5 into 0.5 2.389 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.389 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.389 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.389 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.389 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.389 * [taylor]: Taking taylor expansion of 1.0 in n 2.389 * [backup-simplify]: Simplify 1.0 into 1.0 2.389 * [taylor]: Taking taylor expansion of (log PI) in n 2.389 * [taylor]: Taking taylor expansion of PI in n 2.389 * [backup-simplify]: Simplify PI into PI 2.390 * [backup-simplify]: Simplify (log PI) into (log PI) 2.390 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.391 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.391 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.391 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.391 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.391 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.391 * [taylor]: Taking taylor expansion of 1.0 in n 2.391 * [backup-simplify]: Simplify 1.0 into 1.0 2.392 * [taylor]: Taking taylor expansion of (log n) in n 2.392 * [taylor]: Taking taylor expansion of n in n 2.392 * [backup-simplify]: Simplify 0 into 0 2.392 * [backup-simplify]: Simplify 1 into 1 2.392 * [backup-simplify]: Simplify (log 1) into 0 2.392 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.392 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.392 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.392 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.392 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.392 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.392 * [taylor]: Taking taylor expansion of 1.0 in n 2.392 * [backup-simplify]: Simplify 1.0 into 1.0 2.392 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.392 * [taylor]: Taking taylor expansion of 2.0 in n 2.392 * [backup-simplify]: Simplify 2.0 into 2.0 2.393 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.393 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.394 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.395 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 2.395 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 2.397 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 2.397 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 2.398 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 2.398 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.398 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.398 * [taylor]: Taking taylor expansion of 2.0 in n 2.398 * [backup-simplify]: Simplify 2.0 into 2.0 2.398 * [taylor]: Taking taylor expansion of (* n PI) in n 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 * [taylor]: Taking taylor expansion of PI in n 2.398 * [backup-simplify]: Simplify PI into PI 2.399 * [backup-simplify]: Simplify (* 0 PI) into 0 2.399 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.400 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.401 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.402 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.402 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))) in n 2.402 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) in n 2.402 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) in n 2.402 * [taylor]: Taking taylor expansion of +nan.0 in n 2.402 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.402 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 2.402 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 2.402 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 2.402 * [taylor]: Taking taylor expansion of 0.5 in n 2.402 * [backup-simplify]: Simplify 0.5 into 0.5 2.402 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 2.402 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 2.402 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.402 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.402 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.402 * [taylor]: Taking taylor expansion of 1.0 in n 2.402 * [backup-simplify]: Simplify 1.0 into 1.0 2.402 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.402 * [taylor]: Taking taylor expansion of 2.0 in n 2.402 * [backup-simplify]: Simplify 2.0 into 2.0 2.402 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.403 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.404 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.404 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 2.404 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.404 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.404 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.404 * [taylor]: Taking taylor expansion of 1.0 in n 2.404 * [backup-simplify]: Simplify 1.0 into 1.0 2.404 * [taylor]: Taking taylor expansion of (log n) in n 2.404 * [taylor]: Taking taylor expansion of n in n 2.404 * [backup-simplify]: Simplify 0 into 0 2.404 * [backup-simplify]: Simplify 1 into 1 2.404 * [backup-simplify]: Simplify (log 1) into 0 2.404 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.404 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.405 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.405 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.405 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.405 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.405 * [taylor]: Taking taylor expansion of 1.0 in n 2.405 * [backup-simplify]: Simplify 1.0 into 1.0 2.405 * [taylor]: Taking taylor expansion of (log PI) in n 2.405 * [taylor]: Taking taylor expansion of PI in n 2.405 * [backup-simplify]: Simplify PI into PI 2.405 * [backup-simplify]: Simplify (log PI) into (log PI) 2.406 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.407 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.407 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.408 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 2.409 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 2.410 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 2.412 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 2.412 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) in n 2.412 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n 2.412 * [taylor]: Taking taylor expansion of +nan.0 in n 2.412 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.412 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n 2.412 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 2.412 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.412 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.412 * [taylor]: Taking taylor expansion of 0.5 in n 2.413 * [backup-simplify]: Simplify 0.5 into 0.5 2.413 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.413 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.413 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.413 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.413 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.413 * [taylor]: Taking taylor expansion of 1.0 in n 2.413 * [backup-simplify]: Simplify 1.0 into 1.0 2.413 * [taylor]: Taking taylor expansion of (log PI) in n 2.413 * [taylor]: Taking taylor expansion of PI in n 2.413 * [backup-simplify]: Simplify PI into PI 2.413 * [backup-simplify]: Simplify (log PI) into (log PI) 2.415 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.416 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.416 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.416 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.416 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.416 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.416 * [taylor]: Taking taylor expansion of 1.0 in n 2.416 * [backup-simplify]: Simplify 1.0 into 1.0 2.416 * [taylor]: Taking taylor expansion of (log n) in n 2.416 * [taylor]: Taking taylor expansion of n in n 2.416 * [backup-simplify]: Simplify 0 into 0 2.416 * [backup-simplify]: Simplify 1 into 1 2.417 * [backup-simplify]: Simplify (log 1) into 0 2.417 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.417 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.418 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.418 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.418 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.418 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.418 * [taylor]: Taking taylor expansion of 1.0 in n 2.418 * [backup-simplify]: Simplify 1.0 into 1.0 2.418 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.418 * [taylor]: Taking taylor expansion of 2.0 in n 2.418 * [backup-simplify]: Simplify 2.0 into 2.0 2.418 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.419 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.421 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.421 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 2.422 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 2.424 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 2.425 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 2.427 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 2.427 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 2.427 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.427 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.427 * [taylor]: Taking taylor expansion of 2.0 in n 2.427 * [backup-simplify]: Simplify 2.0 into 2.0 2.427 * [taylor]: Taking taylor expansion of (* n PI) in n 2.427 * [taylor]: Taking taylor expansion of n in n 2.427 * [backup-simplify]: Simplify 0 into 0 2.427 * [backup-simplify]: Simplify 1 into 1 2.427 * [taylor]: Taking taylor expansion of PI in n 2.427 * [backup-simplify]: Simplify PI into PI 2.427 * [backup-simplify]: Simplify (* 0 PI) into 0 2.428 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.429 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.431 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.432 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.434 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.435 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.438 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n))) 2.441 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) into (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) 2.442 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 2.444 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.445 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.448 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 2.451 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)) 2.453 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2))) into (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2))) 2.456 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2)))))))) 2.466 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) 2.477 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2)))))))))) 2.490 * [backup-simplify]: Simplify (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))) 2.500 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))) 2.511 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n))))))))))))))) 2.534 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n))))))))))))))) (pow (* 1 k) 2)) (+ (* (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))) (* 1 k)) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) k)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow k 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (pow k 2)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log n) 2) (pow k 2))))))))))))))))))))))) 2.535 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 k))) (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) into (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) 2.535 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in (k n) around 0 2.535 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n 2.535 * [taylor]: Taking taylor expansion of 1.0 in n 2.535 * [backup-simplify]: Simplify 1.0 into 1.0 2.535 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n 2.535 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.535 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.536 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.536 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.536 * [taylor]: Taking taylor expansion of 0.5 in n 2.536 * [backup-simplify]: Simplify 0.5 into 0.5 2.536 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.536 * [taylor]: Taking taylor expansion of 1.0 in n 2.536 * [backup-simplify]: Simplify 1.0 into 1.0 2.536 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.536 * [taylor]: Taking taylor expansion of k in n 2.536 * [backup-simplify]: Simplify k into k 2.536 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.536 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.536 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.536 * [taylor]: Taking taylor expansion of 2.0 in n 2.536 * [backup-simplify]: Simplify 2.0 into 2.0 2.536 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.536 * [taylor]: Taking taylor expansion of PI in n 2.536 * [backup-simplify]: Simplify PI into PI 2.536 * [taylor]: Taking taylor expansion of n in n 2.536 * [backup-simplify]: Simplify 0 into 0 2.536 * [backup-simplify]: Simplify 1 into 1 2.537 * [backup-simplify]: Simplify (/ PI 1) into PI 2.537 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.538 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.538 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.538 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.538 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.540 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.541 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 2.542 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 2.542 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.542 * [taylor]: Taking taylor expansion of k in n 2.542 * [backup-simplify]: Simplify k into k 2.542 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.542 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.543 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 2.543 * [taylor]: Taking taylor expansion of 1.0 in k 2.543 * [backup-simplify]: Simplify 1.0 into 1.0 2.543 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 2.543 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.543 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.543 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.543 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.543 * [taylor]: Taking taylor expansion of 0.5 in k 2.543 * [backup-simplify]: Simplify 0.5 into 0.5 2.543 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.543 * [taylor]: Taking taylor expansion of 1.0 in k 2.543 * [backup-simplify]: Simplify 1.0 into 1.0 2.543 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.543 * [taylor]: Taking taylor expansion of k in k 2.543 * [backup-simplify]: Simplify 0 into 0 2.543 * [backup-simplify]: Simplify 1 into 1 2.543 * [backup-simplify]: Simplify (/ 1 1) into 1 2.543 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.543 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.543 * [taylor]: Taking taylor expansion of 2.0 in k 2.543 * [backup-simplify]: Simplify 2.0 into 2.0 2.544 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.544 * [taylor]: Taking taylor expansion of PI in k 2.544 * [backup-simplify]: Simplify PI into PI 2.544 * [taylor]: Taking taylor expansion of n in k 2.544 * [backup-simplify]: Simplify n into n 2.544 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.544 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.544 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.544 * [backup-simplify]: Simplify (- 1) into -1 2.545 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.545 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.545 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.545 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 2.546 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.546 * [taylor]: Taking taylor expansion of k in k 2.546 * [backup-simplify]: Simplify 0 into 0 2.546 * [backup-simplify]: Simplify 1 into 1 2.546 * [backup-simplify]: Simplify (sqrt 0) into 0 2.548 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.548 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 2.548 * [taylor]: Taking taylor expansion of 1.0 in k 2.548 * [backup-simplify]: Simplify 1.0 into 1.0 2.548 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 2.548 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.548 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.548 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.548 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.548 * [taylor]: Taking taylor expansion of 0.5 in k 2.548 * [backup-simplify]: Simplify 0.5 into 0.5 2.548 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.548 * [taylor]: Taking taylor expansion of 1.0 in k 2.548 * [backup-simplify]: Simplify 1.0 into 1.0 2.548 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.548 * [taylor]: Taking taylor expansion of k in k 2.548 * [backup-simplify]: Simplify 0 into 0 2.548 * [backup-simplify]: Simplify 1 into 1 2.548 * [backup-simplify]: Simplify (/ 1 1) into 1 2.548 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.548 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.548 * [taylor]: Taking taylor expansion of 2.0 in k 2.548 * [backup-simplify]: Simplify 2.0 into 2.0 2.548 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.548 * [taylor]: Taking taylor expansion of PI in k 2.548 * [backup-simplify]: Simplify PI into PI 2.548 * [taylor]: Taking taylor expansion of n in k 2.548 * [backup-simplify]: Simplify n into n 2.548 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.548 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.549 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.549 * [backup-simplify]: Simplify (- 1) into -1 2.549 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.549 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.549 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.550 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 2.550 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.550 * [taylor]: Taking taylor expansion of k in k 2.550 * [backup-simplify]: Simplify 0 into 0 2.550 * [backup-simplify]: Simplify 1 into 1 2.550 * [backup-simplify]: Simplify (sqrt 0) into 0 2.551 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.551 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 0) into 0 2.551 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.551 * [taylor]: Taking taylor expansion of 0 in n 2.551 * [backup-simplify]: Simplify 0 into 0 2.551 * [backup-simplify]: Simplify 0 into 0 2.552 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 2.552 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 2.552 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 2.552 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 2.552 * [taylor]: Taking taylor expansion of +nan.0 in n 2.552 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.552 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 2.552 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 2.552 * [taylor]: Taking taylor expansion of 0.5 in n 2.552 * [backup-simplify]: Simplify 0.5 into 0.5 2.552 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 2.552 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.552 * [taylor]: Taking taylor expansion of 1.0 in n 2.552 * [backup-simplify]: Simplify 1.0 into 1.0 2.552 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.552 * [taylor]: Taking taylor expansion of k in n 2.552 * [backup-simplify]: Simplify k into k 2.552 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.552 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.552 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.553 * [taylor]: Taking taylor expansion of 2.0 in n 2.553 * [backup-simplify]: Simplify 2.0 into 2.0 2.553 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.553 * [taylor]: Taking taylor expansion of PI in n 2.553 * [backup-simplify]: Simplify PI into PI 2.553 * [taylor]: Taking taylor expansion of n in n 2.553 * [backup-simplify]: Simplify 0 into 0 2.553 * [backup-simplify]: Simplify 1 into 1 2.553 * [backup-simplify]: Simplify (/ PI 1) into PI 2.553 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.554 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.554 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.554 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.555 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.556 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 2.556 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 2.557 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 2.558 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 2.559 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 2.560 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 2.560 * [backup-simplify]: Simplify 0 into 0 2.562 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.562 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 2.563 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 2.563 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 2.563 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 2.563 * [taylor]: Taking taylor expansion of +nan.0 in n 2.563 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.563 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 2.563 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 2.563 * [taylor]: Taking taylor expansion of 0.5 in n 2.563 * [backup-simplify]: Simplify 0.5 into 0.5 2.563 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 2.563 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.563 * [taylor]: Taking taylor expansion of 1.0 in n 2.563 * [backup-simplify]: Simplify 1.0 into 1.0 2.563 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.563 * [taylor]: Taking taylor expansion of k in n 2.563 * [backup-simplify]: Simplify k into k 2.563 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.563 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.563 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.563 * [taylor]: Taking taylor expansion of 2.0 in n 2.563 * [backup-simplify]: Simplify 2.0 into 2.0 2.563 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.563 * [taylor]: Taking taylor expansion of PI in n 2.563 * [backup-simplify]: Simplify PI into PI 2.563 * [taylor]: Taking taylor expansion of n in n 2.563 * [backup-simplify]: Simplify 0 into 0 2.563 * [backup-simplify]: Simplify 1 into 1 2.564 * [backup-simplify]: Simplify (/ PI 1) into PI 2.564 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.565 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.565 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.565 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.566 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.566 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 2.567 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 2.568 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 2.569 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 2.569 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 2.570 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 2.571 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.571 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.572 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.573 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.573 * [backup-simplify]: Simplify (- 0) into 0 2.573 * [backup-simplify]: Simplify (+ 0 0) into 0 2.574 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.575 * [backup-simplify]: Simplify (+ (* (- 1.0 (/ 1 k)) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.576 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into 0 2.577 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.578 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into 0 2.578 * [backup-simplify]: Simplify (- 0) into 0 2.578 * [backup-simplify]: Simplify 0 into 0 2.578 * [backup-simplify]: Simplify 0 into 0 2.581 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.582 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 2.584 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 2.584 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 2.584 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 2.584 * [taylor]: Taking taylor expansion of +nan.0 in n 2.584 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.584 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 2.584 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 2.584 * [taylor]: Taking taylor expansion of 0.5 in n 2.584 * [backup-simplify]: Simplify 0.5 into 0.5 2.584 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 2.584 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.584 * [taylor]: Taking taylor expansion of 1.0 in n 2.584 * [backup-simplify]: Simplify 1.0 into 1.0 2.584 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.584 * [taylor]: Taking taylor expansion of k in n 2.584 * [backup-simplify]: Simplify k into k 2.584 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.584 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.584 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.584 * [taylor]: Taking taylor expansion of 2.0 in n 2.584 * [backup-simplify]: Simplify 2.0 into 2.0 2.584 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.584 * [taylor]: Taking taylor expansion of PI in n 2.584 * [backup-simplify]: Simplify PI into PI 2.584 * [taylor]: Taking taylor expansion of n in n 2.584 * [backup-simplify]: Simplify 0 into 0 2.585 * [backup-simplify]: Simplify 1 into 1 2.585 * [backup-simplify]: Simplify (/ PI 1) into PI 2.586 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.587 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.587 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.587 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.592 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.593 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 2.594 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 2.596 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 2.597 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 2.599 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 2.600 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 2.605 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3)))))))) 2.606 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 2.606 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k n) around 0 2.606 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 2.606 * [taylor]: Taking taylor expansion of 1.0 in n 2.606 * [backup-simplify]: Simplify 1.0 into 1.0 2.606 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 2.606 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.606 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.606 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.606 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.606 * [taylor]: Taking taylor expansion of 0.5 in n 2.606 * [backup-simplify]: Simplify 0.5 into 0.5 2.606 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.606 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.606 * [taylor]: Taking taylor expansion of k in n 2.606 * [backup-simplify]: Simplify k into k 2.606 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.606 * [taylor]: Taking taylor expansion of 1.0 in n 2.607 * [backup-simplify]: Simplify 1.0 into 1.0 2.607 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.607 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.607 * [taylor]: Taking taylor expansion of -2.0 in n 2.607 * [backup-simplify]: Simplify -2.0 into -2.0 2.607 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.607 * [taylor]: Taking taylor expansion of PI in n 2.607 * [backup-simplify]: Simplify PI into PI 2.607 * [taylor]: Taking taylor expansion of n in n 2.607 * [backup-simplify]: Simplify 0 into 0 2.607 * [backup-simplify]: Simplify 1 into 1 2.607 * [backup-simplify]: Simplify (/ PI 1) into PI 2.608 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.609 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.609 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.609 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.611 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.612 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 2.613 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 2.613 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.613 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.613 * [taylor]: Taking taylor expansion of -1 in n 2.613 * [backup-simplify]: Simplify -1 into -1 2.613 * [taylor]: Taking taylor expansion of k in n 2.613 * [backup-simplify]: Simplify k into k 2.613 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.613 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.614 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.614 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.615 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) 2.615 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 2.615 * [taylor]: Taking taylor expansion of 1.0 in k 2.615 * [backup-simplify]: Simplify 1.0 into 1.0 2.615 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 2.615 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.615 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.615 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.615 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.615 * [taylor]: Taking taylor expansion of 0.5 in k 2.615 * [backup-simplify]: Simplify 0.5 into 0.5 2.615 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.615 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.615 * [taylor]: Taking taylor expansion of k in k 2.616 * [backup-simplify]: Simplify 0 into 0 2.616 * [backup-simplify]: Simplify 1 into 1 2.616 * [backup-simplify]: Simplify (/ 1 1) into 1 2.616 * [taylor]: Taking taylor expansion of 1.0 in k 2.616 * [backup-simplify]: Simplify 1.0 into 1.0 2.616 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.616 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.616 * [taylor]: Taking taylor expansion of -2.0 in k 2.616 * [backup-simplify]: Simplify -2.0 into -2.0 2.616 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.616 * [taylor]: Taking taylor expansion of PI in k 2.616 * [backup-simplify]: Simplify PI into PI 2.616 * [taylor]: Taking taylor expansion of n in k 2.616 * [backup-simplify]: Simplify n into n 2.616 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.616 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.617 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.617 * [backup-simplify]: Simplify (+ 1 0) into 1 2.617 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.618 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.618 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) 2.618 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.618 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.618 * [taylor]: Taking taylor expansion of -1 in k 2.618 * [backup-simplify]: Simplify -1 into -1 2.618 * [taylor]: Taking taylor expansion of k in k 2.618 * [backup-simplify]: Simplify 0 into 0 2.618 * [backup-simplify]: Simplify 1 into 1 2.619 * [backup-simplify]: Simplify (/ -1 1) into -1 2.619 * [backup-simplify]: Simplify (sqrt 0) into 0 2.621 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.621 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) 2.621 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 2.621 * [taylor]: Taking taylor expansion of 1.0 in k 2.621 * [backup-simplify]: Simplify 1.0 into 1.0 2.621 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 2.621 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.621 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.621 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.621 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.621 * [taylor]: Taking taylor expansion of 0.5 in k 2.621 * [backup-simplify]: Simplify 0.5 into 0.5 2.621 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.621 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.621 * [taylor]: Taking taylor expansion of k in k 2.621 * [backup-simplify]: Simplify 0 into 0 2.621 * [backup-simplify]: Simplify 1 into 1 2.622 * [backup-simplify]: Simplify (/ 1 1) into 1 2.622 * [taylor]: Taking taylor expansion of 1.0 in k 2.622 * [backup-simplify]: Simplify 1.0 into 1.0 2.622 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.622 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.622 * [taylor]: Taking taylor expansion of -2.0 in k 2.622 * [backup-simplify]: Simplify -2.0 into -2.0 2.622 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.622 * [taylor]: Taking taylor expansion of PI in k 2.622 * [backup-simplify]: Simplify PI into PI 2.622 * [taylor]: Taking taylor expansion of n in k 2.622 * [backup-simplify]: Simplify n into n 2.622 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.622 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.622 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.623 * [backup-simplify]: Simplify (+ 1 0) into 1 2.623 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.623 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.624 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) 2.624 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.624 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.624 * [taylor]: Taking taylor expansion of -1 in k 2.624 * [backup-simplify]: Simplify -1 into -1 2.624 * [taylor]: Taking taylor expansion of k in k 2.624 * [backup-simplify]: Simplify 0 into 0 2.624 * [backup-simplify]: Simplify 1 into 1 2.624 * [backup-simplify]: Simplify (/ -1 1) into -1 2.624 * [backup-simplify]: Simplify (sqrt 0) into 0 2.625 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.625 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) 2.626 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) 2.626 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 2.626 * [taylor]: Taking taylor expansion of +nan.0 in n 2.626 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.626 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 2.626 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 2.626 * [taylor]: Taking taylor expansion of 0.5 in n 2.626 * [backup-simplify]: Simplify 0.5 into 0.5 2.626 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 2.626 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.626 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.626 * [taylor]: Taking taylor expansion of -2.0 in n 2.626 * [backup-simplify]: Simplify -2.0 into -2.0 2.626 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.626 * [taylor]: Taking taylor expansion of PI in n 2.626 * [backup-simplify]: Simplify PI into PI 2.626 * [taylor]: Taking taylor expansion of n in n 2.626 * [backup-simplify]: Simplify 0 into 0 2.626 * [backup-simplify]: Simplify 1 into 1 2.626 * [backup-simplify]: Simplify (/ PI 1) into PI 2.626 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.627 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.627 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.627 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.627 * [taylor]: Taking taylor expansion of k in n 2.627 * [backup-simplify]: Simplify k into k 2.627 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.627 * [taylor]: Taking taylor expansion of 1.0 in n 2.627 * [backup-simplify]: Simplify 1.0 into 1.0 2.628 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.628 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.629 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 2.630 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 2.631 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 2.631 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 2.632 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 2.633 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.635 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.636 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) 2.636 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) 2.636 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n 2.637 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 2.637 * [taylor]: Taking taylor expansion of +nan.0 in n 2.637 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.637 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 2.637 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 2.637 * [taylor]: Taking taylor expansion of 0.5 in n 2.637 * [backup-simplify]: Simplify 0.5 into 0.5 2.637 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 2.637 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.637 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.637 * [taylor]: Taking taylor expansion of -2.0 in n 2.637 * [backup-simplify]: Simplify -2.0 into -2.0 2.637 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.637 * [taylor]: Taking taylor expansion of PI in n 2.637 * [backup-simplify]: Simplify PI into PI 2.637 * [taylor]: Taking taylor expansion of n in n 2.637 * [backup-simplify]: Simplify 0 into 0 2.637 * [backup-simplify]: Simplify 1 into 1 2.637 * [backup-simplify]: Simplify (/ PI 1) into PI 2.637 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.638 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.638 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.638 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.638 * [taylor]: Taking taylor expansion of k in n 2.638 * [backup-simplify]: Simplify k into k 2.638 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.638 * [taylor]: Taking taylor expansion of 1.0 in n 2.638 * [backup-simplify]: Simplify 1.0 into 1.0 2.639 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.639 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.640 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 2.641 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 2.642 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 2.643 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 2.643 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 2.644 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 2.645 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.645 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.646 * [backup-simplify]: Simplify (+ 0 0) into 0 2.646 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.647 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.648 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.649 * [backup-simplify]: Simplify (+ (* (- (log (* -2.0 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.650 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into 0 2.651 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.652 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into 0 2.652 * [backup-simplify]: Simplify 0 into 0 2.653 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.655 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.656 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) 2.658 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) 2.658 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n 2.658 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 2.658 * [taylor]: Taking taylor expansion of +nan.0 in n 2.658 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.658 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 2.658 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 2.658 * [taylor]: Taking taylor expansion of 0.5 in n 2.658 * [backup-simplify]: Simplify 0.5 into 0.5 2.658 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 2.658 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.658 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.658 * [taylor]: Taking taylor expansion of -2.0 in n 2.658 * [backup-simplify]: Simplify -2.0 into -2.0 2.658 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.658 * [taylor]: Taking taylor expansion of PI in n 2.658 * [backup-simplify]: Simplify PI into PI 2.658 * [taylor]: Taking taylor expansion of n in n 2.658 * [backup-simplify]: Simplify 0 into 0 2.658 * [backup-simplify]: Simplify 1 into 1 2.659 * [backup-simplify]: Simplify (/ PI 1) into PI 2.659 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.660 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.660 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.660 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.660 * [taylor]: Taking taylor expansion of k in n 2.661 * [backup-simplify]: Simplify k into k 2.661 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.661 * [taylor]: Taking taylor expansion of 1.0 in n 2.661 * [backup-simplify]: Simplify 1.0 into 1.0 2.662 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.662 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.664 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 2.665 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 2.666 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 2.668 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 2.669 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 2.670 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 2.675 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) into (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)))))))) 2.676 * * * [progress]: simplifying candidates 2.680 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) 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n PI)) (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) k)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow k 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (pow k 2)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log n) 2) (pow k 2))))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3)))))))) (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)))))))) 2.685 * * [simplify]: iteration 0: 361 enodes 2.809 * * [simplify]: iteration 1: 1013 enodes 3.508 * * [simplify]: iteration 2: 4865 enodes 4.670 * * [simplify]: iteration complete: 5000 enodes 4.670 * * [simplify]: Extracting #0: cost 129 inf + 0 4.673 * * [simplify]: Extracting #1: cost 758 inf + 2 4.682 * * [simplify]: Extracting #2: cost 1373 inf + 2524 4.708 * * [simplify]: Extracting #3: cost 1241 inf + 76633 4.769 * * [simplify]: Extracting #4: cost 552 inf + 291583 4.847 * * [simplify]: Extracting #5: cost 332 inf + 429815 4.936 * * [simplify]: Extracting #6: cost 338 inf + 465869 5.078 * * [simplify]: Extracting #7: cost 270 inf + 514394 5.259 * * [simplify]: Extracting #8: cost 74 inf + 703108 5.406 * * [simplify]: Extracting #9: cost 23 inf + 759463 5.598 * * [simplify]: Extracting #10: cost 3 inf + 798776 5.800 * * [simplify]: Extracting #11: cost 0 inf + 804622 5.976 * * [simplify]: Extracting #12: cost 0 inf + 803812 6.132 * * [simplify]: Extracting #13: cost 0 inf + 803337 6.326 * * [simplify]: Extracting #14: cost 0 inf + 803102 6.490 * * [simplify]: Extracting #15: cost 0 inf + 803042 6.676 * * [simplify]: Extracting #16: cost 0 inf + 803022 6.884 * [simplify]: Simplified to: (expm1 (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (log1p (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (* (/ (- 1.0 k) 2.0) (log (* PI (* n 2.0)))) (* (/ (- 1.0 k) 2.0) (log (* PI (* n 2.0)))) (* (/ (- 1.0 k) 2.0) (log (* PI (* n 2.0)))) (* (/ (- 1.0 k) 2.0) (log (* PI (* n 2.0)))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* PI (* n 2.0)) (/ 1.0 2.0)) (pow (* PI (* n 2.0)) (/ k 2.0)) (pow (* PI (* n 2.0)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* PI (* n 2.0)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* PI (* n 2.0)) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow (* PI (* n 2.0)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* PI (* n 2.0)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* PI (* n 2.0)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* PI (* n 2.0)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* PI (* n 2.0)) (sqrt (- 1.0 k))) (pow (* PI (* n 2.0)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* PI (* n 2.0)) (/ 1 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k))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* (/ 1.0 (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))) (log1p (* (/ 1.0 (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))) (fma (log (* PI (* n 2.0))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* PI (* n 2.0))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* PI (* n 2.0))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* PI (* n 2.0))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* PI (* n 2.0))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* PI (* n 2.0))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* PI (* n 2.0))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* PI (* n 2.0))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* PI (* n 2.0))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* PI (* n 2.0))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* PI (* n 2.0))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (exp (* (/ 1.0 (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))) (/ (* (* (* 1.0 (* 1.0 1.0)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))) (* (sqrt k) k)) (* (* (* (/ 1.0 (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))) (* (pow (* PI (* n 2.0)) (/ 1.0 2.0)) 1.0) (* (sqrt k) (pow (* PI (* n 2.0)) (/ k 2.0))) (* (sqrt (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* PI (* n 2.0)) (/ (/ (- 1.0 k) 2) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* PI (* n 2.0)) (/ (/ (- 1.0 k) 2) 2.0))) (* (sqrt (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* PI (* n 2.0)) (/ (/ (- 1.0 k) 2) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* PI (* n 2.0)) (/ (/ (- 1.0 k) 2) 2.0))) (* (sqrt (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* PI (* n 2.0)) (/ (/ (- 1.0 k) 2) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* PI (* n 2.0)) (/ (/ (- 1.0 k) 2) 2.0))) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (* (cbrt (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))) (/ 1.0 (sqrt k))) (/ (* (sqrt (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) 1.0) (sqrt k)) (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (pow (* PI (* n 2.0)) (/ (/ (- 1.0 k) 2) 2.0))) (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (cbrt (/ 1.0 (sqrt k)))) (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (sqrt (/ 1.0 (sqrt k)))) (/ (cbrt 1.0) (/ (cbrt (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))) (/ (* (cbrt 1.0) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (sqrt (cbrt k))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (/ (* (cbrt 1.0) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (sqrt k)) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (/ (* (cbrt 1.0) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (* (sqrt 1.0) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (cbrt (sqrt k))) (/ (* (sqrt 1.0) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (sqrt (cbrt k))) (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))) (/ (* (sqrt 1.0) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))) (/ (* (sqrt 1.0) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (cbrt (sqrt k))) (/ (* 1.0 (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (sqrt (cbrt k))) (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt (sqrt k)))) (* (/ 1.0 (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt (sqrt k)))) (* (/ 1.0 (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (sqrt k)) (/ (* (pow (* PI (* n 2.0)) (/ 1.0 2.0)) 1.0) (sqrt k)) (* 1.0 (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (fma (* (* (log (* 2.0 PI)) 0.25) (* (log n) (exp (* (log (* PI (* n 2.0))) 0.5)))) (* k k) (- (fma (* (log (* 2.0 PI)) (* (log (* 2.0 PI)) (exp (* (log (* PI (* n 2.0))) 0.5)))) (* (* k k) 0.125) (fma (* 0.125 (exp (* (log (* PI (* n 2.0))) 0.5))) (* (* k k) (* (log n) (log n))) (exp (* (log (* PI (* n 2.0))) 0.5)))) (* 0.5 (* k (+ (* (log n) (exp (* (log (* PI (* n 2.0))) 0.5))) (* (log (* 2.0 PI)) (exp (* (log (* PI (* n 2.0))) 0.5)))))))) (exp (* (- 1.0 k) (* (log (* PI (* n 2.0))) 0.5))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* PI (* n 2.0)) (* PI (* n 2.0)) (* PI (* n 2.0)) (- (fma (* k k) +nan.0 (fma +nan.0 k (- +nan.0)))) (- (- (/ +nan.0 (* k k)) (- (/ +nan.0 k) (/ (/ +nan.0 (* k k)) k)))) (- (/ (- +nan.0) (* k k)) (+ (/ (- +nan.0) k) +nan.0)) (+ (fma (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (* k k) (+ (* (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (- (* (log n) (* k k)))) (- (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (fma (* (* (log (* 2.0 PI)) k) (* (log (* 2.0 PI)) k)) (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (- (fma +nan.0 (* (* (log n) (* k k)) (* (log (* 2.0 PI)) (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5))) (+ (* (- +nan.0) (* k (* (log (* 2.0 PI)) (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)))) (- (* (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (* (log n) k)) (* +nan.0 (- (* (* k k) (* (log (* 2.0 PI)) (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5))) (* (* (* (log n) k) (* (log n) k)) (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)))))))))))) (* (* k (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (- +nan.0))) (+ (* +nan.0 (- (/ (exp (* (- 1.0 k) (* (log (* PI (* n 2.0))) 0.5))) k) (/ (exp (* (- 1.0 k) (* (log (* PI (* n 2.0))) 0.5))) (* k (* k k))))) (/ (- (* +nan.0 (exp (* (- 1.0 k) (* (log (* PI (* n 2.0))) 0.5))))) (* k k))) (+ (* +nan.0 (- (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k) (/ (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k) k))) (* (- +nan.0) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))) 6.897 * * * [progress]: adding candidates to table 7.929 * * [progress]: iteration 2 / 4 7.929 * * * [progress]: picking best candidate 7.992 * * * * [pick]: Picked # 7.993 * * * [progress]: localizing error 8.031 * * * [progress]: generating rewritten candidates 8.031 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 8.038 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 8.061 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 8.066 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1) 8.111 * * * [progress]: generating series expansions 8.111 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 8.111 * [backup-simplify]: Simplify (pow n (/ (- 1.0 k) 2.0)) into (pow n (* 0.5 (- 1.0 k))) 8.111 * [approximate]: Taking taylor expansion of (pow n (* 0.5 (- 1.0 k))) in (n k) around 0 8.111 * [taylor]: Taking taylor expansion of (pow n (* 0.5 (- 1.0 k))) in k 8.112 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log n))) in k 8.112 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log n)) in k 8.112 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 8.112 * [taylor]: Taking taylor expansion of 0.5 in k 8.112 * [backup-simplify]: Simplify 0.5 into 0.5 8.112 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.112 * [taylor]: Taking taylor expansion of 1.0 in k 8.112 * [backup-simplify]: Simplify 1.0 into 1.0 8.112 * [taylor]: Taking taylor expansion of k in k 8.112 * [backup-simplify]: Simplify 0 into 0 8.112 * [backup-simplify]: Simplify 1 into 1 8.112 * [taylor]: Taking taylor expansion of (log n) in k 8.112 * [taylor]: Taking taylor expansion of n in k 8.112 * [backup-simplify]: Simplify n into n 8.112 * [backup-simplify]: Simplify (log n) into (log n) 8.113 * [backup-simplify]: Simplify (- 0) into 0 8.113 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.114 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 8.114 * [backup-simplify]: Simplify (* 0.5 (log n)) into (* 0.5 (log n)) 8.114 * [backup-simplify]: Simplify (exp (* 0.5 (log n))) into (pow n 0.5) 8.114 * [taylor]: Taking taylor expansion of (pow n (* 0.5 (- 1.0 k))) in n 8.114 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log n))) in n 8.114 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log n)) in n 8.114 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 8.114 * [taylor]: Taking taylor expansion of 0.5 in n 8.114 * [backup-simplify]: Simplify 0.5 into 0.5 8.114 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.114 * [taylor]: Taking taylor expansion of 1.0 in n 8.114 * [backup-simplify]: Simplify 1.0 into 1.0 8.114 * [taylor]: Taking taylor expansion of k in n 8.114 * [backup-simplify]: Simplify k into k 8.114 * [taylor]: Taking taylor expansion of (log n) in n 8.114 * [taylor]: Taking taylor expansion of n in n 8.114 * [backup-simplify]: Simplify 0 into 0 8.114 * [backup-simplify]: Simplify 1 into 1 8.115 * [backup-simplify]: Simplify (log 1) into 0 8.115 * [backup-simplify]: Simplify (- k) into (- k) 8.115 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.115 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 8.116 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 8.116 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (log n)) into (* 0.5 (* (- 1.0 k) (log n))) 8.116 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (log n)))) into (exp (* 0.5 (* (- 1.0 k) (log n)))) 8.116 * [taylor]: Taking taylor expansion of (pow n (* 0.5 (- 1.0 k))) in n 8.116 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log n))) in n 8.116 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log n)) in n 8.116 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 8.116 * [taylor]: Taking taylor expansion of 0.5 in n 8.116 * [backup-simplify]: Simplify 0.5 into 0.5 8.116 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.116 * [taylor]: Taking taylor expansion of 1.0 in n 8.116 * [backup-simplify]: Simplify 1.0 into 1.0 8.116 * [taylor]: Taking taylor expansion of k in n 8.116 * [backup-simplify]: Simplify k into k 8.116 * [taylor]: Taking taylor expansion of (log n) in n 8.116 * [taylor]: Taking taylor expansion of n in n 8.117 * [backup-simplify]: Simplify 0 into 0 8.117 * [backup-simplify]: Simplify 1 into 1 8.117 * [backup-simplify]: Simplify (log 1) into 0 8.117 * [backup-simplify]: Simplify (- k) into (- k) 8.117 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.117 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 8.118 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 8.118 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (log n)) into (* 0.5 (* (- 1.0 k) (log n))) 8.118 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (log n)))) into (exp (* 0.5 (* (- 1.0 k) (log n)))) 8.118 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (log n)))) in k 8.118 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (log n))) in k 8.118 * [taylor]: Taking taylor expansion of 0.5 in k 8.118 * [backup-simplify]: Simplify 0.5 into 0.5 8.118 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (log n)) in k 8.118 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.118 * [taylor]: Taking taylor expansion of 1.0 in k 8.118 * [backup-simplify]: Simplify 1.0 into 1.0 8.118 * [taylor]: Taking taylor expansion of k in k 8.118 * [backup-simplify]: Simplify 0 into 0 8.119 * [backup-simplify]: Simplify 1 into 1 8.119 * [taylor]: Taking taylor expansion of (log n) in k 8.119 * [taylor]: Taking taylor expansion of n in k 8.119 * [backup-simplify]: Simplify n into n 8.119 * [backup-simplify]: Simplify (log n) into (log n) 8.119 * [backup-simplify]: Simplify (- 0) into 0 8.120 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.120 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 8.120 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (log n))) into (* 0.5 (log n)) 8.120 * [backup-simplify]: Simplify (exp (* 0.5 (log n))) into (pow n 0.5) 8.120 * [backup-simplify]: Simplify (pow n 0.5) into (pow n 0.5) 8.122 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 8.122 * [backup-simplify]: Simplify (- 0) into 0 8.122 * [backup-simplify]: Simplify (+ 0 0) into 0 8.123 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 8.124 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 8.124 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (log n))) into 0 8.125 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 8.125 * [taylor]: Taking taylor expansion of 0 in k 8.125 * [backup-simplify]: Simplify 0 into 0 8.125 * [backup-simplify]: Simplify 0 into 0 8.126 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 8.127 * [backup-simplify]: Simplify (- 1) into -1 8.127 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.128 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (log n))) into (- (log n)) 8.128 * [backup-simplify]: Simplify (+ (* 0.5 (- (log n))) (* 0 (* 1.0 (log n)))) into (- (* 0.5 (log n))) 8.128 * [backup-simplify]: Simplify (* (exp (* 0.5 (log n))) (+ (* (/ (pow (- (* 0.5 (log n))) 1) 1)))) into (* -0.5 (* (pow (pow n 1.0) 0.5) (log n))) 8.129 * [backup-simplify]: Simplify (* -0.5 (* (pow (pow n 1.0) 0.5) (log n))) into (* -0.5 (* (pow (pow n 1.0) 0.5) (log n))) 8.132 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 8.132 * [backup-simplify]: Simplify (- 0) into 0 8.132 * [backup-simplify]: Simplify (+ 0 0) into 0 8.133 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 8.134 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 8.134 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0 8.136 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.136 * [taylor]: Taking taylor expansion of 0 in k 8.136 * [backup-simplify]: Simplify 0 into 0 8.136 * [backup-simplify]: Simplify 0 into 0 8.136 * [backup-simplify]: Simplify 0 into 0 8.138 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 8.139 * [backup-simplify]: Simplify (- 0) into 0 8.139 * [backup-simplify]: Simplify (+ 0 0) into 0 8.140 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (log n)))) into 0 8.141 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (log n))) (* 0 (* 1.0 (log n))))) into 0 8.142 * [backup-simplify]: Simplify (* (exp (* 0.5 (log n))) (+ (* (/ (pow (- (* 0.5 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (pow n 1.0) 0.5) (pow (log n) 2))) 8.142 * [backup-simplify]: Simplify (* 0.125 (* (pow (pow n 1.0) 0.5) (pow (log n) 2))) into (* 0.125 (* (pow (pow n 1.0) 0.5) (pow (log n) 2))) 8.144 * [backup-simplify]: Simplify (+ (* (* 0.125 (* (pow (pow n 1.0) 0.5) (pow (log n) 2))) (pow (* k 1) 2)) (+ (* (* -0.5 (* (pow (pow n 1.0) 0.5) (log n))) (* k 1)) (pow n 0.5))) into (- (+ (* 0.125 (* (pow (pow n 1.0) 0.5) (* (pow (log n) 2) (pow k 2)))) (pow n 0.5)) (* 0.5 (* (pow (pow n 1.0) 0.5) (* (log n) k)))) 8.144 * [backup-simplify]: Simplify (pow (/ 1 n) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) 8.144 * [approximate]: Taking taylor expansion of (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 8.144 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) in k 8.144 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n)))) in k 8.144 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n))) in k 8.144 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 8.144 * [taylor]: Taking taylor expansion of 0.5 in k 8.144 * [backup-simplify]: Simplify 0.5 into 0.5 8.144 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.144 * [taylor]: Taking taylor expansion of 1.0 in k 8.144 * [backup-simplify]: Simplify 1.0 into 1.0 8.144 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.145 * [taylor]: Taking taylor expansion of k in k 8.145 * [backup-simplify]: Simplify 0 into 0 8.145 * [backup-simplify]: Simplify 1 into 1 8.145 * [backup-simplify]: Simplify (/ 1 1) into 1 8.145 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k 8.145 * [taylor]: Taking taylor expansion of (/ 1 n) in k 8.145 * [taylor]: Taking taylor expansion of n in k 8.145 * [backup-simplify]: Simplify n into n 8.145 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n) 8.145 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n)) 8.146 * [backup-simplify]: Simplify (- 1) into -1 8.146 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.147 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 8.147 * [backup-simplify]: Simplify (* -0.5 (log (/ 1 n))) into (* -0.5 (log (/ 1 n))) 8.147 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ 1 n))))) 8.147 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) in n 8.147 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n)))) in n 8.147 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n))) in n 8.147 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 8.147 * [taylor]: Taking taylor expansion of 0.5 in n 8.147 * [backup-simplify]: Simplify 0.5 into 0.5 8.147 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.147 * [taylor]: Taking taylor expansion of 1.0 in n 8.147 * [backup-simplify]: Simplify 1.0 into 1.0 8.148 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.148 * [taylor]: Taking taylor expansion of k in n 8.148 * [backup-simplify]: Simplify k into k 8.148 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.148 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 8.148 * [taylor]: Taking taylor expansion of (/ 1 n) in n 8.148 * [taylor]: Taking taylor expansion of n in n 8.148 * [backup-simplify]: Simplify 0 into 0 8.148 * [backup-simplify]: Simplify 1 into 1 8.148 * [backup-simplify]: Simplify (/ 1 1) into 1 8.149 * [backup-simplify]: Simplify (log 1) into 0 8.149 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.149 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.149 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 8.149 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 8.150 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log n))) into (* -0.5 (* (- 1.0 (/ 1 k)) (log n))) 8.150 * [backup-simplify]: Simplify (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) into (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) 8.150 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) in n 8.150 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n)))) in n 8.150 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n))) in n 8.150 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 8.150 * [taylor]: Taking taylor expansion of 0.5 in n 8.150 * [backup-simplify]: Simplify 0.5 into 0.5 8.150 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.150 * [taylor]: Taking taylor expansion of 1.0 in n 8.150 * [backup-simplify]: Simplify 1.0 into 1.0 8.150 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.150 * [taylor]: Taking taylor expansion of k in n 8.150 * [backup-simplify]: Simplify k into k 8.150 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.150 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 8.150 * [taylor]: Taking taylor expansion of (/ 1 n) in n 8.150 * [taylor]: Taking taylor expansion of n in n 8.151 * [backup-simplify]: Simplify 0 into 0 8.151 * [backup-simplify]: Simplify 1 into 1 8.151 * [backup-simplify]: Simplify (/ 1 1) into 1 8.152 * [backup-simplify]: Simplify (log 1) into 0 8.152 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.152 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.152 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 8.153 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 8.153 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log n))) into (* -0.5 (* (- 1.0 (/ 1 k)) (log n))) 8.153 * [backup-simplify]: Simplify (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) into (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) 8.153 * [taylor]: Taking taylor expansion of (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) in k 8.153 * [taylor]: Taking taylor expansion of (* -0.5 (* (- 1.0 (/ 1 k)) (log n))) in k 8.153 * [taylor]: Taking taylor expansion of -0.5 in k 8.153 * [backup-simplify]: Simplify -0.5 into -0.5 8.153 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log n)) in k 8.154 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.154 * [taylor]: Taking taylor expansion of 1.0 in k 8.154 * [backup-simplify]: Simplify 1.0 into 1.0 8.154 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.154 * [taylor]: Taking taylor expansion of k in k 8.154 * [backup-simplify]: Simplify 0 into 0 8.154 * [backup-simplify]: Simplify 1 into 1 8.154 * [backup-simplify]: Simplify (/ 1 1) into 1 8.154 * [taylor]: Taking taylor expansion of (log n) in k 8.154 * [taylor]: Taking taylor expansion of n in k 8.154 * [backup-simplify]: Simplify n into n 8.154 * [backup-simplify]: Simplify (log n) into (log n) 8.155 * [backup-simplify]: Simplify (- 1) into -1 8.155 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.155 * [backup-simplify]: Simplify (* -1 (log n)) into (* -1 (log n)) 8.155 * [backup-simplify]: Simplify (* -0.5 (* -1 (log n))) into (* 0.5 (log n)) 8.156 * [backup-simplify]: Simplify (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) into (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) 8.156 * [backup-simplify]: Simplify (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) into (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) 8.157 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 8.158 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 8.158 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.159 * [backup-simplify]: Simplify (- 0) into 0 8.159 * [backup-simplify]: Simplify (+ 0 0) into 0 8.160 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 8.160 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 8.161 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 8.162 * [backup-simplify]: Simplify (* (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 8.162 * [taylor]: Taking taylor expansion of 0 in k 8.162 * [backup-simplify]: Simplify 0 into 0 8.162 * [backup-simplify]: Simplify 0 into 0 8.162 * [backup-simplify]: Simplify 0 into 0 8.163 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.166 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 8.166 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.166 * [backup-simplify]: Simplify (- 0) into 0 8.167 * [backup-simplify]: Simplify (+ 0 0) into 0 8.168 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 8.168 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 8.169 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 8.171 * [backup-simplify]: Simplify (* (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.171 * [taylor]: Taking taylor expansion of 0 in k 8.171 * [backup-simplify]: Simplify 0 into 0 8.171 * [backup-simplify]: Simplify 0 into 0 8.171 * [backup-simplify]: Simplify 0 into 0 8.171 * [backup-simplify]: Simplify 0 into 0 8.172 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.177 * [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 8.178 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.178 * [backup-simplify]: Simplify (- 0) into 0 8.179 * [backup-simplify]: Simplify (+ 0 0) into 0 8.180 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 8.186 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 8.187 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 8.189 * [backup-simplify]: Simplify (* (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 8.189 * [taylor]: Taking taylor expansion of 0 in k 8.189 * [backup-simplify]: Simplify 0 into 0 8.189 * [backup-simplify]: Simplify 0 into 0 8.190 * [backup-simplify]: Simplify (exp (* -0.5 (* (- 1.0 (/ 1 (/ 1 k))) (log (/ 1 n))))) into (exp (* -0.5 (* (- 1.0 k) (log (/ 1 n))))) 8.190 * [backup-simplify]: Simplify (pow (/ 1 (- n)) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) 8.190 * [approximate]: Taking taylor expansion of (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 8.190 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) in k 8.190 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) in k 8.190 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n))) in k 8.190 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 8.190 * [taylor]: Taking taylor expansion of 0.5 in k 8.190 * [backup-simplify]: Simplify 0.5 into 0.5 8.190 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.190 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.190 * [taylor]: Taking taylor expansion of k in k 8.190 * [backup-simplify]: Simplify 0 into 0 8.190 * [backup-simplify]: Simplify 1 into 1 8.191 * [backup-simplify]: Simplify (/ 1 1) into 1 8.191 * [taylor]: Taking taylor expansion of 1.0 in k 8.191 * [backup-simplify]: Simplify 1.0 into 1.0 8.191 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k 8.191 * [taylor]: Taking taylor expansion of (/ -1 n) in k 8.191 * [taylor]: Taking taylor expansion of -1 in k 8.191 * [backup-simplify]: Simplify -1 into -1 8.191 * [taylor]: Taking taylor expansion of n in k 8.191 * [backup-simplify]: Simplify n into n 8.191 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n) 8.191 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n)) 8.192 * [backup-simplify]: Simplify (+ 1 0) into 1 8.192 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 8.192 * [backup-simplify]: Simplify (* 0.5 (log (/ -1 n))) into (* 0.5 (log (/ -1 n))) 8.193 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) into (exp (* 0.5 (* (log (/ -1 n)) (+ (/ 1 k) 1.0)))) 8.193 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) in n 8.193 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) in n 8.193 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n))) in n 8.193 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 8.193 * [taylor]: Taking taylor expansion of 0.5 in n 8.193 * [backup-simplify]: Simplify 0.5 into 0.5 8.193 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.193 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.193 * [taylor]: Taking taylor expansion of k in n 8.193 * [backup-simplify]: Simplify k into k 8.193 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.193 * [taylor]: Taking taylor expansion of 1.0 in n 8.193 * [backup-simplify]: Simplify 1.0 into 1.0 8.193 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 8.193 * [taylor]: Taking taylor expansion of (/ -1 n) in n 8.193 * [taylor]: Taking taylor expansion of -1 in n 8.193 * [backup-simplify]: Simplify -1 into -1 8.193 * [taylor]: Taking taylor expansion of n in n 8.193 * [backup-simplify]: Simplify 0 into 0 8.193 * [backup-simplify]: Simplify 1 into 1 8.194 * [backup-simplify]: Simplify (/ -1 1) into -1 8.194 * [backup-simplify]: Simplify (log -1) into (log -1) 8.195 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.195 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 8.196 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 8.196 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log -1) (log n))) into (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0))) 8.197 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 8.197 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) in n 8.197 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) in n 8.197 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n))) in n 8.197 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 8.197 * [taylor]: Taking taylor expansion of 0.5 in n 8.197 * [backup-simplify]: Simplify 0.5 into 0.5 8.197 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.197 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.197 * [taylor]: Taking taylor expansion of k in n 8.197 * [backup-simplify]: Simplify k into k 8.197 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.197 * [taylor]: Taking taylor expansion of 1.0 in n 8.197 * [backup-simplify]: Simplify 1.0 into 1.0 8.197 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 8.197 * [taylor]: Taking taylor expansion of (/ -1 n) in n 8.197 * [taylor]: Taking taylor expansion of -1 in n 8.197 * [backup-simplify]: Simplify -1 into -1 8.197 * [taylor]: Taking taylor expansion of n in n 8.197 * [backup-simplify]: Simplify 0 into 0 8.197 * [backup-simplify]: Simplify 1 into 1 8.198 * [backup-simplify]: Simplify (/ -1 1) into -1 8.198 * [backup-simplify]: Simplify (log -1) into (log -1) 8.199 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.199 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 8.200 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 8.200 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log -1) (log n))) into (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0))) 8.201 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 8.201 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) in k 8.201 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0))) in k 8.201 * [taylor]: Taking taylor expansion of 0.5 in k 8.201 * [backup-simplify]: Simplify 0.5 into 0.5 8.201 * [taylor]: Taking taylor expansion of (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)) in k 8.201 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k 8.201 * [taylor]: Taking taylor expansion of (log -1) in k 8.201 * [taylor]: Taking taylor expansion of -1 in k 8.201 * [backup-simplify]: Simplify -1 into -1 8.202 * [backup-simplify]: Simplify (log -1) into (log -1) 8.202 * [taylor]: Taking taylor expansion of (log n) in k 8.202 * [taylor]: Taking taylor expansion of n in k 8.202 * [backup-simplify]: Simplify n into n 8.202 * [backup-simplify]: Simplify (log n) into (log n) 8.202 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.202 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.202 * [taylor]: Taking taylor expansion of k in k 8.202 * [backup-simplify]: Simplify 0 into 0 8.202 * [backup-simplify]: Simplify 1 into 1 8.202 * [backup-simplify]: Simplify (/ 1 1) into 1 8.203 * [taylor]: Taking taylor expansion of 1.0 in k 8.203 * [backup-simplify]: Simplify 1.0 into 1.0 8.203 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.203 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n)) 8.204 * [backup-simplify]: Simplify (+ 1 0) into 1 8.204 * [backup-simplify]: Simplify (* (- (log -1) (log n)) 1) into (- (log -1) (log n)) 8.205 * [backup-simplify]: Simplify (* 0.5 (- (log -1) (log n))) into (* 0.5 (- (log -1) (log n))) 8.205 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 8.206 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 8.207 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 8.209 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 8.209 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.209 * [backup-simplify]: Simplify (+ 0 0) into 0 8.210 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 8.211 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 8.211 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log -1) (log n)))) into 0 8.213 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 8.213 * [taylor]: Taking taylor expansion of 0 in k 8.213 * [backup-simplify]: Simplify 0 into 0 8.213 * [backup-simplify]: Simplify 0 into 0 8.213 * [backup-simplify]: Simplify 0 into 0 8.214 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.216 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0 8.217 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.217 * [backup-simplify]: Simplify (+ 0 0) into 0 8.217 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 8.218 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 8.219 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0 8.220 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.220 * [taylor]: Taking taylor expansion of 0 in k 8.220 * [backup-simplify]: Simplify 0 into 0 8.220 * [backup-simplify]: Simplify 0 into 0 8.220 * [backup-simplify]: Simplify 0 into 0 8.220 * [backup-simplify]: Simplify 0 into 0 8.221 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.223 * [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 8.224 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.224 * [backup-simplify]: Simplify (+ 0 0) into 0 8.225 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 8.226 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 8.226 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -1) (log n)))))) into 0 8.228 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 8.228 * [taylor]: Taking taylor expansion of 0 in k 8.228 * [backup-simplify]: Simplify 0 into 0 8.228 * [backup-simplify]: Simplify 0 into 0 8.228 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log (/ -1 n))) (- 1.0 k)))) 8.228 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 8.229 * [backup-simplify]: Simplify (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) 8.229 * [approximate]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in (k) around 0 8.229 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in k 8.229 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI)))) in k 8.229 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI))) in k 8.229 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 8.229 * [taylor]: Taking taylor expansion of 0.5 in k 8.229 * [backup-simplify]: Simplify 0.5 into 0.5 8.229 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.229 * [taylor]: Taking taylor expansion of 1.0 in k 8.229 * [backup-simplify]: Simplify 1.0 into 1.0 8.229 * [taylor]: Taking taylor expansion of k in k 8.229 * [backup-simplify]: Simplify 0 into 0 8.229 * [backup-simplify]: Simplify 1 into 1 8.229 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.229 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.229 * [taylor]: Taking taylor expansion of 2.0 in k 8.229 * [backup-simplify]: Simplify 2.0 into 2.0 8.229 * [taylor]: Taking taylor expansion of PI in k 8.229 * [backup-simplify]: Simplify PI into PI 8.230 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.231 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.231 * [backup-simplify]: Simplify (- 0) into 0 8.231 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.232 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 8.233 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 8.234 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 PI)))) into (pow (* 2.0 PI) 0.5) 8.235 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in k 8.235 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI)))) in k 8.235 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI))) in k 8.235 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 8.235 * [taylor]: Taking taylor expansion of 0.5 in k 8.235 * [backup-simplify]: Simplify 0.5 into 0.5 8.235 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.235 * [taylor]: Taking taylor expansion of 1.0 in k 8.235 * [backup-simplify]: Simplify 1.0 into 1.0 8.235 * [taylor]: Taking taylor expansion of k in k 8.235 * [backup-simplify]: Simplify 0 into 0 8.235 * [backup-simplify]: Simplify 1 into 1 8.235 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.235 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.235 * [taylor]: Taking taylor expansion of 2.0 in k 8.235 * [backup-simplify]: Simplify 2.0 into 2.0 8.235 * [taylor]: Taking taylor expansion of PI in k 8.235 * [backup-simplify]: Simplify PI into PI 8.235 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.236 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.236 * [backup-simplify]: Simplify (- 0) into 0 8.236 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.237 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 8.238 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 8.239 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 PI)))) into (pow (* 2.0 PI) 0.5) 8.240 * [backup-simplify]: Simplify (pow (* 2.0 PI) 0.5) into (pow (* 2.0 PI) 0.5) 8.241 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.242 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.242 * [backup-simplify]: Simplify (- 1) into -1 8.243 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.244 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 8.248 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 PI)))) into (- (* 0.5 (log (* 2.0 PI)))) 8.262 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 PI)))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 1) 1)))) into (* -0.5 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) 8.270 * [backup-simplify]: Simplify (* -0.5 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) into (* -0.5 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (log (* 2.0 PI)))) 8.271 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.275 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.276 * [backup-simplify]: Simplify (- 0) into 0 8.276 * [backup-simplify]: Simplify (+ 0 0) into 0 8.278 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 8.279 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 PI))))) into 0 8.297 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 PI)))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) 8.307 * [backup-simplify]: Simplify (* 0.125 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) into (* 0.125 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) 8.318 * [backup-simplify]: Simplify (+ (* (* 0.125 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) (pow k 2)) (+ (* (* -0.5 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (log (* 2.0 PI)))) k) (pow (* 2.0 PI) 0.5))) into (- (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (pow (* 2.0 PI) 0.5)) (* 0.5 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (log (* 2.0 PI)) k)))) 8.318 * [backup-simplify]: Simplify (pow (* 2.0 PI) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) 8.318 * [approximate]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in (k) around 0 8.318 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in k 8.318 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) in k 8.318 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI))) in k 8.318 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 8.318 * [taylor]: Taking taylor expansion of 0.5 in k 8.318 * [backup-simplify]: Simplify 0.5 into 0.5 8.318 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.318 * [taylor]: Taking taylor expansion of 1.0 in k 8.318 * [backup-simplify]: Simplify 1.0 into 1.0 8.318 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.318 * [taylor]: Taking taylor expansion of k in k 8.318 * [backup-simplify]: Simplify 0 into 0 8.318 * [backup-simplify]: Simplify 1 into 1 8.319 * [backup-simplify]: Simplify (/ 1 1) into 1 8.319 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.319 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.319 * [taylor]: Taking taylor expansion of 2.0 in k 8.319 * [backup-simplify]: Simplify 2.0 into 2.0 8.319 * [taylor]: Taking taylor expansion of PI in k 8.319 * [backup-simplify]: Simplify PI into PI 8.319 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.320 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.320 * [backup-simplify]: Simplify (- 1) into -1 8.320 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.321 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 8.327 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 PI))) into (* -0.5 (log (* 2.0 PI))) 8.328 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) 8.328 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in k 8.328 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) in k 8.328 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI))) in k 8.328 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 8.328 * [taylor]: Taking taylor expansion of 0.5 in k 8.328 * [backup-simplify]: Simplify 0.5 into 0.5 8.328 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.328 * [taylor]: Taking taylor expansion of 1.0 in k 8.328 * [backup-simplify]: Simplify 1.0 into 1.0 8.328 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.328 * [taylor]: Taking taylor expansion of k in k 8.328 * [backup-simplify]: Simplify 0 into 0 8.328 * [backup-simplify]: Simplify 1 into 1 8.329 * [backup-simplify]: Simplify (/ 1 1) into 1 8.329 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.329 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.329 * [taylor]: Taking taylor expansion of 2.0 in k 8.329 * [backup-simplify]: Simplify 2.0 into 2.0 8.329 * [taylor]: Taking taylor expansion of PI in k 8.329 * [backup-simplify]: Simplify PI into PI 8.329 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.330 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.330 * [backup-simplify]: Simplify (- 1) into -1 8.330 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.331 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 8.332 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 PI))) into (* -0.5 (log (* 2.0 PI))) 8.333 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) 8.333 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) 8.334 * [backup-simplify]: Simplify 0 into 0 8.334 * [backup-simplify]: Simplify 0 into 0 8.334 * [backup-simplify]: Simplify 0 into 0 8.334 * [backup-simplify]: Simplify 0 into 0 8.334 * [backup-simplify]: Simplify 0 into 0 8.334 * [backup-simplify]: Simplify 0 into 0 8.334 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (log (* 2.0 PI))))) into (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) 8.335 * [backup-simplify]: Simplify (pow (* 2.0 PI) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) 8.335 * [approximate]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in (k) around 0 8.335 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in k 8.335 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) in k 8.335 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI))) in k 8.335 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 8.335 * [taylor]: Taking taylor expansion of 0.5 in k 8.335 * [backup-simplify]: Simplify 0.5 into 0.5 8.335 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.335 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.335 * [taylor]: Taking taylor expansion of k in k 8.335 * [backup-simplify]: Simplify 0 into 0 8.335 * [backup-simplify]: Simplify 1 into 1 8.335 * [backup-simplify]: Simplify (/ 1 1) into 1 8.335 * [taylor]: Taking taylor expansion of 1.0 in k 8.335 * [backup-simplify]: Simplify 1.0 into 1.0 8.335 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.335 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.335 * [taylor]: Taking taylor expansion of 2.0 in k 8.336 * [backup-simplify]: Simplify 2.0 into 2.0 8.336 * [taylor]: Taking taylor expansion of PI in k 8.336 * [backup-simplify]: Simplify PI into PI 8.336 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.337 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.338 * [backup-simplify]: Simplify (+ 1 0) into 1 8.338 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 8.340 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 8.342 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 8.342 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in k 8.342 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) in k 8.342 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI))) in k 8.342 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 8.342 * [taylor]: Taking taylor expansion of 0.5 in k 8.342 * [backup-simplify]: Simplify 0.5 into 0.5 8.342 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.342 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.342 * [taylor]: Taking taylor expansion of k in k 8.342 * [backup-simplify]: Simplify 0 into 0 8.342 * [backup-simplify]: Simplify 1 into 1 8.343 * [backup-simplify]: Simplify (/ 1 1) into 1 8.343 * [taylor]: Taking taylor expansion of 1.0 in k 8.343 * [backup-simplify]: Simplify 1.0 into 1.0 8.343 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.343 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.343 * [taylor]: Taking taylor expansion of 2.0 in k 8.343 * [backup-simplify]: Simplify 2.0 into 2.0 8.343 * [taylor]: Taking taylor expansion of PI in k 8.343 * [backup-simplify]: Simplify PI into PI 8.343 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.345 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.345 * [backup-simplify]: Simplify (+ 1 0) into 1 8.345 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 8.347 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 8.349 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 8.350 * [backup-simplify]: Simplify (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 8.350 * [backup-simplify]: Simplify 0 into 0 8.350 * [backup-simplify]: Simplify 0 into 0 8.350 * [backup-simplify]: Simplify 0 into 0 8.350 * [backup-simplify]: Simplify 0 into 0 8.350 * [backup-simplify]: Simplify 0 into 0 8.350 * [backup-simplify]: Simplify 0 into 0 8.352 * [backup-simplify]: Simplify (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) 8.352 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 8.352 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 8.352 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 8.352 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 8.352 * [taylor]: Taking taylor expansion of 1.0 in k 8.352 * [backup-simplify]: Simplify 1.0 into 1.0 8.352 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.352 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.352 * [taylor]: Taking taylor expansion of k in k 8.352 * [backup-simplify]: Simplify 0 into 0 8.352 * [backup-simplify]: Simplify 1 into 1 8.353 * [backup-simplify]: Simplify (/ 1 1) into 1 8.353 * [backup-simplify]: Simplify (sqrt 0) into 0 8.354 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.354 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 8.354 * [taylor]: Taking taylor expansion of 1.0 in k 8.354 * [backup-simplify]: Simplify 1.0 into 1.0 8.355 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.355 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.355 * [taylor]: Taking taylor expansion of k in k 8.355 * [backup-simplify]: Simplify 0 into 0 8.355 * [backup-simplify]: Simplify 1 into 1 8.355 * [backup-simplify]: Simplify (/ 1 1) into 1 8.355 * [backup-simplify]: Simplify (sqrt 0) into 0 8.357 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.357 * [backup-simplify]: Simplify (* 1.0 0) into 0 8.357 * [backup-simplify]: Simplify 0 into 0 8.359 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 8.359 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.360 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 8.363 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.365 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 8.365 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.366 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.370 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.373 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 8.373 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.374 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 8.375 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 8.375 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 8.375 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 8.375 * [taylor]: Taking taylor expansion of 1.0 in k 8.375 * [backup-simplify]: Simplify 1.0 into 1.0 8.375 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.375 * [taylor]: Taking taylor expansion of k in k 8.375 * [backup-simplify]: Simplify 0 into 0 8.375 * [backup-simplify]: Simplify 1 into 1 8.375 * [backup-simplify]: Simplify (sqrt 0) into 0 8.377 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.377 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 8.377 * [taylor]: Taking taylor expansion of 1.0 in k 8.377 * [backup-simplify]: Simplify 1.0 into 1.0 8.377 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.377 * [taylor]: Taking taylor expansion of k in k 8.377 * [backup-simplify]: Simplify 0 into 0 8.377 * [backup-simplify]: Simplify 1 into 1 8.377 * [backup-simplify]: Simplify (sqrt 0) into 0 8.378 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.379 * [backup-simplify]: Simplify (* 1.0 0) into 0 8.379 * [backup-simplify]: Simplify 0 into 0 8.380 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 8.381 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.384 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.387 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 8.387 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.391 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.394 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 8.394 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.396 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 8.396 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 8.396 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 8.396 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 8.396 * [taylor]: Taking taylor expansion of 1.0 in k 8.396 * [backup-simplify]: Simplify 1.0 into 1.0 8.396 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.396 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.396 * [taylor]: Taking taylor expansion of -1 in k 8.397 * [backup-simplify]: Simplify -1 into -1 8.397 * [taylor]: Taking taylor expansion of k in k 8.397 * [backup-simplify]: Simplify 0 into 0 8.397 * [backup-simplify]: Simplify 1 into 1 8.397 * [backup-simplify]: Simplify (/ -1 1) into -1 8.398 * [backup-simplify]: Simplify (sqrt 0) into 0 8.399 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.399 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 8.399 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 8.399 * [taylor]: Taking taylor expansion of 1.0 in k 8.400 * [backup-simplify]: Simplify 1.0 into 1.0 8.400 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.400 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.400 * [taylor]: Taking taylor expansion of -1 in k 8.400 * [backup-simplify]: Simplify -1 into -1 8.400 * [taylor]: Taking taylor expansion of k in k 8.400 * [backup-simplify]: Simplify 0 into 0 8.400 * [backup-simplify]: Simplify 1 into 1 8.400 * [backup-simplify]: Simplify (/ -1 1) into -1 8.401 * [backup-simplify]: Simplify (sqrt 0) into 0 8.402 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.403 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 8.403 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.404 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 8.407 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.409 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 8.410 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.411 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.415 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.419 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 8.420 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.421 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 8.421 * * * * [progress]: [ 4 / 4 ] generating series at (2 1) 8.422 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) 8.422 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in (k) around 0 8.422 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 8.422 * [taylor]: Taking taylor expansion of 1.0 in k 8.422 * [backup-simplify]: Simplify 1.0 into 1.0 8.422 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 8.422 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in k 8.422 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI)))) in k 8.422 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI))) in k 8.422 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 8.422 * [taylor]: Taking taylor expansion of 0.5 in k 8.422 * [backup-simplify]: Simplify 0.5 into 0.5 8.422 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.422 * [taylor]: Taking taylor expansion of 1.0 in k 8.422 * [backup-simplify]: Simplify 1.0 into 1.0 8.422 * [taylor]: Taking taylor expansion of k in k 8.422 * [backup-simplify]: Simplify 0 into 0 8.422 * [backup-simplify]: Simplify 1 into 1 8.422 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.422 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.423 * [taylor]: Taking taylor expansion of 2.0 in k 8.423 * [backup-simplify]: Simplify 2.0 into 2.0 8.423 * [taylor]: Taking taylor expansion of PI in k 8.423 * [backup-simplify]: Simplify PI into PI 8.423 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.424 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.425 * [backup-simplify]: Simplify (- 0) into 0 8.425 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.425 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 8.427 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 8.430 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 PI)))) into (pow (* 2.0 PI) 0.5) 8.430 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.430 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.430 * [taylor]: Taking taylor expansion of k in k 8.430 * [backup-simplify]: Simplify 0 into 0 8.430 * [backup-simplify]: Simplify 1 into 1 8.430 * [backup-simplify]: Simplify (/ 1 1) into 1 8.431 * [backup-simplify]: Simplify (sqrt 0) into 0 8.432 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.432 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 8.432 * [taylor]: Taking taylor expansion of 1.0 in k 8.432 * [backup-simplify]: Simplify 1.0 into 1.0 8.432 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 8.432 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in k 8.432 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI)))) in k 8.432 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI))) in k 8.432 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 8.432 * [taylor]: Taking taylor expansion of 0.5 in k 8.432 * [backup-simplify]: Simplify 0.5 into 0.5 8.432 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.432 * [taylor]: Taking taylor expansion of 1.0 in k 8.432 * [backup-simplify]: Simplify 1.0 into 1.0 8.432 * [taylor]: Taking taylor expansion of k in k 8.432 * [backup-simplify]: Simplify 0 into 0 8.432 * [backup-simplify]: Simplify 1 into 1 8.432 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.432 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.432 * [taylor]: Taking taylor expansion of 2.0 in k 8.432 * [backup-simplify]: Simplify 2.0 into 2.0 8.432 * [taylor]: Taking taylor expansion of PI in k 8.432 * [backup-simplify]: Simplify PI into PI 8.433 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.434 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.434 * [backup-simplify]: Simplify (- 0) into 0 8.435 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.436 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 8.438 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 8.440 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 PI)))) into (pow (* 2.0 PI) 0.5) 8.440 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.440 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.440 * [taylor]: Taking taylor expansion of k in k 8.440 * [backup-simplify]: Simplify 0 into 0 8.440 * [backup-simplify]: Simplify 1 into 1 8.441 * [backup-simplify]: Simplify (/ 1 1) into 1 8.441 * [backup-simplify]: Simplify (sqrt 0) into 0 8.443 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.443 * [backup-simplify]: Simplify (* (pow (* 2.0 PI) 0.5) 0) into 0 8.444 * [backup-simplify]: Simplify (* 1.0 0) into 0 8.444 * [backup-simplify]: Simplify 0 into 0 8.445 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.446 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.447 * [backup-simplify]: Simplify (- 1) into -1 8.447 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.449 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 8.453 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 PI)))) into (- (* 0.5 (log (* 2.0 PI)))) 8.465 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 PI)))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 1) 1)))) into (* -0.5 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) 8.476 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 PI) 0.5) +nan.0) (* (* -0.5 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) 0)) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))) 8.482 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)))) (* 0 0)) into (- (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) 8.485 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))) 8.485 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 8.487 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.488 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.490 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.490 * [backup-simplify]: Simplify (- 0) into 0 8.491 * [backup-simplify]: Simplify (+ 0 0) into 0 8.491 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 8.492 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 PI))))) into 0 8.502 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 PI)))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) 8.514 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 PI) 0.5) +nan.0) (+ (* (* -0.5 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) +nan.0) (* (* 0.125 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) 0))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))))) 8.531 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)))) (* 0 0))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))))) 8.549 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))))) 8.550 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.554 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.556 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.562 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 8.562 * [backup-simplify]: Simplify (- 0) into 0 8.563 * [backup-simplify]: Simplify (+ 0 0) into 0 8.564 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 8.567 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 PI)))))) into 0 8.595 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 PI)))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 3) 6)) (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 3))) 8.621 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 PI) 0.5) +nan.0) (+ (* (* -0.5 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) +nan.0) (+ (* (* 0.125 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) +nan.0) (* (* -0.020833333333333332 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 3))) 0)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))))))) 8.672 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)))))))) (+ (* 0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)))) (* 0 0)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))))))) 8.707 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))))))) 8.761 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))))))) (pow k 2)) (+ (* (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))))) k) (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (pow k 2))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) k)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (log (* 2.0 PI)) (pow k 2)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (log (* 2.0 PI)) k)))))))))))))) 8.762 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 k))) (pow (* 2.0 PI) (/ (- 1.0 (/ 1 k)) 2.0))) into (* 1.0 (* (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) 8.762 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in (k) around 0 8.762 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 8.762 * [taylor]: Taking taylor expansion of 1.0 in k 8.762 * [backup-simplify]: Simplify 1.0 into 1.0 8.762 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 8.762 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in k 8.762 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) in k 8.762 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI))) in k 8.762 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 8.762 * [taylor]: Taking taylor expansion of 0.5 in k 8.762 * [backup-simplify]: Simplify 0.5 into 0.5 8.762 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.762 * [taylor]: Taking taylor expansion of 1.0 in k 8.762 * [backup-simplify]: Simplify 1.0 into 1.0 8.762 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.762 * [taylor]: Taking taylor expansion of k in k 8.762 * [backup-simplify]: Simplify 0 into 0 8.762 * [backup-simplify]: Simplify 1 into 1 8.763 * [backup-simplify]: Simplify (/ 1 1) into 1 8.763 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.763 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.763 * [taylor]: Taking taylor expansion of 2.0 in k 8.763 * [backup-simplify]: Simplify 2.0 into 2.0 8.763 * [taylor]: Taking taylor expansion of PI in k 8.763 * [backup-simplify]: Simplify PI into PI 8.763 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.764 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.764 * [backup-simplify]: Simplify (- 1) into -1 8.764 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.764 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 8.766 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 PI))) into (* -0.5 (log (* 2.0 PI))) 8.766 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) 8.766 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.766 * [taylor]: Taking taylor expansion of k in k 8.766 * [backup-simplify]: Simplify 0 into 0 8.766 * [backup-simplify]: Simplify 1 into 1 8.767 * [backup-simplify]: Simplify (sqrt 0) into 0 8.768 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.768 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 8.768 * [taylor]: Taking taylor expansion of 1.0 in k 8.768 * [backup-simplify]: Simplify 1.0 into 1.0 8.768 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 8.768 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in k 8.768 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) in k 8.768 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI))) in k 8.768 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 8.768 * [taylor]: Taking taylor expansion of 0.5 in k 8.768 * [backup-simplify]: Simplify 0.5 into 0.5 8.768 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.768 * [taylor]: Taking taylor expansion of 1.0 in k 8.768 * [backup-simplify]: Simplify 1.0 into 1.0 8.768 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.768 * [taylor]: Taking taylor expansion of k in k 8.768 * [backup-simplify]: Simplify 0 into 0 8.768 * [backup-simplify]: Simplify 1 into 1 8.768 * [backup-simplify]: Simplify (/ 1 1) into 1 8.768 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.768 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.768 * [taylor]: Taking taylor expansion of 2.0 in k 8.768 * [backup-simplify]: Simplify 2.0 into 2.0 8.768 * [taylor]: Taking taylor expansion of PI in k 8.768 * [backup-simplify]: Simplify PI into PI 8.769 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.769 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.769 * [backup-simplify]: Simplify (- 1) into -1 8.770 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.770 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 8.771 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 PI))) into (* -0.5 (log (* 2.0 PI))) 8.772 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) 8.772 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.772 * [taylor]: Taking taylor expansion of k in k 8.772 * [backup-simplify]: Simplify 0 into 0 8.772 * [backup-simplify]: Simplify 1 into 1 8.772 * [backup-simplify]: Simplify (sqrt 0) into 0 8.773 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.774 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) 0) into 0 8.774 * [backup-simplify]: Simplify (* 1.0 0) into 0 8.774 * [backup-simplify]: Simplify 0 into 0 8.775 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))) 8.776 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))) 8.778 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))) 8.781 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.783 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))) 8.786 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))) 8.787 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))) 8.791 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.793 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))) 8.797 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))) 8.799 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))) 8.803 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (log (* 2.0 PI))))))) (pow (/ 1 k) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (log (* 2.0 PI))))))) (pow (/ 1 k) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (log (* 2.0 PI))))))) (/ 1 k)))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) (pow k 3))) (- (* +nan.0 (/ (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) (pow k 2)))))))) 8.804 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* 2.0 PI) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* 1.0 (/ (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 8.804 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k) around 0 8.804 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 8.804 * [taylor]: Taking taylor expansion of 1.0 in k 8.804 * [backup-simplify]: Simplify 1.0 into 1.0 8.804 * [taylor]: Taking taylor expansion of (/ (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 8.804 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in k 8.804 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) in k 8.804 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI))) in k 8.804 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 8.804 * [taylor]: Taking taylor expansion of 0.5 in k 8.805 * [backup-simplify]: Simplify 0.5 into 0.5 8.805 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.805 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.805 * [taylor]: Taking taylor expansion of k in k 8.805 * [backup-simplify]: Simplify 0 into 0 8.805 * [backup-simplify]: Simplify 1 into 1 8.805 * [backup-simplify]: Simplify (/ 1 1) into 1 8.805 * [taylor]: Taking taylor expansion of 1.0 in k 8.805 * [backup-simplify]: Simplify 1.0 into 1.0 8.805 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.805 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.805 * [taylor]: Taking taylor expansion of 2.0 in k 8.805 * [backup-simplify]: Simplify 2.0 into 2.0 8.805 * [taylor]: Taking taylor expansion of PI in k 8.805 * [backup-simplify]: Simplify PI into PI 8.806 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.807 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.807 * [backup-simplify]: Simplify (+ 1 0) into 1 8.808 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 8.810 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 8.812 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 8.812 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.812 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.812 * [taylor]: Taking taylor expansion of -1 in k 8.812 * [backup-simplify]: Simplify -1 into -1 8.812 * [taylor]: Taking taylor expansion of k in k 8.812 * [backup-simplify]: Simplify 0 into 0 8.812 * [backup-simplify]: Simplify 1 into 1 8.812 * [backup-simplify]: Simplify (/ -1 1) into -1 8.813 * [backup-simplify]: Simplify (sqrt 0) into 0 8.814 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.816 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))) 8.816 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 8.816 * [taylor]: Taking taylor expansion of 1.0 in k 8.816 * [backup-simplify]: Simplify 1.0 into 1.0 8.816 * [taylor]: Taking taylor expansion of (/ (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 8.816 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in k 8.816 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) in k 8.816 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI))) in k 8.816 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 8.816 * [taylor]: Taking taylor expansion of 0.5 in k 8.816 * [backup-simplify]: Simplify 0.5 into 0.5 8.816 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.816 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.816 * [taylor]: Taking taylor expansion of k in k 8.816 * [backup-simplify]: Simplify 0 into 0 8.816 * [backup-simplify]: Simplify 1 into 1 8.817 * [backup-simplify]: Simplify (/ 1 1) into 1 8.817 * [taylor]: Taking taylor expansion of 1.0 in k 8.817 * [backup-simplify]: Simplify 1.0 into 1.0 8.817 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.817 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.817 * [taylor]: Taking taylor expansion of 2.0 in k 8.817 * [backup-simplify]: Simplify 2.0 into 2.0 8.817 * [taylor]: Taking taylor expansion of PI in k 8.817 * [backup-simplify]: Simplify PI into PI 8.817 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.818 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.819 * [backup-simplify]: Simplify (+ 1 0) into 1 8.819 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 8.821 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 8.822 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 8.822 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.822 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.823 * [taylor]: Taking taylor expansion of -1 in k 8.823 * [backup-simplify]: Simplify -1 into -1 8.823 * [taylor]: Taking taylor expansion of k in k 8.823 * [backup-simplify]: Simplify 0 into 0 8.823 * [backup-simplify]: Simplify 1 into 1 8.823 * [backup-simplify]: Simplify (/ -1 1) into -1 8.823 * [backup-simplify]: Simplify (sqrt 0) into 0 8.825 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.826 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))) 8.827 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))) 8.829 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))) 8.830 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 8.833 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.835 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) 8.838 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) 8.839 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) 8.840 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.844 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.848 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) 8.852 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) 8.853 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) 8.864 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (/ 1 (- k))) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 (/ 1 (- k))) 1.0))))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))))))))) 8.864 * * * [progress]: simplifying candidates 8.869 * [simplify]: Simplifying: (expm1 (pow n (/ (- 1.0 k) 2.0))) (log1p (pow n (/ (- 1.0 k) 2.0))) (* (log n) (/ (- 1.0 k) 2.0)) (* (log n) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow n (/ 1.0 2.0)) (pow n (/ k 2.0)) (pow n (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow n (sqrt (/ (- 1.0 k) 2.0))) (pow n (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow n (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow n (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow n (/ (sqrt (- 1.0 k)) 1)) (pow n (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ 1 (sqrt 2.0))) (pow n (/ 1 1)) (pow n (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow n (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow n (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ 1 (sqrt 2.0))) (pow n (/ 1 1)) (pow n 1) (pow n (- 1.0 k)) (pow (* (cbrt n) (cbrt n)) (/ (- 1.0 k) 2.0)) (pow (cbrt n) (/ (- 1.0 k) 2.0)) (pow (sqrt n) (/ (- 1.0 k) 2.0)) (pow (sqrt n) (/ (- 1.0 k) 2.0)) (pow 1 (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow n (/ (- 1.0 k) 2.0))) (exp (pow n (/ (- 1.0 k) 2.0))) (* (cbrt (pow n (/ (- 1.0 k) 2.0))) (cbrt (pow n (/ (- 1.0 k) 2.0)))) (cbrt (pow n (/ (- 1.0 k) 2.0))) (* (* (pow n (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0))) (sqrt (pow n (/ (- 1.0 k) 2.0))) (sqrt (pow n (/ (- 1.0 k) 2.0))) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (log1p (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (+ (log 2.0) (log PI)) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 PI)) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 PI)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ 1.0 2.0)) (pow (* 2.0 PI) (/ k 2.0)) (pow (* 2.0 PI) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* 2.0 PI) (sqrt (/ (- 1.0 k) 2.0))) (pow (* 2.0 PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* 2.0 PI) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 PI) (/ (sqrt (- 1.0 k)) 1)) (pow (* 2.0 PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ 1 (sqrt 2.0))) (pow (* 2.0 PI) (/ 1 1)) (pow (* 2.0 PI) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 PI) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* 2.0 PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ 1 (sqrt 2.0))) (pow (* 2.0 PI) (/ 1 1)) (pow (* 2.0 PI) 1) (pow (* 2.0 PI) (- 1.0 k)) (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)) (log (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (exp (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 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(/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ 1.0 2.0))) (* 1.0 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (- (+ (* 0.125 (* (pow (pow n 1.0) 0.5) (* (pow (log n) 2) (pow k 2)))) (pow n 0.5)) (* 0.5 (* (pow (pow n 1.0) 0.5) (* (log n) k)))) (exp (* -0.5 (* (- 1.0 k) (log (/ 1 n))))) (exp (* 0.5 (* (- (log -1) (log (/ -1 n))) (- 1.0 k)))) (- (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (pow (* 2.0 PI) 0.5)) (* 0.5 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (log (* 2.0 PI)) k)))) (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (pow k 2))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) k)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (log (* 2.0 PI)) (pow k 2)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (log (* 2.0 PI)) k)))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) (pow k 3))) (- (* +nan.0 (/ (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))))))))) 8.876 * * [simplify]: iteration 0: 334 enodes 9.034 * * [simplify]: iteration 1: 928 enodes 9.586 * * [simplify]: iteration 2: 3775 enodes 10.657 * * [simplify]: iteration complete: 5000 enodes 10.657 * * [simplify]: Extracting #0: cost 147 inf + 0 10.659 * * [simplify]: Extracting #1: cost 819 inf + 44 10.670 * * [simplify]: Extracting #2: cost 1414 inf + 6076 10.686 * * [simplify]: Extracting #3: cost 1131 inf + 99124 10.749 * * [simplify]: Extracting #4: cost 588 inf + 285543 10.833 * * [simplify]: Extracting #5: cost 234 inf + 450186 10.951 * * [simplify]: Extracting #6: cost 44 inf + 574894 11.085 * * [simplify]: Extracting #7: cost 7 inf + 592554 11.215 * * [simplify]: Extracting #8: cost 0 inf + 595072 11.364 * * [simplify]: Extracting #9: cost 0 inf + 595017 11.520 * [simplify]: Simplified to: (expm1 (pow n (/ (- 1.0 k) 2.0))) (log1p (pow n (/ (- 1.0 k) 2.0))) (* (log n) (/ (- 1.0 k) 2.0)) (* (log n) (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (pow n (/ 1.0 2.0)) (pow n (/ k 2.0)) (pow n (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow n (sqrt (/ (- 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(sqrt k)) (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* (/ 1.0 (sqrt k)) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (log1p (* (/ 1.0 (sqrt k)) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (fma (/ (- 1.0 k) 2.0) (log (* PI 2.0)) (log (/ 1.0 (sqrt k)))) (fma (/ (- 1.0 k) 2.0) (log (* PI 2.0)) (log (/ 1.0 (sqrt k)))) (fma (/ (- 1.0 k) 2.0) (log (* PI 2.0)) (log (/ 1.0 (sqrt k)))) (fma (/ (- 1.0 k) 2.0) (log (* PI 2.0)) (log (/ 1.0 (sqrt k)))) (fma (/ (- 1.0 k) 2.0) (log (* PI 2.0)) (log (/ 1.0 (sqrt k)))) (fma (/ (- 1.0 k) 2.0) (log (* PI 2.0)) (log (/ 1.0 (sqrt k)))) (fma (/ (- 1.0 k) 2.0) (log (* PI 2.0)) (log (/ 1.0 (sqrt k)))) (fma (/ (- 1.0 k) 2.0) (log (* PI 2.0)) (log (/ 1.0 (sqrt k)))) (fma (/ (- 1.0 k) 2.0) (log (* PI 2.0)) (log (/ 1.0 (sqrt k)))) (exp (* (/ 1.0 (sqrt k)) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (* (* (* (/ (/ (* 1.0 (* 1.0 1.0)) (sqrt k)) k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (* (* (* (/ 1.0 (sqrt k)) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (* (pow (* PI 2.0) (/ 1.0 2.0)) 1.0) (* (pow (* PI 2.0) (/ k 2.0)) (sqrt k)) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* PI 2.0) (/ (- 1.0 k) (* 2.0 2)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* PI 2.0) (/ (- 1.0 k) (* 2.0 2)))) (/ (* (sqrt 1.0) (sqrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (sqrt (sqrt k))) (/ (* (sqrt 1.0) (sqrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (sqrt (sqrt k))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* PI 2.0) (/ (- 1.0 k) (* 2.0 2)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* PI 2.0) (/ (- 1.0 k) (* 2.0 2)))) (/ (* (sqrt 1.0) (sqrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (sqrt (sqrt k))) (/ (* (sqrt 1.0) (sqrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (sqrt (sqrt k))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* PI 2.0) (/ (- 1.0 k) (* 2.0 2)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* PI 2.0) (/ (- 1.0 k) (* 2.0 2)))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (* (cbrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (cbrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (/ 1.0 (sqrt k))) (/ 1.0 (/ (sqrt k) (sqrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0))))) (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (pow (* PI 2.0) (/ (- 1.0 k) (* 2.0 2)))) (* (pow (* PI 2.0) (/ (- 1.0 k) 2.0)) (cbrt (/ 1.0 (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (/ (* (pow (* PI 2.0) (/ (- 1.0 k) 2.0)) (cbrt 1.0)) (sqrt (cbrt k))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (* (pow (* PI 2.0) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt k))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (* (pow (* PI 2.0) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt k))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (/ (* (pow (* PI 2.0) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt (cbrt k))) (/ (* (pow (* PI 2.0) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt (sqrt k))) (/ (* (sqrt 1.0) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (* (pow (* PI 2.0) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt (sqrt k))) (/ (* (sqrt 1.0) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (* (pow (* PI 2.0) (/ (- 1.0 k) 2.0)) 1.0) (cbrt (sqrt k))) (/ 1.0 (/ (sqrt (cbrt k)) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (/ (* (pow (* PI 2.0) (/ (- 1.0 k) 2.0)) 1.0) (sqrt (sqrt k))) (* (/ 1.0 (sqrt k)) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (/ (* (pow (* PI 2.0) (/ (- 1.0 k) 2.0)) 1.0) (sqrt (sqrt k))) (* (/ 1.0 (sqrt k)) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (/ (pow (* PI 2.0) (/ (- 1.0 k) 2.0)) (sqrt k)) (* (/ 1.0 (sqrt k)) (pow (* PI 2.0) (/ 1.0 2.0))) (* (pow (* PI 2.0) (/ (- 1.0 k) 2.0)) 1.0) (- (fma (pow (pow n 1.0) 0.5) (* (* (* k (log n)) (* k (log n))) 0.125) (pow n 0.5)) (* (pow (pow n 1.0) 0.5) (* (* k (log n)) 0.5))) (exp (* -0.5 (- (* (- 1.0 k) (log n))))) (exp (* (- (log -1) (log (/ -1 n))) (* (- 1.0 k) 0.5))) (- (fma (* 0.125 (* (* (log (* PI 2.0)) k) (* (log (* PI 2.0)) k))) (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (exp (* (log (* PI 2.0)) 0.5))) (* 0.5 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (log (* PI 2.0)) k)))) (exp (* (* (log (* PI 2.0)) 0.5) (- 1.0 k))) (exp (* (* (log (* PI 2.0)) 0.5) (- 1.0 k))) (- (- (fma (* +nan.0 k) k (* +nan.0 k)) +nan.0)) (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) (/ (/ +nan.0 k) (* k k)))) (+ (- (/ +nan.0 k) +nan.0) (/ (- +nan.0) (* k k))) (fma (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)) (- (* (* (log (* PI 2.0)) k) (* (log (* PI 2.0)) k))) (- (fma (* (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)) k) k (- (* (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)) k) (* (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)) (fma (* (log (* PI 2.0)) k) k (- (* (log (* PI 2.0)) k)))))) (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)))) (fma (- (/ (exp (* (* (log (* PI 2.0)) 0.5) (- 1.0 k))) k)) +nan.0 (fma (/ (/ (exp (* (* (log (* PI 2.0)) 0.5) (- 1.0 k))) k) k) (/ +nan.0 k) (- (* (/ +nan.0 k) (/ (exp (* (* (log (* PI 2.0)) 0.5) (- 1.0 k))) k))))) (fma +nan.0 (- (/ (exp (* (* (log (* PI 2.0)) 0.5) (- 1.0 k))) k)) (* +nan.0 (- (/ (/ (exp (* (* (log (* PI 2.0)) 0.5) (- 1.0 k))) k) k) (exp (* (* (log (* PI 2.0)) 0.5) (- 1.0 k)))))) 11.546 * * * [progress]: adding candidates to table 12.763 * * [progress]: iteration 3 / 4 12.763 * * * [progress]: picking best candidate 12.855 * * * * [pick]: Picked # 12.855 * * * [progress]: localizing error 12.921 * * * [progress]: generating rewritten candidates 12.921 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 12.934 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 12.952 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 12.999 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 1) 13.020 * * * [progress]: generating series expansions 13.020 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 13.020 * [backup-simplify]: Simplify (pow n (/ (- 1.0 k) 2.0)) into (pow n (* 0.5 (- 1.0 k))) 13.020 * [approximate]: Taking taylor expansion of (pow n (* 0.5 (- 1.0 k))) in (n k) around 0 13.020 * [taylor]: Taking taylor expansion of (pow n (* 0.5 (- 1.0 k))) in k 13.020 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log n))) in k 13.020 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log n)) in k 13.020 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 13.020 * [taylor]: Taking taylor expansion of 0.5 in k 13.020 * [backup-simplify]: Simplify 0.5 into 0.5 13.020 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 13.020 * [taylor]: Taking taylor expansion of 1.0 in k 13.021 * [backup-simplify]: Simplify 1.0 into 1.0 13.021 * [taylor]: Taking taylor expansion of k in k 13.021 * [backup-simplify]: Simplify 0 into 0 13.021 * [backup-simplify]: Simplify 1 into 1 13.021 * [taylor]: Taking taylor expansion of (log n) in k 13.021 * [taylor]: Taking taylor expansion of n in k 13.021 * [backup-simplify]: Simplify n into n 13.021 * [backup-simplify]: Simplify (log n) into (log n) 13.021 * [backup-simplify]: Simplify (- 0) into 0 13.022 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 13.022 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 13.023 * [backup-simplify]: Simplify (* 0.5 (log n)) into (* 0.5 (log n)) 13.023 * [backup-simplify]: Simplify (exp (* 0.5 (log n))) into (pow n 0.5) 13.023 * [taylor]: Taking taylor expansion of (pow n (* 0.5 (- 1.0 k))) in n 13.023 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log n))) in n 13.023 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log n)) in n 13.023 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 13.023 * [taylor]: Taking taylor expansion of 0.5 in n 13.023 * [backup-simplify]: Simplify 0.5 into 0.5 13.023 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 13.023 * [taylor]: Taking taylor expansion of 1.0 in n 13.023 * [backup-simplify]: Simplify 1.0 into 1.0 13.023 * [taylor]: Taking taylor expansion of k in n 13.023 * [backup-simplify]: Simplify k into k 13.023 * [taylor]: Taking taylor expansion of (log n) in n 13.023 * [taylor]: Taking taylor expansion of n in n 13.023 * [backup-simplify]: Simplify 0 into 0 13.023 * [backup-simplify]: Simplify 1 into 1 13.023 * [backup-simplify]: Simplify (log 1) into 0 13.024 * [backup-simplify]: Simplify (- k) into (- k) 13.024 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 13.024 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 13.024 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 13.024 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (log n)) into (* 0.5 (* (- 1.0 k) (log n))) 13.024 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (log n)))) into (exp (* 0.5 (* (- 1.0 k) (log n)))) 13.025 * [taylor]: Taking taylor expansion of (pow n (* 0.5 (- 1.0 k))) in n 13.025 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log n))) in n 13.025 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log n)) in n 13.025 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 13.025 * [taylor]: Taking taylor expansion of 0.5 in n 13.025 * [backup-simplify]: Simplify 0.5 into 0.5 13.025 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 13.025 * [taylor]: Taking taylor expansion of 1.0 in n 13.025 * [backup-simplify]: Simplify 1.0 into 1.0 13.025 * [taylor]: Taking taylor expansion of k in n 13.025 * [backup-simplify]: Simplify k into k 13.025 * [taylor]: Taking taylor expansion of (log n) in n 13.025 * [taylor]: Taking taylor expansion of n in n 13.025 * [backup-simplify]: Simplify 0 into 0 13.025 * [backup-simplify]: Simplify 1 into 1 13.025 * [backup-simplify]: Simplify (log 1) into 0 13.025 * [backup-simplify]: Simplify (- k) into (- k) 13.025 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 13.025 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 13.026 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 13.026 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (log n)) into (* 0.5 (* (- 1.0 k) (log n))) 13.026 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (log n)))) into (exp (* 0.5 (* (- 1.0 k) (log n)))) 13.026 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (log n)))) in k 13.026 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (log n))) in k 13.026 * [taylor]: Taking taylor expansion of 0.5 in k 13.026 * [backup-simplify]: Simplify 0.5 into 0.5 13.027 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (log n)) in k 13.027 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 13.027 * [taylor]: Taking taylor expansion of 1.0 in k 13.027 * [backup-simplify]: Simplify 1.0 into 1.0 13.027 * [taylor]: Taking taylor expansion of k in k 13.027 * [backup-simplify]: Simplify 0 into 0 13.027 * [backup-simplify]: Simplify 1 into 1 13.027 * [taylor]: Taking taylor expansion of (log n) in k 13.027 * [taylor]: Taking taylor expansion of n in k 13.027 * [backup-simplify]: Simplify n into n 13.027 * [backup-simplify]: Simplify (log n) into (log n) 13.027 * [backup-simplify]: Simplify (- 0) into 0 13.028 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 13.028 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 13.028 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (log n))) into (* 0.5 (log n)) 13.028 * [backup-simplify]: Simplify (exp (* 0.5 (log n))) into (pow n 0.5) 13.028 * [backup-simplify]: Simplify (pow n 0.5) into (pow n 0.5) 13.029 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 13.030 * [backup-simplify]: Simplify (- 0) into 0 13.030 * [backup-simplify]: Simplify (+ 0 0) into 0 13.031 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 13.031 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 13.031 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (log n))) into 0 13.032 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 13.032 * [taylor]: Taking taylor expansion of 0 in k 13.032 * [backup-simplify]: Simplify 0 into 0 13.032 * [backup-simplify]: Simplify 0 into 0 13.033 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 13.034 * [backup-simplify]: Simplify (- 1) into -1 13.034 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.035 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (log n))) into (- (log n)) 13.035 * [backup-simplify]: Simplify (+ (* 0.5 (- (log n))) (* 0 (* 1.0 (log n)))) into (- (* 0.5 (log n))) 13.035 * [backup-simplify]: Simplify (* (exp (* 0.5 (log n))) (+ (* (/ (pow (- (* 0.5 (log n))) 1) 1)))) into (* -0.5 (* (pow (pow n 1.0) 0.5) (log n))) 13.035 * [backup-simplify]: Simplify (* -0.5 (* (pow (pow n 1.0) 0.5) (log n))) into (* -0.5 (* (pow (pow n 1.0) 0.5) (log n))) 13.038 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 13.039 * [backup-simplify]: Simplify (- 0) into 0 13.039 * [backup-simplify]: Simplify (+ 0 0) into 0 13.040 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 13.040 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 13.041 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0 13.042 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.042 * [taylor]: Taking taylor expansion of 0 in k 13.042 * [backup-simplify]: Simplify 0 into 0 13.043 * [backup-simplify]: Simplify 0 into 0 13.043 * [backup-simplify]: Simplify 0 into 0 13.044 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 13.045 * [backup-simplify]: Simplify (- 0) into 0 13.045 * [backup-simplify]: Simplify (+ 0 0) into 0 13.046 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (log n)))) into 0 13.047 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (log n))) (* 0 (* 1.0 (log n))))) into 0 13.048 * [backup-simplify]: Simplify (* (exp (* 0.5 (log n))) (+ (* (/ (pow (- (* 0.5 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (pow n 1.0) 0.5) (pow (log n) 2))) 13.048 * [backup-simplify]: Simplify (* 0.125 (* (pow (pow n 1.0) 0.5) (pow (log n) 2))) into (* 0.125 (* (pow (pow n 1.0) 0.5) (pow (log n) 2))) 13.049 * [backup-simplify]: Simplify (+ (* (* 0.125 (* (pow (pow n 1.0) 0.5) (pow (log n) 2))) (pow (* k 1) 2)) (+ (* (* -0.5 (* (pow (pow n 1.0) 0.5) (log n))) (* k 1)) (pow n 0.5))) into (- (+ (* 0.125 (* (pow (pow n 1.0) 0.5) (* (pow (log n) 2) (pow k 2)))) (pow n 0.5)) (* 0.5 (* (pow (pow n 1.0) 0.5) (* (log n) k)))) 13.050 * [backup-simplify]: Simplify (pow (/ 1 n) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) 13.050 * [approximate]: Taking taylor expansion of (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 13.050 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) in k 13.050 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n)))) in k 13.050 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n))) in k 13.050 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 13.050 * [taylor]: Taking taylor expansion of 0.5 in k 13.050 * [backup-simplify]: Simplify 0.5 into 0.5 13.050 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.050 * [taylor]: Taking taylor expansion of 1.0 in k 13.050 * [backup-simplify]: Simplify 1.0 into 1.0 13.050 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.050 * [taylor]: Taking taylor expansion of k in k 13.050 * [backup-simplify]: Simplify 0 into 0 13.050 * [backup-simplify]: Simplify 1 into 1 13.050 * [backup-simplify]: Simplify (/ 1 1) into 1 13.050 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k 13.050 * [taylor]: Taking taylor expansion of (/ 1 n) in k 13.051 * [taylor]: Taking taylor expansion of n in k 13.051 * [backup-simplify]: Simplify n into n 13.051 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n) 13.051 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n)) 13.051 * [backup-simplify]: Simplify (- 1) into -1 13.051 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.052 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 13.052 * [backup-simplify]: Simplify (* -0.5 (log (/ 1 n))) into (* -0.5 (log (/ 1 n))) 13.052 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ 1 n))))) 13.052 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) in n 13.052 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n)))) in n 13.052 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n))) in n 13.052 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 13.052 * [taylor]: Taking taylor expansion of 0.5 in n 13.052 * [backup-simplify]: Simplify 0.5 into 0.5 13.052 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 13.053 * [taylor]: Taking taylor expansion of 1.0 in n 13.053 * [backup-simplify]: Simplify 1.0 into 1.0 13.053 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.053 * [taylor]: Taking taylor expansion of k in n 13.053 * [backup-simplify]: Simplify k into k 13.053 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.053 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 13.053 * [taylor]: Taking taylor expansion of (/ 1 n) in n 13.053 * [taylor]: Taking taylor expansion of n in n 13.053 * [backup-simplify]: Simplify 0 into 0 13.053 * [backup-simplify]: Simplify 1 into 1 13.053 * [backup-simplify]: Simplify (/ 1 1) into 1 13.054 * [backup-simplify]: Simplify (log 1) into 0 13.054 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 13.054 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 13.054 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 13.055 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.055 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log n))) into (* -0.5 (* (- 1.0 (/ 1 k)) (log n))) 13.055 * [backup-simplify]: Simplify (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) into (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) 13.055 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) in n 13.055 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n)))) in n 13.055 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n))) in n 13.055 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 13.055 * [taylor]: Taking taylor expansion of 0.5 in n 13.055 * [backup-simplify]: Simplify 0.5 into 0.5 13.055 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 13.055 * [taylor]: Taking taylor expansion of 1.0 in n 13.055 * [backup-simplify]: Simplify 1.0 into 1.0 13.055 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.055 * [taylor]: Taking taylor expansion of k in n 13.055 * [backup-simplify]: Simplify k into k 13.055 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.055 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 13.055 * [taylor]: Taking taylor expansion of (/ 1 n) in n 13.055 * [taylor]: Taking taylor expansion of n in n 13.055 * [backup-simplify]: Simplify 0 into 0 13.055 * [backup-simplify]: Simplify 1 into 1 13.056 * [backup-simplify]: Simplify (/ 1 1) into 1 13.056 * [backup-simplify]: Simplify (log 1) into 0 13.056 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 13.056 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 13.057 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 13.057 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.057 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log n))) into (* -0.5 (* (- 1.0 (/ 1 k)) (log n))) 13.057 * [backup-simplify]: Simplify (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) into (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) 13.057 * [taylor]: Taking taylor expansion of (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) in k 13.058 * [taylor]: Taking taylor expansion of (* -0.5 (* (- 1.0 (/ 1 k)) (log n))) in k 13.058 * [taylor]: Taking taylor expansion of -0.5 in k 13.058 * [backup-simplify]: Simplify -0.5 into -0.5 13.058 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log n)) in k 13.058 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.058 * [taylor]: Taking taylor expansion of 1.0 in k 13.058 * [backup-simplify]: Simplify 1.0 into 1.0 13.058 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.058 * [taylor]: Taking taylor expansion of k in k 13.058 * [backup-simplify]: Simplify 0 into 0 13.058 * [backup-simplify]: Simplify 1 into 1 13.058 * [backup-simplify]: Simplify (/ 1 1) into 1 13.058 * [taylor]: Taking taylor expansion of (log n) in k 13.058 * [taylor]: Taking taylor expansion of n in k 13.058 * [backup-simplify]: Simplify n into n 13.058 * [backup-simplify]: Simplify (log n) into (log n) 13.059 * [backup-simplify]: Simplify (- 1) into -1 13.059 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.059 * [backup-simplify]: Simplify (* -1 (log n)) into (* -1 (log n)) 13.059 * [backup-simplify]: Simplify (* -0.5 (* -1 (log n))) into (* 0.5 (log n)) 13.060 * [backup-simplify]: Simplify (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) into (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) 13.060 * [backup-simplify]: Simplify (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) into (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) 13.061 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 13.062 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 13.062 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.062 * [backup-simplify]: Simplify (- 0) into 0 13.063 * [backup-simplify]: Simplify (+ 0 0) into 0 13.063 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 13.064 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.064 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 13.065 * [backup-simplify]: Simplify (* (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 13.065 * [taylor]: Taking taylor expansion of 0 in k 13.065 * [backup-simplify]: Simplify 0 into 0 13.065 * [backup-simplify]: Simplify 0 into 0 13.065 * [backup-simplify]: Simplify 0 into 0 13.066 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.069 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 13.069 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.069 * [backup-simplify]: Simplify (- 0) into 0 13.070 * [backup-simplify]: Simplify (+ 0 0) into 0 13.071 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 13.071 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.072 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 13.073 * [backup-simplify]: Simplify (* (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.073 * [taylor]: Taking taylor expansion of 0 in k 13.073 * [backup-simplify]: Simplify 0 into 0 13.073 * [backup-simplify]: Simplify 0 into 0 13.073 * [backup-simplify]: Simplify 0 into 0 13.073 * [backup-simplify]: Simplify 0 into 0 13.074 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.079 * [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 13.080 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.080 * [backup-simplify]: Simplify (- 0) into 0 13.081 * [backup-simplify]: Simplify (+ 0 0) into 0 13.082 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 13.082 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.083 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 13.085 * [backup-simplify]: Simplify (* (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.085 * [taylor]: Taking taylor expansion of 0 in k 13.085 * [backup-simplify]: Simplify 0 into 0 13.085 * [backup-simplify]: Simplify 0 into 0 13.086 * [backup-simplify]: Simplify (exp (* -0.5 (* (- 1.0 (/ 1 (/ 1 k))) (log (/ 1 n))))) into (exp (* -0.5 (* (- 1.0 k) (log (/ 1 n))))) 13.086 * [backup-simplify]: Simplify (pow (/ 1 (- n)) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) 13.086 * [approximate]: Taking taylor expansion of (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 13.086 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) in k 13.086 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) in k 13.086 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n))) in k 13.086 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 13.086 * [taylor]: Taking taylor expansion of 0.5 in k 13.086 * [backup-simplify]: Simplify 0.5 into 0.5 13.086 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.086 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.086 * [taylor]: Taking taylor expansion of k in k 13.086 * [backup-simplify]: Simplify 0 into 0 13.086 * [backup-simplify]: Simplify 1 into 1 13.087 * [backup-simplify]: Simplify (/ 1 1) into 1 13.087 * [taylor]: Taking taylor expansion of 1.0 in k 13.087 * [backup-simplify]: Simplify 1.0 into 1.0 13.087 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k 13.087 * [taylor]: Taking taylor expansion of (/ -1 n) in k 13.087 * [taylor]: Taking taylor expansion of -1 in k 13.087 * [backup-simplify]: Simplify -1 into -1 13.087 * [taylor]: Taking taylor expansion of n in k 13.087 * [backup-simplify]: Simplify n into n 13.087 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n) 13.087 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n)) 13.087 * [backup-simplify]: Simplify (+ 1 0) into 1 13.088 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 13.088 * [backup-simplify]: Simplify (* 0.5 (log (/ -1 n))) into (* 0.5 (log (/ -1 n))) 13.088 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) into (exp (* 0.5 (* (log (/ -1 n)) (+ (/ 1 k) 1.0)))) 13.088 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) in n 13.088 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) in n 13.088 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n))) in n 13.088 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 13.088 * [taylor]: Taking taylor expansion of 0.5 in n 13.088 * [backup-simplify]: Simplify 0.5 into 0.5 13.088 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 13.088 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.088 * [taylor]: Taking taylor expansion of k in n 13.088 * [backup-simplify]: Simplify k into k 13.089 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.089 * [taylor]: Taking taylor expansion of 1.0 in n 13.089 * [backup-simplify]: Simplify 1.0 into 1.0 13.089 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 13.089 * [taylor]: Taking taylor expansion of (/ -1 n) in n 13.089 * [taylor]: Taking taylor expansion of -1 in n 13.089 * [backup-simplify]: Simplify -1 into -1 13.089 * [taylor]: Taking taylor expansion of n in n 13.089 * [backup-simplify]: Simplify 0 into 0 13.089 * [backup-simplify]: Simplify 1 into 1 13.095 * [backup-simplify]: Simplify (/ -1 1) into -1 13.095 * [backup-simplify]: Simplify (log -1) into (log -1) 13.095 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 13.096 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 13.096 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 13.097 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log -1) (log n))) into (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0))) 13.098 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 13.098 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) in n 13.098 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) in n 13.098 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n))) in n 13.098 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 13.098 * [taylor]: Taking taylor expansion of 0.5 in n 13.098 * [backup-simplify]: Simplify 0.5 into 0.5 13.098 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 13.098 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.098 * [taylor]: Taking taylor expansion of k in n 13.098 * [backup-simplify]: Simplify k into k 13.098 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.098 * [taylor]: Taking taylor expansion of 1.0 in n 13.098 * [backup-simplify]: Simplify 1.0 into 1.0 13.098 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 13.098 * [taylor]: Taking taylor expansion of (/ -1 n) in n 13.098 * [taylor]: Taking taylor expansion of -1 in n 13.098 * [backup-simplify]: Simplify -1 into -1 13.098 * [taylor]: Taking taylor expansion of n in n 13.098 * [backup-simplify]: Simplify 0 into 0 13.098 * [backup-simplify]: Simplify 1 into 1 13.099 * [backup-simplify]: Simplify (/ -1 1) into -1 13.099 * [backup-simplify]: Simplify (log -1) into (log -1) 13.099 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 13.099 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 13.100 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 13.101 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log -1) (log n))) into (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0))) 13.101 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 13.101 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) in k 13.101 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0))) in k 13.101 * [taylor]: Taking taylor expansion of 0.5 in k 13.101 * [backup-simplify]: Simplify 0.5 into 0.5 13.102 * [taylor]: Taking taylor expansion of (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)) in k 13.102 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k 13.102 * [taylor]: Taking taylor expansion of (log -1) in k 13.102 * [taylor]: Taking taylor expansion of -1 in k 13.102 * [backup-simplify]: Simplify -1 into -1 13.102 * [backup-simplify]: Simplify (log -1) into (log -1) 13.102 * [taylor]: Taking taylor expansion of (log n) in k 13.102 * [taylor]: Taking taylor expansion of n in k 13.102 * [backup-simplify]: Simplify n into n 13.102 * [backup-simplify]: Simplify (log n) into (log n) 13.102 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.102 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.102 * [taylor]: Taking taylor expansion of k in k 13.102 * [backup-simplify]: Simplify 0 into 0 13.102 * [backup-simplify]: Simplify 1 into 1 13.103 * [backup-simplify]: Simplify (/ 1 1) into 1 13.103 * [taylor]: Taking taylor expansion of 1.0 in k 13.103 * [backup-simplify]: Simplify 1.0 into 1.0 13.103 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.103 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n)) 13.104 * [backup-simplify]: Simplify (+ 1 0) into 1 13.104 * [backup-simplify]: Simplify (* (- (log -1) (log n)) 1) into (- (log -1) (log n)) 13.105 * [backup-simplify]: Simplify (* 0.5 (- (log -1) (log n))) into (* 0.5 (- (log -1) (log n))) 13.106 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 13.106 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 13.107 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 13.109 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 13.109 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.109 * [backup-simplify]: Simplify (+ 0 0) into 0 13.110 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 13.111 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 13.111 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log -1) (log n)))) into 0 13.112 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 13.112 * [taylor]: Taking taylor expansion of 0 in k 13.112 * [backup-simplify]: Simplify 0 into 0 13.113 * [backup-simplify]: Simplify 0 into 0 13.113 * [backup-simplify]: Simplify 0 into 0 13.114 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.116 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0 13.117 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.117 * [backup-simplify]: Simplify (+ 0 0) into 0 13.118 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 13.119 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 13.120 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0 13.121 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.122 * [taylor]: Taking taylor expansion of 0 in k 13.122 * [backup-simplify]: Simplify 0 into 0 13.122 * [backup-simplify]: Simplify 0 into 0 13.122 * [backup-simplify]: Simplify 0 into 0 13.122 * [backup-simplify]: Simplify 0 into 0 13.123 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.128 * [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 13.128 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.129 * [backup-simplify]: Simplify (+ 0 0) into 0 13.130 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 13.131 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 13.132 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -1) (log n)))))) into 0 13.134 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.134 * [taylor]: Taking taylor expansion of 0 in k 13.134 * [backup-simplify]: Simplify 0 into 0 13.134 * [backup-simplify]: Simplify 0 into 0 13.135 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log (/ -1 n))) (- 1.0 k)))) 13.135 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 13.135 * [backup-simplify]: Simplify (pow PI (/ (- 1.0 k) 2.0)) into (pow PI (* 0.5 (- 1.0 k))) 13.136 * [approximate]: Taking taylor expansion of (pow PI (* 0.5 (- 1.0 k))) in (k) around 0 13.136 * [taylor]: Taking taylor expansion of (pow PI (* 0.5 (- 1.0 k))) in k 13.136 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log PI))) in k 13.136 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log PI)) in k 13.136 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 13.136 * [taylor]: Taking taylor expansion of 0.5 in k 13.136 * [backup-simplify]: Simplify 0.5 into 0.5 13.136 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 13.136 * [taylor]: Taking taylor expansion of 1.0 in k 13.136 * [backup-simplify]: Simplify 1.0 into 1.0 13.136 * [taylor]: Taking taylor expansion of k in k 13.136 * [backup-simplify]: Simplify 0 into 0 13.136 * [backup-simplify]: Simplify 1 into 1 13.136 * [taylor]: Taking taylor expansion of (log PI) in k 13.136 * [taylor]: Taking taylor expansion of PI in k 13.136 * [backup-simplify]: Simplify PI into PI 13.136 * [backup-simplify]: Simplify (log PI) into (log PI) 13.137 * [backup-simplify]: Simplify (- 0) into 0 13.137 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 13.138 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 13.139 * [backup-simplify]: Simplify (* 0.5 (log PI)) into (* 0.5 (log PI)) 13.140 * [backup-simplify]: Simplify (exp (* 0.5 (log PI))) into (pow PI 0.5) 13.140 * [taylor]: Taking taylor expansion of (pow PI (* 0.5 (- 1.0 k))) in k 13.140 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log PI))) in k 13.140 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log PI)) in k 13.141 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 13.141 * [taylor]: Taking taylor expansion of 0.5 in k 13.141 * [backup-simplify]: Simplify 0.5 into 0.5 13.141 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 13.141 * [taylor]: Taking taylor expansion of 1.0 in k 13.141 * [backup-simplify]: Simplify 1.0 into 1.0 13.141 * [taylor]: Taking taylor expansion of k in k 13.141 * [backup-simplify]: Simplify 0 into 0 13.141 * [backup-simplify]: Simplify 1 into 1 13.141 * [taylor]: Taking taylor expansion of (log PI) in k 13.141 * [taylor]: Taking taylor expansion of PI in k 13.141 * [backup-simplify]: Simplify PI into PI 13.141 * [backup-simplify]: Simplify (log PI) into (log PI) 13.142 * [backup-simplify]: Simplify (- 0) into 0 13.142 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 13.142 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 13.143 * [backup-simplify]: Simplify (* 0.5 (log PI)) into (* 0.5 (log PI)) 13.145 * [backup-simplify]: Simplify (exp (* 0.5 (log PI))) into (pow PI 0.5) 13.146 * [backup-simplify]: Simplify (pow PI 0.5) into (pow PI 0.5) 13.147 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 13.148 * [backup-simplify]: Simplify (- 1) into -1 13.148 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.150 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 13.152 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log PI))) into (- (* 0.5 (log PI))) 13.162 * [backup-simplify]: Simplify (* (exp (* 0.5 (log PI))) (+ (* (/ (pow (- (* 0.5 (log PI))) 1) 1)))) into (* -0.5 (* (log PI) (pow (pow PI 1.0) 0.5))) 13.166 * [backup-simplify]: Simplify (* -0.5 (* (log PI) (pow (pow PI 1.0) 0.5))) into (* -0.5 (* (log PI) (pow (pow PI 1.0) 0.5))) 13.169 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 13.170 * [backup-simplify]: Simplify (- 0) into 0 13.170 * [backup-simplify]: Simplify (+ 0 0) into 0 13.171 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 13.172 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log PI)))) into 0 13.185 * [backup-simplify]: Simplify (* (exp (* 0.5 (log PI))) (+ (* (/ (pow (- (* 0.5 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (log PI) 2) (pow (pow PI 1.0) 0.5))) 13.189 * [backup-simplify]: Simplify (* 0.125 (* (pow (log PI) 2) (pow (pow PI 1.0) 0.5))) into (* 0.125 (* (pow (log PI) 2) (pow (pow PI 1.0) 0.5))) 13.199 * [backup-simplify]: Simplify (+ (* (* 0.125 (* (pow (log PI) 2) (pow (pow PI 1.0) 0.5))) (pow k 2)) (+ (* (* -0.5 (* (log PI) (pow (pow PI 1.0) 0.5))) k) (pow PI 0.5))) into (- (+ (pow PI 0.5) (* 0.125 (* (* (pow (log PI) 2) (pow k 2)) (pow (pow PI 1.0) 0.5)))) (* 0.5 (* (* (log PI) k) (pow (pow PI 1.0) 0.5)))) 13.199 * [backup-simplify]: Simplify (pow PI (/ (- 1.0 (/ 1 k)) 2.0)) into (pow PI (* 0.5 (- 1.0 (/ 1 k)))) 13.199 * [approximate]: Taking taylor expansion of (pow PI (* 0.5 (- 1.0 (/ 1 k)))) in (k) around 0 13.199 * [taylor]: Taking taylor expansion of (pow PI (* 0.5 (- 1.0 (/ 1 k)))) in k 13.199 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log PI))) in k 13.199 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log PI)) in k 13.199 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 13.199 * [taylor]: Taking taylor expansion of 0.5 in k 13.199 * [backup-simplify]: Simplify 0.5 into 0.5 13.200 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.200 * [taylor]: Taking taylor expansion of 1.0 in k 13.200 * [backup-simplify]: Simplify 1.0 into 1.0 13.200 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.200 * [taylor]: Taking taylor expansion of k in k 13.200 * [backup-simplify]: Simplify 0 into 0 13.200 * [backup-simplify]: Simplify 1 into 1 13.200 * [backup-simplify]: Simplify (/ 1 1) into 1 13.200 * [taylor]: Taking taylor expansion of (log PI) in k 13.200 * [taylor]: Taking taylor expansion of PI in k 13.200 * [backup-simplify]: Simplify PI into PI 13.201 * [backup-simplify]: Simplify (log PI) into (log PI) 13.201 * [backup-simplify]: Simplify (- 1) into -1 13.201 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.202 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 13.203 * [backup-simplify]: Simplify (* -0.5 (log PI)) into (* -0.5 (log PI)) 13.203 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log PI))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log PI)))) 13.203 * [taylor]: Taking taylor expansion of (pow PI (* 0.5 (- 1.0 (/ 1 k)))) in k 13.203 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log PI))) in k 13.203 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log PI)) in k 13.204 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 13.204 * [taylor]: Taking taylor expansion of 0.5 in k 13.204 * [backup-simplify]: Simplify 0.5 into 0.5 13.204 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.204 * [taylor]: Taking taylor expansion of 1.0 in k 13.204 * [backup-simplify]: Simplify 1.0 into 1.0 13.204 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.204 * [taylor]: Taking taylor expansion of k in k 13.204 * [backup-simplify]: Simplify 0 into 0 13.204 * [backup-simplify]: Simplify 1 into 1 13.204 * [backup-simplify]: Simplify (/ 1 1) into 1 13.204 * [taylor]: Taking taylor expansion of (log PI) in k 13.204 * [taylor]: Taking taylor expansion of PI in k 13.204 * [backup-simplify]: Simplify PI into PI 13.205 * [backup-simplify]: Simplify (log PI) into (log PI) 13.205 * [backup-simplify]: Simplify (- 1) into -1 13.206 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.206 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 13.207 * [backup-simplify]: Simplify (* -0.5 (log PI)) into (* -0.5 (log PI)) 13.208 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log PI))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log PI)))) 13.208 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log PI)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log PI)))) 13.208 * [backup-simplify]: Simplify 0 into 0 13.208 * [backup-simplify]: Simplify 0 into 0 13.208 * [backup-simplify]: Simplify 0 into 0 13.208 * [backup-simplify]: Simplify 0 into 0 13.208 * [backup-simplify]: Simplify 0 into 0 13.209 * [backup-simplify]: Simplify 0 into 0 13.209 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (log PI)))) into (exp (* 0.5 (* (- 1.0 k) (log PI)))) 13.209 * [backup-simplify]: Simplify (pow PI (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow PI (* 0.5 (+ (/ 1 k) 1.0))) 13.209 * [approximate]: Taking taylor expansion of (pow PI (* 0.5 (+ (/ 1 k) 1.0))) in (k) around 0 13.209 * [taylor]: Taking taylor expansion of (pow PI (* 0.5 (+ (/ 1 k) 1.0))) in k 13.209 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log PI))) in k 13.209 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log PI)) in k 13.209 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 13.210 * [taylor]: Taking taylor expansion of 0.5 in k 13.210 * [backup-simplify]: Simplify 0.5 into 0.5 13.210 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.210 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.210 * [taylor]: Taking taylor expansion of k in k 13.210 * [backup-simplify]: Simplify 0 into 0 13.210 * [backup-simplify]: Simplify 1 into 1 13.210 * [backup-simplify]: Simplify (/ 1 1) into 1 13.210 * [taylor]: Taking taylor expansion of 1.0 in k 13.210 * [backup-simplify]: Simplify 1.0 into 1.0 13.210 * [taylor]: Taking taylor expansion of (log PI) in k 13.210 * [taylor]: Taking taylor expansion of PI in k 13.210 * [backup-simplify]: Simplify PI into PI 13.211 * [backup-simplify]: Simplify (log PI) into (log PI) 13.211 * [backup-simplify]: Simplify (+ 1 0) into 1 13.211 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 13.213 * [backup-simplify]: Simplify (* 0.5 (log PI)) into (* 0.5 (log PI)) 13.213 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log PI))) into (exp (* 0.5 (* (log PI) (+ (/ 1 k) 1.0)))) 13.213 * [taylor]: Taking taylor expansion of (pow PI (* 0.5 (+ (/ 1 k) 1.0))) in k 13.213 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log PI))) in k 13.213 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log PI)) in k 13.213 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 13.213 * [taylor]: Taking taylor expansion of 0.5 in k 13.213 * [backup-simplify]: Simplify 0.5 into 0.5 13.213 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.213 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.213 * [taylor]: Taking taylor expansion of k in k 13.213 * [backup-simplify]: Simplify 0 into 0 13.213 * [backup-simplify]: Simplify 1 into 1 13.214 * [backup-simplify]: Simplify (/ 1 1) into 1 13.214 * [taylor]: Taking taylor expansion of 1.0 in k 13.214 * [backup-simplify]: Simplify 1.0 into 1.0 13.214 * [taylor]: Taking taylor expansion of (log PI) in k 13.214 * [taylor]: Taking taylor expansion of PI in k 13.214 * [backup-simplify]: Simplify PI into PI 13.214 * [backup-simplify]: Simplify (log PI) into (log PI) 13.215 * [backup-simplify]: Simplify (+ 1 0) into 1 13.215 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 13.216 * [backup-simplify]: Simplify (* 0.5 (log PI)) into (* 0.5 (log PI)) 13.217 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log PI))) into (exp (* 0.5 (* (log PI) (+ (/ 1 k) 1.0)))) 13.218 * [backup-simplify]: Simplify (exp (* 0.5 (* (log PI) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (log PI) (+ (/ 1 k) 1.0)))) 13.218 * [backup-simplify]: Simplify 0 into 0 13.218 * [backup-simplify]: Simplify 0 into 0 13.218 * [backup-simplify]: Simplify 0 into 0 13.218 * [backup-simplify]: Simplify 0 into 0 13.218 * [backup-simplify]: Simplify 0 into 0 13.218 * [backup-simplify]: Simplify 0 into 0 13.219 * [backup-simplify]: Simplify (exp (* 0.5 (* (log PI) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (log PI)))) 13.219 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 13.219 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0))) into (* 1.0 (* (pow 2.0 (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) 13.219 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow 2.0 (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in (k) around 0 13.219 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow 2.0 (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 13.219 * [taylor]: Taking taylor expansion of 1.0 in k 13.219 * [backup-simplify]: Simplify 1.0 into 1.0 13.219 * [taylor]: Taking taylor expansion of (* (pow 2.0 (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 13.219 * [taylor]: Taking taylor expansion of (pow 2.0 (* 0.5 (- 1.0 k))) in k 13.219 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log 2.0))) in k 13.219 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log 2.0)) in k 13.219 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 13.219 * [taylor]: Taking taylor expansion of 0.5 in k 13.219 * [backup-simplify]: Simplify 0.5 into 0.5 13.219 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 13.219 * [taylor]: Taking taylor expansion of 1.0 in k 13.219 * [backup-simplify]: Simplify 1.0 into 1.0 13.219 * [taylor]: Taking taylor expansion of k in k 13.219 * [backup-simplify]: Simplify 0 into 0 13.220 * [backup-simplify]: Simplify 1 into 1 13.220 * [taylor]: Taking taylor expansion of (log 2.0) in k 13.220 * [taylor]: Taking taylor expansion of 2.0 in k 13.220 * [backup-simplify]: Simplify 2.0 into 2.0 13.220 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 13.220 * [backup-simplify]: Simplify (- 0) into 0 13.221 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 13.221 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 13.222 * [backup-simplify]: Simplify (* 0.5 (log 2.0)) into (* 0.5 (log 2.0)) 13.224 * [backup-simplify]: Simplify (exp (* 0.5 (log 2.0))) into (pow 2.0 0.5) 13.224 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 13.224 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.224 * [taylor]: Taking taylor expansion of k in k 13.224 * [backup-simplify]: Simplify 0 into 0 13.224 * [backup-simplify]: Simplify 1 into 1 13.224 * [backup-simplify]: Simplify (/ 1 1) into 1 13.225 * [backup-simplify]: Simplify (sqrt 0) into 0 13.226 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.226 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow 2.0 (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 13.226 * [taylor]: Taking taylor expansion of 1.0 in k 13.226 * [backup-simplify]: Simplify 1.0 into 1.0 13.226 * [taylor]: Taking taylor expansion of (* (pow 2.0 (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 13.226 * [taylor]: Taking taylor expansion of (pow 2.0 (* 0.5 (- 1.0 k))) in k 13.226 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log 2.0))) in k 13.226 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log 2.0)) in k 13.226 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 13.226 * [taylor]: Taking taylor expansion of 0.5 in k 13.226 * [backup-simplify]: Simplify 0.5 into 0.5 13.226 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 13.227 * [taylor]: Taking taylor expansion of 1.0 in k 13.227 * [backup-simplify]: Simplify 1.0 into 1.0 13.227 * [taylor]: Taking taylor expansion of k in k 13.227 * [backup-simplify]: Simplify 0 into 0 13.227 * [backup-simplify]: Simplify 1 into 1 13.227 * [taylor]: Taking taylor expansion of (log 2.0) in k 13.227 * [taylor]: Taking taylor expansion of 2.0 in k 13.227 * [backup-simplify]: Simplify 2.0 into 2.0 13.227 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 13.227 * [backup-simplify]: Simplify (- 0) into 0 13.228 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 13.228 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 13.229 * [backup-simplify]: Simplify (* 0.5 (log 2.0)) into (* 0.5 (log 2.0)) 13.231 * [backup-simplify]: Simplify (exp (* 0.5 (log 2.0))) into (pow 2.0 0.5) 13.231 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 13.231 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.231 * [taylor]: Taking taylor expansion of k in k 13.231 * [backup-simplify]: Simplify 0 into 0 13.231 * [backup-simplify]: Simplify 1 into 1 13.231 * [backup-simplify]: Simplify (/ 1 1) into 1 13.232 * [backup-simplify]: Simplify (sqrt 0) into 0 13.233 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.234 * [backup-simplify]: Simplify (* (pow 2.0 0.5) 0) into 0 13.234 * [backup-simplify]: Simplify (* 1.0 0) into 0 13.234 * [backup-simplify]: Simplify 0 into 0 13.236 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 13.236 * [backup-simplify]: Simplify (- 1) into -1 13.236 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.238 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 13.241 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log 2.0))) into (- (* 0.5 (log 2.0))) 13.256 * [backup-simplify]: Simplify (* (exp (* 0.5 (log 2.0))) (+ (* (/ (pow (- (* 0.5 (log 2.0))) 1) 1)))) into (* -0.5 (* (pow (pow 2.0 1.0) 0.5) (log 2.0))) 13.259 * [backup-simplify]: Simplify (+ (* (pow 2.0 0.5) +nan.0) (* (* -0.5 (* (pow (pow 2.0 1.0) 0.5) (log 2.0))) 0)) into (- (* +nan.0 (pow (pow 2.0 1.0) 0.5))) 13.262 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (pow (pow 2.0 1.0) 0.5)))) (* 0 0)) into (- (* +nan.0 (pow (pow 2.0 1.0) 0.5))) 13.264 * [backup-simplify]: Simplify (- (* +nan.0 (pow (pow 2.0 1.0) 0.5))) into (- (* +nan.0 (pow (pow 2.0 1.0) 0.5))) 13.264 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 13.266 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.268 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2.0 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2.0 1)))) 2) into 0 13.268 * [backup-simplify]: Simplify (- 0) into 0 13.269 * [backup-simplify]: Simplify (+ 0 0) into 0 13.269 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 13.270 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log 2.0)))) into 0 13.276 * [backup-simplify]: Simplify (* (exp (* 0.5 (log 2.0))) (+ (* (/ (pow (- (* 0.5 (log 2.0))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (pow 2.0 1.0) 0.5) (pow (log 2.0) 2))) 13.284 * [backup-simplify]: Simplify (+ (* (pow 2.0 0.5) +nan.0) (+ (* (* -0.5 (* (pow (pow 2.0 1.0) 0.5) (log 2.0))) +nan.0) (* (* 0.125 (* (pow (pow 2.0 1.0) 0.5) (pow (log 2.0) 2))) 0))) into (- (+ (* +nan.0 (pow (pow 2.0 1.0) 0.5)) (- (* +nan.0 (* (pow (pow 2.0 1.0) 0.5) (log 2.0)))))) 13.294 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (pow (pow 2.0 1.0) 0.5)) (- (* +nan.0 (* (pow (pow 2.0 1.0) 0.5) (log 2.0))))))) (+ (* 0 (- (* +nan.0 (pow (pow 2.0 1.0) 0.5)))) (* 0 0))) into (- (+ (* +nan.0 (pow (pow 2.0 1.0) 0.5)) (- (* +nan.0 (* (pow (pow 2.0 1.0) 0.5) (log 2.0)))))) 13.300 * [backup-simplify]: Simplify (- (+ (* +nan.0 (pow (pow 2.0 1.0) 0.5)) (- (* +nan.0 (* (pow (pow 2.0 1.0) 0.5) (log 2.0)))))) into (- (+ (* +nan.0 (pow (pow 2.0 1.0) 0.5)) (- (* +nan.0 (* (pow (pow 2.0 1.0) 0.5) (log 2.0)))))) 13.300 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.303 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.305 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2.0 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2.0 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2.0 1)))) 6) into 0 13.306 * [backup-simplify]: Simplify (- 0) into 0 13.306 * [backup-simplify]: Simplify (+ 0 0) into 0 13.307 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 13.308 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log 2.0))))) into 0 13.316 * [backup-simplify]: Simplify (* (exp (* 0.5 (log 2.0))) (+ (* (/ (pow (- (* 0.5 (log 2.0))) 3) 6)) (* (/ (pow (- (* 0.5 (log 2.0))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (pow 2.0 1.0) 0.5) (pow (log 2.0) 3))) 13.334 * [backup-simplify]: Simplify (+ (* (pow 2.0 0.5) +nan.0) (+ (* (* -0.5 (* (pow (pow 2.0 1.0) 0.5) (log 2.0))) +nan.0) (+ (* (* 0.125 (* (pow (pow 2.0 1.0) 0.5) (pow (log 2.0) 2))) +nan.0) (* (* -0.020833333333333332 (* (pow (pow 2.0 1.0) 0.5) (pow (log 2.0) 3))) 0)))) into (- (+ (* +nan.0 (pow (pow 2.0 1.0) 0.5)) (- (+ (* +nan.0 (* (pow (pow 2.0 1.0) 0.5) (pow (log 2.0) 2))) (- (* +nan.0 (* (pow (pow 2.0 1.0) 0.5) (log 2.0)))))))) 13.361 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (pow (pow 2.0 1.0) 0.5)) (- (+ (* +nan.0 (* (pow (pow 2.0 1.0) 0.5) (pow (log 2.0) 2))) (- (* +nan.0 (* (pow (pow 2.0 1.0) 0.5) (log 2.0))))))))) (+ (* 0 (- (+ (* +nan.0 (pow (pow 2.0 1.0) 0.5)) (- (* +nan.0 (* (pow (pow 2.0 1.0) 0.5) (log 2.0))))))) (+ (* 0 (- (* +nan.0 (pow (pow 2.0 1.0) 0.5)))) (* 0 0)))) into (- (+ (* +nan.0 (pow (pow 2.0 1.0) 0.5)) (- (+ (* +nan.0 (* (pow (pow 2.0 1.0) 0.5) (pow (log 2.0) 2))) (- (* +nan.0 (* (pow (pow 2.0 1.0) 0.5) (log 2.0)))))))) 13.374 * [backup-simplify]: Simplify (- (+ (* +nan.0 (pow (pow 2.0 1.0) 0.5)) (- (+ (* +nan.0 (* (pow (pow 2.0 1.0) 0.5) (pow (log 2.0) 2))) (- (* +nan.0 (* (pow (pow 2.0 1.0) 0.5) (log 2.0)))))))) into (- (+ (* +nan.0 (pow (pow 2.0 1.0) 0.5)) (- (+ (* +nan.0 (* (pow (pow 2.0 1.0) 0.5) (pow (log 2.0) 2))) (- (* +nan.0 (* (pow (pow 2.0 1.0) 0.5) (log 2.0)))))))) 13.410 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (pow (pow 2.0 1.0) 0.5)) (- (+ (* +nan.0 (* (pow (pow 2.0 1.0) 0.5) (pow (log 2.0) 2))) (- (* +nan.0 (* (pow (pow 2.0 1.0) 0.5) (log 2.0)))))))) (pow k 2)) (+ (* (- (+ (* +nan.0 (pow (pow 2.0 1.0) 0.5)) (- (* +nan.0 (* (pow (pow 2.0 1.0) 0.5) (log 2.0)))))) k) (- (* +nan.0 (pow (pow 2.0 1.0) 0.5))))) into (- (+ (* +nan.0 (* (pow (pow 2.0 1.0) 0.5) (pow k 2))) (- (+ (* +nan.0 (pow (pow 2.0 1.0) 0.5)) (- (+ (* +nan.0 (* (* (log 2.0) (pow k 2)) (pow (pow 2.0 1.0) 0.5))) (- (+ (* +nan.0 (* (* k (log 2.0)) (pow (pow 2.0 1.0) 0.5))) (- (+ (* +nan.0 (* (pow (pow 2.0 1.0) 0.5) k)) (- (* +nan.0 (* (* (pow (log 2.0) 2) (pow k 2)) (pow (pow 2.0 1.0) 0.5)))))))))))))) 13.410 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 k))) (pow 2.0 (/ (- 1.0 (/ 1 k)) 2.0))) into (* 1.0 (* (pow 2.0 (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) 13.410 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow 2.0 (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in (k) around 0 13.410 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow 2.0 (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 13.410 * [taylor]: Taking taylor expansion of 1.0 in k 13.410 * [backup-simplify]: Simplify 1.0 into 1.0 13.410 * [taylor]: Taking taylor expansion of (* (pow 2.0 (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 13.410 * [taylor]: Taking taylor expansion of (pow 2.0 (* 0.5 (- 1.0 (/ 1 k)))) in k 13.411 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log 2.0))) in k 13.411 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log 2.0)) in k 13.411 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 13.411 * [taylor]: Taking taylor expansion of 0.5 in k 13.411 * [backup-simplify]: Simplify 0.5 into 0.5 13.411 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.411 * [taylor]: Taking taylor expansion of 1.0 in k 13.411 * [backup-simplify]: Simplify 1.0 into 1.0 13.411 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.411 * [taylor]: Taking taylor expansion of k in k 13.411 * [backup-simplify]: Simplify 0 into 0 13.411 * [backup-simplify]: Simplify 1 into 1 13.411 * [backup-simplify]: Simplify (/ 1 1) into 1 13.411 * [taylor]: Taking taylor expansion of (log 2.0) in k 13.411 * [taylor]: Taking taylor expansion of 2.0 in k 13.411 * [backup-simplify]: Simplify 2.0 into 2.0 13.412 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 13.412 * [backup-simplify]: Simplify (- 1) into -1 13.412 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.413 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 13.414 * [backup-simplify]: Simplify (* -0.5 (log 2.0)) into (* -0.5 (log 2.0)) 13.414 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log 2.0))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) 13.414 * [taylor]: Taking taylor expansion of (sqrt k) in k 13.414 * [taylor]: Taking taylor expansion of k in k 13.414 * [backup-simplify]: Simplify 0 into 0 13.414 * [backup-simplify]: Simplify 1 into 1 13.415 * [backup-simplify]: Simplify (sqrt 0) into 0 13.416 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.416 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow 2.0 (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 13.417 * [taylor]: Taking taylor expansion of 1.0 in k 13.417 * [backup-simplify]: Simplify 1.0 into 1.0 13.417 * [taylor]: Taking taylor expansion of (* (pow 2.0 (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 13.417 * [taylor]: Taking taylor expansion of (pow 2.0 (* 0.5 (- 1.0 (/ 1 k)))) in k 13.417 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log 2.0))) in k 13.417 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log 2.0)) in k 13.417 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 13.417 * [taylor]: Taking taylor expansion of 0.5 in k 13.417 * [backup-simplify]: Simplify 0.5 into 0.5 13.417 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.417 * [taylor]: Taking taylor expansion of 1.0 in k 13.417 * [backup-simplify]: Simplify 1.0 into 1.0 13.417 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.417 * [taylor]: Taking taylor expansion of k in k 13.417 * [backup-simplify]: Simplify 0 into 0 13.417 * [backup-simplify]: Simplify 1 into 1 13.417 * [backup-simplify]: Simplify (/ 1 1) into 1 13.417 * [taylor]: Taking taylor expansion of (log 2.0) in k 13.417 * [taylor]: Taking taylor expansion of 2.0 in k 13.417 * [backup-simplify]: Simplify 2.0 into 2.0 13.418 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 13.418 * [backup-simplify]: Simplify (- 1) into -1 13.419 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.419 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 13.420 * [backup-simplify]: Simplify (* -0.5 (log 2.0)) into (* -0.5 (log 2.0)) 13.420 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log 2.0))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) 13.420 * [taylor]: Taking taylor expansion of (sqrt k) in k 13.421 * [taylor]: Taking taylor expansion of k in k 13.421 * [backup-simplify]: Simplify 0 into 0 13.421 * [backup-simplify]: Simplify 1 into 1 13.421 * [backup-simplify]: Simplify (sqrt 0) into 0 13.422 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.423 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) 0) into 0 13.423 * [backup-simplify]: Simplify (* 1.0 0) into 0 13.423 * [backup-simplify]: Simplify 0 into 0 13.424 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))))) 13.425 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))))) 13.426 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))))) 13.429 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.430 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))))) 13.432 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))))) 13.432 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))))) 13.436 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.437 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))))) 13.439 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))))) 13.440 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))))) 13.442 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (log 2.0)))))) (pow (/ 1 k) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (log 2.0)))))) (pow (/ 1 k) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (log 2.0)))))) (/ 1 k)))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (log 2.0)))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (log 2.0)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (log 2.0)))) (pow k 3)))))))) 13.443 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow 2.0 (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* 1.0 (/ (pow 2.0 (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 13.443 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow 2.0 (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k) around 0 13.443 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow 2.0 (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 13.443 * [taylor]: Taking taylor expansion of 1.0 in k 13.443 * [backup-simplify]: Simplify 1.0 into 1.0 13.443 * [taylor]: Taking taylor expansion of (/ (pow 2.0 (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 13.443 * [taylor]: Taking taylor expansion of (pow 2.0 (* 0.5 (+ (/ 1 k) 1.0))) in k 13.443 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log 2.0))) in k 13.443 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log 2.0)) in k 13.443 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 13.443 * [taylor]: Taking taylor expansion of 0.5 in k 13.443 * [backup-simplify]: Simplify 0.5 into 0.5 13.443 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.443 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.443 * [taylor]: Taking taylor expansion of k in k 13.443 * [backup-simplify]: Simplify 0 into 0 13.443 * [backup-simplify]: Simplify 1 into 1 13.444 * [backup-simplify]: Simplify (/ 1 1) into 1 13.444 * [taylor]: Taking taylor expansion of 1.0 in k 13.444 * [backup-simplify]: Simplify 1.0 into 1.0 13.444 * [taylor]: Taking taylor expansion of (log 2.0) in k 13.444 * [taylor]: Taking taylor expansion of 2.0 in k 13.444 * [backup-simplify]: Simplify 2.0 into 2.0 13.444 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 13.445 * [backup-simplify]: Simplify (+ 1 0) into 1 13.445 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 13.446 * [backup-simplify]: Simplify (* 0.5 (log 2.0)) into (* 0.5 (log 2.0)) 13.446 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log 2.0))) into (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))) 13.446 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 13.447 * [taylor]: Taking taylor expansion of (/ -1 k) in k 13.447 * [taylor]: Taking taylor expansion of -1 in k 13.447 * [backup-simplify]: Simplify -1 into -1 13.447 * [taylor]: Taking taylor expansion of k in k 13.447 * [backup-simplify]: Simplify 0 into 0 13.447 * [backup-simplify]: Simplify 1 into 1 13.447 * [backup-simplify]: Simplify (/ -1 1) into -1 13.447 * [backup-simplify]: Simplify (sqrt 0) into 0 13.449 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 13.449 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0))))) 13.449 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow 2.0 (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 13.449 * [taylor]: Taking taylor expansion of 1.0 in k 13.449 * [backup-simplify]: Simplify 1.0 into 1.0 13.449 * [taylor]: Taking taylor expansion of (/ (pow 2.0 (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 13.449 * [taylor]: Taking taylor expansion of (pow 2.0 (* 0.5 (+ (/ 1 k) 1.0))) in k 13.449 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log 2.0))) in k 13.450 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log 2.0)) in k 13.450 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 13.450 * [taylor]: Taking taylor expansion of 0.5 in k 13.450 * [backup-simplify]: Simplify 0.5 into 0.5 13.450 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.450 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.450 * [taylor]: Taking taylor expansion of k in k 13.450 * [backup-simplify]: Simplify 0 into 0 13.450 * [backup-simplify]: Simplify 1 into 1 13.450 * [backup-simplify]: Simplify (/ 1 1) into 1 13.450 * [taylor]: Taking taylor expansion of 1.0 in k 13.450 * [backup-simplify]: Simplify 1.0 into 1.0 13.450 * [taylor]: Taking taylor expansion of (log 2.0) in k 13.450 * [taylor]: Taking taylor expansion of 2.0 in k 13.450 * [backup-simplify]: Simplify 2.0 into 2.0 13.451 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 13.451 * [backup-simplify]: Simplify (+ 1 0) into 1 13.451 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 13.452 * [backup-simplify]: Simplify (* 0.5 (log 2.0)) into (* 0.5 (log 2.0)) 13.453 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log 2.0))) into (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))) 13.453 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 13.453 * [taylor]: Taking taylor expansion of (/ -1 k) in k 13.453 * [taylor]: Taking taylor expansion of -1 in k 13.453 * [backup-simplify]: Simplify -1 into -1 13.453 * [taylor]: Taking taylor expansion of k in k 13.453 * [backup-simplify]: Simplify 0 into 0 13.453 * [backup-simplify]: Simplify 1 into 1 13.453 * [backup-simplify]: Simplify (/ -1 1) into -1 13.455 * [backup-simplify]: Simplify (sqrt 0) into 0 13.456 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 13.457 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0))))) 13.457 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0))))) 13.458 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0))))) 13.459 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 13.462 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.463 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))))) 13.472 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))))) 13.472 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))))) 13.473 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.477 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.480 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))))) 13.481 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))))) 13.482 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))))) 13.484 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (/ 1 (- k))) (* +nan.0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 (/ 1 (- k))) 1.0))))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (log 2.0)))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (log 2.0)))) k)) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (log 2.0)))))))))) 13.485 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 1) 13.485 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 13.485 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 13.485 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 13.485 * [taylor]: Taking taylor expansion of 1.0 in k 13.485 * [backup-simplify]: Simplify 1.0 into 1.0 13.485 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 13.485 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.485 * [taylor]: Taking taylor expansion of k in k 13.485 * [backup-simplify]: Simplify 0 into 0 13.485 * [backup-simplify]: Simplify 1 into 1 13.485 * [backup-simplify]: Simplify (/ 1 1) into 1 13.486 * [backup-simplify]: Simplify (sqrt 0) into 0 13.487 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.487 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 13.487 * [taylor]: Taking taylor expansion of 1.0 in k 13.487 * [backup-simplify]: Simplify 1.0 into 1.0 13.487 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 13.487 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.487 * [taylor]: Taking taylor expansion of k in k 13.487 * [backup-simplify]: Simplify 0 into 0 13.487 * [backup-simplify]: Simplify 1 into 1 13.488 * [backup-simplify]: Simplify (/ 1 1) into 1 13.488 * [backup-simplify]: Simplify (sqrt 0) into 0 13.490 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.490 * [backup-simplify]: Simplify (* 1.0 0) into 0 13.490 * [backup-simplify]: Simplify 0 into 0 13.492 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 13.492 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.493 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 13.496 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.498 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 13.498 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.500 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.504 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.506 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 13.506 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.508 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 13.508 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 13.508 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 13.508 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 13.508 * [taylor]: Taking taylor expansion of 1.0 in k 13.508 * [backup-simplify]: Simplify 1.0 into 1.0 13.508 * [taylor]: Taking taylor expansion of (sqrt k) in k 13.508 * [taylor]: Taking taylor expansion of k in k 13.508 * [backup-simplify]: Simplify 0 into 0 13.508 * [backup-simplify]: Simplify 1 into 1 13.508 * [backup-simplify]: Simplify (sqrt 0) into 0 13.510 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.510 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 13.510 * [taylor]: Taking taylor expansion of 1.0 in k 13.510 * [backup-simplify]: Simplify 1.0 into 1.0 13.510 * [taylor]: Taking taylor expansion of (sqrt k) in k 13.510 * [taylor]: Taking taylor expansion of k in k 13.510 * [backup-simplify]: Simplify 0 into 0 13.510 * [backup-simplify]: Simplify 1 into 1 13.510 * [backup-simplify]: Simplify (sqrt 0) into 0 13.512 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.512 * [backup-simplify]: Simplify (* 1.0 0) into 0 13.512 * [backup-simplify]: Simplify 0 into 0 13.514 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 13.514 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.517 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.519 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 13.519 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.523 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.525 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 13.526 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.528 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 13.528 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 13.528 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 13.528 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 13.528 * [taylor]: Taking taylor expansion of 1.0 in k 13.528 * [backup-simplify]: Simplify 1.0 into 1.0 13.528 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 13.528 * [taylor]: Taking taylor expansion of (/ -1 k) in k 13.528 * [taylor]: Taking taylor expansion of -1 in k 13.528 * [backup-simplify]: Simplify -1 into -1 13.528 * [taylor]: Taking taylor expansion of k in k 13.528 * [backup-simplify]: Simplify 0 into 0 13.528 * [backup-simplify]: Simplify 1 into 1 13.529 * [backup-simplify]: Simplify (/ -1 1) into -1 13.529 * [backup-simplify]: Simplify (sqrt 0) into 0 13.530 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 13.531 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 13.531 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 13.531 * [taylor]: Taking taylor expansion of 1.0 in k 13.531 * [backup-simplify]: Simplify 1.0 into 1.0 13.531 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 13.531 * [taylor]: Taking taylor expansion of (/ -1 k) in k 13.531 * [taylor]: Taking taylor expansion of -1 in k 13.531 * [backup-simplify]: Simplify -1 into -1 13.531 * [taylor]: Taking taylor expansion of k in k 13.531 * [backup-simplify]: Simplify 0 into 0 13.531 * [backup-simplify]: Simplify 1 into 1 13.532 * [backup-simplify]: Simplify (/ -1 1) into -1 13.532 * [backup-simplify]: Simplify (sqrt 0) into 0 13.533 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 13.533 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 13.533 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.533 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 13.535 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.537 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 13.537 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.538 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.540 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.543 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 13.543 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.544 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 13.544 * * * [progress]: simplifying candidates 13.546 * [simplify]: Simplifying: (expm1 (pow n (/ (- 1.0 k) 2.0))) (log1p (pow n (/ (- 1.0 k) 2.0))) (* (log n) (/ (- 1.0 k) 2.0)) (* (log n) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow n (/ 1.0 2.0)) (pow n (/ k 2.0)) (pow n (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow n (sqrt (/ (- 1.0 k) 2.0))) (pow n (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow n (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow n (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow n (/ (sqrt (- 1.0 k)) 1)) (pow n (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ 1 (sqrt 2.0))) (pow n (/ 1 1)) (pow n (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow n (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow n (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ 1 (sqrt 2.0))) (pow n (/ 1 1)) (pow n 1) (pow n (- 1.0 k)) (pow (* (cbrt n) (cbrt n)) (/ (- 1.0 k) 2.0)) (pow (cbrt n) (/ (- 1.0 k) 2.0)) (pow (sqrt n) (/ (- 1.0 k) 2.0)) (pow (sqrt n) (/ (- 1.0 k) 2.0)) (pow 1 (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow n (/ (- 1.0 k) 2.0))) (exp (pow n (/ (- 1.0 k) 2.0))) (* (cbrt (pow n (/ (- 1.0 k) 2.0))) (cbrt (pow n (/ (- 1.0 k) 2.0)))) (cbrt (pow n (/ (- 1.0 k) 2.0))) (* (* (pow n (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0))) (sqrt (pow n (/ (- 1.0 k) 2.0))) (sqrt (pow n (/ (- 1.0 k) 2.0))) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (pow PI (/ (- 1.0 k) 2.0))) (log1p (pow PI (/ (- 1.0 k) 2.0))) (* (log PI) (/ (- 1.0 k) 2.0)) (* (log PI) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow PI (/ 1.0 2.0)) (pow PI (/ k 2.0)) (pow PI (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow PI (sqrt (/ (- 1.0 k) 2.0))) (pow PI (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow PI (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow PI (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow PI (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow PI (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow PI (/ (sqrt (- 1.0 k)) 1)) (pow PI (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow PI (/ 1 (sqrt 2.0))) (pow PI (/ 1 1)) (pow PI (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow PI (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow PI (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow PI (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow PI (/ 1 (sqrt 2.0))) (pow PI (/ 1 1)) (pow PI 1) (pow PI (- 1.0 k)) (pow (* (cbrt PI) (cbrt PI)) (/ (- 1.0 k) 2.0)) (pow (cbrt PI) (/ (- 1.0 k) 2.0)) (pow (sqrt PI) (/ (- 1.0 k) 2.0)) (pow (sqrt PI) (/ (- 1.0 k) 2.0)) (pow 1 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)) (log (pow PI (/ (- 1.0 k) 2.0))) (exp (pow PI (/ (- 1.0 k) 2.0))) (* (cbrt (pow PI (/ (- 1.0 k) 2.0))) (cbrt (pow PI (/ (- 1.0 k) 2.0)))) (cbrt (pow PI (/ (- 1.0 k) 2.0))) (* (* (pow PI (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))) (pow PI (/ (- 1.0 k) 2.0))) (sqrt (pow PI (/ (- 1.0 k) 2.0))) (sqrt (pow PI (/ (- 1.0 k) 2.0))) (pow PI (/ (/ (- 1.0 k) 2.0) 2)) (pow PI (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0)))) (log1p (* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0)))) (+ (- (log 1.0) (log (sqrt k))) (* (log 2.0) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log 2.0) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (log (pow 2.0 (/ (- 1.0 k) 2.0)))) (+ (log (/ 1.0 (sqrt k))) (* (log 2.0) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log 2.0) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (log (pow 2.0 (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0)))) (exp (* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0)))) (* (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0))) (pow 2.0 (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0))) (pow 2.0 (/ (- 1.0 k) 2.0)))) (* (cbrt (* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0)))) (* 1.0 (pow 2.0 (/ 1.0 2.0))) (* (sqrt k) (pow 2.0 (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (sqrt 2.0) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (sqrt 2.0) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow 2.0 (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow 2.0 (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow 2.0 (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow 2.0 (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (sqrt 2.0) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (sqrt 2.0) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow 2.0 (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow 2.0 (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow 2.0 (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow 2.0 (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (sqrt 2.0) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (sqrt 2.0) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow 2.0 (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow 2.0 (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow 2.0 (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow 2.0 (/ (/ (- 1.0 k) 2.0) 2))) (* (/ 1.0 (sqrt k)) (pow (* (cbrt 2.0) (cbrt 2.0)) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (sqrt 2.0) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow 1 (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow 2.0 (/ (- 1.0 k) 2.0))) (cbrt (pow 2.0 (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (sqrt k)) (sqrt (pow 2.0 (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) 1) (* (/ 1.0 (sqrt k)) (pow 2.0 (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (/ 1.0 (sqrt k))) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ 1 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow 2.0 (/ 1.0 2.0))) (* 1.0 (pow 2.0 (/ (- 1.0 k) 2.0))) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (- (+ (* 0.125 (* (pow (pow n 1.0) 0.5) (* (pow (log n) 2) (pow k 2)))) (pow n 0.5)) (* 0.5 (* (pow (pow n 1.0) 0.5) (* (log n) k)))) (exp (* -0.5 (* (- 1.0 k) (log (/ 1 n))))) (exp (* 0.5 (* (- (log -1) (log (/ -1 n))) (- 1.0 k)))) (- (+ (pow PI 0.5) (* 0.125 (* (* (pow (log PI) 2) (pow k 2)) (pow (pow PI 1.0) 0.5)))) (* 0.5 (* (* (log PI) k) (pow (pow PI 1.0) 0.5)))) (exp (* 0.5 (* (- 1.0 k) (log PI)))) (exp (* 0.5 (* (- 1.0 k) (log PI)))) (- (+ (* +nan.0 (* (pow (pow 2.0 1.0) 0.5) (pow k 2))) (- (+ (* +nan.0 (pow (pow 2.0 1.0) 0.5)) (- (+ (* +nan.0 (* (* (log 2.0) (pow k 2)) (pow (pow 2.0 1.0) 0.5))) (- (+ (* +nan.0 (* (* k (log 2.0)) (pow (pow 2.0 1.0) 0.5))) (- (+ (* +nan.0 (* (pow (pow 2.0 1.0) 0.5) k)) (- (* +nan.0 (* (* (pow (log 2.0) 2) (pow k 2)) (pow (pow 2.0 1.0) 0.5)))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (log 2.0)))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (log 2.0)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (log 2.0)))) (pow k 3)))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (log 2.0)))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (log 2.0)))) k)) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (log 2.0)))))))))) (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 13.550 * * [simplify]: iteration 0: 353 enodes 13.727 * * [simplify]: iteration 1: 973 enodes 14.398 * * [simplify]: iteration 2: 4088 enodes 15.339 * * [simplify]: iteration complete: 5000 enodes 15.339 * * [simplify]: Extracting #0: cost 152 inf + 0 15.343 * * [simplify]: Extracting #1: cost 813 inf + 45 15.353 * * [simplify]: Extracting #2: cost 1462 inf + 7240 15.394 * * [simplify]: Extracting #3: cost 1119 inf + 115550 15.476 * * [simplify]: Extracting #4: cost 523 inf + 344124 15.581 * * [simplify]: Extracting #5: cost 135 inf + 515745 15.677 * * [simplify]: Extracting #6: cost 17 inf + 562205 15.803 * * [simplify]: Extracting #7: cost 1 inf + 570539 15.961 * * [simplify]: Extracting #8: cost 0 inf + 570292 16.068 * * [simplify]: Extracting #9: cost 0 inf + 570002 16.214 * [simplify]: Simplified to: (expm1 (pow n (/ (- 1.0 k) 2.0))) (log1p (pow n (/ (- 1.0 k) 2.0))) (* (/ (- 1.0 k) 2.0) (log n)) (* (/ (- 1.0 k) 2.0) (log n)) (/ (- 1.0 k) 2.0) (pow n (/ 1.0 2.0)) (pow n (/ k 2.0)) (pow n (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow n (sqrt (/ (- 1.0 k) 2.0))) (pow n (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow n (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow n (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow n (/ (/ (sqrt (- 1.0 k)) (cbrt 2.0)) (cbrt 2.0))) (pow n (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow n (sqrt (- 1.0 k))) (pow n (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ 1 (sqrt 2.0))) n (pow n (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow n (+ (sqrt 1.0) (sqrt k))) (pow n (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ 1 (sqrt 2.0))) n n (pow n (- 1.0 k)) (pow (* (cbrt n) (cbrt n)) (/ (- 1.0 k) 2.0)) (pow (cbrt n) (/ (- 1.0 k) 2.0)) (pow (sqrt n) (/ (- 1.0 k) 2.0)) (pow (sqrt n) (/ (- 1.0 k) 2.0)) 1 (pow n (/ (- 1.0 k) 2.0)) (* (/ (- 1.0 k) 2.0) (log n)) (exp (pow n (/ (- 1.0 k) 2.0))) (* (cbrt (pow n (/ (- 1.0 k) 2.0))) (cbrt (pow n (/ (- 1.0 k) 2.0)))) (cbrt (pow n (/ (- 1.0 k) 2.0))) (* (pow n (/ (- 1.0 k) 2.0)) (* (pow n (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))) (sqrt (pow n (/ (- 1.0 k) 2.0))) (sqrt (pow n (/ (- 1.0 k) 2.0))) (pow n (/ (/ (- 1.0 k) 2) 2.0)) (pow n (/ (/ (- 1.0 k) 2) 2.0)) (expm1 (pow PI (/ (- 1.0 k) 2.0))) (log1p (pow PI (/ (- 1.0 k) 2.0))) (* (log PI) (/ (- 1.0 k) 2.0)) (* (log PI) (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (pow PI (/ 1.0 2.0)) (pow PI (/ k 2.0)) (pow PI (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow PI (sqrt (/ (- 1.0 k) 2.0))) (pow PI (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow PI (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow PI (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow PI (/ (/ (sqrt (- 1.0 k)) (cbrt 2.0)) (cbrt 2.0))) (pow PI (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow PI (sqrt (- 1.0 k))) (pow PI (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow PI (/ 1 (sqrt 2.0))) PI (pow PI (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow PI (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow PI (+ (sqrt 1.0) (sqrt k))) (pow PI (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow PI (/ 1 (sqrt 2.0))) PI PI (pow PI (- 1.0 k)) (pow (* (cbrt PI) (cbrt PI)) (/ (- 1.0 k) 2.0)) (pow (cbrt PI) (/ (- 1.0 k) 2.0)) (pow (sqrt PI) (/ (- 1.0 k) 2.0)) (pow (sqrt PI) (/ (- 1.0 k) 2.0)) 1 (pow PI (/ (- 1.0 k) 2.0)) (* (log PI) (/ (- 1.0 k) 2.0)) (exp (pow PI (/ (- 1.0 k) 2.0))) (* (cbrt (pow PI (/ (- 1.0 k) 2.0))) (cbrt (pow PI (/ (- 1.0 k) 2.0)))) (cbrt (pow PI (/ (- 1.0 k) 2.0))) (* (pow PI (/ (- 1.0 k) 2.0)) (* (pow PI (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)))) (sqrt (pow PI (/ (- 1.0 k) 2.0))) (sqrt (pow PI (/ (- 1.0 k) 2.0))) (pow PI (/ (/ (- 1.0 k) 2) 2.0)) (pow PI (/ (/ (- 1.0 k) 2) 2.0)) (expm1 (/ (* 1.0 (pow 2.0 (/ (- 1.0 k) 2.0))) (sqrt k))) (log1p (/ (* 1.0 (pow 2.0 (/ (- 1.0 k) 2.0))) (sqrt k))) (fma (log 2.0) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log 2.0) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log 2.0) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log 2.0) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log 2.0) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log 2.0) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log 2.0) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (exp (/ (* 1.0 (pow 2.0 (/ (- 1.0 k) 2.0))) (sqrt k))) (/ (* (* 1.0 1.0) (* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0))) (pow 2.0 (/ (- 1.0 k) 2.0)))) (/ k (/ 1.0 (sqrt k)))) (* (/ (* 1.0 (pow 2.0 (/ (- 1.0 k) 2.0))) (sqrt k)) (* (/ (* 1.0 (pow 2.0 (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (* 1.0 (pow 2.0 (/ (- 1.0 k) 2.0))) (sqrt k)))) (* (cbrt (/ (* 1.0 (pow 2.0 (/ (- 1.0 k) 2.0))) (sqrt k))) (cbrt (/ (* 1.0 (pow 2.0 (/ (- 1.0 k) 2.0))) (sqrt k)))) (cbrt (/ (* 1.0 (pow 2.0 (/ (- 1.0 k) 2.0))) (sqrt k))) (* (/ (* 1.0 (pow 2.0 (/ (- 1.0 k) 2.0))) (sqrt k)) (* (/ (* 1.0 (pow 2.0 (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (* 1.0 (pow 2.0 (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (* 1.0 (pow 2.0 (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow 2.0 (/ (- 1.0 k) 2.0))) (sqrt k))) (* 1.0 (pow 2.0 (/ 1.0 2.0))) (* (pow 2.0 (/ k 2.0)) (sqrt k)) (* (sqrt (/ 1.0 (sqrt k))) (pow (sqrt 2.0) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (sqrt 2.0) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow 2.0 (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow 2.0 (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow 2.0 (/ (/ (- 1.0 k) 2) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow 2.0 (/ (/ (- 1.0 k) 2) 2.0))) (/ (* (sqrt 1.0) (pow (sqrt 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (/ (* (sqrt 1.0) (pow (sqrt 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow 2.0 (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow 2.0 (/ (- 1.0 k) 2.0)))) (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (pow 2.0 (/ (/ (- 1.0 k) 2) 2.0)))) (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (pow 2.0 (/ (/ (- 1.0 k) 2) 2.0)))) (/ (* (sqrt 1.0) (pow (sqrt 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (/ (* (sqrt 1.0) (pow (sqrt 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow 2.0 (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow 2.0 (/ (- 1.0 k) 2.0)))) (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (pow 2.0 (/ (/ (- 1.0 k) 2) 2.0)))) (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (pow 2.0 (/ (/ (- 1.0 k) 2) 2.0)))) (/ (* (pow (* (cbrt 2.0) (cbrt 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (/ (* (pow (sqrt 2.0) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (/ 1.0 (sqrt k)) (* (* (/ 1.0 (sqrt k)) (cbrt (pow 2.0 (/ (- 1.0 k) 2.0)))) (cbrt (pow 2.0 (/ (- 1.0 k) 2.0)))) (* (sqrt (pow 2.0 (/ (- 1.0 k) 2.0))) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k)) (/ (* 1.0 (pow 2.0 (/ (/ (- 1.0 k) 2) 2.0))) (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (cbrt (/ 1.0 (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (pow 2.0 (/ (- 1.0 k) 2.0))) (/ (cbrt 1.0) (/ (cbrt (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0)))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0))) (/ (* (pow 2.0 (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (cbrt (sqrt k))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow 2.0 (/ (- 1.0 k) 2.0))) (/ (* (pow 2.0 (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt (sqrt k))) (/ (* (pow 2.0 (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt k)) (/ (* (pow 2.0 (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt (sqrt k))) (/ (* (pow 2.0 (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt k)) (/ (* (pow 2.0 (/ (- 1.0 k) 2.0)) 1.0) (cbrt (sqrt k))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt (cbrt k)))) (/ (* (pow 2.0 (/ (- 1.0 k) 2.0)) 1.0) (sqrt (sqrt k))) (/ (* 1.0 (pow 2.0 (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (* (pow 2.0 (/ (- 1.0 k) 2.0)) 1.0) (sqrt (sqrt k))) (/ (* 1.0 (pow 2.0 (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (* 1.0 (pow 2.0 (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (pow 2.0 (/ (- 1.0 k) 2.0)) (sqrt k)) (* (/ 1.0 (sqrt k)) (pow 2.0 (/ 1.0 2.0))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) 1.0) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (* (/ (* 1.0 1.0) k) (/ 1.0 (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (/ (sqrt 1.0) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ (/ 1.0 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (fma (* (* k (log n)) (* k (log n))) (* 0.125 (pow (pow n 1.0) 0.5)) (- (pow n 0.5) (* (pow (pow n 1.0) 0.5) (* (* (log n) k) 0.5)))) (exp (- (* (* -0.5 (- 1.0 k)) (log n)))) (exp (* (- (log -1) (- (log -1) (log n))) (* 0.5 (- 1.0 k)))) (fma (* (* (* k (log PI)) (* k (log PI))) (pow (pow PI 1.0) 0.5)) 0.125 (- (pow PI 0.5) (* (* k (log PI)) (* (pow (pow PI 1.0) 0.5) 0.5)))) (exp (* 0.5 (* (log PI) (- 1.0 k)))) (exp (* 0.5 (* (log PI) (- 1.0 k)))) (- (- (fma (* k k) (* (pow (pow 2.0 1.0) 0.5) +nan.0) (fma (* (* k k) (log 2.0)) (* (pow (pow 2.0 1.0) 0.5) +nan.0) (- (fma (* (log 2.0) k) (* (pow (pow 2.0 1.0) 0.5) +nan.0) (fma (* (pow (pow 2.0 1.0) 0.5) +nan.0) (- k) (* (* (* (log 2.0) k) (* (log 2.0) k)) (* (pow (pow 2.0 1.0) 0.5) +nan.0))))))) (* (pow (pow 2.0 1.0) 0.5) +nan.0))) (fma +nan.0 (- (/ (exp (* (* (- 1.0 k) (log 2.0)) 0.5)) k) (/ (/ (exp (* (* (- 1.0 k) (log 2.0)) 0.5)) (* k k)) k)) (- (* +nan.0 (/ (exp (* (* (- 1.0 k) (log 2.0)) 0.5)) (* k k))))) (fma +nan.0 (- (/ (exp (* (* (- 1.0 k) (log 2.0)) 0.5)) k) (exp (* (* (- 1.0 k) (log 2.0)) 0.5))) (- (* +nan.0 (/ (exp (* (* (- 1.0 k) (log 2.0)) 0.5)) (* k k))))) (- (- (fma k (* k +nan.0) (* k +nan.0)) +nan.0)) (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) (/ (/ +nan.0 (* k k)) k))) (+ (- (/ +nan.0 k) +nan.0) (/ (- +nan.0) (* k k))) 16.238 * * * [progress]: adding candidates to table 17.610 * * [progress]: iteration 4 / 4 17.610 * * * [progress]: picking best candidate 17.654 * * * * [pick]: Picked # 17.654 * * * [progress]: localizing error 17.741 * * * [progress]: generating rewritten candidates 17.741 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 17.748 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2 2 1) 17.762 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1 2 1) 17.776 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1) 17.962 * * * [progress]: generating series expansions 17.963 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 17.963 * [backup-simplify]: Simplify (pow n (/ (- 1.0 k) 2.0)) into (pow n (* 0.5 (- 1.0 k))) 17.963 * [approximate]: Taking taylor expansion of (pow n (* 0.5 (- 1.0 k))) in (n k) around 0 17.963 * [taylor]: Taking taylor expansion of (pow n (* 0.5 (- 1.0 k))) in k 17.963 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log n))) in k 17.963 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log n)) in k 17.963 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 17.963 * [taylor]: Taking taylor expansion of 0.5 in k 17.963 * [backup-simplify]: Simplify 0.5 into 0.5 17.963 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 17.963 * [taylor]: Taking taylor expansion of 1.0 in k 17.963 * [backup-simplify]: Simplify 1.0 into 1.0 17.963 * [taylor]: Taking taylor expansion of k in k 17.963 * [backup-simplify]: Simplify 0 into 0 17.963 * [backup-simplify]: Simplify 1 into 1 17.963 * [taylor]: Taking taylor expansion of (log n) in k 17.963 * [taylor]: Taking taylor expansion of n in k 17.963 * [backup-simplify]: Simplify n into n 17.963 * [backup-simplify]: Simplify (log n) into (log n) 17.964 * [backup-simplify]: Simplify (- 0) into 0 17.964 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 17.965 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 17.965 * [backup-simplify]: Simplify (* 0.5 (log n)) into (* 0.5 (log n)) 17.965 * [backup-simplify]: Simplify (exp (* 0.5 (log n))) into (pow n 0.5) 17.965 * [taylor]: Taking taylor expansion of (pow n (* 0.5 (- 1.0 k))) in n 17.965 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log n))) in n 17.965 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log n)) in n 17.965 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 17.965 * [taylor]: Taking taylor expansion of 0.5 in n 17.965 * [backup-simplify]: Simplify 0.5 into 0.5 17.965 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 17.965 * [taylor]: Taking taylor expansion of 1.0 in n 17.965 * [backup-simplify]: Simplify 1.0 into 1.0 17.965 * [taylor]: Taking taylor expansion of k in n 17.965 * [backup-simplify]: Simplify k into k 17.965 * [taylor]: Taking taylor expansion of (log n) in n 17.965 * [taylor]: Taking taylor expansion of n in n 17.965 * [backup-simplify]: Simplify 0 into 0 17.965 * [backup-simplify]: Simplify 1 into 1 17.966 * [backup-simplify]: Simplify (log 1) into 0 17.966 * [backup-simplify]: Simplify (- k) into (- k) 17.966 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 17.966 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 17.967 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.967 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (log n)) into (* 0.5 (* (- 1.0 k) (log n))) 17.967 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (log n)))) into (exp (* 0.5 (* (- 1.0 k) (log n)))) 17.967 * [taylor]: Taking taylor expansion of (pow n (* 0.5 (- 1.0 k))) in n 17.967 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log n))) in n 17.967 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log n)) in n 17.967 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 17.967 * [taylor]: Taking taylor expansion of 0.5 in n 17.967 * [backup-simplify]: Simplify 0.5 into 0.5 17.967 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 17.967 * [taylor]: Taking taylor expansion of 1.0 in n 17.967 * [backup-simplify]: Simplify 1.0 into 1.0 17.967 * [taylor]: Taking taylor expansion of k in n 17.967 * [backup-simplify]: Simplify k into k 17.967 * [taylor]: Taking taylor expansion of (log n) in n 17.967 * [taylor]: Taking taylor expansion of n in n 17.967 * [backup-simplify]: Simplify 0 into 0 17.967 * [backup-simplify]: Simplify 1 into 1 17.968 * [backup-simplify]: Simplify (log 1) into 0 17.968 * [backup-simplify]: Simplify (- k) into (- k) 17.968 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 17.968 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 17.969 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.969 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (log n)) into (* 0.5 (* (- 1.0 k) (log n))) 17.969 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (log n)))) into (exp (* 0.5 (* (- 1.0 k) (log n)))) 17.969 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (log n)))) in k 17.969 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (log n))) in k 17.969 * [taylor]: Taking taylor expansion of 0.5 in k 17.969 * [backup-simplify]: Simplify 0.5 into 0.5 17.969 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (log n)) in k 17.969 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 17.969 * [taylor]: Taking taylor expansion of 1.0 in k 17.969 * [backup-simplify]: Simplify 1.0 into 1.0 17.969 * [taylor]: Taking taylor expansion of k in k 17.969 * [backup-simplify]: Simplify 0 into 0 17.969 * [backup-simplify]: Simplify 1 into 1 17.969 * [taylor]: Taking taylor expansion of (log n) in k 17.969 * [taylor]: Taking taylor expansion of n in k 17.969 * [backup-simplify]: Simplify n into n 17.969 * [backup-simplify]: Simplify (log n) into (log n) 17.970 * [backup-simplify]: Simplify (- 0) into 0 17.970 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 17.970 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 17.971 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (log n))) into (* 0.5 (log n)) 17.971 * [backup-simplify]: Simplify (exp (* 0.5 (log n))) into (pow n 0.5) 17.971 * [backup-simplify]: Simplify (pow n 0.5) into (pow n 0.5) 17.972 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 17.973 * [backup-simplify]: Simplify (- 0) into 0 17.973 * [backup-simplify]: Simplify (+ 0 0) into 0 17.973 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 17.974 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.974 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (log n))) into 0 17.975 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 17.975 * [taylor]: Taking taylor expansion of 0 in k 17.975 * [backup-simplify]: Simplify 0 into 0 17.975 * [backup-simplify]: Simplify 0 into 0 17.976 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 17.977 * [backup-simplify]: Simplify (- 1) into -1 17.977 * [backup-simplify]: Simplify (+ 0 -1) into -1 17.978 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (log n))) into (- (log n)) 17.978 * [backup-simplify]: Simplify (+ (* 0.5 (- (log n))) (* 0 (* 1.0 (log n)))) into (- (* 0.5 (log n))) 17.978 * [backup-simplify]: Simplify (* (exp (* 0.5 (log n))) (+ (* (/ (pow (- (* 0.5 (log n))) 1) 1)))) into (* -0.5 (* (pow (pow n 1.0) 0.5) (log n))) 17.979 * [backup-simplify]: Simplify (* -0.5 (* (pow (pow n 1.0) 0.5) (log n))) into (* -0.5 (* (pow (pow n 1.0) 0.5) (log n))) 17.982 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 17.982 * [backup-simplify]: Simplify (- 0) into 0 17.983 * [backup-simplify]: Simplify (+ 0 0) into 0 17.983 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 17.984 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.984 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0 17.986 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.986 * [taylor]: Taking taylor expansion of 0 in k 17.986 * [backup-simplify]: Simplify 0 into 0 17.986 * [backup-simplify]: Simplify 0 into 0 17.986 * [backup-simplify]: Simplify 0 into 0 17.988 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 17.989 * [backup-simplify]: Simplify (- 0) into 0 17.989 * [backup-simplify]: Simplify (+ 0 0) into 0 17.990 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (log n)))) into 0 17.991 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (log n))) (* 0 (* 1.0 (log n))))) into 0 17.992 * [backup-simplify]: Simplify (* (exp (* 0.5 (log n))) (+ (* (/ (pow (- (* 0.5 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (pow n 1.0) 0.5) (pow (log n) 2))) 17.992 * [backup-simplify]: Simplify (* 0.125 (* (pow (pow n 1.0) 0.5) (pow (log n) 2))) into (* 0.125 (* (pow (pow n 1.0) 0.5) (pow (log n) 2))) 17.993 * [backup-simplify]: Simplify (+ (* (* 0.125 (* (pow (pow n 1.0) 0.5) (pow (log n) 2))) (pow (* k 1) 2)) (+ (* (* -0.5 (* (pow (pow n 1.0) 0.5) (log n))) (* k 1)) (pow n 0.5))) into (- (+ (* 0.125 (* (pow (pow n 1.0) 0.5) (* (pow (log n) 2) (pow k 2)))) (pow n 0.5)) (* 0.5 (* (pow (pow n 1.0) 0.5) (* (log n) k)))) 17.994 * [backup-simplify]: Simplify (pow (/ 1 n) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) 17.994 * [approximate]: Taking taylor expansion of (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 17.994 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) in k 17.994 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n)))) in k 17.994 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n))) in k 17.994 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 17.994 * [taylor]: Taking taylor expansion of 0.5 in k 17.994 * [backup-simplify]: Simplify 0.5 into 0.5 17.994 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 17.994 * [taylor]: Taking taylor expansion of 1.0 in k 17.994 * [backup-simplify]: Simplify 1.0 into 1.0 17.994 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.994 * [taylor]: Taking taylor expansion of k in k 17.994 * [backup-simplify]: Simplify 0 into 0 17.995 * [backup-simplify]: Simplify 1 into 1 17.995 * [backup-simplify]: Simplify (/ 1 1) into 1 17.995 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k 17.995 * [taylor]: Taking taylor expansion of (/ 1 n) in k 17.995 * [taylor]: Taking taylor expansion of n in k 17.995 * [backup-simplify]: Simplify n into n 17.995 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n) 17.995 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n)) 17.996 * [backup-simplify]: Simplify (- 1) into -1 17.996 * [backup-simplify]: Simplify (+ 0 -1) into -1 17.997 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 17.997 * [backup-simplify]: Simplify (* -0.5 (log (/ 1 n))) into (* -0.5 (log (/ 1 n))) 17.997 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ 1 n))))) 17.997 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) in n 17.997 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n)))) in n 17.997 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n))) in n 17.997 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 17.997 * [taylor]: Taking taylor expansion of 0.5 in n 17.997 * [backup-simplify]: Simplify 0.5 into 0.5 17.997 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 17.997 * [taylor]: Taking taylor expansion of 1.0 in n 17.997 * [backup-simplify]: Simplify 1.0 into 1.0 17.997 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.997 * [taylor]: Taking taylor expansion of k in n 17.997 * [backup-simplify]: Simplify k into k 17.997 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.997 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 17.998 * [taylor]: Taking taylor expansion of (/ 1 n) in n 17.998 * [taylor]: Taking taylor expansion of n in n 17.998 * [backup-simplify]: Simplify 0 into 0 17.998 * [backup-simplify]: Simplify 1 into 1 17.998 * [backup-simplify]: Simplify (/ 1 1) into 1 17.998 * [backup-simplify]: Simplify (log 1) into 0 17.998 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 17.999 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 17.999 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 17.999 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.999 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log n))) into (* -0.5 (* (- 1.0 (/ 1 k)) (log n))) 18.000 * [backup-simplify]: Simplify (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) into (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) 18.000 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) in n 18.000 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n)))) in n 18.000 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n))) in n 18.000 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 18.000 * [taylor]: Taking taylor expansion of 0.5 in n 18.000 * [backup-simplify]: Simplify 0.5 into 0.5 18.000 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 18.000 * [taylor]: Taking taylor expansion of 1.0 in n 18.000 * [backup-simplify]: Simplify 1.0 into 1.0 18.000 * [taylor]: Taking taylor expansion of (/ 1 k) in n 18.000 * [taylor]: Taking taylor expansion of k in n 18.000 * [backup-simplify]: Simplify k into k 18.000 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 18.000 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 18.000 * [taylor]: Taking taylor expansion of (/ 1 n) in n 18.000 * [taylor]: Taking taylor expansion of n in n 18.000 * [backup-simplify]: Simplify 0 into 0 18.000 * [backup-simplify]: Simplify 1 into 1 18.000 * [backup-simplify]: Simplify (/ 1 1) into 1 18.001 * [backup-simplify]: Simplify (log 1) into 0 18.001 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 18.001 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 18.001 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 18.002 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 18.002 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log n))) into (* -0.5 (* (- 1.0 (/ 1 k)) (log n))) 18.002 * [backup-simplify]: Simplify (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) into (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) 18.002 * [taylor]: Taking taylor expansion of (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) in k 18.002 * [taylor]: Taking taylor expansion of (* -0.5 (* (- 1.0 (/ 1 k)) (log n))) in k 18.002 * [taylor]: Taking taylor expansion of -0.5 in k 18.002 * [backup-simplify]: Simplify -0.5 into -0.5 18.002 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log n)) in k 18.002 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 18.002 * [taylor]: Taking taylor expansion of 1.0 in k 18.002 * [backup-simplify]: Simplify 1.0 into 1.0 18.002 * [taylor]: Taking taylor expansion of (/ 1 k) in k 18.002 * [taylor]: Taking taylor expansion of k in k 18.002 * [backup-simplify]: Simplify 0 into 0 18.002 * [backup-simplify]: Simplify 1 into 1 18.003 * [backup-simplify]: Simplify (/ 1 1) into 1 18.003 * [taylor]: Taking taylor expansion of (log n) in k 18.003 * [taylor]: Taking taylor expansion of n in k 18.003 * [backup-simplify]: Simplify n into n 18.003 * [backup-simplify]: Simplify (log n) into (log n) 18.003 * [backup-simplify]: Simplify (- 1) into -1 18.004 * [backup-simplify]: Simplify (+ 0 -1) into -1 18.004 * [backup-simplify]: Simplify (* -1 (log n)) into (* -1 (log n)) 18.004 * [backup-simplify]: Simplify (* -0.5 (* -1 (log n))) into (* 0.5 (log n)) 18.004 * [backup-simplify]: Simplify (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) into (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) 18.004 * [backup-simplify]: Simplify (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) into (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) 18.005 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 18.006 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 18.006 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 18.007 * [backup-simplify]: Simplify (- 0) into 0 18.007 * [backup-simplify]: Simplify (+ 0 0) into 0 18.008 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 18.008 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 18.008 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 18.009 * [backup-simplify]: Simplify (* (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 18.009 * [taylor]: Taking taylor expansion of 0 in k 18.009 * [backup-simplify]: Simplify 0 into 0 18.009 * [backup-simplify]: Simplify 0 into 0 18.009 * [backup-simplify]: Simplify 0 into 0 18.010 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 18.013 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 18.013 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 18.013 * [backup-simplify]: Simplify (- 0) into 0 18.014 * [backup-simplify]: Simplify (+ 0 0) into 0 18.015 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 18.015 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 18.016 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 18.017 * [backup-simplify]: Simplify (* (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 18.017 * [taylor]: Taking taylor expansion of 0 in k 18.017 * [backup-simplify]: Simplify 0 into 0 18.017 * [backup-simplify]: Simplify 0 into 0 18.017 * [backup-simplify]: Simplify 0 into 0 18.018 * [backup-simplify]: Simplify 0 into 0 18.019 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 18.024 * [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 18.024 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 18.024 * [backup-simplify]: Simplify (- 0) into 0 18.025 * [backup-simplify]: Simplify (+ 0 0) into 0 18.026 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 18.027 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 18.028 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 18.030 * [backup-simplify]: Simplify (* (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 18.030 * [taylor]: Taking taylor expansion of 0 in k 18.030 * [backup-simplify]: Simplify 0 into 0 18.030 * [backup-simplify]: Simplify 0 into 0 18.030 * [backup-simplify]: Simplify (exp (* -0.5 (* (- 1.0 (/ 1 (/ 1 k))) (log (/ 1 n))))) into (exp (* -0.5 (* (- 1.0 k) (log (/ 1 n))))) 18.030 * [backup-simplify]: Simplify (pow (/ 1 (- n)) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) 18.030 * [approximate]: Taking taylor expansion of (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 18.030 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) in k 18.030 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) in k 18.030 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n))) in k 18.030 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 18.030 * [taylor]: Taking taylor expansion of 0.5 in k 18.031 * [backup-simplify]: Simplify 0.5 into 0.5 18.031 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 18.031 * [taylor]: Taking taylor expansion of (/ 1 k) in k 18.031 * [taylor]: Taking taylor expansion of k in k 18.031 * [backup-simplify]: Simplify 0 into 0 18.031 * [backup-simplify]: Simplify 1 into 1 18.031 * [backup-simplify]: Simplify (/ 1 1) into 1 18.031 * [taylor]: Taking taylor expansion of 1.0 in k 18.031 * [backup-simplify]: Simplify 1.0 into 1.0 18.031 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k 18.031 * [taylor]: Taking taylor expansion of (/ -1 n) in k 18.031 * [taylor]: Taking taylor expansion of -1 in k 18.031 * [backup-simplify]: Simplify -1 into -1 18.031 * [taylor]: Taking taylor expansion of n in k 18.031 * [backup-simplify]: Simplify n into n 18.031 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n) 18.031 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n)) 18.032 * [backup-simplify]: Simplify (+ 1 0) into 1 18.032 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 18.033 * [backup-simplify]: Simplify (* 0.5 (log (/ -1 n))) into (* 0.5 (log (/ -1 n))) 18.033 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) into (exp (* 0.5 (* (log (/ -1 n)) (+ (/ 1 k) 1.0)))) 18.033 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) in n 18.033 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) in n 18.033 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n))) in n 18.033 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 18.033 * [taylor]: Taking taylor expansion of 0.5 in n 18.033 * [backup-simplify]: Simplify 0.5 into 0.5 18.033 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 18.033 * [taylor]: Taking taylor expansion of (/ 1 k) in n 18.033 * [taylor]: Taking taylor expansion of k in n 18.033 * [backup-simplify]: Simplify k into k 18.033 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 18.033 * [taylor]: Taking taylor expansion of 1.0 in n 18.033 * [backup-simplify]: Simplify 1.0 into 1.0 18.033 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 18.033 * [taylor]: Taking taylor expansion of (/ -1 n) in n 18.033 * [taylor]: Taking taylor expansion of -1 in n 18.033 * [backup-simplify]: Simplify -1 into -1 18.033 * [taylor]: Taking taylor expansion of n in n 18.033 * [backup-simplify]: Simplify 0 into 0 18.033 * [backup-simplify]: Simplify 1 into 1 18.034 * [backup-simplify]: Simplify (/ -1 1) into -1 18.034 * [backup-simplify]: Simplify (log -1) into (log -1) 18.034 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 18.035 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 18.035 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 18.036 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log -1) (log n))) into (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0))) 18.037 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 18.037 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) in n 18.037 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) in n 18.037 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n))) in n 18.037 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 18.037 * [taylor]: Taking taylor expansion of 0.5 in n 18.037 * [backup-simplify]: Simplify 0.5 into 0.5 18.037 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 18.037 * [taylor]: Taking taylor expansion of (/ 1 k) in n 18.037 * [taylor]: Taking taylor expansion of k in n 18.037 * [backup-simplify]: Simplify k into k 18.037 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 18.037 * [taylor]: Taking taylor expansion of 1.0 in n 18.037 * [backup-simplify]: Simplify 1.0 into 1.0 18.037 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 18.037 * [taylor]: Taking taylor expansion of (/ -1 n) in n 18.037 * [taylor]: Taking taylor expansion of -1 in n 18.037 * [backup-simplify]: Simplify -1 into -1 18.037 * [taylor]: Taking taylor expansion of n in n 18.037 * [backup-simplify]: Simplify 0 into 0 18.037 * [backup-simplify]: Simplify 1 into 1 18.038 * [backup-simplify]: Simplify (/ -1 1) into -1 18.038 * [backup-simplify]: Simplify (log -1) into (log -1) 18.038 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 18.039 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 18.039 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 18.040 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log -1) (log n))) into (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0))) 18.041 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 18.041 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) in k 18.041 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0))) in k 18.041 * [taylor]: Taking taylor expansion of 0.5 in k 18.041 * [backup-simplify]: Simplify 0.5 into 0.5 18.041 * [taylor]: Taking taylor expansion of (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)) in k 18.041 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k 18.041 * [taylor]: Taking taylor expansion of (log -1) in k 18.041 * [taylor]: Taking taylor expansion of -1 in k 18.041 * [backup-simplify]: Simplify -1 into -1 18.041 * [backup-simplify]: Simplify (log -1) into (log -1) 18.041 * [taylor]: Taking taylor expansion of (log n) in k 18.041 * [taylor]: Taking taylor expansion of n in k 18.042 * [backup-simplify]: Simplify n into n 18.042 * [backup-simplify]: Simplify (log n) into (log n) 18.042 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 18.042 * [taylor]: Taking taylor expansion of (/ 1 k) in k 18.042 * [taylor]: Taking taylor expansion of k in k 18.042 * [backup-simplify]: Simplify 0 into 0 18.042 * [backup-simplify]: Simplify 1 into 1 18.042 * [backup-simplify]: Simplify (/ 1 1) into 1 18.042 * [taylor]: Taking taylor expansion of 1.0 in k 18.042 * [backup-simplify]: Simplify 1.0 into 1.0 18.042 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 18.043 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n)) 18.043 * [backup-simplify]: Simplify (+ 1 0) into 1 18.044 * [backup-simplify]: Simplify (* (- (log -1) (log n)) 1) into (- (log -1) (log n)) 18.044 * [backup-simplify]: Simplify (* 0.5 (- (log -1) (log n))) into (* 0.5 (- (log -1) (log n))) 18.045 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 18.045 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 18.052 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 18.053 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 18.054 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 18.054 * [backup-simplify]: Simplify (+ 0 0) into 0 18.054 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 18.055 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 18.055 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log -1) (log n)))) into 0 18.056 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 18.056 * [taylor]: Taking taylor expansion of 0 in k 18.056 * [backup-simplify]: Simplify 0 into 0 18.056 * [backup-simplify]: Simplify 0 into 0 18.056 * [backup-simplify]: Simplify 0 into 0 18.057 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 18.058 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0 18.058 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 18.059 * [backup-simplify]: Simplify (+ 0 0) into 0 18.059 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 18.060 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 18.060 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0 18.061 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 18.061 * [taylor]: Taking taylor expansion of 0 in k 18.061 * [backup-simplify]: Simplify 0 into 0 18.061 * [backup-simplify]: Simplify 0 into 0 18.062 * [backup-simplify]: Simplify 0 into 0 18.062 * [backup-simplify]: Simplify 0 into 0 18.062 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 18.065 * [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 18.065 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 18.066 * [backup-simplify]: Simplify (+ 0 0) into 0 18.066 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 18.067 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 18.068 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -1) (log n)))))) into 0 18.069 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 18.069 * [taylor]: Taking taylor expansion of 0 in k 18.069 * [backup-simplify]: Simplify 0 into 0 18.069 * [backup-simplify]: Simplify 0 into 0 18.070 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log (/ -1 n))) (- 1.0 k)))) 18.070 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2 2 1) 18.070 * [backup-simplify]: Simplify (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) 18.070 * [approximate]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in (k) around 0 18.071 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in k 18.071 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI)))) in k 18.071 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI))) in k 18.071 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 18.071 * [taylor]: Taking taylor expansion of 0.5 in k 18.071 * [backup-simplify]: Simplify 0.5 into 0.5 18.071 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 18.071 * [taylor]: Taking taylor expansion of 1.0 in k 18.071 * [backup-simplify]: Simplify 1.0 into 1.0 18.071 * [taylor]: Taking taylor expansion of k in k 18.071 * [backup-simplify]: Simplify 0 into 0 18.071 * [backup-simplify]: Simplify 1 into 1 18.071 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 18.071 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 18.071 * [taylor]: Taking taylor expansion of 2.0 in k 18.071 * [backup-simplify]: Simplify 2.0 into 2.0 18.071 * [taylor]: Taking taylor expansion of PI in k 18.071 * [backup-simplify]: Simplify PI into PI 18.071 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 18.072 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 18.072 * [backup-simplify]: Simplify (- 0) into 0 18.072 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 18.073 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 18.074 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 18.075 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 PI)))) into (pow (* 2.0 PI) 0.5) 18.075 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in k 18.075 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI)))) in k 18.075 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI))) in k 18.075 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 18.075 * [taylor]: Taking taylor expansion of 0.5 in k 18.075 * [backup-simplify]: Simplify 0.5 into 0.5 18.075 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 18.075 * [taylor]: Taking taylor expansion of 1.0 in k 18.076 * [backup-simplify]: Simplify 1.0 into 1.0 18.076 * [taylor]: Taking taylor expansion of k in k 18.076 * [backup-simplify]: Simplify 0 into 0 18.076 * [backup-simplify]: Simplify 1 into 1 18.076 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 18.076 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 18.076 * [taylor]: Taking taylor expansion of 2.0 in k 18.076 * [backup-simplify]: Simplify 2.0 into 2.0 18.076 * [taylor]: Taking taylor expansion of PI in k 18.076 * [backup-simplify]: Simplify PI into PI 18.076 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 18.077 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 18.077 * [backup-simplify]: Simplify (- 0) into 0 18.077 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 18.077 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 18.079 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 18.080 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 PI)))) into (pow (* 2.0 PI) 0.5) 18.082 * [backup-simplify]: Simplify (pow (* 2.0 PI) 0.5) into (pow (* 2.0 PI) 0.5) 18.083 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 18.085 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 18.085 * [backup-simplify]: Simplify (- 1) into -1 18.086 * [backup-simplify]: Simplify (+ 0 -1) into -1 18.087 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 18.091 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 PI)))) into (- (* 0.5 (log (* 2.0 PI)))) 18.103 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 PI)))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 1) 1)))) into (* -0.5 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) 18.110 * [backup-simplify]: Simplify (* -0.5 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) into (* -0.5 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (log (* 2.0 PI)))) 18.111 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 18.113 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 18.113 * [backup-simplify]: Simplify (- 0) into 0 18.113 * [backup-simplify]: Simplify (+ 0 0) into 0 18.114 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 18.115 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 PI))))) into 0 18.124 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 PI)))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) 18.130 * [backup-simplify]: Simplify (* 0.125 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) into (* 0.125 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) 18.140 * [backup-simplify]: Simplify (+ (* (* 0.125 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) (pow k 2)) (+ (* (* -0.5 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (log (* 2.0 PI)))) k) (pow (* 2.0 PI) 0.5))) into (- (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (pow (* 2.0 PI) 0.5)) (* 0.5 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (log (* 2.0 PI)) k)))) 18.141 * [backup-simplify]: Simplify (pow (* 2.0 PI) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) 18.141 * [approximate]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in (k) around 0 18.141 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in k 18.141 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) in k 18.141 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI))) in k 18.141 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 18.141 * [taylor]: Taking taylor expansion of 0.5 in k 18.141 * [backup-simplify]: Simplify 0.5 into 0.5 18.141 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 18.141 * [taylor]: Taking taylor expansion of 1.0 in k 18.141 * [backup-simplify]: Simplify 1.0 into 1.0 18.141 * [taylor]: Taking taylor expansion of (/ 1 k) in k 18.141 * [taylor]: Taking taylor expansion of k in k 18.141 * [backup-simplify]: Simplify 0 into 0 18.141 * [backup-simplify]: Simplify 1 into 1 18.141 * [backup-simplify]: Simplify (/ 1 1) into 1 18.141 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 18.142 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 18.142 * [taylor]: Taking taylor expansion of 2.0 in k 18.142 * [backup-simplify]: Simplify 2.0 into 2.0 18.142 * [taylor]: Taking taylor expansion of PI in k 18.142 * [backup-simplify]: Simplify PI into PI 18.142 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 18.143 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 18.143 * [backup-simplify]: Simplify (- 1) into -1 18.143 * [backup-simplify]: Simplify (+ 0 -1) into -1 18.143 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 18.144 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 PI))) into (* -0.5 (log (* 2.0 PI))) 18.145 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) 18.145 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in k 18.145 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) in k 18.145 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI))) in k 18.145 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 18.145 * [taylor]: Taking taylor expansion of 0.5 in k 18.145 * [backup-simplify]: Simplify 0.5 into 0.5 18.145 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 18.145 * [taylor]: Taking taylor expansion of 1.0 in k 18.145 * [backup-simplify]: Simplify 1.0 into 1.0 18.145 * [taylor]: Taking taylor expansion of (/ 1 k) in k 18.145 * [taylor]: Taking taylor expansion of k in k 18.145 * [backup-simplify]: Simplify 0 into 0 18.145 * [backup-simplify]: Simplify 1 into 1 18.146 * [backup-simplify]: Simplify (/ 1 1) into 1 18.146 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 18.146 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 18.146 * [taylor]: Taking taylor expansion of 2.0 in k 18.146 * [backup-simplify]: Simplify 2.0 into 2.0 18.146 * [taylor]: Taking taylor expansion of PI in k 18.146 * [backup-simplify]: Simplify PI into PI 18.146 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 18.147 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 18.147 * [backup-simplify]: Simplify (- 1) into -1 18.147 * [backup-simplify]: Simplify (+ 0 -1) into -1 18.148 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 18.149 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 PI))) into (* -0.5 (log (* 2.0 PI))) 18.149 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) 18.150 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) 18.150 * [backup-simplify]: Simplify 0 into 0 18.150 * [backup-simplify]: Simplify 0 into 0 18.150 * [backup-simplify]: Simplify 0 into 0 18.150 * [backup-simplify]: Simplify 0 into 0 18.150 * [backup-simplify]: Simplify 0 into 0 18.150 * [backup-simplify]: Simplify 0 into 0 18.151 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (log (* 2.0 PI))))) into (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) 18.152 * [backup-simplify]: Simplify (pow (* 2.0 PI) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) 18.152 * [approximate]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in (k) around 0 18.152 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in k 18.152 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) in k 18.152 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI))) in k 18.152 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 18.152 * [taylor]: Taking taylor expansion of 0.5 in k 18.152 * [backup-simplify]: Simplify 0.5 into 0.5 18.152 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 18.152 * [taylor]: Taking taylor expansion of (/ 1 k) in k 18.152 * [taylor]: Taking taylor expansion of k in k 18.152 * [backup-simplify]: Simplify 0 into 0 18.152 * [backup-simplify]: Simplify 1 into 1 18.152 * [backup-simplify]: Simplify (/ 1 1) into 1 18.152 * [taylor]: Taking taylor expansion of 1.0 in k 18.152 * [backup-simplify]: Simplify 1.0 into 1.0 18.152 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 18.152 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 18.152 * [taylor]: Taking taylor expansion of 2.0 in k 18.152 * [backup-simplify]: Simplify 2.0 into 2.0 18.152 * [taylor]: Taking taylor expansion of PI in k 18.152 * [backup-simplify]: Simplify PI into PI 18.153 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 18.153 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 18.154 * [backup-simplify]: Simplify (+ 1 0) into 1 18.160 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 18.162 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 18.163 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 18.163 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in k 18.164 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) in k 18.164 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI))) in k 18.164 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 18.164 * [taylor]: Taking taylor expansion of 0.5 in k 18.164 * [backup-simplify]: Simplify 0.5 into 0.5 18.164 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 18.164 * [taylor]: Taking taylor expansion of (/ 1 k) in k 18.164 * [taylor]: Taking taylor expansion of k in k 18.164 * [backup-simplify]: Simplify 0 into 0 18.164 * [backup-simplify]: Simplify 1 into 1 18.164 * [backup-simplify]: Simplify (/ 1 1) into 1 18.164 * [taylor]: Taking taylor expansion of 1.0 in k 18.164 * [backup-simplify]: Simplify 1.0 into 1.0 18.164 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 18.164 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 18.164 * [taylor]: Taking taylor expansion of 2.0 in k 18.164 * [backup-simplify]: Simplify 2.0 into 2.0 18.164 * [taylor]: Taking taylor expansion of PI in k 18.165 * [backup-simplify]: Simplify PI into PI 18.165 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 18.166 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 18.167 * [backup-simplify]: Simplify (+ 1 0) into 1 18.167 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 18.169 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 18.170 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 18.172 * [backup-simplify]: Simplify (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 18.172 * [backup-simplify]: Simplify 0 into 0 18.172 * [backup-simplify]: Simplify 0 into 0 18.172 * [backup-simplify]: Simplify 0 into 0 18.172 * [backup-simplify]: Simplify 0 into 0 18.172 * [backup-simplify]: Simplify 0 into 0 18.172 * [backup-simplify]: Simplify 0 into 0 18.173 * [backup-simplify]: Simplify (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) 18.173 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1 2 1) 18.174 * [backup-simplify]: Simplify (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) 18.174 * [approximate]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in (k) around 0 18.174 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in k 18.174 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI)))) in k 18.174 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI))) in k 18.174 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 18.174 * [taylor]: Taking taylor expansion of 0.5 in k 18.174 * [backup-simplify]: Simplify 0.5 into 0.5 18.174 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 18.174 * [taylor]: Taking taylor expansion of 1.0 in k 18.174 * [backup-simplify]: Simplify 1.0 into 1.0 18.174 * [taylor]: Taking taylor expansion of k in k 18.175 * [backup-simplify]: Simplify 0 into 0 18.175 * [backup-simplify]: Simplify 1 into 1 18.175 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 18.175 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 18.175 * [taylor]: Taking taylor expansion of 2.0 in k 18.175 * [backup-simplify]: Simplify 2.0 into 2.0 18.175 * [taylor]: Taking taylor expansion of PI in k 18.175 * [backup-simplify]: Simplify PI into PI 18.175 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 18.176 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 18.177 * [backup-simplify]: Simplify (- 0) into 0 18.177 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 18.178 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 18.180 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 18.182 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 PI)))) into (pow (* 2.0 PI) 0.5) 18.182 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in k 18.183 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI)))) in k 18.183 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI))) in k 18.183 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 18.183 * [taylor]: Taking taylor expansion of 0.5 in k 18.183 * [backup-simplify]: Simplify 0.5 into 0.5 18.183 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 18.183 * [taylor]: Taking taylor expansion of 1.0 in k 18.183 * [backup-simplify]: Simplify 1.0 into 1.0 18.183 * [taylor]: Taking taylor expansion of k in k 18.183 * [backup-simplify]: Simplify 0 into 0 18.183 * [backup-simplify]: Simplify 1 into 1 18.183 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 18.183 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 18.183 * [taylor]: Taking taylor expansion of 2.0 in k 18.183 * [backup-simplify]: Simplify 2.0 into 2.0 18.183 * [taylor]: Taking taylor expansion of PI in k 18.183 * [backup-simplify]: Simplify PI into PI 18.184 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 18.184 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 18.185 * [backup-simplify]: Simplify (- 0) into 0 18.185 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 18.185 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 18.186 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 18.188 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 PI)))) into (pow (* 2.0 PI) 0.5) 18.189 * [backup-simplify]: Simplify (pow (* 2.0 PI) 0.5) into (pow (* 2.0 PI) 0.5) 18.189 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 18.190 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 18.191 * [backup-simplify]: Simplify (- 1) into -1 18.191 * [backup-simplify]: Simplify (+ 0 -1) into -1 18.192 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 18.194 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 PI)))) into (- (* 0.5 (log (* 2.0 PI)))) 18.202 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 PI)))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 1) 1)))) into (* -0.5 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) 18.206 * [backup-simplify]: Simplify (* -0.5 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) into (* -0.5 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (log (* 2.0 PI)))) 18.207 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 18.209 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 18.209 * [backup-simplify]: Simplify (- 0) into 0 18.209 * [backup-simplify]: Simplify (+ 0 0) into 0 18.210 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 18.211 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 PI))))) into 0 18.221 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 PI)))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) 18.227 * [backup-simplify]: Simplify (* 0.125 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) into (* 0.125 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) 18.242 * [backup-simplify]: Simplify (+ (* (* 0.125 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) (pow k 2)) (+ (* (* -0.5 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (log (* 2.0 PI)))) k) (pow (* 2.0 PI) 0.5))) into (- (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (pow (* 2.0 PI) 0.5)) (* 0.5 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (log (* 2.0 PI)) k)))) 18.243 * [backup-simplify]: Simplify (pow (* 2.0 PI) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) 18.243 * [approximate]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in (k) around 0 18.243 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in k 18.243 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) in k 18.243 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI))) in k 18.243 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 18.243 * [taylor]: Taking taylor expansion of 0.5 in k 18.244 * [backup-simplify]: Simplify 0.5 into 0.5 18.244 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 18.244 * [taylor]: Taking taylor expansion of 1.0 in k 18.244 * [backup-simplify]: Simplify 1.0 into 1.0 18.244 * [taylor]: Taking taylor expansion of (/ 1 k) in k 18.244 * [taylor]: Taking taylor expansion of k in k 18.244 * [backup-simplify]: Simplify 0 into 0 18.244 * [backup-simplify]: Simplify 1 into 1 18.244 * [backup-simplify]: Simplify (/ 1 1) into 1 18.244 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 18.244 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 18.244 * [taylor]: Taking taylor expansion of 2.0 in k 18.244 * [backup-simplify]: Simplify 2.0 into 2.0 18.244 * [taylor]: Taking taylor expansion of PI in k 18.244 * [backup-simplify]: Simplify PI into PI 18.245 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 18.246 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 18.246 * [backup-simplify]: Simplify (- 1) into -1 18.247 * [backup-simplify]: Simplify (+ 0 -1) into -1 18.247 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 18.249 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 PI))) into (* -0.5 (log (* 2.0 PI))) 18.250 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) 18.250 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in k 18.251 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) in k 18.251 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI))) in k 18.251 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 18.251 * [taylor]: Taking taylor expansion of 0.5 in k 18.251 * [backup-simplify]: Simplify 0.5 into 0.5 18.251 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 18.251 * [taylor]: Taking taylor expansion of 1.0 in k 18.251 * [backup-simplify]: Simplify 1.0 into 1.0 18.251 * [taylor]: Taking taylor expansion of (/ 1 k) in k 18.251 * [taylor]: Taking taylor expansion of k in k 18.251 * [backup-simplify]: Simplify 0 into 0 18.251 * [backup-simplify]: Simplify 1 into 1 18.251 * [backup-simplify]: Simplify (/ 1 1) into 1 18.251 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 18.251 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 18.251 * [taylor]: Taking taylor expansion of 2.0 in k 18.251 * [backup-simplify]: Simplify 2.0 into 2.0 18.251 * [taylor]: Taking taylor expansion of PI in k 18.251 * [backup-simplify]: Simplify PI into PI 18.252 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 18.253 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 18.253 * [backup-simplify]: Simplify (- 1) into -1 18.254 * [backup-simplify]: Simplify (+ 0 -1) into -1 18.254 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 18.256 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 PI))) into (* -0.5 (log (* 2.0 PI))) 18.257 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) 18.259 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) 18.259 * [backup-simplify]: Simplify 0 into 0 18.259 * [backup-simplify]: Simplify 0 into 0 18.259 * [backup-simplify]: Simplify 0 into 0 18.259 * [backup-simplify]: Simplify 0 into 0 18.259 * [backup-simplify]: Simplify 0 into 0 18.259 * [backup-simplify]: Simplify 0 into 0 18.260 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (log (* 2.0 PI))))) into (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) 18.261 * [backup-simplify]: Simplify (pow (* 2.0 PI) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) 18.261 * [approximate]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in (k) around 0 18.261 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in k 18.261 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) in k 18.261 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI))) in k 18.261 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 18.261 * [taylor]: Taking taylor expansion of 0.5 in k 18.261 * [backup-simplify]: Simplify 0.5 into 0.5 18.261 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 18.261 * [taylor]: Taking taylor expansion of (/ 1 k) in k 18.261 * [taylor]: Taking taylor expansion of k in k 18.261 * [backup-simplify]: Simplify 0 into 0 18.261 * [backup-simplify]: Simplify 1 into 1 18.262 * [backup-simplify]: Simplify (/ 1 1) into 1 18.262 * [taylor]: Taking taylor expansion of 1.0 in k 18.262 * [backup-simplify]: Simplify 1.0 into 1.0 18.262 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 18.262 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 18.262 * [taylor]: Taking taylor expansion of 2.0 in k 18.262 * [backup-simplify]: Simplify 2.0 into 2.0 18.262 * [taylor]: Taking taylor expansion of PI in k 18.262 * [backup-simplify]: Simplify PI into PI 18.263 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 18.264 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 18.264 * [backup-simplify]: Simplify (+ 1 0) into 1 18.264 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 18.266 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 18.267 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 18.268 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in k 18.268 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) in k 18.268 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI))) in k 18.268 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 18.268 * [taylor]: Taking taylor expansion of 0.5 in k 18.268 * [backup-simplify]: Simplify 0.5 into 0.5 18.268 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 18.268 * [taylor]: Taking taylor expansion of (/ 1 k) in k 18.268 * [taylor]: Taking taylor expansion of k in k 18.268 * [backup-simplify]: Simplify 0 into 0 18.268 * [backup-simplify]: Simplify 1 into 1 18.268 * [backup-simplify]: Simplify (/ 1 1) into 1 18.268 * [taylor]: Taking taylor expansion of 1.0 in k 18.268 * [backup-simplify]: Simplify 1.0 into 1.0 18.268 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 18.268 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 18.268 * [taylor]: Taking taylor expansion of 2.0 in k 18.268 * [backup-simplify]: Simplify 2.0 into 2.0 18.268 * [taylor]: Taking taylor expansion of PI in k 18.269 * [backup-simplify]: Simplify PI into PI 18.269 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 18.270 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 18.271 * [backup-simplify]: Simplify (+ 1 0) into 1 18.271 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 18.273 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 18.274 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 18.275 * [backup-simplify]: Simplify (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 18.275 * [backup-simplify]: Simplify 0 into 0 18.275 * [backup-simplify]: Simplify 0 into 0 18.275 * [backup-simplify]: Simplify 0 into 0 18.275 * [backup-simplify]: Simplify 0 into 0 18.276 * [backup-simplify]: Simplify 0 into 0 18.276 * [backup-simplify]: Simplify 0 into 0 18.277 * [backup-simplify]: Simplify (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) 18.277 * * * * [progress]: [ 4 / 4 ] generating series at (2 1) 18.279 * [backup-simplify]: Simplify (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))) into (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 PI) (* 0.5 (- 1.0 k)))) (sqrt (/ 1 k))) 18.279 * [approximate]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 PI) (* 0.5 (- 1.0 k)))) (sqrt (/ 1 k))) in (k) around 0 18.279 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 PI) (* 0.5 (- 1.0 k)))) (sqrt (/ 1 k))) in k 18.279 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* 2.0 PI) (* 0.5 (- 1.0 k)))) in k 18.279 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 18.279 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 18.279 * [taylor]: Taking taylor expansion of 1.0 in k 18.279 * [backup-simplify]: Simplify 1.0 into 1.0 18.287 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 18.288 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 18.288 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in k 18.288 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI)))) in k 18.288 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI))) in k 18.288 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 18.288 * [taylor]: Taking taylor expansion of 0.5 in k 18.288 * [backup-simplify]: Simplify 0.5 into 0.5 18.288 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 18.288 * [taylor]: Taking taylor expansion of 1.0 in k 18.288 * [backup-simplify]: Simplify 1.0 into 1.0 18.288 * [taylor]: Taking taylor expansion of k in k 18.288 * [backup-simplify]: Simplify 0 into 0 18.288 * [backup-simplify]: Simplify 1 into 1 18.288 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 18.288 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 18.288 * [taylor]: Taking taylor expansion of 2.0 in k 18.288 * [backup-simplify]: Simplify 2.0 into 2.0 18.288 * [taylor]: Taking taylor expansion of PI in k 18.288 * [backup-simplify]: Simplify PI into PI 18.289 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 18.290 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 18.290 * [backup-simplify]: Simplify (- 0) into 0 18.291 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 18.291 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 18.293 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 18.296 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 PI)))) into (pow (* 2.0 PI) 0.5) 18.296 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 18.296 * [taylor]: Taking taylor expansion of (/ 1 k) in k 18.296 * [taylor]: Taking taylor expansion of k in k 18.296 * [backup-simplify]: Simplify 0 into 0 18.296 * [backup-simplify]: Simplify 1 into 1 18.296 * [backup-simplify]: Simplify (/ 1 1) into 1 18.297 * [backup-simplify]: Simplify (sqrt 0) into 0 18.298 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 18.298 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 PI) (* 0.5 (- 1.0 k)))) (sqrt (/ 1 k))) in k 18.298 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* 2.0 PI) (* 0.5 (- 1.0 k)))) in k 18.298 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 18.298 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 18.299 * [taylor]: Taking taylor expansion of 1.0 in k 18.299 * [backup-simplify]: Simplify 1.0 into 1.0 18.299 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 18.300 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 18.300 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in k 18.300 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI)))) in k 18.300 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI))) in k 18.300 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 18.300 * [taylor]: Taking taylor expansion of 0.5 in k 18.300 * [backup-simplify]: Simplify 0.5 into 0.5 18.300 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 18.300 * [taylor]: Taking taylor expansion of 1.0 in k 18.300 * [backup-simplify]: Simplify 1.0 into 1.0 18.300 * [taylor]: Taking taylor expansion of k in k 18.300 * [backup-simplify]: Simplify 0 into 0 18.300 * [backup-simplify]: Simplify 1 into 1 18.300 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 18.300 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 18.300 * [taylor]: Taking taylor expansion of 2.0 in k 18.300 * [backup-simplify]: Simplify 2.0 into 2.0 18.300 * [taylor]: Taking taylor expansion of PI in k 18.300 * [backup-simplify]: Simplify PI into PI 18.301 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 18.302 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 18.302 * [backup-simplify]: Simplify (- 0) into 0 18.303 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 18.303 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 18.305 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 18.308 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 PI)))) into (pow (* 2.0 PI) 0.5) 18.308 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 18.308 * [taylor]: Taking taylor expansion of (/ 1 k) in k 18.308 * [taylor]: Taking taylor expansion of k in k 18.308 * [backup-simplify]: Simplify 0 into 0 18.308 * [backup-simplify]: Simplify 1 into 1 18.309 * [backup-simplify]: Simplify (/ 1 1) into 1 18.309 * [backup-simplify]: Simplify (sqrt 0) into 0 18.310 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 18.312 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 18.314 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (pow (* 2.0 PI) 0.5)) into (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (sqrt 1.0) 2)) 18.315 * [backup-simplify]: Simplify (* (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (sqrt 1.0) 2)) 0) into 0 18.315 * [backup-simplify]: Simplify 0 into 0 18.315 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 18.316 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 18.317 * [backup-simplify]: Simplify (- 1) into -1 18.317 * [backup-simplify]: Simplify (+ 0 -1) into -1 18.318 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 18.320 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 PI)))) into (- (* 0.5 (log (* 2.0 PI)))) 18.328 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 PI)))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 1) 1)))) into (* -0.5 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) 18.328 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0 18.338 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) (* -0.5 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI))))) (* 0 (pow (* 2.0 PI) 0.5))) into (- (* 0.5 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (log (* 2.0 PI)))))) 18.346 * [backup-simplify]: Simplify (+ (* (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (sqrt 1.0) 2)) +nan.0) (* (- (* 0.5 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (log (* 2.0 PI)))))) 0)) into (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (pow (sqrt 1.0) 2)))) 18.352 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (pow (sqrt 1.0) 2)))) into (- (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (sqrt 1.0) 2)))) 18.352 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 18.354 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 18.355 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 18.357 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 18.357 * [backup-simplify]: Simplify (- 0) into 0 18.358 * [backup-simplify]: Simplify (+ 0 0) into 0 18.358 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 18.360 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 PI))))) into 0 18.371 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 PI)))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) 18.372 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0 18.373 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0 18.395 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) (* 0.125 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 2)))) (+ (* 0 (* -0.5 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI))))) (* 0 (pow (* 2.0 PI) 0.5)))) into (* 0.125 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (pow (log (* 2.0 PI)) 2)))) 18.429 * [backup-simplify]: Simplify (+ (* (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (sqrt 1.0) 2)) +nan.0) (+ (* (- (* 0.5 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (log (* 2.0 PI)))))) +nan.0) (* (* 0.125 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (pow (log (* 2.0 PI)) 2)))) 0))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (pow (sqrt 1.0) 2))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (log (* 2.0 PI)))))))) 18.445 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (pow (sqrt 1.0) 2))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (log (* 2.0 PI)))))))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (sqrt 1.0) 2))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (log (* 2.0 PI)))))))) 18.446 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 18.448 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 18.449 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 18.453 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 18.454 * [backup-simplify]: Simplify (- 0) into 0 18.454 * [backup-simplify]: Simplify (+ 0 0) into 0 18.455 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 18.458 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 PI)))))) into 0 18.477 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 PI)))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 3) 6)) (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 3))) 18.479 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0 18.480 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0 18.505 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) (* -0.020833333333333332 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 3)))) (+ (* 0 (* 0.125 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 2)))) (+ (* 0 (* -0.5 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI))))) (* 0 (pow (* 2.0 PI) 0.5))))) into (- (* 0.020833333333333332 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (pow (log (* 2.0 PI)) 3))))) 18.582 * [backup-simplify]: Simplify (+ (* (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (sqrt 1.0) 2)) +nan.0) (+ (* (- (* 0.5 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (log (* 2.0 PI)))))) +nan.0) (+ (* (* 0.125 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (pow (log (* 2.0 PI)) 2)))) +nan.0) (* (- (* 0.020833333333333332 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (pow (log (* 2.0 PI)) 3))))) 0)))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (pow (sqrt 1.0) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (pow (log (* 2.0 PI)) 2)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (log (* 2.0 PI)))))))))) 18.630 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (pow (sqrt 1.0) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (pow (log (* 2.0 PI)) 2)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (log (* 2.0 PI)))))))))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (sqrt 1.0) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (pow (log (* 2.0 PI)) 2)))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (log (* 2.0 PI)))))))))) 18.699 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (sqrt 1.0) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (pow (log (* 2.0 PI)) 2)))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (log (* 2.0 PI)))))))))) (pow k 2)) (+ (* (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (sqrt 1.0) 2))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (log (* 2.0 PI)))))))) k) (- (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (sqrt 1.0) 2)))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (* (log (* 2.0 PI)) k)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (* (pow (log (* 2.0 PI)) 2) (pow k 2))))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (pow (sqrt 1.0) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (* (log (* 2.0 PI)) (pow k 2))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (pow (sqrt 1.0) 2) k)))))))))))))) 18.700 * [backup-simplify]: Simplify (* (* (sqrt (/ 1.0 (sqrt (/ 1 k)))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 (/ 1 k)) 2.0)))) (* (sqrt (/ 1.0 (sqrt (/ 1 k)))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 (/ 1 k)) 2.0))))) into (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k))))) (sqrt k)) 18.700 * [approximate]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k))))) (sqrt k)) in (k) around 0 18.700 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k))))) (sqrt k)) in k 18.700 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k))))) in k 18.700 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 18.700 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 18.700 * [taylor]: Taking taylor expansion of 1.0 in k 18.700 * [backup-simplify]: Simplify 1.0 into 1.0 18.701 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 18.702 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 18.702 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in k 18.702 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) in k 18.702 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI))) in k 18.702 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 18.702 * [taylor]: Taking taylor expansion of 0.5 in k 18.702 * [backup-simplify]: Simplify 0.5 into 0.5 18.702 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 18.702 * [taylor]: Taking taylor expansion of 1.0 in k 18.702 * [backup-simplify]: Simplify 1.0 into 1.0 18.702 * [taylor]: Taking taylor expansion of (/ 1 k) in k 18.702 * [taylor]: Taking taylor expansion of k in k 18.702 * [backup-simplify]: Simplify 0 into 0 18.702 * [backup-simplify]: Simplify 1 into 1 18.702 * [backup-simplify]: Simplify (/ 1 1) into 1 18.702 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 18.702 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 18.703 * [taylor]: Taking taylor expansion of 2.0 in k 18.703 * [backup-simplify]: Simplify 2.0 into 2.0 18.703 * [taylor]: Taking taylor expansion of PI in k 18.703 * [backup-simplify]: Simplify PI into PI 18.703 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 18.704 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 18.705 * [backup-simplify]: Simplify (- 1) into -1 18.705 * [backup-simplify]: Simplify (+ 0 -1) into -1 18.705 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 18.707 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 PI))) into (* -0.5 (log (* 2.0 PI))) 18.708 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) 18.708 * [taylor]: Taking taylor expansion of (sqrt k) in k 18.708 * [taylor]: Taking taylor expansion of k in k 18.708 * [backup-simplify]: Simplify 0 into 0 18.708 * [backup-simplify]: Simplify 1 into 1 18.709 * [backup-simplify]: Simplify (sqrt 0) into 0 18.710 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 18.710 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k))))) (sqrt k)) in k 18.711 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k))))) in k 18.711 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 18.711 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 18.711 * [taylor]: Taking taylor expansion of 1.0 in k 18.711 * [backup-simplify]: Simplify 1.0 into 1.0 18.711 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 18.712 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 18.712 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in k 18.712 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) in k 18.712 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI))) in k 18.712 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 18.712 * [taylor]: Taking taylor expansion of 0.5 in k 18.712 * [backup-simplify]: Simplify 0.5 into 0.5 18.712 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 18.712 * [taylor]: Taking taylor expansion of 1.0 in k 18.712 * [backup-simplify]: Simplify 1.0 into 1.0 18.712 * [taylor]: Taking taylor expansion of (/ 1 k) in k 18.712 * [taylor]: Taking taylor expansion of k in k 18.712 * [backup-simplify]: Simplify 0 into 0 18.712 * [backup-simplify]: Simplify 1 into 1 18.713 * [backup-simplify]: Simplify (/ 1 1) into 1 18.713 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 18.713 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 18.713 * [taylor]: Taking taylor expansion of 2.0 in k 18.713 * [backup-simplify]: Simplify 2.0 into 2.0 18.713 * [taylor]: Taking taylor expansion of PI in k 18.713 * [backup-simplify]: Simplify PI into PI 18.714 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 18.715 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 18.715 * [backup-simplify]: Simplify (- 1) into -1 18.716 * [backup-simplify]: Simplify (+ 0 -1) into -1 18.716 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 18.718 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 PI))) into (* -0.5 (log (* 2.0 PI))) 18.720 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) 18.720 * [taylor]: Taking taylor expansion of (sqrt k) in k 18.720 * [taylor]: Taking taylor expansion of k in k 18.720 * [backup-simplify]: Simplify 0 into 0 18.720 * [backup-simplify]: Simplify 1 into 1 18.721 * [backup-simplify]: Simplify (sqrt 0) into 0 18.723 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 18.724 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 18.726 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))) 18.729 * [backup-simplify]: Simplify (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))) 0) into 0 18.729 * [backup-simplify]: Simplify 0 into 0 18.730 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0 18.732 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))) into 0 18.736 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))))) 18.739 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))))) 18.742 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 18.743 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0 18.744 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0 18.747 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))))) into 0 18.750 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))))) 18.752 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))))) 18.756 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 18.758 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0 18.759 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0 18.762 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))))) into 0 18.765 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))))) 18.767 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))))) 18.775 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (log (* 2.0 PI)))))))) (pow (/ 1 k) 3)) (+ (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (log (* 2.0 PI)))))))) (pow (/ 1 k) 2)) (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (log (* 2.0 PI)))))))) (/ 1 k)))) into (- (+ (* +nan.0 (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k))))) (pow k 3))) (- (+ (* +nan.0 (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k))))) k)) (- (* +nan.0 (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k))))) (pow k 2)))))))) 18.777 * [backup-simplify]: Simplify (* (* (sqrt (/ 1.0 (sqrt (/ 1 (- k))))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 (/ 1 (- k))) 2.0)))) (* (sqrt (/ 1.0 (sqrt (/ 1 (- k))))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 (/ 1 (- k))) 2.0))))) into (/ (* (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) (pow (sqrt 1.0) 2)) (sqrt (/ -1 k))) 18.777 * [approximate]: Taking taylor expansion of (/ (* (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) (pow (sqrt 1.0) 2)) (sqrt (/ -1 k))) in (k) around 0 18.777 * [taylor]: Taking taylor expansion of (/ (* (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) (pow (sqrt 1.0) 2)) (sqrt (/ -1 k))) in k 18.777 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) (pow (sqrt 1.0) 2)) in k 18.778 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in k 18.778 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) in k 18.778 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI))) in k 18.778 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 18.778 * [taylor]: Taking taylor expansion of 0.5 in k 18.778 * [backup-simplify]: Simplify 0.5 into 0.5 18.778 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 18.778 * [taylor]: Taking taylor expansion of (/ 1 k) in k 18.778 * [taylor]: Taking taylor expansion of k in k 18.778 * [backup-simplify]: Simplify 0 into 0 18.778 * [backup-simplify]: Simplify 1 into 1 18.778 * [backup-simplify]: Simplify (/ 1 1) into 1 18.778 * [taylor]: Taking taylor expansion of 1.0 in k 18.778 * [backup-simplify]: Simplify 1.0 into 1.0 18.778 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 18.778 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 18.779 * [taylor]: Taking taylor expansion of 2.0 in k 18.779 * [backup-simplify]: Simplify 2.0 into 2.0 18.779 * [taylor]: Taking taylor expansion of PI in k 18.779 * [backup-simplify]: Simplify PI into PI 18.780 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 18.781 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 18.781 * [backup-simplify]: Simplify (+ 1 0) into 1 18.782 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 18.784 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 18.785 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 18.785 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 18.785 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 18.785 * [taylor]: Taking taylor expansion of 1.0 in k 18.785 * [backup-simplify]: Simplify 1.0 into 1.0 18.786 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 18.786 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 18.786 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 18.786 * [taylor]: Taking taylor expansion of (/ -1 k) in k 18.786 * [taylor]: Taking taylor expansion of -1 in k 18.787 * [backup-simplify]: Simplify -1 into -1 18.787 * [taylor]: Taking taylor expansion of k in k 18.787 * [backup-simplify]: Simplify 0 into 0 18.787 * [backup-simplify]: Simplify 1 into 1 18.787 * [backup-simplify]: Simplify (/ -1 1) into -1 18.787 * [backup-simplify]: Simplify (sqrt 0) into 0 18.789 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 18.790 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 18.792 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) (pow (sqrt 1.0) 2)) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))) 18.795 * [backup-simplify]: Simplify (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))) +nan.0) into (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) 18.795 * [taylor]: Taking taylor expansion of (/ (* (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) (pow (sqrt 1.0) 2)) (sqrt (/ -1 k))) in k 18.795 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) (pow (sqrt 1.0) 2)) in k 18.795 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in k 18.795 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) in k 18.795 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI))) in k 18.795 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 18.795 * [taylor]: Taking taylor expansion of 0.5 in k 18.795 * [backup-simplify]: Simplify 0.5 into 0.5 18.795 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 18.795 * [taylor]: Taking taylor expansion of (/ 1 k) in k 18.795 * [taylor]: Taking taylor expansion of k in k 18.795 * [backup-simplify]: Simplify 0 into 0 18.795 * [backup-simplify]: Simplify 1 into 1 18.796 * [backup-simplify]: Simplify (/ 1 1) into 1 18.796 * [taylor]: Taking taylor expansion of 1.0 in k 18.796 * [backup-simplify]: Simplify 1.0 into 1.0 18.796 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 18.796 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 18.796 * [taylor]: Taking taylor expansion of 2.0 in k 18.796 * [backup-simplify]: Simplify 2.0 into 2.0 18.796 * [taylor]: Taking taylor expansion of PI in k 18.796 * [backup-simplify]: Simplify PI into PI 18.796 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 18.797 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 18.798 * [backup-simplify]: Simplify (+ 1 0) into 1 18.798 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 18.800 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 18.801 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 18.801 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 18.802 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 18.802 * [taylor]: Taking taylor expansion of 1.0 in k 18.802 * [backup-simplify]: Simplify 1.0 into 1.0 18.802 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 18.803 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 18.803 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 18.803 * [taylor]: Taking taylor expansion of (/ -1 k) in k 18.803 * [taylor]: Taking taylor expansion of -1 in k 18.803 * [backup-simplify]: Simplify -1 into -1 18.803 * [taylor]: Taking taylor expansion of k in k 18.803 * [backup-simplify]: Simplify 0 into 0 18.803 * [backup-simplify]: Simplify 1 into 1 18.803 * [backup-simplify]: Simplify (/ -1 1) into -1 18.804 * [backup-simplify]: Simplify (sqrt 0) into 0 18.811 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 18.812 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 18.813 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) (pow (sqrt 1.0) 2)) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))) 18.814 * [backup-simplify]: Simplify (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))) +nan.0) into (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) 18.816 * [backup-simplify]: Simplify (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) 18.816 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0 18.817 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 0) (* 0 (pow (sqrt 1.0) 2))) into 0 18.818 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 18.820 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 18.822 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))))) 18.823 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))))) 18.824 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0 18.824 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0 18.826 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 0) (+ (* 0 0) (* 0 (pow (sqrt 1.0) 2)))) into 0 18.826 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 18.829 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 18.832 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))))) 18.834 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))))) 18.841 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 (/ 1 (- k))) 1.0))))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 (/ 1 (- k))) 1.0))))))) (/ 1 (- k))) (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 (/ 1 (- k))) 1.0)))))))) into (- (+ (* +nan.0 (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k))))) k)) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))))) (- (* +nan.0 (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k))))) (pow k 2)))))))) 18.841 * * * [progress]: simplifying candidates 18.846 * [simplify]: Simplifying: (expm1 (pow n (/ (- 1.0 k) 2.0))) (log1p (pow n (/ (- 1.0 k) 2.0))) (* (log n) (/ (- 1.0 k) 2.0)) (* (log n) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow n (/ 1.0 2.0)) (pow n (/ k 2.0)) (pow n (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow n (sqrt (/ (- 1.0 k) 2.0))) (pow n (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow n (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow n (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow n (/ (sqrt (- 1.0 k)) 1)) (pow n (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ 1 (sqrt 2.0))) (pow n (/ 1 1)) (pow n (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow n (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow n (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ 1 (sqrt 2.0))) (pow n (/ 1 1)) (pow n 1) (pow n (- 1.0 k)) (pow (* (cbrt n) (cbrt n)) (/ (- 1.0 k) 2.0)) (pow (cbrt n) (/ (- 1.0 k) 2.0)) (pow (sqrt n) (/ (- 1.0 k) 2.0)) (pow (sqrt n) (/ (- 1.0 k) 2.0)) (pow 1 (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow n (/ (- 1.0 k) 2.0))) (exp (pow n (/ (- 1.0 k) 2.0))) (* (cbrt (pow n (/ (- 1.0 k) 2.0))) (cbrt (pow n (/ (- 1.0 k) 2.0)))) (cbrt (pow n (/ (- 1.0 k) 2.0))) (* (* (pow n (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0))) (sqrt (pow n (/ (- 1.0 k) 2.0))) (sqrt (pow n (/ (- 1.0 k) 2.0))) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (log1p (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (+ (log 2.0) (log PI)) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 PI)) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 PI)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ 1.0 2.0)) (pow (* 2.0 PI) (/ k 2.0)) (pow (* 2.0 PI) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* 2.0 PI) (sqrt (/ (- 1.0 k) 2.0))) (pow (* 2.0 PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* 2.0 PI) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 PI) (/ (sqrt (- 1.0 k)) 1)) (pow (* 2.0 PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ 1 (sqrt 2.0))) (pow (* 2.0 PI) (/ 1 1)) (pow (* 2.0 PI) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 PI) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* 2.0 PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ 1 (sqrt 2.0))) (pow (* 2.0 PI) (/ 1 1)) (pow (* 2.0 PI) 1) (pow (* 2.0 PI) (- 1.0 k)) (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)) (log (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (exp (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (log1p (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (+ (log 2.0) (log PI)) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 PI)) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 PI)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 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2.0))))) (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (sqrt 1.0) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))) (* (* (sqrt 1.0) (sqrt (pow (* 2.0 PI) (/ 1.0 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))) (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 PI) (/ 1.0 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))) (* (* (sqrt 1.0) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))) (- (+ (* 0.125 (* (pow (pow n 1.0) 0.5) (* (pow (log n) 2) (pow k 2)))) (pow n 0.5)) (* 0.5 (* (pow (pow n 1.0) 0.5) (* (log n) k)))) (exp (* -0.5 (* (- 1.0 k) (log (/ 1 n))))) (exp (* 0.5 (* (- (log -1) (log (/ -1 n))) (- 1.0 k)))) (- (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (pow (* 2.0 PI) 0.5)) (* 0.5 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (log (* 2.0 PI)) k)))) (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) (- (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (pow (* 2.0 PI) 0.5)) (* 0.5 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (log (* 2.0 PI)) k)))) (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (* (log (* 2.0 PI)) k)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (* (pow (log (* 2.0 PI)) 2) (pow k 2))))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (pow (sqrt 1.0) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (pow (sqrt 1.0) 2) (* (log (* 2.0 PI)) (pow k 2))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (pow (sqrt 1.0) 2) k)))))))))))))) (- (+ (* +nan.0 (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k))))) (pow k 3))) (- (+ (* +nan.0 (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k))))) k)) (- (* +nan.0 (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k))))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k))))) k)) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))))) (- (* +nan.0 (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k))))) (pow k 2)))))))) 18.853 * * [simplify]: iteration 0: 281 enodes 18.962 * * [simplify]: iteration 1: 842 enodes 19.453 * * [simplify]: iteration 2: 3531 enodes 20.402 * * [simplify]: iteration complete: 5001 enodes 20.402 * * [simplify]: Extracting #0: cost 96 inf + 0 20.404 * * [simplify]: Extracting #1: cost 645 inf + 3 20.408 * * [simplify]: Extracting #2: cost 1343 inf + 2380 20.424 * * [simplify]: Extracting #3: cost 1320 inf + 45341 20.455 * * [simplify]: Extracting #4: cost 929 inf + 227402 20.580 * * [simplify]: Extracting #5: cost 379 inf + 451245 20.745 * * [simplify]: Extracting #6: cost 114 inf + 603865 20.922 * * [simplify]: Extracting #7: cost 13 inf + 676939 21.085 * * [simplify]: Extracting #8: cost 0 inf + 686607 21.247 * * [simplify]: Extracting #9: cost 0 inf + 686247 21.382 * * [simplify]: Extracting #10: cost 0 inf + 686207 21.528 * [simplify]: Simplified to: (expm1 (pow n (/ (- 1.0 k) 2.0))) (log1p (pow n (/ (- 1.0 k) 2.0))) (/ (* (log n) (- 1.0 k)) 2.0) (/ (* (log n) (- 1.0 k)) 2.0) (/ (- 1.0 k) 2.0) (pow n (/ 1.0 2.0)) (pow n (/ k 2.0)) (pow n (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow n (sqrt (/ (- 1.0 k) 2.0))) (pow n (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow n (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow n (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow n (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow n (sqrt (- 1.0 k))) (pow n (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ 1 (sqrt 2.0))) n (pow n (/ (/ (+ (sqrt 1.0) (sqrt k)) (cbrt 2.0)) (cbrt 2.0))) (pow n (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow n (+ (sqrt 1.0) (sqrt k))) (pow n (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ 1 (sqrt 2.0))) n n (pow n (- 1.0 k)) (pow (* (cbrt n) (cbrt n)) (/ (- 1.0 k) 2.0)) (pow (cbrt n) (/ (- 1.0 k) 2.0)) (pow (sqrt n) (/ (- 1.0 k) 2.0)) (pow (sqrt n) (/ (- 1.0 k) 2.0)) 1 (pow n (/ (- 1.0 k) 2.0)) (/ (* (log n) (- 1.0 k)) 2.0) (exp (pow n (/ (- 1.0 k) 2.0))) (* (cbrt (pow n (/ (- 1.0 k) 2.0))) (cbrt (pow n (/ (- 1.0 k) 2.0)))) (cbrt (pow n (/ (- 1.0 k) 2.0))) (* (pow n (/ (- 1.0 k) 2.0)) (* (pow n (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))) (sqrt (pow n (/ (- 1.0 k) 2.0))) (sqrt (pow n (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) (* 2 2.0))) (pow n (/ (- 1.0 k) (* 2 2.0))) (expm1 (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (log1p (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (* (log (* PI 2.0)) (/ (- 1.0 k) 2.0)) (* (log (* PI 2.0)) (/ (- 1.0 k) 2.0)) (* (log (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* PI 2.0) (/ 1.0 2.0)) (pow (* PI 2.0) (/ k 2.0)) (pow (* PI 2.0) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* PI 2.0) (sqrt (/ (- 1.0 k) 2.0))) (pow (* PI 2.0) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow (* PI 2.0) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* PI 2.0) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* PI 2.0) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* PI 2.0) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* PI 2.0) (sqrt (- 1.0 k))) (pow (* PI 2.0) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* PI 2.0) (/ 1 (sqrt 2.0))) (* PI 2.0) (pow (* PI 2.0) (/ (/ (+ (sqrt 1.0) (sqrt k)) (cbrt 2.0)) (cbrt 2.0))) (pow (* PI 2.0) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* PI 2.0) (+ (sqrt 1.0) (sqrt k))) (pow (* PI 2.0) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* PI 2.0) (/ 1 (sqrt 2.0))) (* PI 2.0) (* PI 2.0) (exp (* (log (* PI 2.0)) (- 1.0 k))) (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)) (* (log (* PI 2.0)) (/ (- 1.0 k) 2.0)) (exp (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (cbrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (* (* (pow (* PI 2.0) (/ (- 1.0 k) 2.0)) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (sqrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (sqrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (pow (* PI 2.0) (/ (- 1.0 k) (* 2 2.0))) (pow (* PI 2.0) (/ (- 1.0 k) (* 2 2.0))) (expm1 (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (log1p (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (* (log (* PI 2.0)) (/ (- 1.0 k) 2.0)) (* (log (* PI 2.0)) (/ (- 1.0 k) 2.0)) (* (log (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* PI 2.0) (/ 1.0 2.0)) (pow (* PI 2.0) (/ k 2.0)) (pow (* PI 2.0) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* PI 2.0) (sqrt (/ (- 1.0 k) 2.0))) (pow (* PI 2.0) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow (* PI 2.0) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* PI 2.0) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* PI 2.0) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* PI 2.0) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* PI 2.0) (sqrt (- 1.0 k))) (pow (* PI 2.0) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* PI 2.0) (/ 1 (sqrt 2.0))) (* PI 2.0) (pow (* PI 2.0) (/ (/ (+ (sqrt 1.0) (sqrt k)) (cbrt 2.0)) (cbrt 2.0))) (pow (* PI 2.0) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* PI 2.0) (+ (sqrt 1.0) (sqrt k))) (pow (* PI 2.0) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* PI 2.0) (/ 1 (sqrt 2.0))) (* PI 2.0) (* PI 2.0) (exp (* (log (* PI 2.0)) (- 1.0 k))) (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)) (* (log (* PI 2.0)) (/ (- 1.0 k) 2.0)) (exp (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (cbrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (* (* (pow (* PI 2.0) (/ (- 1.0 k) 2.0)) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (sqrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (sqrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (pow (* PI 2.0) (/ (- 1.0 k) (* 2 2.0))) (pow (* PI 2.0) (/ (- 1.0 k) (* 2 2.0))) (expm1 (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))))) (log1p (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))))) 1 2 2 2 2 (* (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))))) (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) 2 2 (fma (log (* PI 2.0)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* PI 2.0)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* PI 2.0)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* PI 2.0)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* PI 2.0)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (exp (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))))) (* (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))))) (* (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))))) (* (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))))) (* (cbrt (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))))) (cbrt (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))))) (cbrt (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))))) (* (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))))) (sqrt (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))))) (sqrt (/ 1.0 (/ (sqrt k) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))))) (* 1.0 (pow (* PI 2.0) (/ 1.0 2.0))) (* (pow (* PI 2.0) (/ k 2.0)) (sqrt k)) (* (* (pow (* PI 2.0) (/ 1.0 2.0)) (sqrt (/ 1.0 (sqrt k)))) (sqrt 1.0)) (* (sqrt (sqrt k)) (pow (* PI 2.0) (/ k 2.0))) (* (* (sqrt (pow (* PI 2.0) (/ 1.0 2.0))) 1.0) (sqrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (* (sqrt (pow (* PI 2.0) (/ k 2.0))) (sqrt k)) (* (* (pow (* PI 2.0) (/ 1.0 2.0)) (sqrt (/ 1.0 (sqrt k)))) (sqrt 1.0)) (* (sqrt (sqrt k)) (pow (* PI 2.0) (/ k 2.0))) (* (/ 1.0 (sqrt k)) (pow (* PI 2.0) (/ 1.0 2.0))) (pow (* PI 2.0) (/ k 2.0)) (* (* (sqrt (pow (* PI 2.0) (/ 1.0 2.0))) (sqrt 1.0)) (* (sqrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (sqrt (/ 1.0 (sqrt k))))) (* (sqrt (sqrt k)) (sqrt (pow (* PI 2.0) (/ k 2.0)))) (* (* (sqrt (pow (* PI 2.0) (/ 1.0 2.0))) 1.0) (sqrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (* (sqrt (pow (* PI 2.0) (/ k 2.0))) (sqrt k)) (* (* (sqrt (pow (* PI 2.0) (/ 1.0 2.0))) (sqrt 1.0)) (* (sqrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (sqrt (/ 1.0 (sqrt k))))) (* (sqrt (sqrt k)) (sqrt (pow (* PI 2.0) (/ k 2.0)))) (* 1.0 (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (sqrt k) (/ 1.0 (sqrt k)) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)) 1 2 2 2 2 (* (/ 1.0 (sqrt k)) (sqrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (* (* (sqrt (pow (* PI 2.0) (/ 1.0 2.0))) (sqrt 1.0)) (* (sqrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (sqrt (/ 1.0 (sqrt k))))) (* (sqrt (pow (* PI 2.0) (/ 1.0 2.0))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0))))) (* (* (pow (* PI 2.0) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt (/ 1.0 (sqrt k)))) (* (* (sqrt (pow (* PI 2.0) (/ 1.0 2.0))) (sqrt 1.0)) (* (sqrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (sqrt (/ 1.0 (sqrt k))))) (* (sqrt (pow (* PI 2.0) (/ 1.0 2.0))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* PI 2.0) (/ (- 1.0 k) 2.0))))) (* (* (pow (* PI 2.0) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt (/ 1.0 (sqrt k)))) (fma (* (pow (pow n 1.0) 0.5) 0.125) (* (* k (log n)) (* k (log n))) (- (pow n 0.5) (* (pow (pow n 1.0) 0.5) (* (* k (log n)) 0.5)))) (exp (* (* (- 1.0 k) -0.5) (- (log n)))) (exp (* (+ (- (log -1) (log -1)) (log n)) (* (- 1.0 k) 0.5))) (- (fma (* 0.125 (* (* k (log (* PI 2.0))) (* k (log (* PI 2.0))))) (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (exp (* 0.5 (log (* PI 2.0))))) (* (* 0.5 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)) (* (log (* PI 2.0)) k))) (exp (* (* 0.5 (log (* PI 2.0))) (- 1.0 k))) (exp (* (* 0.5 (log (* PI 2.0))) (- 1.0 k))) (- (fma (* 0.125 (* (* k (log (* PI 2.0))) (* k (log (* PI 2.0))))) (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (exp (* 0.5 (log (* PI 2.0))))) (* (* 0.5 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)) (* (log (* PI 2.0)) k))) (exp (* (* 0.5 (log (* PI 2.0))) (- 1.0 k))) (exp (* (* 0.5 (log (* PI 2.0))) (- 1.0 k))) (- (fma (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) 1.0) (* (* k k) +nan.0) (fma (* (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) 1.0) (* (log (* PI 2.0)) k)) (- +nan.0) (fma (- +nan.0) (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) 1.0) (fma +nan.0 (fma (* (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) 1.0) (* k k)) (log (* PI 2.0)) (* (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) 1.0) (- k))) (* (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) 1.0) (* (* (* k (log (* PI 2.0))) (* k (log (* PI 2.0)))) +nan.0))))))) (fma +nan.0 (- (* (/ 1.0 (* k k)) (/ (exp (* (* 0.5 (log (* PI 2.0))) (- 1.0 k))) k))) (- (/ (* (* +nan.0 1.0) (exp (* (* 0.5 (log (* PI 2.0))) (- 1.0 k)))) k) (/ (/ (* (* +nan.0 1.0) (exp (* (* 0.5 (log (* PI 2.0))) (- 1.0 k)))) k) k))) (- (+ (- (/ (* (* +nan.0 1.0) (exp (* (* 0.5 (log (* PI 2.0))) (- 1.0 k)))) k) (* (* +nan.0 1.0) (exp (* (* 0.5 (log (* PI 2.0))) (- 1.0 k))))) (/ (/ (* (* +nan.0 1.0) (exp (* (* 0.5 (log (* PI 2.0))) (- 1.0 k)))) k) k))) 21.546 * * * [progress]: adding candidates to table 23.427 * [progress]: [Phase 3 of 3] Extracting. 23.427 * * [regime]: Finding splitpoints for: (# # # # # # # # # #) 23.431 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 23.431 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # # # # #) 23.555 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # #) 23.628 * * * * [regimes]: Trying to branch on n from (# # # # # # # # # #) 23.746 * * * * [regimes]: Trying to branch on k from (# # # # # # # # # #) 23.896 * * * [regime]: Found split indices: #