50.032 * [progress]: [Phase 1 of 3] Setting up. 0.002 * * * [progress]: [1/2] Preparing points 0.162 * * * [progress]: [2/2] Setting up program. 0.168 * [progress]: [Phase 2 of 3] Improving. 0.168 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.169 * * [simplify]: Extracting # 0 : cost 0 0.169 * * [simplify]: Extracting # 1 : cost 0 0.169 * * [simplify]: Extracting # 2 : cost 0 0.169 * * [simplify]: Extracting # 3 : cost 0 0.169 * * [simplify]: Extracting # 4 : cost 0 0.169 * * [simplify]: Extracting # 5 : cost 0 0.169 * * [simplify]: Extracting # 6 : cost 0 0.169 * * [simplify]: Extracting # 7 : cost 0 0.169 * * [simplify]: iteration 0 : 13 enodes (cost 16 ) 0.175 * * [simplify]: Extracting # 0 : cost 0 0.175 * * [simplify]: Extracting # 1 : cost 0 0.175 * * [simplify]: Extracting # 2 : cost 0 0.175 * * [simplify]: Extracting # 3 : cost 0 0.176 * * [simplify]: Extracting # 4 : cost 0 0.176 * * [simplify]: Extracting # 5 : cost 0 0.176 * * [simplify]: iteration 1 : 29 enodes (cost 16 ) 0.183 * * [simplify]: Extracting # 0 : cost 0 0.183 * * [simplify]: Extracting # 1 : cost 0 0.183 * * [simplify]: Extracting # 2 : cost 0 0.183 * * [simplify]: Extracting # 3 : cost 0 0.184 * * [simplify]: Extracting # 4 : cost 0 0.184 * * [simplify]: iteration 2 : 59 enodes (cost 16 ) 0.195 * * [simplify]: Extracting # 0 : cost 0 0.195 * * [simplify]: Extracting # 1 : cost 0 0.195 * * [simplify]: Extracting # 2 : cost 0 0.195 * * [simplify]: Extracting # 3 : cost 0 0.196 * * [simplify]: Extracting # 4 : cost 0 0.196 * * [simplify]: iteration 3 : 120 enodes (cost 16 ) 0.265 * * [simplify]: Extracting # 0 : cost 0 0.265 * * [simplify]: Extracting # 1 : cost 0 0.266 * * [simplify]: Extracting # 2 : cost 0 0.267 * * [simplify]: Extracting # 3 : cost 0 0.267 * * [simplify]: Extracting # 4 : cost 0 0.268 * * [simplify]: iteration 4 : 330 enodes (cost 16 ) 0.513 * * [simplify]: Extracting # 0 : cost 0 0.521 * * [simplify]: Extracting # 1 : cost 0 0.524 * * [simplify]: Extracting # 2 : cost 0 0.527 * * [simplify]: Extracting # 3 : cost 0 0.530 * * [simplify]: Extracting # 4 : cost 0 0.533 * * [simplify]: Extracting # 5 : cost 0 0.535 * * [simplify]: iteration 5 : 1545 enodes (cost 16 ) 1.676 * * [simplify]: Extracting # 0 : cost 0 1.727 * * [simplify]: Extracting # 1 : cost 0 1.734 * * [simplify]: Extracting # 2 : cost 0 1.740 * * [simplify]: Extracting # 3 : cost 0 1.747 * * [simplify]: Extracting # 4 : cost 0 1.755 * * [simplify]: iteration done: 5000 enodes (cost 16 ) 1.755 * [simplify]: Simplified to: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1.755 * * [progress]: iteration 1 / 4 1.755 * * * [progress]: picking best candidate 1.762 * * * * [pick]: Picked # 1.762 * * * [progress]: localizing error 1.793 * * * [progress]: generating rewritten candidates 1.793 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 1.829 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 1.835 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 1.858 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 1.930 * * * [progress]: generating series expansions 1.930 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 1.931 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 1.931 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 1.931 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.931 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.931 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.931 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.931 * [taylor]: Taking taylor expansion of 0.5 in k 1.931 * [backup-simplify]: Simplify 0.5 into 0.5 1.931 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.931 * [taylor]: Taking taylor expansion of 1.0 in k 1.931 * [backup-simplify]: Simplify 1.0 into 1.0 1.931 * [taylor]: Taking taylor expansion of k in k 1.931 * [backup-simplify]: Simplify 0 into 0 1.931 * [backup-simplify]: Simplify 1 into 1 1.932 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.932 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.932 * [taylor]: Taking taylor expansion of 2.0 in k 1.932 * [backup-simplify]: Simplify 2.0 into 2.0 1.932 * [taylor]: Taking taylor expansion of (* n PI) in k 1.932 * [taylor]: Taking taylor expansion of n in k 1.932 * [backup-simplify]: Simplify n into n 1.932 * [taylor]: Taking taylor expansion of PI in k 1.932 * [backup-simplify]: Simplify PI into PI 1.932 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.932 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.932 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.933 * [backup-simplify]: Simplify (- 0) into 0 1.933 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.933 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 1.934 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 1.934 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 1.934 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.934 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.934 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.934 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.934 * [taylor]: Taking taylor expansion of 0.5 in n 1.934 * [backup-simplify]: Simplify 0.5 into 0.5 1.934 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.934 * [taylor]: Taking taylor expansion of 1.0 in n 1.934 * [backup-simplify]: Simplify 1.0 into 1.0 1.934 * [taylor]: Taking taylor expansion of k in n 1.934 * [backup-simplify]: Simplify k into k 1.934 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.934 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.934 * [taylor]: Taking taylor expansion of 2.0 in n 1.934 * [backup-simplify]: Simplify 2.0 into 2.0 1.934 * [taylor]: Taking taylor expansion of (* n PI) in n 1.934 * [taylor]: Taking taylor expansion of n in n 1.934 * [backup-simplify]: Simplify 0 into 0 1.934 * [backup-simplify]: Simplify 1 into 1 1.934 * [taylor]: Taking taylor expansion of PI in n 1.934 * [backup-simplify]: Simplify PI into PI 1.935 * [backup-simplify]: Simplify (* 0 PI) into 0 1.935 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.937 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.938 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.940 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.940 * [backup-simplify]: Simplify (- k) into (- k) 1.940 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.940 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.941 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.943 * [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)))) 1.944 * [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))))) 1.944 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.944 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.944 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.944 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.944 * [taylor]: Taking taylor expansion of 0.5 in n 1.944 * [backup-simplify]: Simplify 0.5 into 0.5 1.944 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.944 * [taylor]: Taking taylor expansion of 1.0 in n 1.944 * [backup-simplify]: Simplify 1.0 into 1.0 1.944 * [taylor]: Taking taylor expansion of k in n 1.944 * [backup-simplify]: Simplify k into k 1.944 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.944 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.944 * [taylor]: Taking taylor expansion of 2.0 in n 1.944 * [backup-simplify]: Simplify 2.0 into 2.0 1.944 * [taylor]: Taking taylor expansion of (* n PI) in n 1.944 * [taylor]: Taking taylor expansion of n in n 1.944 * [backup-simplify]: Simplify 0 into 0 1.944 * [backup-simplify]: Simplify 1 into 1 1.944 * [taylor]: Taking taylor expansion of PI in n 1.945 * [backup-simplify]: Simplify PI into PI 1.945 * [backup-simplify]: Simplify (* 0 PI) into 0 1.945 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.947 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.949 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.950 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.950 * [backup-simplify]: Simplify (- k) into (- k) 1.950 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.950 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.952 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.953 * [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)))) 1.954 * [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))))) 1.954 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.954 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.954 * [taylor]: Taking taylor expansion of 0.5 in k 1.954 * [backup-simplify]: Simplify 0.5 into 0.5 1.954 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.954 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.954 * [taylor]: Taking taylor expansion of 1.0 in k 1.954 * [backup-simplify]: Simplify 1.0 into 1.0 1.955 * [taylor]: Taking taylor expansion of k in k 1.955 * [backup-simplify]: Simplify 0 into 0 1.955 * [backup-simplify]: Simplify 1 into 1 1.955 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.955 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.955 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.955 * [taylor]: Taking taylor expansion of 2.0 in k 1.955 * [backup-simplify]: Simplify 2.0 into 2.0 1.955 * [taylor]: Taking taylor expansion of PI in k 1.955 * [backup-simplify]: Simplify PI into PI 1.955 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.956 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.956 * [taylor]: Taking taylor expansion of (log n) in k 1.956 * [taylor]: Taking taylor expansion of n in k 1.956 * [backup-simplify]: Simplify n into n 1.956 * [backup-simplify]: Simplify (log n) into (log n) 1.957 * [backup-simplify]: Simplify (- 0) into 0 1.957 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.958 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 1.959 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 1.961 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 1.962 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.963 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.964 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.970 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.972 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.973 * [backup-simplify]: Simplify (- 0) into 0 1.973 * [backup-simplify]: Simplify (+ 0 0) into 0 1.974 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 1.975 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.976 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 1.978 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.978 * [taylor]: Taking taylor expansion of 0 in k 1.978 * [backup-simplify]: Simplify 0 into 0 1.978 * [backup-simplify]: Simplify 0 into 0 1.979 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.981 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.982 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.982 * [backup-simplify]: Simplify (+ 0 0) into 0 1.983 * [backup-simplify]: Simplify (- 1) into -1 1.983 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.985 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 1.987 * [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)))) 1.991 * [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)))))) 1.994 * [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)))))) 1.996 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.997 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.001 * [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 2.001 * [backup-simplify]: Simplify (- 0) into 0 2.002 * [backup-simplify]: Simplify (+ 0 0) into 0 2.003 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.004 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.006 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.008 * [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 2.008 * [taylor]: Taking taylor expansion of 0 in k 2.009 * [backup-simplify]: Simplify 0 into 0 2.009 * [backup-simplify]: Simplify 0 into 0 2.009 * [backup-simplify]: Simplify 0 into 0 2.010 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.013 * [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 2.015 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.016 * [backup-simplify]: Simplify (+ 0 0) into 0 2.016 * [backup-simplify]: Simplify (- 0) into 0 2.016 * [backup-simplify]: Simplify (+ 0 0) into 0 2.018 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.021 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.025 * [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 (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 2.031 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 2.043 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 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 (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 2.044 * [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)))) 2.044 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 2.044 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.044 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.044 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.044 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.044 * [taylor]: Taking taylor expansion of 0.5 in k 2.044 * [backup-simplify]: Simplify 0.5 into 0.5 2.044 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.044 * [taylor]: Taking taylor expansion of 1.0 in k 2.044 * [backup-simplify]: Simplify 1.0 into 1.0 2.044 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.044 * [taylor]: Taking taylor expansion of k in k 2.044 * [backup-simplify]: Simplify 0 into 0 2.044 * [backup-simplify]: Simplify 1 into 1 2.045 * [backup-simplify]: Simplify (/ 1 1) into 1 2.045 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.045 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.045 * [taylor]: Taking taylor expansion of 2.0 in k 2.045 * [backup-simplify]: Simplify 2.0 into 2.0 2.045 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.045 * [taylor]: Taking taylor expansion of PI in k 2.045 * [backup-simplify]: Simplify PI into PI 2.045 * [taylor]: Taking taylor expansion of n in k 2.045 * [backup-simplify]: Simplify n into n 2.045 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.045 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.045 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.046 * [backup-simplify]: Simplify (- 1) into -1 2.046 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.047 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.047 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.047 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 2.047 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.047 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.047 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.047 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.047 * [taylor]: Taking taylor expansion of 0.5 in n 2.047 * [backup-simplify]: Simplify 0.5 into 0.5 2.047 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.047 * [taylor]: Taking taylor expansion of 1.0 in n 2.047 * [backup-simplify]: Simplify 1.0 into 1.0 2.047 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.048 * [taylor]: Taking taylor expansion of k in n 2.048 * [backup-simplify]: Simplify k into k 2.048 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.048 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.048 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.048 * [taylor]: Taking taylor expansion of 2.0 in n 2.048 * [backup-simplify]: Simplify 2.0 into 2.0 2.048 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.048 * [taylor]: Taking taylor expansion of PI in n 2.048 * [backup-simplify]: Simplify PI into PI 2.048 * [taylor]: Taking taylor expansion of n in n 2.048 * [backup-simplify]: Simplify 0 into 0 2.048 * [backup-simplify]: Simplify 1 into 1 2.048 * [backup-simplify]: Simplify (/ PI 1) into PI 2.049 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.050 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.050 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.050 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.050 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.051 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.052 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.053 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.053 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.053 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.053 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.053 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.053 * [taylor]: Taking taylor expansion of 0.5 in n 2.053 * [backup-simplify]: Simplify 0.5 into 0.5 2.053 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.053 * [taylor]: Taking taylor expansion of 1.0 in n 2.053 * [backup-simplify]: Simplify 1.0 into 1.0 2.053 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.053 * [taylor]: Taking taylor expansion of k in n 2.053 * [backup-simplify]: Simplify k into k 2.053 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.053 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.053 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.053 * [taylor]: Taking taylor expansion of 2.0 in n 2.053 * [backup-simplify]: Simplify 2.0 into 2.0 2.053 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.053 * [taylor]: Taking taylor expansion of PI in n 2.053 * [backup-simplify]: Simplify PI into PI 2.053 * [taylor]: Taking taylor expansion of n in n 2.054 * [backup-simplify]: Simplify 0 into 0 2.054 * [backup-simplify]: Simplify 1 into 1 2.054 * [backup-simplify]: Simplify (/ PI 1) into PI 2.054 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.055 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.055 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.055 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.055 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.056 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.057 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.058 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.058 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.058 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.058 * [taylor]: Taking taylor expansion of 0.5 in k 2.058 * [backup-simplify]: Simplify 0.5 into 0.5 2.058 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.058 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.058 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.058 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.058 * [taylor]: Taking taylor expansion of 2.0 in k 2.058 * [backup-simplify]: Simplify 2.0 into 2.0 2.058 * [taylor]: Taking taylor expansion of PI in k 2.058 * [backup-simplify]: Simplify PI into PI 2.058 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.059 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.059 * [taylor]: Taking taylor expansion of (log n) in k 2.059 * [taylor]: Taking taylor expansion of n in k 2.059 * [backup-simplify]: Simplify n into n 2.059 * [backup-simplify]: Simplify (log n) into (log n) 2.059 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.059 * [taylor]: Taking taylor expansion of 1.0 in k 2.059 * [backup-simplify]: Simplify 1.0 into 1.0 2.059 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.059 * [taylor]: Taking taylor expansion of k in k 2.059 * [backup-simplify]: Simplify 0 into 0 2.059 * [backup-simplify]: Simplify 1 into 1 2.060 * [backup-simplify]: Simplify (/ 1 1) into 1 2.060 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.061 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.061 * [backup-simplify]: Simplify (- 1) into -1 2.061 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.062 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.063 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 2.063 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.064 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.065 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.065 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.066 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.066 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.066 * [backup-simplify]: Simplify (- 0) into 0 2.067 * [backup-simplify]: Simplify (+ 0 0) into 0 2.067 * [backup-simplify]: Simplify (+ (* 0.5 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 (- (log (* 2.0 PI)) (log n)))) into 0 2.070 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.070 * [taylor]: Taking taylor expansion of 0 in k 2.070 * [backup-simplify]: Simplify 0 into 0 2.070 * [backup-simplify]: Simplify 0 into 0 2.070 * [backup-simplify]: Simplify 0 into 0 2.071 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.071 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.073 * [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 2.073 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.073 * [backup-simplify]: Simplify (- 0) into 0 2.074 * [backup-simplify]: Simplify (+ 0 0) into 0 2.074 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.075 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.076 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.077 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.077 * [taylor]: Taking taylor expansion of 0 in k 2.077 * [backup-simplify]: Simplify 0 into 0 2.077 * [backup-simplify]: Simplify 0 into 0 2.077 * [backup-simplify]: Simplify 0 into 0 2.077 * [backup-simplify]: Simplify 0 into 0 2.078 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.079 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.085 * [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 2.085 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.086 * [backup-simplify]: Simplify (- 0) into 0 2.086 * [backup-simplify]: Simplify (+ 0 0) into 0 2.087 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.089 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.091 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.094 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.094 * [taylor]: Taking taylor expansion of 0 in k 2.094 * [backup-simplify]: Simplify 0 into 0 2.094 * [backup-simplify]: Simplify 0 into 0 2.095 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 2.096 * [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))) 2.096 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 2.096 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.096 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.096 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.096 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.096 * [taylor]: Taking taylor expansion of 0.5 in k 2.096 * [backup-simplify]: Simplify 0.5 into 0.5 2.096 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.096 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.096 * [taylor]: Taking taylor expansion of k in k 2.096 * [backup-simplify]: Simplify 0 into 0 2.096 * [backup-simplify]: Simplify 1 into 1 2.097 * [backup-simplify]: Simplify (/ 1 1) into 1 2.097 * [taylor]: Taking taylor expansion of 1.0 in k 2.097 * [backup-simplify]: Simplify 1.0 into 1.0 2.097 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.097 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.097 * [taylor]: Taking taylor expansion of -2.0 in k 2.097 * [backup-simplify]: Simplify -2.0 into -2.0 2.097 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.097 * [taylor]: Taking taylor expansion of PI in k 2.097 * [backup-simplify]: Simplify PI into PI 2.097 * [taylor]: Taking taylor expansion of n in k 2.097 * [backup-simplify]: Simplify n into n 2.097 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.097 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.097 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.097 * [backup-simplify]: Simplify (+ 1 0) into 1 2.097 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.098 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.098 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 2.098 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.098 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.098 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.098 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.098 * [taylor]: Taking taylor expansion of 0.5 in n 2.098 * [backup-simplify]: Simplify 0.5 into 0.5 2.098 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.098 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.098 * [taylor]: Taking taylor expansion of k in n 2.098 * [backup-simplify]: Simplify k into k 2.098 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.098 * [taylor]: Taking taylor expansion of 1.0 in n 2.098 * [backup-simplify]: Simplify 1.0 into 1.0 2.098 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.098 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.098 * [taylor]: Taking taylor expansion of -2.0 in n 2.098 * [backup-simplify]: Simplify -2.0 into -2.0 2.098 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.098 * [taylor]: Taking taylor expansion of PI in n 2.098 * [backup-simplify]: Simplify PI into PI 2.098 * [taylor]: Taking taylor expansion of n in n 2.098 * [backup-simplify]: Simplify 0 into 0 2.098 * [backup-simplify]: Simplify 1 into 1 2.098 * [backup-simplify]: Simplify (/ PI 1) into PI 2.099 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.099 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.100 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.100 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.100 * [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 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.105 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.105 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.105 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.105 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.105 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.105 * [taylor]: Taking taylor expansion of 0.5 in n 2.105 * [backup-simplify]: Simplify 0.5 into 0.5 2.105 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.105 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.105 * [taylor]: Taking taylor expansion of k in n 2.105 * [backup-simplify]: Simplify k into k 2.105 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.105 * [taylor]: Taking taylor expansion of 1.0 in n 2.105 * [backup-simplify]: Simplify 1.0 into 1.0 2.105 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.105 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.105 * [taylor]: Taking taylor expansion of -2.0 in n 2.105 * [backup-simplify]: Simplify -2.0 into -2.0 2.105 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.105 * [taylor]: Taking taylor expansion of PI in n 2.105 * [backup-simplify]: Simplify PI into PI 2.106 * [taylor]: Taking taylor expansion of n in n 2.106 * [backup-simplify]: Simplify 0 into 0 2.106 * [backup-simplify]: Simplify 1 into 1 2.106 * [backup-simplify]: Simplify (/ PI 1) into PI 2.106 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.107 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.107 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.107 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.108 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.109 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.109 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.109 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.109 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.109 * [taylor]: Taking taylor expansion of 0.5 in k 2.109 * [backup-simplify]: Simplify 0.5 into 0.5 2.110 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.110 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.110 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.110 * [taylor]: Taking taylor expansion of k in k 2.110 * [backup-simplify]: Simplify 0 into 0 2.110 * [backup-simplify]: Simplify 1 into 1 2.110 * [backup-simplify]: Simplify (/ 1 1) into 1 2.110 * [taylor]: Taking taylor expansion of 1.0 in k 2.110 * [backup-simplify]: Simplify 1.0 into 1.0 2.110 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.110 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.110 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.110 * [taylor]: Taking taylor expansion of -2.0 in k 2.110 * [backup-simplify]: Simplify -2.0 into -2.0 2.110 * [taylor]: Taking taylor expansion of PI in k 2.110 * [backup-simplify]: Simplify PI into PI 2.110 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.111 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.111 * [taylor]: Taking taylor expansion of (log n) in k 2.111 * [taylor]: Taking taylor expansion of n in k 2.111 * [backup-simplify]: Simplify n into n 2.111 * [backup-simplify]: Simplify (log n) into (log n) 2.111 * [backup-simplify]: Simplify (+ 1 0) into 1 2.111 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.112 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.113 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.113 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 2.114 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.115 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.116 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.117 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.119 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.119 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.119 * [backup-simplify]: Simplify (+ 0 0) into 0 2.120 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.121 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.123 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.125 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.125 * [taylor]: Taking taylor expansion of 0 in k 2.125 * [backup-simplify]: Simplify 0 into 0 2.125 * [backup-simplify]: Simplify 0 into 0 2.125 * [backup-simplify]: Simplify 0 into 0 2.126 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.127 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.131 * [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 2.131 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.131 * [backup-simplify]: Simplify (+ 0 0) into 0 2.132 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.134 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.135 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.138 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.138 * [taylor]: Taking taylor expansion of 0 in k 2.138 * [backup-simplify]: Simplify 0 into 0 2.138 * [backup-simplify]: Simplify 0 into 0 2.138 * [backup-simplify]: Simplify 0 into 0 2.138 * [backup-simplify]: Simplify 0 into 0 2.139 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.141 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.147 * [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 2.147 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.148 * [backup-simplify]: Simplify (+ 0 0) into 0 2.149 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.150 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.152 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.155 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.155 * [taylor]: Taking taylor expansion of 0 in k 2.156 * [backup-simplify]: Simplify 0 into 0 2.156 * [backup-simplify]: Simplify 0 into 0 2.157 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 2.157 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 2.157 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 2.157 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 2.157 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 2.157 * [taylor]: Taking taylor expansion of 1.0 in k 2.157 * [backup-simplify]: Simplify 1.0 into 1.0 2.157 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.157 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.158 * [taylor]: Taking taylor expansion of k in k 2.158 * [backup-simplify]: Simplify 0 into 0 2.158 * [backup-simplify]: Simplify 1 into 1 2.158 * [backup-simplify]: Simplify (/ 1 1) into 1 2.159 * [backup-simplify]: Simplify (sqrt 0) into 0 2.160 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.160 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 2.160 * [taylor]: Taking taylor expansion of 1.0 in k 2.160 * [backup-simplify]: Simplify 1.0 into 1.0 2.160 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.160 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.160 * [taylor]: Taking taylor expansion of k in k 2.160 * [backup-simplify]: Simplify 0 into 0 2.160 * [backup-simplify]: Simplify 1 into 1 2.161 * [backup-simplify]: Simplify (/ 1 1) into 1 2.161 * [backup-simplify]: Simplify (sqrt 0) into 0 2.163 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.163 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.163 * [backup-simplify]: Simplify 0 into 0 2.165 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 2.165 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.166 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.169 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.170 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 2.170 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.170 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.173 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.174 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 2.174 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.175 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 2.175 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 2.175 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 2.175 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 2.175 * [taylor]: Taking taylor expansion of 1.0 in k 2.175 * [backup-simplify]: Simplify 1.0 into 1.0 2.175 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.175 * [taylor]: Taking taylor expansion of k in k 2.175 * [backup-simplify]: Simplify 0 into 0 2.175 * [backup-simplify]: Simplify 1 into 1 2.176 * [backup-simplify]: Simplify (sqrt 0) into 0 2.176 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.176 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 2.177 * [taylor]: Taking taylor expansion of 1.0 in k 2.177 * [backup-simplify]: Simplify 1.0 into 1.0 2.177 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.177 * [taylor]: Taking taylor expansion of k in k 2.177 * [backup-simplify]: Simplify 0 into 0 2.177 * [backup-simplify]: Simplify 1 into 1 2.177 * [backup-simplify]: Simplify (sqrt 0) into 0 2.178 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.178 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.178 * [backup-simplify]: Simplify 0 into 0 2.179 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 2.179 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.181 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.182 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 2.183 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.185 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.186 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 2.187 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.188 * [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)))))))) 2.188 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 2.188 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 2.188 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 2.188 * [taylor]: Taking taylor expansion of 1.0 in k 2.188 * [backup-simplify]: Simplify 1.0 into 1.0 2.188 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.188 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.188 * [taylor]: Taking taylor expansion of -1 in k 2.188 * [backup-simplify]: Simplify -1 into -1 2.188 * [taylor]: Taking taylor expansion of k in k 2.188 * [backup-simplify]: Simplify 0 into 0 2.188 * [backup-simplify]: Simplify 1 into 1 2.188 * [backup-simplify]: Simplify (/ -1 1) into -1 2.188 * [backup-simplify]: Simplify (sqrt 0) into 0 2.189 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.190 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 2.190 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 2.190 * [taylor]: Taking taylor expansion of 1.0 in k 2.190 * [backup-simplify]: Simplify 1.0 into 1.0 2.190 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.190 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.190 * [taylor]: Taking taylor expansion of -1 in k 2.190 * [backup-simplify]: Simplify -1 into -1 2.190 * [taylor]: Taking taylor expansion of k in k 2.190 * [backup-simplify]: Simplify 0 into 0 2.190 * [backup-simplify]: Simplify 1 into 1 2.190 * [backup-simplify]: Simplify (/ -1 1) into -1 2.190 * [backup-simplify]: Simplify (sqrt 0) into 0 2.191 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.191 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 2.192 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.192 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.194 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.195 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 2.196 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.196 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.199 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.201 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 2.201 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.202 * [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))))) 2.202 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 2.202 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.202 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 2.202 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.202 * [taylor]: Taking taylor expansion of 2.0 in n 2.203 * [backup-simplify]: Simplify 2.0 into 2.0 2.203 * [taylor]: Taking taylor expansion of (* n PI) in n 2.203 * [taylor]: Taking taylor expansion of n in n 2.203 * [backup-simplify]: Simplify 0 into 0 2.203 * [backup-simplify]: Simplify 1 into 1 2.203 * [taylor]: Taking taylor expansion of PI in n 2.203 * [backup-simplify]: Simplify PI into PI 2.203 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.203 * [taylor]: Taking taylor expansion of 2.0 in n 2.203 * [backup-simplify]: Simplify 2.0 into 2.0 2.203 * [taylor]: Taking taylor expansion of (* n PI) in n 2.203 * [taylor]: Taking taylor expansion of n in n 2.203 * [backup-simplify]: Simplify 0 into 0 2.203 * [backup-simplify]: Simplify 1 into 1 2.203 * [taylor]: Taking taylor expansion of PI in n 2.203 * [backup-simplify]: Simplify PI into PI 2.203 * [backup-simplify]: Simplify (* 0 PI) into 0 2.203 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.203 * [backup-simplify]: Simplify 0 into 0 2.204 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.205 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.206 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.206 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.207 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.207 * [backup-simplify]: Simplify 0 into 0 2.207 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.208 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.208 * [backup-simplify]: Simplify 0 into 0 2.209 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.210 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.210 * [backup-simplify]: Simplify 0 into 0 2.210 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.212 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 2.212 * [backup-simplify]: Simplify 0 into 0 2.213 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.215 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 2.215 * [backup-simplify]: Simplify 0 into 0 2.221 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.224 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.224 * [backup-simplify]: Simplify 0 into 0 2.224 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.225 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 2.225 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 2.225 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.225 * [taylor]: Taking taylor expansion of 2.0 in n 2.225 * [backup-simplify]: Simplify 2.0 into 2.0 2.225 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.225 * [taylor]: Taking taylor expansion of PI in n 2.225 * [backup-simplify]: Simplify PI into PI 2.225 * [taylor]: Taking taylor expansion of n in n 2.225 * [backup-simplify]: Simplify 0 into 0 2.225 * [backup-simplify]: Simplify 1 into 1 2.226 * [backup-simplify]: Simplify (/ PI 1) into PI 2.226 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.226 * [taylor]: Taking taylor expansion of 2.0 in n 2.226 * [backup-simplify]: Simplify 2.0 into 2.0 2.226 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.226 * [taylor]: Taking taylor expansion of PI in n 2.226 * [backup-simplify]: Simplify PI into PI 2.226 * [taylor]: Taking taylor expansion of n in n 2.226 * [backup-simplify]: Simplify 0 into 0 2.226 * [backup-simplify]: Simplify 1 into 1 2.226 * [backup-simplify]: Simplify (/ PI 1) into PI 2.227 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.228 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.228 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.229 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.229 * [backup-simplify]: Simplify 0 into 0 2.230 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.231 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.231 * [backup-simplify]: Simplify 0 into 0 2.232 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.234 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.234 * [backup-simplify]: Simplify 0 into 0 2.235 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.236 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.236 * [backup-simplify]: Simplify 0 into 0 2.237 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.239 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.239 * [backup-simplify]: Simplify 0 into 0 2.240 * [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 2.242 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.242 * [backup-simplify]: Simplify 0 into 0 2.243 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 2.243 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 2.243 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 2.243 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) 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 (/ PI n) in n 2.243 * [taylor]: Taking taylor expansion of PI in n 2.243 * [backup-simplify]: Simplify PI into PI 2.244 * [taylor]: Taking taylor expansion of n in n 2.244 * [backup-simplify]: Simplify 0 into 0 2.244 * [backup-simplify]: Simplify 1 into 1 2.244 * [backup-simplify]: Simplify (/ PI 1) into PI 2.244 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.244 * [taylor]: Taking taylor expansion of -2.0 in n 2.244 * [backup-simplify]: Simplify -2.0 into -2.0 2.244 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.244 * [taylor]: Taking taylor expansion of PI in n 2.244 * [backup-simplify]: Simplify PI into PI 2.244 * [taylor]: Taking taylor expansion of n in n 2.244 * [backup-simplify]: Simplify 0 into 0 2.244 * [backup-simplify]: Simplify 1 into 1 2.245 * [backup-simplify]: Simplify (/ PI 1) into PI 2.245 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.246 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.247 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.247 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.248 * [backup-simplify]: Simplify 0 into 0 2.249 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.250 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.250 * [backup-simplify]: Simplify 0 into 0 2.251 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.251 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.252 * [backup-simplify]: Simplify 0 into 0 2.252 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.253 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.253 * [backup-simplify]: Simplify 0 into 0 2.254 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.254 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.254 * [backup-simplify]: Simplify 0 into 0 2.255 * [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 2.256 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.256 * [backup-simplify]: Simplify 0 into 0 2.256 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 2.256 * * * * [progress]: [ 4 / 4 ] generating series at (2) 2.257 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) 2.257 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in (k n) around 0 2.257 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 2.257 * [taylor]: Taking taylor expansion of 1.0 in n 2.257 * [backup-simplify]: Simplify 1.0 into 1.0 2.257 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 2.257 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.257 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.257 * [taylor]: Taking taylor expansion of k in n 2.257 * [backup-simplify]: Simplify k into k 2.257 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.257 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 2.257 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.257 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 2.257 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.257 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.258 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.258 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.258 * [taylor]: Taking taylor expansion of 0.5 in n 2.258 * [backup-simplify]: Simplify 0.5 into 0.5 2.258 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.258 * [taylor]: Taking taylor expansion of 1.0 in n 2.258 * [backup-simplify]: Simplify 1.0 into 1.0 2.258 * [taylor]: Taking taylor expansion of k in n 2.258 * [backup-simplify]: Simplify k into k 2.258 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.258 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.258 * [taylor]: Taking taylor expansion of 2.0 in n 2.258 * [backup-simplify]: Simplify 2.0 into 2.0 2.258 * [taylor]: Taking taylor expansion of (* n PI) in n 2.258 * [taylor]: Taking taylor expansion of n in n 2.258 * [backup-simplify]: Simplify 0 into 0 2.258 * [backup-simplify]: Simplify 1 into 1 2.258 * [taylor]: Taking taylor expansion of PI in n 2.258 * [backup-simplify]: Simplify PI into PI 2.258 * [backup-simplify]: Simplify (* 0 PI) into 0 2.258 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.259 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.260 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.261 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.261 * [backup-simplify]: Simplify (- k) into (- k) 2.261 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.261 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.262 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.263 * [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)))) 2.263 * [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))))) 2.263 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 2.263 * [taylor]: Taking taylor expansion of 1.0 in k 2.263 * [backup-simplify]: Simplify 1.0 into 1.0 2.263 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 2.263 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.263 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.263 * [taylor]: Taking taylor expansion of k in k 2.263 * [backup-simplify]: Simplify 0 into 0 2.264 * [backup-simplify]: Simplify 1 into 1 2.264 * [backup-simplify]: Simplify (/ 1 1) into 1 2.264 * [backup-simplify]: Simplify (sqrt 0) into 0 2.265 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.265 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.265 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.265 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.265 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.265 * [taylor]: Taking taylor expansion of 0.5 in k 2.265 * [backup-simplify]: Simplify 0.5 into 0.5 2.265 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.265 * [taylor]: Taking taylor expansion of 1.0 in k 2.265 * [backup-simplify]: Simplify 1.0 into 1.0 2.265 * [taylor]: Taking taylor expansion of k in k 2.265 * [backup-simplify]: Simplify 0 into 0 2.265 * [backup-simplify]: Simplify 1 into 1 2.265 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.265 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.265 * [taylor]: Taking taylor expansion of 2.0 in k 2.265 * [backup-simplify]: Simplify 2.0 into 2.0 2.265 * [taylor]: Taking taylor expansion of (* n PI) in k 2.265 * [taylor]: Taking taylor expansion of n in k 2.265 * [backup-simplify]: Simplify n into n 2.265 * [taylor]: Taking taylor expansion of PI in k 2.265 * [backup-simplify]: Simplify PI into PI 2.265 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.265 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.265 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.266 * [backup-simplify]: Simplify (- 0) into 0 2.266 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.266 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.266 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.266 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.266 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 2.266 * [taylor]: Taking taylor expansion of 1.0 in k 2.266 * [backup-simplify]: Simplify 1.0 into 1.0 2.266 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 2.266 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.266 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.266 * [taylor]: Taking taylor expansion of k in k 2.266 * [backup-simplify]: Simplify 0 into 0 2.267 * [backup-simplify]: Simplify 1 into 1 2.267 * [backup-simplify]: Simplify (/ 1 1) into 1 2.267 * [backup-simplify]: Simplify (sqrt 0) into 0 2.268 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.268 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.268 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.268 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.268 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.268 * [taylor]: Taking taylor expansion of 0.5 in k 2.268 * [backup-simplify]: Simplify 0.5 into 0.5 2.268 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.268 * [taylor]: Taking taylor expansion of 1.0 in k 2.268 * [backup-simplify]: Simplify 1.0 into 1.0 2.268 * [taylor]: Taking taylor expansion of k in k 2.268 * [backup-simplify]: Simplify 0 into 0 2.268 * [backup-simplify]: Simplify 1 into 1 2.268 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.268 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.268 * [taylor]: Taking taylor expansion of 2.0 in k 2.268 * [backup-simplify]: Simplify 2.0 into 2.0 2.268 * [taylor]: Taking taylor expansion of (* n PI) in k 2.268 * [taylor]: Taking taylor expansion of n in k 2.268 * [backup-simplify]: Simplify n into n 2.268 * [taylor]: Taking taylor expansion of PI in k 2.268 * [backup-simplify]: Simplify PI into PI 2.268 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.268 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.268 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.269 * [backup-simplify]: Simplify (- 0) into 0 2.269 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.269 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.269 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.269 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.269 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 2.270 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.270 * [taylor]: Taking taylor expansion of 0 in n 2.270 * [backup-simplify]: Simplify 0 into 0 2.270 * [backup-simplify]: Simplify 0 into 0 2.270 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 2.270 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 2.271 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 2.271 * [backup-simplify]: Simplify (- 1) into -1 2.271 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.272 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 2.273 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 2.273 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1)))) into (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 2.274 * [backup-simplify]: Simplify (+ (* 0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 2.275 * [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))) 2.275 * [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 2.276 * [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 2.276 * [taylor]: Taking taylor expansion of +nan.0 in n 2.276 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.276 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 2.276 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.276 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.276 * [taylor]: Taking taylor expansion of 0.5 in n 2.276 * [backup-simplify]: Simplify 0.5 into 0.5 2.276 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.276 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.276 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.276 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.276 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.276 * [taylor]: Taking taylor expansion of 1.0 in n 2.276 * [backup-simplify]: Simplify 1.0 into 1.0 2.276 * [taylor]: Taking taylor expansion of (log PI) in n 2.276 * [taylor]: Taking taylor expansion of PI in n 2.276 * [backup-simplify]: Simplify PI into PI 2.276 * [backup-simplify]: Simplify (log PI) into (log PI) 2.277 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.278 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.278 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.278 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.278 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.278 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.278 * [taylor]: Taking taylor expansion of 1.0 in n 2.278 * [backup-simplify]: Simplify 1.0 into 1.0 2.278 * [taylor]: Taking taylor expansion of (log n) in n 2.278 * [taylor]: Taking taylor expansion of n in n 2.278 * [backup-simplify]: Simplify 0 into 0 2.278 * [backup-simplify]: Simplify 1 into 1 2.278 * [backup-simplify]: Simplify (log 1) into 0 2.278 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.278 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.279 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.279 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.279 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.279 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.279 * [taylor]: Taking taylor expansion of 1.0 in n 2.279 * [backup-simplify]: Simplify 1.0 into 1.0 2.279 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.279 * [taylor]: Taking taylor expansion of 2.0 in n 2.279 * [backup-simplify]: Simplify 2.0 into 2.0 2.279 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.280 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.281 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.282 * [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) 2.283 * [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) 2.285 * [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)) 2.286 * [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))) 2.288 * [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) 2.289 * [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)) 2.291 * [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))) 2.292 * [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))) 2.292 * [backup-simplify]: Simplify 0 into 0 2.293 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 2.294 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 2.296 * [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 2.296 * [backup-simplify]: Simplify (- 0) into 0 2.296 * [backup-simplify]: Simplify (+ 0 0) into 0 2.297 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 2.298 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 2.299 * [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 (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 2.300 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.303 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.307 * [backup-simplify]: Simplify (+ (* 0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5)))) into (- (+ (* +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 PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) 2.312 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +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 PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))) (+ (* 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)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) 2.312 * [taylor]: Taking taylor expansion of (- (+ (* +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 PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) in n 2.312 * [taylor]: Taking taylor expansion of (+ (* +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 PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))) in n 2.312 * [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 2.312 * [taylor]: Taking taylor expansion of +nan.0 in n 2.312 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.312 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 2.312 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.312 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.312 * [taylor]: Taking taylor expansion of 0.5 in n 2.312 * [backup-simplify]: Simplify 0.5 into 0.5 2.312 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.312 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.312 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.312 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.312 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.312 * [taylor]: Taking taylor expansion of 1.0 in n 2.312 * [backup-simplify]: Simplify 1.0 into 1.0 2.312 * [taylor]: Taking taylor expansion of (log PI) in n 2.312 * [taylor]: Taking taylor expansion of PI in n 2.312 * [backup-simplify]: Simplify PI into PI 2.313 * [backup-simplify]: Simplify (log PI) into (log PI) 2.313 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.314 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.314 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.314 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.314 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.314 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.314 * [taylor]: Taking taylor expansion of 1.0 in n 2.314 * [backup-simplify]: Simplify 1.0 into 1.0 2.314 * [taylor]: Taking taylor expansion of (log n) in n 2.315 * [taylor]: Taking taylor expansion of n in n 2.315 * [backup-simplify]: Simplify 0 into 0 2.315 * [backup-simplify]: Simplify 1 into 1 2.315 * [backup-simplify]: Simplify (log 1) into 0 2.315 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.315 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.315 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.315 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.315 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.315 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.315 * [taylor]: Taking taylor expansion of 1.0 in n 2.315 * [backup-simplify]: Simplify 1.0 into 1.0 2.315 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.315 * [taylor]: Taking taylor expansion of 2.0 in n 2.315 * [backup-simplify]: Simplify 2.0 into 2.0 2.316 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.316 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.317 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.317 * [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) 2.318 * [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) 2.319 * [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)) 2.320 * [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) 2.321 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))) in n 2.321 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 2.321 * [taylor]: Taking taylor expansion of +nan.0 in n 2.321 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.321 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 2.321 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 2.321 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 2.321 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 2.321 * [taylor]: Taking taylor expansion of 0.5 in n 2.321 * [backup-simplify]: Simplify 0.5 into 0.5 2.321 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 2.321 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 2.321 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.321 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.321 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.321 * [taylor]: Taking taylor expansion of 1.0 in n 2.321 * [backup-simplify]: Simplify 1.0 into 1.0 2.321 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.321 * [taylor]: Taking taylor expansion of 2.0 in n 2.321 * [backup-simplify]: Simplify 2.0 into 2.0 2.322 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.322 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.323 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.323 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 2.323 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.323 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.323 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.323 * [taylor]: Taking taylor expansion of 1.0 in n 2.323 * [backup-simplify]: Simplify 1.0 into 1.0 2.323 * [taylor]: Taking taylor expansion of (log PI) in n 2.323 * [taylor]: Taking taylor expansion of PI in n 2.323 * [backup-simplify]: Simplify PI into PI 2.323 * [backup-simplify]: Simplify (log PI) into (log PI) 2.324 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.325 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.325 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.325 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.325 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.325 * [taylor]: Taking taylor expansion of 1.0 in n 2.325 * [backup-simplify]: Simplify 1.0 into 1.0 2.325 * [taylor]: Taking taylor expansion of (log n) in n 2.325 * [taylor]: Taking taylor expansion of n in n 2.325 * [backup-simplify]: Simplify 0 into 0 2.325 * [backup-simplify]: Simplify 1 into 1 2.325 * [backup-simplify]: Simplify (log 1) into 0 2.326 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.326 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.326 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.326 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.327 * [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) 2.328 * [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)) 2.329 * [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))) 2.330 * [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) 2.330 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.330 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.330 * [taylor]: Taking taylor expansion of 2.0 in n 2.330 * [backup-simplify]: Simplify 2.0 into 2.0 2.330 * [taylor]: Taking taylor expansion of (* n PI) in n 2.330 * [taylor]: Taking taylor expansion of n in n 2.330 * [backup-simplify]: Simplify 0 into 0 2.330 * [backup-simplify]: Simplify 1 into 1 2.330 * [taylor]: Taking taylor expansion of PI in n 2.330 * [backup-simplify]: Simplify PI into PI 2.330 * [backup-simplify]: Simplify (* 0 PI) into 0 2.330 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.331 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.332 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.333 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.334 * [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)) 2.335 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.337 * [backup-simplify]: Simplify (* (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) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 2.338 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 2.343 * [backup-simplify]: Simplify (- (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))) 2.347 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (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)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 2.351 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (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)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 2.355 * [backup-simplify]: Simplify (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (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)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 2.356 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 2.356 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 2.357 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 2.358 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.358 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.358 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 2.359 * [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 2.360 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 2.360 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 2.361 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 2.362 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 2.363 * [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 2.364 * [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 2.366 * [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 2.367 * [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 2.367 * [backup-simplify]: Simplify (- 0) into 0 2.367 * [backup-simplify]: Simplify 0 into 0 2.367 * [backup-simplify]: Simplify 0 into 0 2.368 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.369 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 2.370 * [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 2.371 * [backup-simplify]: Simplify (- 0) into 0 2.371 * [backup-simplify]: Simplify (+ 0 0) into 0 2.372 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 2.373 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 2.375 * [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 (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 2.376 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.380 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.386 * [backup-simplify]: Simplify (+ (* 0 (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))))) into (- (+ (* +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 PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 2.398 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +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 PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 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)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))) (+ (* 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 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 2.398 * [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 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) in n 2.398 * [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 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))) in n 2.398 * [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 2.398 * [taylor]: Taking taylor expansion of +nan.0 in n 2.398 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.398 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 2.398 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 2.398 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 2.398 * [taylor]: Taking taylor expansion of 0.5 in n 2.398 * [backup-simplify]: Simplify 0.5 into 0.5 2.398 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 2.398 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 2.398 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.398 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.398 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.398 * [taylor]: Taking taylor expansion of 1.0 in n 2.399 * [backup-simplify]: Simplify 1.0 into 1.0 2.399 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.399 * [taylor]: Taking taylor expansion of 2.0 in n 2.399 * [backup-simplify]: Simplify 2.0 into 2.0 2.399 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.400 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.402 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.402 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 2.402 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.402 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.402 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) 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 n) in n 2.402 * [taylor]: Taking taylor expansion of n in n 2.402 * [backup-simplify]: Simplify 0 into 0 2.402 * [backup-simplify]: Simplify 1 into 1 2.403 * [backup-simplify]: Simplify (log 1) into 0 2.403 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.403 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.403 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.403 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.403 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.404 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) 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 PI) in n 2.404 * [taylor]: Taking taylor expansion of PI in n 2.404 * [backup-simplify]: Simplify PI into PI 2.404 * [backup-simplify]: Simplify (log PI) into (log PI) 2.405 * [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) 2.408 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.409 * [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) 2.411 * [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)) 2.412 * [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))) 2.414 * [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) 2.414 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))) in n 2.414 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) in n 2.414 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 2.414 * [taylor]: Taking taylor expansion of +nan.0 in n 2.414 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.414 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 2.414 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 2.414 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 2.414 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 2.414 * [taylor]: Taking taylor expansion of 0.5 in n 2.414 * [backup-simplify]: Simplify 0.5 into 0.5 2.414 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 2.414 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 2.414 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.414 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.414 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.414 * [taylor]: Taking taylor expansion of 1.0 in n 2.414 * [backup-simplify]: Simplify 1.0 into 1.0 2.414 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.414 * [taylor]: Taking taylor expansion of 2.0 in n 2.414 * [backup-simplify]: Simplify 2.0 into 2.0 2.415 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.416 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.417 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.417 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 2.417 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.417 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.417 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.417 * [taylor]: Taking taylor expansion of 1.0 in n 2.417 * [backup-simplify]: Simplify 1.0 into 1.0 2.417 * [taylor]: Taking taylor expansion of (log PI) in n 2.417 * [taylor]: Taking taylor expansion of PI in n 2.417 * [backup-simplify]: Simplify PI into PI 2.418 * [backup-simplify]: Simplify (log PI) into (log PI) 2.419 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.420 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.420 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.420 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.420 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.420 * [taylor]: Taking taylor expansion of 1.0 in n 2.420 * [backup-simplify]: Simplify 1.0 into 1.0 2.420 * [taylor]: Taking taylor expansion of (log n) in n 2.421 * [taylor]: Taking taylor expansion of n in n 2.421 * [backup-simplify]: Simplify 0 into 0 2.421 * [backup-simplify]: Simplify 1 into 1 2.421 * [backup-simplify]: Simplify (log 1) into 0 2.421 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.421 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.422 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.422 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.423 * [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) 2.425 * [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)) 2.426 * [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))) 2.428 * [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) 2.428 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.428 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.428 * [taylor]: Taking taylor expansion of 2.0 in n 2.428 * [backup-simplify]: Simplify 2.0 into 2.0 2.428 * [taylor]: Taking taylor expansion of (* n PI) in n 2.428 * [taylor]: Taking taylor expansion of n in n 2.428 * [backup-simplify]: Simplify 0 into 0 2.428 * [backup-simplify]: Simplify 1 into 1 2.428 * [taylor]: Taking taylor expansion of PI in n 2.428 * [backup-simplify]: Simplify PI into PI 2.428 * [backup-simplify]: Simplify (* 0 PI) into 0 2.429 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.430 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.432 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.433 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.433 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) in n 2.433 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n 2.433 * [taylor]: Taking taylor expansion of +nan.0 in n 2.433 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.433 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n 2.434 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 2.434 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 2.434 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 2.434 * [taylor]: Taking taylor expansion of 0.5 in n 2.434 * [backup-simplify]: Simplify 0.5 into 0.5 2.434 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 2.434 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 2.434 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.434 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.434 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.434 * [taylor]: Taking taylor expansion of 1.0 in n 2.434 * [backup-simplify]: Simplify 1.0 into 1.0 2.434 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.434 * [taylor]: Taking taylor expansion of 2.0 in n 2.434 * [backup-simplify]: Simplify 2.0 into 2.0 2.434 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.435 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.437 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.437 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 2.437 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.437 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.437 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.437 * [taylor]: Taking taylor expansion of 1.0 in n 2.437 * [backup-simplify]: Simplify 1.0 into 1.0 2.437 * [taylor]: Taking taylor expansion of (log PI) in n 2.437 * [taylor]: Taking taylor expansion of PI in n 2.437 * [backup-simplify]: Simplify PI into PI 2.438 * [backup-simplify]: Simplify (log PI) into (log PI) 2.439 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.440 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.440 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.440 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.440 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.440 * [taylor]: Taking taylor expansion of 1.0 in n 2.440 * [backup-simplify]: Simplify 1.0 into 1.0 2.440 * [taylor]: Taking taylor expansion of (log n) in n 2.440 * [taylor]: Taking taylor expansion of n in n 2.440 * [backup-simplify]: Simplify 0 into 0 2.440 * [backup-simplify]: Simplify 1 into 1 2.440 * [backup-simplify]: Simplify (log 1) into 0 2.440 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.440 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.441 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.441 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.442 * [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) 2.443 * [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)) 2.443 * [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))) 2.444 * [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) 2.444 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 2.444 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.444 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.444 * [taylor]: Taking taylor expansion of 2.0 in n 2.444 * [backup-simplify]: Simplify 2.0 into 2.0 2.444 * [taylor]: Taking taylor expansion of (* n PI) in n 2.445 * [taylor]: Taking taylor expansion of n in n 2.445 * [backup-simplify]: Simplify 0 into 0 2.445 * [backup-simplify]: Simplify 1 into 1 2.445 * [taylor]: Taking taylor expansion of PI in n 2.445 * [backup-simplify]: Simplify PI into PI 2.445 * [backup-simplify]: Simplify (* 0 PI) into 0 2.445 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.446 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.447 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.448 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.449 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.450 * [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)) 2.451 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.452 * [backup-simplify]: Simplify (* (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) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 2.454 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 2.454 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.455 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.457 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 2.458 * [backup-simplify]: Simplify (* (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) (pow (+ (log (* 2.0 PI)) (log n)) 2)) into (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 2.460 * [backup-simplify]: Simplify (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 2.465 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 2.472 * [backup-simplify]: Simplify (+ (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)))))))))))) 2.484 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))) 2.493 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (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)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 2.503 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (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)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (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)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 2.515 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (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)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (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)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 2.542 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (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)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) (pow (* 1 k) 2)) (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (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)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 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 k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) 2.543 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 k))) (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) into (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) 2.543 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in (k n) around 0 2.543 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 2.543 * [taylor]: Taking taylor expansion of 1.0 in n 2.543 * [backup-simplify]: Simplify 1.0 into 1.0 2.543 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 2.543 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.543 * [taylor]: Taking taylor expansion of k in n 2.543 * [backup-simplify]: Simplify k into k 2.543 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.544 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.544 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.544 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.544 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.544 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.544 * [taylor]: Taking taylor expansion of 0.5 in n 2.544 * [backup-simplify]: Simplify 0.5 into 0.5 2.544 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.544 * [taylor]: Taking taylor expansion of 1.0 in n 2.544 * [backup-simplify]: Simplify 1.0 into 1.0 2.544 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.544 * [taylor]: Taking taylor expansion of k in n 2.544 * [backup-simplify]: Simplify k into k 2.544 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.544 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.544 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.544 * [taylor]: Taking taylor expansion of 2.0 in n 2.544 * [backup-simplify]: Simplify 2.0 into 2.0 2.544 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.544 * [taylor]: Taking taylor expansion of PI in n 2.544 * [backup-simplify]: Simplify PI into PI 2.544 * [taylor]: Taking taylor expansion of n in n 2.544 * [backup-simplify]: Simplify 0 into 0 2.544 * [backup-simplify]: Simplify 1 into 1 2.545 * [backup-simplify]: Simplify (/ PI 1) into PI 2.545 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.546 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.546 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.547 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.547 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.548 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.549 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.550 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.550 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 2.551 * [taylor]: Taking taylor expansion of 1.0 in k 2.551 * [backup-simplify]: Simplify 1.0 into 1.0 2.551 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 2.551 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.551 * [taylor]: Taking taylor expansion of k in k 2.551 * [backup-simplify]: Simplify 0 into 0 2.551 * [backup-simplify]: Simplify 1 into 1 2.551 * [backup-simplify]: Simplify (sqrt 0) into 0 2.552 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.552 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.553 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.553 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.553 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.553 * [taylor]: Taking taylor expansion of 0.5 in k 2.553 * [backup-simplify]: Simplify 0.5 into 0.5 2.553 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.553 * [taylor]: Taking taylor expansion of 1.0 in k 2.553 * [backup-simplify]: Simplify 1.0 into 1.0 2.553 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.553 * [taylor]: Taking taylor expansion of k in k 2.553 * [backup-simplify]: Simplify 0 into 0 2.553 * [backup-simplify]: Simplify 1 into 1 2.553 * [backup-simplify]: Simplify (/ 1 1) into 1 2.553 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.553 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.553 * [taylor]: Taking taylor expansion of 2.0 in k 2.553 * [backup-simplify]: Simplify 2.0 into 2.0 2.553 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.553 * [taylor]: Taking taylor expansion of PI in k 2.553 * [backup-simplify]: Simplify PI into PI 2.553 * [taylor]: Taking taylor expansion of n in k 2.554 * [backup-simplify]: Simplify n into n 2.554 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.554 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.554 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.554 * [backup-simplify]: Simplify (- 1) into -1 2.555 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.555 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.555 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.555 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 2.555 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 2.555 * [taylor]: Taking taylor expansion of 1.0 in k 2.556 * [backup-simplify]: Simplify 1.0 into 1.0 2.556 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 2.556 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.556 * [taylor]: Taking taylor expansion of k in k 2.556 * [backup-simplify]: Simplify 0 into 0 2.556 * [backup-simplify]: Simplify 1 into 1 2.556 * [backup-simplify]: Simplify (sqrt 0) into 0 2.557 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.557 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.557 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.557 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.557 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.557 * [taylor]: Taking taylor expansion of 0.5 in k 2.557 * [backup-simplify]: Simplify 0.5 into 0.5 2.558 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.558 * [taylor]: Taking taylor expansion of 1.0 in k 2.558 * [backup-simplify]: Simplify 1.0 into 1.0 2.558 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.558 * [taylor]: Taking taylor expansion of k in k 2.558 * [backup-simplify]: Simplify 0 into 0 2.558 * [backup-simplify]: Simplify 1 into 1 2.558 * [backup-simplify]: Simplify (/ 1 1) into 1 2.558 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.558 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.558 * [taylor]: Taking taylor expansion of 2.0 in k 2.558 * [backup-simplify]: Simplify 2.0 into 2.0 2.558 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.558 * [taylor]: Taking taylor expansion of PI in k 2.558 * [backup-simplify]: Simplify PI into PI 2.558 * [taylor]: Taking taylor expansion of n in k 2.558 * [backup-simplify]: Simplify n into n 2.558 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.558 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.559 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.559 * [backup-simplify]: Simplify (- 1) into -1 2.559 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.560 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.560 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.560 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 2.561 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 2.561 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.561 * [taylor]: Taking taylor expansion of 0 in n 2.561 * [backup-simplify]: Simplify 0 into 0 2.561 * [backup-simplify]: Simplify 0 into 0 2.562 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 2.563 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 2.563 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 2.563 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) 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 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 2.563 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) 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 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 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) 2.566 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.566 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.566 * [taylor]: Taking taylor expansion of 1.0 in n 2.566 * [backup-simplify]: Simplify 1.0 into 1.0 2.566 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.566 * [taylor]: Taking taylor expansion of k in n 2.566 * [backup-simplify]: Simplify k into k 2.566 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.567 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.567 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.568 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.569 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 2.570 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.571 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.573 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 2.574 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 2.576 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 2.576 * [backup-simplify]: Simplify 0 into 0 2.579 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.580 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 2.582 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 2.582 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 2.582 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 2.582 * [taylor]: Taking taylor expansion of +nan.0 in n 2.582 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.582 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 2.582 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 2.582 * [taylor]: Taking taylor expansion of 0.5 in n 2.582 * [backup-simplify]: Simplify 0.5 into 0.5 2.582 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 2.582 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.582 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.582 * [taylor]: Taking taylor expansion of 2.0 in n 2.582 * [backup-simplify]: Simplify 2.0 into 2.0 2.582 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.582 * [taylor]: Taking taylor expansion of PI in n 2.582 * [backup-simplify]: Simplify PI into PI 2.582 * [taylor]: Taking taylor expansion of n in n 2.582 * [backup-simplify]: Simplify 0 into 0 2.582 * [backup-simplify]: Simplify 1 into 1 2.583 * [backup-simplify]: Simplify (/ PI 1) into PI 2.584 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.585 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.585 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.585 * [taylor]: Taking taylor expansion of 1.0 in n 2.585 * [backup-simplify]: Simplify 1.0 into 1.0 2.585 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.585 * [taylor]: Taking taylor expansion of k in n 2.585 * [backup-simplify]: Simplify k into k 2.585 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.592 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.592 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.592 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.593 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 2.595 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.595 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.596 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 2.597 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 2.598 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 2.599 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.599 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.599 * [backup-simplify]: Simplify (- 0) into 0 2.600 * [backup-simplify]: Simplify (+ 0 0) into 0 2.600 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.601 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.602 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.603 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.604 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 2.605 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.606 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 2.606 * [backup-simplify]: Simplify (- 0) into 0 2.606 * [backup-simplify]: Simplify 0 into 0 2.606 * [backup-simplify]: Simplify 0 into 0 2.608 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.609 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 2.610 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 2.610 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 2.610 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 2.610 * [taylor]: Taking taylor expansion of +nan.0 in n 2.610 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.610 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 2.610 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 2.610 * [taylor]: Taking taylor expansion of 0.5 in n 2.610 * [backup-simplify]: Simplify 0.5 into 0.5 2.610 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 2.610 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.610 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.610 * [taylor]: Taking taylor expansion of 2.0 in n 2.610 * [backup-simplify]: Simplify 2.0 into 2.0 2.610 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.610 * [taylor]: Taking taylor expansion of PI in n 2.610 * [backup-simplify]: Simplify PI into PI 2.610 * [taylor]: Taking taylor expansion of n in n 2.610 * [backup-simplify]: Simplify 0 into 0 2.610 * [backup-simplify]: Simplify 1 into 1 2.611 * [backup-simplify]: Simplify (/ PI 1) into PI 2.611 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.612 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.612 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.612 * [taylor]: Taking taylor expansion of 1.0 in n 2.612 * [backup-simplify]: Simplify 1.0 into 1.0 2.612 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.612 * [taylor]: Taking taylor expansion of k in n 2.612 * [backup-simplify]: Simplify k into k 2.612 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.613 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.613 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.613 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.614 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 2.614 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.615 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.616 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 2.617 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 2.618 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 2.620 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) 2.621 * [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)))) 2.621 * [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 2.621 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 2.621 * [taylor]: Taking taylor expansion of 1.0 in n 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 n 2.621 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.621 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.621 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.621 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.621 * [taylor]: Taking taylor expansion of 0.5 in n 2.621 * [backup-simplify]: Simplify 0.5 into 0.5 2.621 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.621 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.621 * [taylor]: Taking taylor expansion of k in n 2.621 * [backup-simplify]: Simplify k into k 2.621 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.621 * [taylor]: Taking taylor expansion of 1.0 in n 2.622 * [backup-simplify]: Simplify 1.0 into 1.0 2.622 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.622 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.622 * [taylor]: Taking taylor expansion of -2.0 in n 2.622 * [backup-simplify]: Simplify -2.0 into -2.0 2.622 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.622 * [taylor]: Taking taylor expansion of PI in n 2.622 * [backup-simplify]: Simplify PI into PI 2.622 * [taylor]: Taking taylor expansion of n in n 2.622 * [backup-simplify]: Simplify 0 into 0 2.622 * [backup-simplify]: Simplify 1 into 1 2.622 * [backup-simplify]: Simplify (/ PI 1) into PI 2.622 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.623 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.623 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.623 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.624 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.625 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.626 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.626 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.626 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.626 * [taylor]: Taking taylor expansion of -1 in n 2.626 * [backup-simplify]: Simplify -1 into -1 2.626 * [taylor]: Taking taylor expansion of k in n 2.626 * [backup-simplify]: Simplify k into k 2.626 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.626 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.626 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.626 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.627 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) 2.627 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 2.627 * [taylor]: Taking taylor expansion of 1.0 in k 2.627 * [backup-simplify]: Simplify 1.0 into 1.0 2.627 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 2.627 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.627 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.627 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.627 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.627 * [taylor]: Taking taylor expansion of 0.5 in k 2.627 * [backup-simplify]: Simplify 0.5 into 0.5 2.627 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.627 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.627 * [taylor]: Taking taylor expansion of k in k 2.627 * [backup-simplify]: Simplify 0 into 0 2.627 * [backup-simplify]: Simplify 1 into 1 2.628 * [backup-simplify]: Simplify (/ 1 1) into 1 2.628 * [taylor]: Taking taylor expansion of 1.0 in k 2.628 * [backup-simplify]: Simplify 1.0 into 1.0 2.628 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.628 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.628 * [taylor]: Taking taylor expansion of -2.0 in k 2.628 * [backup-simplify]: Simplify -2.0 into -2.0 2.628 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.628 * [taylor]: Taking taylor expansion of PI in k 2.628 * [backup-simplify]: Simplify PI into PI 2.628 * [taylor]: Taking taylor expansion of n in k 2.628 * [backup-simplify]: Simplify n into n 2.628 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.628 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.628 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.628 * [backup-simplify]: Simplify (+ 1 0) into 1 2.629 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.629 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.629 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 2.629 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.629 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.629 * [taylor]: Taking taylor expansion of -1 in k 2.629 * [backup-simplify]: Simplify -1 into -1 2.629 * [taylor]: Taking taylor expansion of k in k 2.629 * [backup-simplify]: Simplify 0 into 0 2.629 * [backup-simplify]: Simplify 1 into 1 2.629 * [backup-simplify]: Simplify (/ -1 1) into -1 2.629 * [backup-simplify]: Simplify (sqrt 0) into 0 2.630 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.630 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 2.631 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 2.631 * [taylor]: Taking taylor expansion of 1.0 in k 2.631 * [backup-simplify]: Simplify 1.0 into 1.0 2.631 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 2.631 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.631 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.631 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.631 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.631 * [taylor]: Taking taylor expansion of 0.5 in k 2.631 * [backup-simplify]: Simplify 0.5 into 0.5 2.631 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.631 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.631 * [taylor]: Taking taylor expansion of k in k 2.631 * [backup-simplify]: Simplify 0 into 0 2.631 * [backup-simplify]: Simplify 1 into 1 2.631 * [backup-simplify]: Simplify (/ 1 1) into 1 2.631 * [taylor]: Taking taylor expansion of 1.0 in k 2.631 * [backup-simplify]: Simplify 1.0 into 1.0 2.631 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.631 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.631 * [taylor]: Taking taylor expansion of -2.0 in k 2.631 * [backup-simplify]: Simplify -2.0 into -2.0 2.631 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.631 * [taylor]: Taking taylor expansion of PI in k 2.631 * [backup-simplify]: Simplify PI into PI 2.631 * [taylor]: Taking taylor expansion of n in k 2.631 * [backup-simplify]: Simplify n into n 2.631 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.631 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.631 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.632 * [backup-simplify]: Simplify (+ 1 0) into 1 2.632 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.632 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.632 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 2.632 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.632 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.632 * [taylor]: Taking taylor expansion of -1 in k 2.632 * [backup-simplify]: Simplify -1 into -1 2.632 * [taylor]: Taking taylor expansion of k in k 2.632 * [backup-simplify]: Simplify 0 into 0 2.632 * [backup-simplify]: Simplify 1 into 1 2.633 * [backup-simplify]: Simplify (/ -1 1) into -1 2.633 * [backup-simplify]: Simplify (sqrt 0) into 0 2.634 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.634 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 2.634 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 2.634 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 2.634 * [taylor]: Taking taylor expansion of +nan.0 in n 2.634 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.634 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 2.634 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 2.634 * [taylor]: Taking taylor expansion of 0.5 in n 2.634 * [backup-simplify]: Simplify 0.5 into 0.5 2.634 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 2.634 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.634 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.634 * [taylor]: Taking taylor expansion of k in n 2.634 * [backup-simplify]: Simplify k into k 2.634 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.634 * [taylor]: Taking taylor expansion of 1.0 in n 2.634 * [backup-simplify]: Simplify 1.0 into 1.0 2.634 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.634 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.635 * [taylor]: Taking taylor expansion of -2.0 in n 2.635 * [backup-simplify]: Simplify -2.0 into -2.0 2.635 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.635 * [taylor]: Taking taylor expansion of PI in n 2.635 * [backup-simplify]: Simplify PI into PI 2.635 * [taylor]: Taking taylor expansion of n in n 2.635 * [backup-simplify]: Simplify 0 into 0 2.635 * [backup-simplify]: Simplify 1 into 1 2.635 * [backup-simplify]: Simplify (/ PI 1) into PI 2.635 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.636 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.636 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.637 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.638 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 2.638 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.639 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.640 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 2.641 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 2.641 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.643 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.644 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 2.644 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 2.644 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 2.644 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 2.644 * [taylor]: Taking taylor expansion of +nan.0 in n 2.644 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.644 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 2.644 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 2.644 * [taylor]: Taking taylor expansion of 0.5 in n 2.644 * [backup-simplify]: Simplify 0.5 into 0.5 2.644 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 2.645 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.645 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.645 * [taylor]: Taking taylor expansion of k in n 2.645 * [backup-simplify]: Simplify k into k 2.645 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.645 * [taylor]: Taking taylor expansion of 1.0 in n 2.645 * [backup-simplify]: Simplify 1.0 into 1.0 2.645 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.645 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.645 * [taylor]: Taking taylor expansion of -2.0 in n 2.645 * [backup-simplify]: Simplify -2.0 into -2.0 2.645 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.645 * [taylor]: Taking taylor expansion of PI in n 2.645 * [backup-simplify]: Simplify PI into PI 2.645 * [taylor]: Taking taylor expansion of n in n 2.645 * [backup-simplify]: Simplify 0 into 0 2.645 * [backup-simplify]: Simplify 1 into 1 2.645 * [backup-simplify]: Simplify (/ PI 1) into PI 2.645 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.646 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.646 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.647 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.648 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 2.649 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.649 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.650 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 2.651 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 2.652 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 2.652 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.653 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.654 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.654 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.654 * [backup-simplify]: Simplify (+ 0 0) into 0 2.655 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.656 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.657 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 2.658 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.659 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 2.659 * [backup-simplify]: Simplify 0 into 0 2.660 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.662 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.663 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 2.663 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 2.663 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 2.664 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 2.664 * [taylor]: Taking taylor expansion of +nan.0 in n 2.664 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.664 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 2.664 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 2.664 * [taylor]: Taking taylor expansion of 0.5 in n 2.664 * [backup-simplify]: Simplify 0.5 into 0.5 2.664 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 2.664 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.664 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.664 * [taylor]: Taking taylor expansion of k in n 2.664 * [backup-simplify]: Simplify k into k 2.664 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.664 * [taylor]: Taking taylor expansion of 1.0 in n 2.664 * [backup-simplify]: Simplify 1.0 into 1.0 2.664 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.664 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.664 * [taylor]: Taking taylor expansion of -2.0 in n 2.664 * [backup-simplify]: Simplify -2.0 into -2.0 2.664 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.664 * [taylor]: Taking taylor expansion of PI in n 2.664 * [backup-simplify]: Simplify PI into PI 2.664 * [taylor]: Taking taylor expansion of n in n 2.664 * [backup-simplify]: Simplify 0 into 0 2.664 * [backup-simplify]: Simplify 1 into 1 2.664 * [backup-simplify]: Simplify (/ PI 1) into PI 2.665 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.665 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.665 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.666 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.667 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 2.668 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.668 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.669 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 2.670 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 2.671 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 2.674 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +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))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 2.674 * * * [progress]: simplifying candidates 2.676 * [simplify]: Simplifying: (* (+ (+ (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)) (- (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) (* (* 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) (+ (- (log 1.0) (log (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (+ (log (/ 1.0 (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (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)))) (* (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (* (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)))) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) 1) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (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 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 2.681 * * [simplify]: Extracting # 0 : cost 0 2.682 * * [simplify]: Extracting # 1 : cost 0 2.682 * * [simplify]: Extracting # 2 : cost 0 2.682 * * [simplify]: Extracting # 3 : cost 0 2.683 * * [simplify]: Extracting # 4 : cost 0 2.683 * * [simplify]: Extracting # 5 : cost 0 2.684 * * [simplify]: Extracting # 6 : cost 0 2.684 * * [simplify]: Extracting # 7 : cost 0 2.685 * * [simplify]: Extracting # 8 : cost 0 2.689 * * [simplify]: Extracting # 9 : cost 0 2.690 * * [simplify]: Extracting # 10 : cost 0 2.690 * * [simplify]: Extracting # 11 : cost 0 2.690 * * [simplify]: Extracting # 12 : cost 0 2.691 * * [simplify]: Extracting # 13 : cost 0 2.692 * * [simplify]: Extracting # 14 : cost 0 2.692 * * [simplify]: Extracting # 15 : cost 0 2.693 * * [simplify]: Extracting # 16 : cost 0 2.693 * * [simplify]: Extracting # 17 : cost 0 2.694 * * [simplify]: Extracting # 18 : cost 0 2.694 * * [simplify]: Extracting # 19 : cost 0 2.695 * * [simplify]: Extracting # 20 : cost 0 2.695 * * [simplify]: Extracting # 21 : cost 0 2.696 * * [simplify]: Extracting # 22 : cost 0 2.696 * * [simplify]: Extracting # 23 : cost 0 2.697 * * [simplify]: Extracting # 24 : cost 0 2.697 * * [simplify]: Extracting # 25 : cost 0 2.698 * * [simplify]: Extracting # 26 : cost 0 2.698 * * [simplify]: Extracting # 27 : cost 0 2.699 * * [simplify]: Extracting # 28 : cost 0 2.699 * * [simplify]: Extracting # 29 : cost 0 2.700 * * [simplify]: Extracting # 30 : cost 0 2.700 * * [simplify]: Extracting # 31 : cost 0 2.701 * * [simplify]: Extracting # 32 : cost 0 2.701 * * [simplify]: Extracting # 33 : cost 0 2.702 * * [simplify]: iteration 0 : 361 enodes (cost 2800 ) 2.813 * * [simplify]: Extracting # 0 : cost 0 2.814 * * [simplify]: Extracting # 1 : cost 0 2.816 * * [simplify]: Extracting # 2 : cost 0 2.817 * * [simplify]: Extracting # 3 : cost 0 2.818 * * [simplify]: Extracting # 4 : cost 0 2.820 * * [simplify]: Extracting # 5 : cost 0 2.821 * * [simplify]: Extracting # 6 : cost 0 2.822 * * [simplify]: iteration 1 : 1008 enodes (cost 2643 ) 3.523 * * [simplify]: Extracting # 0 : cost 0 3.533 * * [simplify]: Extracting # 1 : cost 0 3.546 * * [simplify]: Extracting # 2 : cost 0 3.558 * * [simplify]: Extracting # 3 : cost 0 3.564 * * [simplify]: Extracting # 4 : cost 0 3.571 * * [simplify]: Extracting # 5 : cost 0 3.577 * * [simplify]: iteration 2 : 4741 enodes (cost 2477 ) 5.297 * * [simplify]: Extracting # 0 : cost 0 5.310 * * [simplify]: Extracting # 1 : cost 0 5.322 * * [simplify]: Extracting # 2 : cost 0 5.334 * * [simplify]: Extracting # 3 : cost 0 5.346 * * [simplify]: iteration done: 5000 enodes (cost 2477 ) 5.349 * [simplify]: Simplified to: (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 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 (* n PI)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (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))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (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))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (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 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (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)) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (pow 1.0 3) (* k (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (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)) (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) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (pow n 3) (pow PI 3)) (pow 2.0 3)) (* (pow n 3) (pow (* 2.0 PI) 3)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (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) (* n PI) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (pow 1.0 3) (* k (sqrt k))) (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3)) (pow (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (pow (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k)) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (+ (+ (* (* 0.125 (pow k 2)) (+ (* (pow (log (* 2.0 PI)) 2) (pow (* (* 2.0 PI) n) 0.5)) (* (pow (* (* 2.0 PI) n) 0.5) (pow (log n) 2)))) (* (* (pow k 2) (log (* 2.0 PI))) (* (* (pow (* (* 2.0 PI) n) 0.5) (log n)) 0.25))) (pow (* (* 2.0 PI) n) 0.5)) (* 0.5 (* k (+ (* (pow (* (* 2.0 PI) n) 0.5) (log (* 2.0 PI))) (* (pow (* (* 2.0 PI) n) 0.5) (log n)))))) (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (- (* +nan.0 k) (- (* +nan.0 (pow k 2)) +nan.0))) (+ (- (/ +nan.0 (pow k 2))) (- (/ +nan.0 k) (/ +nan.0 (pow k 3)))) (- (+ (- (/ +nan.0 (pow k 2)) (/ +nan.0 k)) +nan.0)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (- (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (- (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (+ (- (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5)))) (+ (- (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5)))) (+ (- (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (* +nan.0 (- (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))) (+ (* +nan.0 (- (/ (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) k) (/ (/ (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) k) k))) (* (- +nan.0) (/ (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (pow k 3)))) (+ (- (* +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)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))) 5.351 * * * [progress]: adding candidates to table 6.046 * * [progress]: iteration 2 / 4 6.046 * * * [progress]: picking best candidate 6.082 * * * * [pick]: Picked # 6.082 * * * [progress]: localizing error 6.107 * * * [progress]: generating rewritten candidates 6.107 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 6.144 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 6.196 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 6.208 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 6.264 * * * [progress]: generating series expansions 6.264 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 6.264 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 6.265 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 6.265 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 6.265 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 6.265 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 6.265 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 6.265 * [taylor]: Taking taylor expansion of 0.25 in k 6.265 * [backup-simplify]: Simplify 0.25 into 0.25 6.265 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.265 * [taylor]: Taking taylor expansion of 1.0 in k 6.265 * [backup-simplify]: Simplify 1.0 into 1.0 6.265 * [taylor]: Taking taylor expansion of k in k 6.265 * [backup-simplify]: Simplify 0 into 0 6.265 * [backup-simplify]: Simplify 1 into 1 6.265 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 6.265 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 6.265 * [taylor]: Taking taylor expansion of 2.0 in k 6.265 * [backup-simplify]: Simplify 2.0 into 2.0 6.265 * [taylor]: Taking taylor expansion of (* n PI) in k 6.265 * [taylor]: Taking taylor expansion of n in k 6.265 * [backup-simplify]: Simplify n into n 6.265 * [taylor]: Taking taylor expansion of PI in k 6.265 * [backup-simplify]: Simplify PI into PI 6.265 * [backup-simplify]: Simplify (* n PI) into (* n PI) 6.265 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 6.265 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 6.265 * [backup-simplify]: Simplify (- 0) into 0 6.266 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.266 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 6.266 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 6.266 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 6.266 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 6.266 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.266 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.266 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 6.266 * [taylor]: Taking taylor expansion of 0.25 in n 6.266 * [backup-simplify]: Simplify 0.25 into 0.25 6.266 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.266 * [taylor]: Taking taylor expansion of 1.0 in n 6.266 * [backup-simplify]: Simplify 1.0 into 1.0 6.266 * [taylor]: Taking taylor expansion of k in n 6.266 * [backup-simplify]: Simplify k into k 6.266 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.266 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.266 * [taylor]: Taking taylor expansion of 2.0 in n 6.266 * [backup-simplify]: Simplify 2.0 into 2.0 6.266 * [taylor]: Taking taylor expansion of (* n PI) in n 6.266 * [taylor]: Taking taylor expansion of n in n 6.266 * [backup-simplify]: Simplify 0 into 0 6.266 * [backup-simplify]: Simplify 1 into 1 6.266 * [taylor]: Taking taylor expansion of PI in n 6.267 * [backup-simplify]: Simplify PI into PI 6.267 * [backup-simplify]: Simplify (* 0 PI) into 0 6.267 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.268 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.269 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.270 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.270 * [backup-simplify]: Simplify (- k) into (- k) 6.270 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.270 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 6.271 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.272 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 6.273 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 6.273 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 6.273 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.273 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.273 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 6.274 * [taylor]: Taking taylor expansion of 0.25 in n 6.274 * [backup-simplify]: Simplify 0.25 into 0.25 6.274 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.274 * [taylor]: Taking taylor expansion of 1.0 in n 6.274 * [backup-simplify]: Simplify 1.0 into 1.0 6.274 * [taylor]: Taking taylor expansion of k in n 6.274 * [backup-simplify]: Simplify k into k 6.274 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.274 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.274 * [taylor]: Taking taylor expansion of 2.0 in n 6.274 * [backup-simplify]: Simplify 2.0 into 2.0 6.274 * [taylor]: Taking taylor expansion of (* n PI) in n 6.274 * [taylor]: Taking taylor expansion of n in n 6.274 * [backup-simplify]: Simplify 0 into 0 6.274 * [backup-simplify]: Simplify 1 into 1 6.274 * [taylor]: Taking taylor expansion of PI in n 6.274 * [backup-simplify]: Simplify PI into PI 6.274 * [backup-simplify]: Simplify (* 0 PI) into 0 6.275 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.276 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.278 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.279 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.279 * [backup-simplify]: Simplify (- k) into (- k) 6.279 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.279 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 6.280 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.281 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 6.283 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 6.283 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 6.283 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 6.283 * [taylor]: Taking taylor expansion of 0.25 in k 6.283 * [backup-simplify]: Simplify 0.25 into 0.25 6.283 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 6.283 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.283 * [taylor]: Taking taylor expansion of 1.0 in k 6.283 * [backup-simplify]: Simplify 1.0 into 1.0 6.283 * [taylor]: Taking taylor expansion of k in k 6.283 * [backup-simplify]: Simplify 0 into 0 6.283 * [backup-simplify]: Simplify 1 into 1 6.283 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 6.283 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.283 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.283 * [taylor]: Taking taylor expansion of 2.0 in k 6.283 * [backup-simplify]: Simplify 2.0 into 2.0 6.283 * [taylor]: Taking taylor expansion of PI in k 6.283 * [backup-simplify]: Simplify PI into PI 6.284 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.285 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.285 * [taylor]: Taking taylor expansion of (log n) in k 6.285 * [taylor]: Taking taylor expansion of n in k 6.285 * [backup-simplify]: Simplify n into n 6.285 * [backup-simplify]: Simplify (log n) into (log n) 6.285 * [backup-simplify]: Simplify (- 0) into 0 6.286 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.287 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 6.288 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 6.289 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 6.290 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 6.291 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 6.292 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 6.293 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 6.295 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.296 * [backup-simplify]: Simplify (- 0) into 0 6.296 * [backup-simplify]: Simplify (+ 0 0) into 0 6.297 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 6.298 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.299 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 6.301 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.301 * [taylor]: Taking taylor expansion of 0 in k 6.301 * [backup-simplify]: Simplify 0 into 0 6.301 * [backup-simplify]: Simplify 0 into 0 6.302 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.304 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.304 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 6.305 * [backup-simplify]: Simplify (+ 0 0) into 0 6.305 * [backup-simplify]: Simplify (- 1) into -1 6.306 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.307 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 6.309 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 6.313 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 6.315 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 6.316 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 6.317 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 6.319 * [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 6.319 * [backup-simplify]: Simplify (- 0) into 0 6.319 * [backup-simplify]: Simplify (+ 0 0) into 0 6.320 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 6.321 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.322 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.323 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.323 * [taylor]: Taking taylor expansion of 0 in k 6.323 * [backup-simplify]: Simplify 0 into 0 6.323 * [backup-simplify]: Simplify 0 into 0 6.323 * [backup-simplify]: Simplify 0 into 0 6.324 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.326 * [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 6.327 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 6.327 * [backup-simplify]: Simplify (+ 0 0) into 0 6.327 * [backup-simplify]: Simplify (- 0) into 0 6.328 * [backup-simplify]: Simplify (+ 0 0) into 0 6.329 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.330 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 6.333 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 6.336 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 6.342 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 6.343 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 6.343 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 6.343 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 6.343 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 6.343 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 6.343 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 6.343 * [taylor]: Taking taylor expansion of 0.25 in k 6.343 * [backup-simplify]: Simplify 0.25 into 0.25 6.343 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.343 * [taylor]: Taking taylor expansion of 1.0 in k 6.343 * [backup-simplify]: Simplify 1.0 into 1.0 6.343 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.343 * [taylor]: Taking taylor expansion of k in k 6.343 * [backup-simplify]: Simplify 0 into 0 6.343 * [backup-simplify]: Simplify 1 into 1 6.343 * [backup-simplify]: Simplify (/ 1 1) into 1 6.343 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 6.343 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 6.343 * [taylor]: Taking taylor expansion of 2.0 in k 6.343 * [backup-simplify]: Simplify 2.0 into 2.0 6.343 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.343 * [taylor]: Taking taylor expansion of PI in k 6.343 * [backup-simplify]: Simplify PI into PI 6.343 * [taylor]: Taking taylor expansion of n in k 6.343 * [backup-simplify]: Simplify n into n 6.344 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.344 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 6.344 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 6.344 * [backup-simplify]: Simplify (- 1) into -1 6.344 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.344 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 6.345 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 6.345 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 6.345 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 6.345 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.345 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.345 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 6.345 * [taylor]: Taking taylor expansion of 0.25 in n 6.345 * [backup-simplify]: Simplify 0.25 into 0.25 6.345 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.345 * [taylor]: Taking taylor expansion of 1.0 in n 6.345 * [backup-simplify]: Simplify 1.0 into 1.0 6.345 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.345 * [taylor]: Taking taylor expansion of k in n 6.345 * [backup-simplify]: Simplify k into k 6.345 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.345 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.345 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.345 * [taylor]: Taking taylor expansion of 2.0 in n 6.345 * [backup-simplify]: Simplify 2.0 into 2.0 6.345 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.345 * [taylor]: Taking taylor expansion of PI in n 6.345 * [backup-simplify]: Simplify PI into PI 6.345 * [taylor]: Taking taylor expansion of n in n 6.345 * [backup-simplify]: Simplify 0 into 0 6.345 * [backup-simplify]: Simplify 1 into 1 6.346 * [backup-simplify]: Simplify (/ PI 1) into PI 6.346 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.346 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.347 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.347 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.347 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 6.348 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.348 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 6.349 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.349 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 6.349 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.349 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.349 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 6.349 * [taylor]: Taking taylor expansion of 0.25 in n 6.349 * [backup-simplify]: Simplify 0.25 into 0.25 6.349 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.349 * [taylor]: Taking taylor expansion of 1.0 in n 6.349 * [backup-simplify]: Simplify 1.0 into 1.0 6.349 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.349 * [taylor]: Taking taylor expansion of k in n 6.349 * [backup-simplify]: Simplify k into k 6.349 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.350 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.350 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.350 * [taylor]: Taking taylor expansion of 2.0 in n 6.350 * [backup-simplify]: Simplify 2.0 into 2.0 6.350 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.350 * [taylor]: Taking taylor expansion of PI in n 6.350 * [backup-simplify]: Simplify PI into PI 6.350 * [taylor]: Taking taylor expansion of n in n 6.350 * [backup-simplify]: Simplify 0 into 0 6.350 * [backup-simplify]: Simplify 1 into 1 6.350 * [backup-simplify]: Simplify (/ PI 1) into PI 6.350 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.351 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.351 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.351 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.351 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 6.352 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.353 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 6.353 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.354 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 6.354 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 6.354 * [taylor]: Taking taylor expansion of 0.25 in k 6.354 * [backup-simplify]: Simplify 0.25 into 0.25 6.354 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 6.354 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 6.354 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.354 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.354 * [taylor]: Taking taylor expansion of 2.0 in k 6.354 * [backup-simplify]: Simplify 2.0 into 2.0 6.354 * [taylor]: Taking taylor expansion of PI in k 6.354 * [backup-simplify]: Simplify PI into PI 6.354 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.355 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.355 * [taylor]: Taking taylor expansion of (log n) in k 6.355 * [taylor]: Taking taylor expansion of n in k 6.355 * [backup-simplify]: Simplify n into n 6.355 * [backup-simplify]: Simplify (log n) into (log n) 6.355 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.355 * [taylor]: Taking taylor expansion of 1.0 in k 6.355 * [backup-simplify]: Simplify 1.0 into 1.0 6.355 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.355 * [taylor]: Taking taylor expansion of k in k 6.355 * [backup-simplify]: Simplify 0 into 0 6.355 * [backup-simplify]: Simplify 1 into 1 6.355 * [backup-simplify]: Simplify (/ 1 1) into 1 6.355 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.356 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 6.356 * [backup-simplify]: Simplify (- 1) into -1 6.356 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.357 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 6.358 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 6.359 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.359 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.360 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.360 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.361 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.361 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.362 * [backup-simplify]: Simplify (- 0) into 0 6.362 * [backup-simplify]: Simplify (+ 0 0) into 0 6.362 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 6.363 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.364 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 6.365 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.365 * [taylor]: Taking taylor expansion of 0 in k 6.365 * [backup-simplify]: Simplify 0 into 0 6.365 * [backup-simplify]: Simplify 0 into 0 6.365 * [backup-simplify]: Simplify 0 into 0 6.366 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.372 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.376 * [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 6.376 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.376 * [backup-simplify]: Simplify (- 0) into 0 6.377 * [backup-simplify]: Simplify (+ 0 0) into 0 6.378 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 6.379 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.381 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 6.383 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.384 * [taylor]: Taking taylor expansion of 0 in k 6.384 * [backup-simplify]: Simplify 0 into 0 6.384 * [backup-simplify]: Simplify 0 into 0 6.384 * [backup-simplify]: Simplify 0 into 0 6.384 * [backup-simplify]: Simplify 0 into 0 6.385 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.386 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.392 * [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 6.392 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.392 * [backup-simplify]: Simplify (- 0) into 0 6.393 * [backup-simplify]: Simplify (+ 0 0) into 0 6.393 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 6.394 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.395 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 6.397 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 6.397 * [taylor]: Taking taylor expansion of 0 in k 6.397 * [backup-simplify]: Simplify 0 into 0 6.397 * [backup-simplify]: Simplify 0 into 0 6.398 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 6.398 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 6.398 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 6.398 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 6.399 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 6.399 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 6.399 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 6.399 * [taylor]: Taking taylor expansion of 0.25 in k 6.399 * [backup-simplify]: Simplify 0.25 into 0.25 6.399 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.399 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.399 * [taylor]: Taking taylor expansion of k in k 6.399 * [backup-simplify]: Simplify 0 into 0 6.399 * [backup-simplify]: Simplify 1 into 1 6.399 * [backup-simplify]: Simplify (/ 1 1) into 1 6.399 * [taylor]: Taking taylor expansion of 1.0 in k 6.399 * [backup-simplify]: Simplify 1.0 into 1.0 6.399 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 6.399 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 6.399 * [taylor]: Taking taylor expansion of -2.0 in k 6.399 * [backup-simplify]: Simplify -2.0 into -2.0 6.399 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.399 * [taylor]: Taking taylor expansion of PI in k 6.399 * [backup-simplify]: Simplify PI into PI 6.399 * [taylor]: Taking taylor expansion of n in k 6.399 * [backup-simplify]: Simplify n into n 6.399 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.399 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 6.399 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 6.400 * [backup-simplify]: Simplify (+ 1 0) into 1 6.400 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 6.400 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 6.400 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 6.400 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 6.400 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.400 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.400 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 6.400 * [taylor]: Taking taylor expansion of 0.25 in n 6.400 * [backup-simplify]: Simplify 0.25 into 0.25 6.400 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.400 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.400 * [taylor]: Taking taylor expansion of k in n 6.400 * [backup-simplify]: Simplify k into k 6.400 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.400 * [taylor]: Taking taylor expansion of 1.0 in n 6.400 * [backup-simplify]: Simplify 1.0 into 1.0 6.400 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.400 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.400 * [taylor]: Taking taylor expansion of -2.0 in n 6.401 * [backup-simplify]: Simplify -2.0 into -2.0 6.401 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.401 * [taylor]: Taking taylor expansion of PI in n 6.401 * [backup-simplify]: Simplify PI into PI 6.401 * [taylor]: Taking taylor expansion of n in n 6.401 * [backup-simplify]: Simplify 0 into 0 6.401 * [backup-simplify]: Simplify 1 into 1 6.401 * [backup-simplify]: Simplify (/ PI 1) into PI 6.401 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.402 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.402 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.402 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 6.403 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.404 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 6.404 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.404 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 6.404 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.404 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.404 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 6.405 * [taylor]: Taking taylor expansion of 0.25 in n 6.405 * [backup-simplify]: Simplify 0.25 into 0.25 6.405 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.405 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.405 * [taylor]: Taking taylor expansion of k in n 6.405 * [backup-simplify]: Simplify k into k 6.405 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.405 * [taylor]: Taking taylor expansion of 1.0 in n 6.405 * [backup-simplify]: Simplify 1.0 into 1.0 6.405 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.405 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.405 * [taylor]: Taking taylor expansion of -2.0 in n 6.405 * [backup-simplify]: Simplify -2.0 into -2.0 6.405 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.405 * [taylor]: Taking taylor expansion of PI in n 6.405 * [backup-simplify]: Simplify PI into PI 6.405 * [taylor]: Taking taylor expansion of n in n 6.405 * [backup-simplify]: Simplify 0 into 0 6.405 * [backup-simplify]: Simplify 1 into 1 6.405 * [backup-simplify]: Simplify (/ PI 1) into PI 6.405 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.406 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.406 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.406 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 6.407 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.408 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 6.409 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.409 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 6.409 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 6.409 * [taylor]: Taking taylor expansion of 0.25 in k 6.409 * [backup-simplify]: Simplify 0.25 into 0.25 6.409 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 6.409 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.409 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.409 * [taylor]: Taking taylor expansion of k in k 6.409 * [backup-simplify]: Simplify 0 into 0 6.409 * [backup-simplify]: Simplify 1 into 1 6.409 * [backup-simplify]: Simplify (/ 1 1) into 1 6.409 * [taylor]: Taking taylor expansion of 1.0 in k 6.409 * [backup-simplify]: Simplify 1.0 into 1.0 6.409 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 6.409 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 6.409 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 6.409 * [taylor]: Taking taylor expansion of -2.0 in k 6.409 * [backup-simplify]: Simplify -2.0 into -2.0 6.409 * [taylor]: Taking taylor expansion of PI in k 6.409 * [backup-simplify]: Simplify PI into PI 6.410 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.410 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.410 * [taylor]: Taking taylor expansion of (log n) in k 6.410 * [taylor]: Taking taylor expansion of n in k 6.410 * [backup-simplify]: Simplify n into n 6.410 * [backup-simplify]: Simplify (log n) into (log n) 6.411 * [backup-simplify]: Simplify (+ 1 0) into 1 6.411 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.411 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 6.412 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 6.413 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 6.413 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.414 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.415 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.415 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 6.416 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 6.416 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.417 * [backup-simplify]: Simplify (+ 0 0) into 0 6.417 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 6.418 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.419 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 6.420 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.420 * [taylor]: Taking taylor expansion of 0 in k 6.420 * [backup-simplify]: Simplify 0 into 0 6.420 * [backup-simplify]: Simplify 0 into 0 6.421 * [backup-simplify]: Simplify 0 into 0 6.422 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.423 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.427 * [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 6.427 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.427 * [backup-simplify]: Simplify (+ 0 0) into 0 6.428 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 6.429 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.430 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 6.431 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.431 * [taylor]: Taking taylor expansion of 0 in k 6.431 * [backup-simplify]: Simplify 0 into 0 6.431 * [backup-simplify]: Simplify 0 into 0 6.431 * [backup-simplify]: Simplify 0 into 0 6.431 * [backup-simplify]: Simplify 0 into 0 6.432 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.432 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.436 * [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 6.436 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.436 * [backup-simplify]: Simplify (+ 0 0) into 0 6.437 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 6.438 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.439 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 6.441 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 6.441 * [taylor]: Taking taylor expansion of 0 in k 6.441 * [backup-simplify]: Simplify 0 into 0 6.441 * [backup-simplify]: Simplify 0 into 0 6.442 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 6.442 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 6.442 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 6.442 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 6.442 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 6.443 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 6.443 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 6.443 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 6.443 * [taylor]: Taking taylor expansion of 0.25 in k 6.443 * [backup-simplify]: Simplify 0.25 into 0.25 6.443 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.443 * [taylor]: Taking taylor expansion of 1.0 in k 6.443 * [backup-simplify]: Simplify 1.0 into 1.0 6.443 * [taylor]: Taking taylor expansion of k in k 6.443 * [backup-simplify]: Simplify 0 into 0 6.443 * [backup-simplify]: Simplify 1 into 1 6.443 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 6.443 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 6.443 * [taylor]: Taking taylor expansion of 2.0 in k 6.443 * [backup-simplify]: Simplify 2.0 into 2.0 6.443 * [taylor]: Taking taylor expansion of (* n PI) in k 6.443 * [taylor]: Taking taylor expansion of n in k 6.443 * [backup-simplify]: Simplify n into n 6.443 * [taylor]: Taking taylor expansion of PI in k 6.443 * [backup-simplify]: Simplify PI into PI 6.443 * [backup-simplify]: Simplify (* n PI) into (* n PI) 6.443 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 6.443 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 6.443 * [backup-simplify]: Simplify (- 0) into 0 6.444 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.444 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 6.444 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 6.444 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 6.444 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 6.444 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.444 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.444 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 6.444 * [taylor]: Taking taylor expansion of 0.25 in n 6.444 * [backup-simplify]: Simplify 0.25 into 0.25 6.444 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.444 * [taylor]: Taking taylor expansion of 1.0 in n 6.444 * [backup-simplify]: Simplify 1.0 into 1.0 6.444 * [taylor]: Taking taylor expansion of k in n 6.444 * [backup-simplify]: Simplify k into k 6.444 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.444 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.444 * [taylor]: Taking taylor expansion of 2.0 in n 6.444 * [backup-simplify]: Simplify 2.0 into 2.0 6.444 * [taylor]: Taking taylor expansion of (* n PI) in n 6.444 * [taylor]: Taking taylor expansion of n in n 6.444 * [backup-simplify]: Simplify 0 into 0 6.444 * [backup-simplify]: Simplify 1 into 1 6.444 * [taylor]: Taking taylor expansion of PI in n 6.444 * [backup-simplify]: Simplify PI into PI 6.445 * [backup-simplify]: Simplify (* 0 PI) into 0 6.445 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.446 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.447 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.447 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.447 * [backup-simplify]: Simplify (- k) into (- k) 6.447 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.448 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 6.448 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.449 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 6.450 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 6.450 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 6.450 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.450 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.450 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 6.450 * [taylor]: Taking taylor expansion of 0.25 in n 6.450 * [backup-simplify]: Simplify 0.25 into 0.25 6.450 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.450 * [taylor]: Taking taylor expansion of 1.0 in n 6.450 * [backup-simplify]: Simplify 1.0 into 1.0 6.450 * [taylor]: Taking taylor expansion of k in n 6.450 * [backup-simplify]: Simplify k into k 6.450 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.450 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.450 * [taylor]: Taking taylor expansion of 2.0 in n 6.450 * [backup-simplify]: Simplify 2.0 into 2.0 6.450 * [taylor]: Taking taylor expansion of (* n PI) in n 6.450 * [taylor]: Taking taylor expansion of n in n 6.450 * [backup-simplify]: Simplify 0 into 0 6.450 * [backup-simplify]: Simplify 1 into 1 6.450 * [taylor]: Taking taylor expansion of PI in n 6.451 * [backup-simplify]: Simplify PI into PI 6.451 * [backup-simplify]: Simplify (* 0 PI) into 0 6.451 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.452 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.453 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.453 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.454 * [backup-simplify]: Simplify (- k) into (- k) 6.454 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.454 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 6.455 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.455 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 6.457 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 6.457 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 6.457 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 6.457 * [taylor]: Taking taylor expansion of 0.25 in k 6.457 * [backup-simplify]: Simplify 0.25 into 0.25 6.457 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 6.457 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.457 * [taylor]: Taking taylor expansion of 1.0 in k 6.457 * [backup-simplify]: Simplify 1.0 into 1.0 6.457 * [taylor]: Taking taylor expansion of k in k 6.457 * [backup-simplify]: Simplify 0 into 0 6.457 * [backup-simplify]: Simplify 1 into 1 6.457 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 6.457 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.457 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.457 * [taylor]: Taking taylor expansion of 2.0 in k 6.457 * [backup-simplify]: Simplify 2.0 into 2.0 6.457 * [taylor]: Taking taylor expansion of PI in k 6.457 * [backup-simplify]: Simplify PI into PI 6.458 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.459 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.459 * [taylor]: Taking taylor expansion of (log n) in k 6.459 * [taylor]: Taking taylor expansion of n in k 6.459 * [backup-simplify]: Simplify n into n 6.459 * [backup-simplify]: Simplify (log n) into (log n) 6.459 * [backup-simplify]: Simplify (- 0) into 0 6.460 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.461 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 6.462 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 6.463 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 6.464 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 6.465 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 6.466 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 6.467 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 6.469 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.470 * [backup-simplify]: Simplify (- 0) into 0 6.470 * [backup-simplify]: Simplify (+ 0 0) into 0 6.470 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 6.472 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.473 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 6.475 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.475 * [taylor]: Taking taylor expansion of 0 in k 6.475 * [backup-simplify]: Simplify 0 into 0 6.475 * [backup-simplify]: Simplify 0 into 0 6.476 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.478 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.478 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 6.479 * [backup-simplify]: Simplify (+ 0 0) into 0 6.479 * [backup-simplify]: Simplify (- 1) into -1 6.480 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.481 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 6.487 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 6.491 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 6.494 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 6.495 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 6.496 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 6.500 * [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 6.501 * [backup-simplify]: Simplify (- 0) into 0 6.501 * [backup-simplify]: Simplify (+ 0 0) into 0 6.502 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 6.503 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.505 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.508 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.508 * [taylor]: Taking taylor expansion of 0 in k 6.508 * [backup-simplify]: Simplify 0 into 0 6.508 * [backup-simplify]: Simplify 0 into 0 6.508 * [backup-simplify]: Simplify 0 into 0 6.509 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.513 * [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 6.515 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 6.515 * [backup-simplify]: Simplify (+ 0 0) into 0 6.515 * [backup-simplify]: Simplify (- 0) into 0 6.516 * [backup-simplify]: Simplify (+ 0 0) into 0 6.518 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.520 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 6.524 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 6.529 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 6.539 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 6.540 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 6.540 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 6.540 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 6.540 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 6.540 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 6.540 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 6.540 * [taylor]: Taking taylor expansion of 0.25 in k 6.540 * [backup-simplify]: Simplify 0.25 into 0.25 6.540 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.540 * [taylor]: Taking taylor expansion of 1.0 in k 6.540 * [backup-simplify]: Simplify 1.0 into 1.0 6.541 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.541 * [taylor]: Taking taylor expansion of k in k 6.541 * [backup-simplify]: Simplify 0 into 0 6.541 * [backup-simplify]: Simplify 1 into 1 6.541 * [backup-simplify]: Simplify (/ 1 1) into 1 6.541 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 6.541 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 6.541 * [taylor]: Taking taylor expansion of 2.0 in k 6.541 * [backup-simplify]: Simplify 2.0 into 2.0 6.541 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.541 * [taylor]: Taking taylor expansion of PI in k 6.541 * [backup-simplify]: Simplify PI into PI 6.541 * [taylor]: Taking taylor expansion of n in k 6.541 * [backup-simplify]: Simplify n into n 6.541 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.541 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 6.541 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 6.542 * [backup-simplify]: Simplify (- 1) into -1 6.542 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.543 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 6.543 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 6.543 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 6.543 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 6.543 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.543 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.543 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 6.543 * [taylor]: Taking taylor expansion of 0.25 in n 6.543 * [backup-simplify]: Simplify 0.25 into 0.25 6.543 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.543 * [taylor]: Taking taylor expansion of 1.0 in n 6.543 * [backup-simplify]: Simplify 1.0 into 1.0 6.544 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.544 * [taylor]: Taking taylor expansion of k in n 6.544 * [backup-simplify]: Simplify k into k 6.544 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.544 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.544 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.544 * [taylor]: Taking taylor expansion of 2.0 in n 6.544 * [backup-simplify]: Simplify 2.0 into 2.0 6.544 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.544 * [taylor]: Taking taylor expansion of PI in n 6.544 * [backup-simplify]: Simplify PI into PI 6.544 * [taylor]: Taking taylor expansion of n in n 6.544 * [backup-simplify]: Simplify 0 into 0 6.544 * [backup-simplify]: Simplify 1 into 1 6.545 * [backup-simplify]: Simplify (/ PI 1) into PI 6.545 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.546 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.546 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.547 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.547 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 6.548 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.549 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 6.551 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.551 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 6.551 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.551 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.551 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 6.551 * [taylor]: Taking taylor expansion of 0.25 in n 6.551 * [backup-simplify]: Simplify 0.25 into 0.25 6.551 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.551 * [taylor]: Taking taylor expansion of 1.0 in n 6.551 * [backup-simplify]: Simplify 1.0 into 1.0 6.551 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.551 * [taylor]: Taking taylor expansion of k in n 6.551 * [backup-simplify]: Simplify k into k 6.551 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.551 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.551 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.551 * [taylor]: Taking taylor expansion of 2.0 in n 6.551 * [backup-simplify]: Simplify 2.0 into 2.0 6.551 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.551 * [taylor]: Taking taylor expansion of PI in n 6.551 * [backup-simplify]: Simplify PI into PI 6.551 * [taylor]: Taking taylor expansion of n in n 6.551 * [backup-simplify]: Simplify 0 into 0 6.551 * [backup-simplify]: Simplify 1 into 1 6.552 * [backup-simplify]: Simplify (/ PI 1) into PI 6.552 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.553 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.553 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.554 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.554 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 6.555 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.556 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 6.558 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.558 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 6.558 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 6.558 * [taylor]: Taking taylor expansion of 0.25 in k 6.558 * [backup-simplify]: Simplify 0.25 into 0.25 6.558 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 6.558 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 6.558 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.558 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.558 * [taylor]: Taking taylor expansion of 2.0 in k 6.558 * [backup-simplify]: Simplify 2.0 into 2.0 6.558 * [taylor]: Taking taylor expansion of PI in k 6.558 * [backup-simplify]: Simplify PI into PI 6.559 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.560 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.560 * [taylor]: Taking taylor expansion of (log n) in k 6.560 * [taylor]: Taking taylor expansion of n in k 6.560 * [backup-simplify]: Simplify n into n 6.560 * [backup-simplify]: Simplify (log n) into (log n) 6.560 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.560 * [taylor]: Taking taylor expansion of 1.0 in k 6.560 * [backup-simplify]: Simplify 1.0 into 1.0 6.560 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.560 * [taylor]: Taking taylor expansion of k in k 6.560 * [backup-simplify]: Simplify 0 into 0 6.560 * [backup-simplify]: Simplify 1 into 1 6.560 * [backup-simplify]: Simplify (/ 1 1) into 1 6.560 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.562 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 6.562 * [backup-simplify]: Simplify (- 1) into -1 6.563 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.564 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 6.565 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 6.566 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.567 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.568 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.569 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.571 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.571 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.572 * [backup-simplify]: Simplify (- 0) into 0 6.572 * [backup-simplify]: Simplify (+ 0 0) into 0 6.573 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 6.574 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.576 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 6.578 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.578 * [taylor]: Taking taylor expansion of 0 in k 6.578 * [backup-simplify]: Simplify 0 into 0 6.578 * [backup-simplify]: Simplify 0 into 0 6.578 * [backup-simplify]: Simplify 0 into 0 6.579 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.580 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.584 * [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 6.584 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.584 * [backup-simplify]: Simplify (- 0) into 0 6.585 * [backup-simplify]: Simplify (+ 0 0) into 0 6.586 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 6.587 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.589 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 6.591 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.591 * [taylor]: Taking taylor expansion of 0 in k 6.591 * [backup-simplify]: Simplify 0 into 0 6.591 * [backup-simplify]: Simplify 0 into 0 6.591 * [backup-simplify]: Simplify 0 into 0 6.591 * [backup-simplify]: Simplify 0 into 0 6.592 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.593 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.599 * [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 6.600 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.600 * [backup-simplify]: Simplify (- 0) into 0 6.600 * [backup-simplify]: Simplify (+ 0 0) into 0 6.602 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 6.603 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.605 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 6.608 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 6.608 * [taylor]: Taking taylor expansion of 0 in k 6.608 * [backup-simplify]: Simplify 0 into 0 6.608 * [backup-simplify]: Simplify 0 into 0 6.609 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 6.610 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 6.610 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 6.610 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 6.610 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 6.610 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 6.610 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 6.611 * [taylor]: Taking taylor expansion of 0.25 in k 6.611 * [backup-simplify]: Simplify 0.25 into 0.25 6.611 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.611 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.611 * [taylor]: Taking taylor expansion of k in k 6.611 * [backup-simplify]: Simplify 0 into 0 6.611 * [backup-simplify]: Simplify 1 into 1 6.611 * [backup-simplify]: Simplify (/ 1 1) into 1 6.611 * [taylor]: Taking taylor expansion of 1.0 in k 6.611 * [backup-simplify]: Simplify 1.0 into 1.0 6.611 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 6.611 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 6.611 * [taylor]: Taking taylor expansion of -2.0 in k 6.611 * [backup-simplify]: Simplify -2.0 into -2.0 6.611 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.611 * [taylor]: Taking taylor expansion of PI in k 6.611 * [backup-simplify]: Simplify PI into PI 6.611 * [taylor]: Taking taylor expansion of n in k 6.612 * [backup-simplify]: Simplify n into n 6.612 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.612 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 6.612 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 6.612 * [backup-simplify]: Simplify (+ 1 0) into 1 6.613 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 6.613 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 6.613 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 6.613 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 6.613 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.614 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.614 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 6.614 * [taylor]: Taking taylor expansion of 0.25 in n 6.614 * [backup-simplify]: Simplify 0.25 into 0.25 6.614 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.614 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.614 * [taylor]: Taking taylor expansion of k in n 6.614 * [backup-simplify]: Simplify k into k 6.614 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.614 * [taylor]: Taking taylor expansion of 1.0 in n 6.614 * [backup-simplify]: Simplify 1.0 into 1.0 6.614 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.614 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.614 * [taylor]: Taking taylor expansion of -2.0 in n 6.614 * [backup-simplify]: Simplify -2.0 into -2.0 6.614 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.614 * [taylor]: Taking taylor expansion of PI in n 6.614 * [backup-simplify]: Simplify PI into PI 6.614 * [taylor]: Taking taylor expansion of n in n 6.614 * [backup-simplify]: Simplify 0 into 0 6.614 * [backup-simplify]: Simplify 1 into 1 6.615 * [backup-simplify]: Simplify (/ PI 1) into PI 6.615 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.616 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.617 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.617 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 6.618 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.619 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 6.621 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.621 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 6.621 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.621 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.621 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 6.621 * [taylor]: Taking taylor expansion of 0.25 in n 6.621 * [backup-simplify]: Simplify 0.25 into 0.25 6.621 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.621 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.621 * [taylor]: Taking taylor expansion of k in n 6.621 * [backup-simplify]: Simplify k into k 6.621 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.621 * [taylor]: Taking taylor expansion of 1.0 in n 6.621 * [backup-simplify]: Simplify 1.0 into 1.0 6.621 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.621 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.621 * [taylor]: Taking taylor expansion of -2.0 in n 6.621 * [backup-simplify]: Simplify -2.0 into -2.0 6.622 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.622 * [taylor]: Taking taylor expansion of PI in n 6.622 * [backup-simplify]: Simplify PI into PI 6.622 * [taylor]: Taking taylor expansion of n in n 6.622 * [backup-simplify]: Simplify 0 into 0 6.622 * [backup-simplify]: Simplify 1 into 1 6.622 * [backup-simplify]: Simplify (/ PI 1) into PI 6.623 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.624 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.624 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.624 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 6.626 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.627 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 6.628 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.628 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 6.628 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 6.628 * [taylor]: Taking taylor expansion of 0.25 in k 6.628 * [backup-simplify]: Simplify 0.25 into 0.25 6.628 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 6.628 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.628 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.628 * [taylor]: Taking taylor expansion of k in k 6.628 * [backup-simplify]: Simplify 0 into 0 6.628 * [backup-simplify]: Simplify 1 into 1 6.629 * [backup-simplify]: Simplify (/ 1 1) into 1 6.629 * [taylor]: Taking taylor expansion of 1.0 in k 6.629 * [backup-simplify]: Simplify 1.0 into 1.0 6.629 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 6.629 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 6.629 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 6.629 * [taylor]: Taking taylor expansion of -2.0 in k 6.629 * [backup-simplify]: Simplify -2.0 into -2.0 6.629 * [taylor]: Taking taylor expansion of PI in k 6.629 * [backup-simplify]: Simplify PI into PI 6.630 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.631 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.631 * [taylor]: Taking taylor expansion of (log n) in k 6.631 * [taylor]: Taking taylor expansion of n in k 6.631 * [backup-simplify]: Simplify n into n 6.631 * [backup-simplify]: Simplify (log n) into (log n) 6.631 * [backup-simplify]: Simplify (+ 1 0) into 1 6.631 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.632 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 6.633 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 6.635 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 6.636 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.642 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.643 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.644 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 6.645 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 6.646 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.646 * [backup-simplify]: Simplify (+ 0 0) into 0 6.646 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 6.648 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.649 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 6.651 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.651 * [taylor]: Taking taylor expansion of 0 in k 6.651 * [backup-simplify]: Simplify 0 into 0 6.651 * [backup-simplify]: Simplify 0 into 0 6.651 * [backup-simplify]: Simplify 0 into 0 6.652 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.653 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.656 * [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 6.657 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.657 * [backup-simplify]: Simplify (+ 0 0) into 0 6.658 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 6.660 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.661 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 6.664 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.664 * [taylor]: Taking taylor expansion of 0 in k 6.664 * [backup-simplify]: Simplify 0 into 0 6.664 * [backup-simplify]: Simplify 0 into 0 6.664 * [backup-simplify]: Simplify 0 into 0 6.664 * [backup-simplify]: Simplify 0 into 0 6.665 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.666 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.672 * [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 6.673 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.673 * [backup-simplify]: Simplify (+ 0 0) into 0 6.674 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 6.676 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.677 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 6.680 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 6.680 * [taylor]: Taking taylor expansion of 0 in k 6.680 * [backup-simplify]: Simplify 0 into 0 6.680 * [backup-simplify]: Simplify 0 into 0 6.681 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 6.681 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 6.681 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 6.681 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 6.681 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 6.681 * [taylor]: Taking taylor expansion of 1.0 in k 6.681 * [backup-simplify]: Simplify 1.0 into 1.0 6.681 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 6.681 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.681 * [taylor]: Taking taylor expansion of k in k 6.681 * [backup-simplify]: Simplify 0 into 0 6.681 * [backup-simplify]: Simplify 1 into 1 6.681 * [backup-simplify]: Simplify (/ 1 1) into 1 6.681 * [backup-simplify]: Simplify (sqrt 0) into 0 6.682 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.682 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 6.682 * [taylor]: Taking taylor expansion of 1.0 in k 6.682 * [backup-simplify]: Simplify 1.0 into 1.0 6.682 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 6.682 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.682 * [taylor]: Taking taylor expansion of k in k 6.682 * [backup-simplify]: Simplify 0 into 0 6.682 * [backup-simplify]: Simplify 1 into 1 6.683 * [backup-simplify]: Simplify (/ 1 1) into 1 6.683 * [backup-simplify]: Simplify (sqrt 0) into 0 6.684 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.684 * [backup-simplify]: Simplify (* 1.0 0) into 0 6.684 * [backup-simplify]: Simplify 0 into 0 6.685 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 6.685 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.686 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 6.687 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 6.688 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 6.689 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.689 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.691 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 6.693 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 6.693 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.694 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 6.694 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 6.694 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 6.694 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 6.694 * [taylor]: Taking taylor expansion of 1.0 in k 6.694 * [backup-simplify]: Simplify 1.0 into 1.0 6.694 * [taylor]: Taking taylor expansion of (sqrt k) in k 6.694 * [taylor]: Taking taylor expansion of k in k 6.694 * [backup-simplify]: Simplify 0 into 0 6.694 * [backup-simplify]: Simplify 1 into 1 6.694 * [backup-simplify]: Simplify (sqrt 0) into 0 6.695 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.695 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 6.695 * [taylor]: Taking taylor expansion of 1.0 in k 6.695 * [backup-simplify]: Simplify 1.0 into 1.0 6.695 * [taylor]: Taking taylor expansion of (sqrt k) in k 6.695 * [taylor]: Taking taylor expansion of k in k 6.695 * [backup-simplify]: Simplify 0 into 0 6.695 * [backup-simplify]: Simplify 1 into 1 6.695 * [backup-simplify]: Simplify (sqrt 0) into 0 6.696 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.696 * [backup-simplify]: Simplify (* 1.0 0) into 0 6.696 * [backup-simplify]: Simplify 0 into 0 6.697 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 6.697 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.699 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 6.700 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 6.701 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.703 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 6.704 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 6.704 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.705 * [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)))))))) 6.705 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 6.705 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 6.705 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 6.705 * [taylor]: Taking taylor expansion of 1.0 in k 6.706 * [backup-simplify]: Simplify 1.0 into 1.0 6.706 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 6.706 * [taylor]: Taking taylor expansion of (/ -1 k) in k 6.706 * [taylor]: Taking taylor expansion of -1 in k 6.706 * [backup-simplify]: Simplify -1 into -1 6.706 * [taylor]: Taking taylor expansion of k in k 6.706 * [backup-simplify]: Simplify 0 into 0 6.706 * [backup-simplify]: Simplify 1 into 1 6.706 * [backup-simplify]: Simplify (/ -1 1) into -1 6.706 * [backup-simplify]: Simplify (sqrt 0) into 0 6.707 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 6.707 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 6.707 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 6.707 * [taylor]: Taking taylor expansion of 1.0 in k 6.707 * [backup-simplify]: Simplify 1.0 into 1.0 6.708 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 6.708 * [taylor]: Taking taylor expansion of (/ -1 k) in k 6.708 * [taylor]: Taking taylor expansion of -1 in k 6.708 * [backup-simplify]: Simplify -1 into -1 6.708 * [taylor]: Taking taylor expansion of k in k 6.708 * [backup-simplify]: Simplify 0 into 0 6.708 * [backup-simplify]: Simplify 1 into 1 6.708 * [backup-simplify]: Simplify (/ -1 1) into -1 6.709 * [backup-simplify]: Simplify (sqrt 0) into 0 6.710 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 6.711 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 6.711 * [backup-simplify]: Simplify +nan.0 into +nan.0 6.712 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 6.715 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 6.717 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 6.718 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.719 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.722 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 6.725 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 6.725 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.726 * [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))))) 6.726 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 6.726 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 6.726 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 6.727 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.727 * [taylor]: Taking taylor expansion of 2.0 in n 6.727 * [backup-simplify]: Simplify 2.0 into 2.0 6.727 * [taylor]: Taking taylor expansion of (* n PI) in n 6.727 * [taylor]: Taking taylor expansion of n in n 6.727 * [backup-simplify]: Simplify 0 into 0 6.727 * [backup-simplify]: Simplify 1 into 1 6.727 * [taylor]: Taking taylor expansion of PI in n 6.727 * [backup-simplify]: Simplify PI into PI 6.727 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.727 * [taylor]: Taking taylor expansion of 2.0 in n 6.727 * [backup-simplify]: Simplify 2.0 into 2.0 6.727 * [taylor]: Taking taylor expansion of (* n PI) in n 6.727 * [taylor]: Taking taylor expansion of n in n 6.727 * [backup-simplify]: Simplify 0 into 0 6.727 * [backup-simplify]: Simplify 1 into 1 6.727 * [taylor]: Taking taylor expansion of PI in n 6.727 * [backup-simplify]: Simplify PI into PI 6.727 * [backup-simplify]: Simplify (* 0 PI) into 0 6.727 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.727 * [backup-simplify]: Simplify 0 into 0 6.728 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.729 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.730 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.730 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 6.731 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 6.731 * [backup-simplify]: Simplify 0 into 0 6.731 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 6.732 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 6.732 * [backup-simplify]: Simplify 0 into 0 6.733 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 6.734 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 6.734 * [backup-simplify]: Simplify 0 into 0 6.735 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 6.736 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 6.736 * [backup-simplify]: Simplify 0 into 0 6.736 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 6.737 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 6.737 * [backup-simplify]: Simplify 0 into 0 6.738 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 6.740 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 6.740 * [backup-simplify]: Simplify 0 into 0 6.740 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 6.740 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 6.740 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 6.740 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.740 * [taylor]: Taking taylor expansion of 2.0 in n 6.740 * [backup-simplify]: Simplify 2.0 into 2.0 6.740 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.740 * [taylor]: Taking taylor expansion of PI in n 6.740 * [backup-simplify]: Simplify PI into PI 6.740 * [taylor]: Taking taylor expansion of n in n 6.740 * [backup-simplify]: Simplify 0 into 0 6.741 * [backup-simplify]: Simplify 1 into 1 6.741 * [backup-simplify]: Simplify (/ PI 1) into PI 6.741 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.741 * [taylor]: Taking taylor expansion of 2.0 in n 6.741 * [backup-simplify]: Simplify 2.0 into 2.0 6.741 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.741 * [taylor]: Taking taylor expansion of PI in n 6.741 * [backup-simplify]: Simplify PI into PI 6.741 * [taylor]: Taking taylor expansion of n in n 6.741 * [backup-simplify]: Simplify 0 into 0 6.741 * [backup-simplify]: Simplify 1 into 1 6.741 * [backup-simplify]: Simplify (/ PI 1) into PI 6.742 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.742 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.743 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.743 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.743 * [backup-simplify]: Simplify 0 into 0 6.744 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.744 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.744 * [backup-simplify]: Simplify 0 into 0 6.745 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.746 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.746 * [backup-simplify]: Simplify 0 into 0 6.746 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.750 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 6.750 * [backup-simplify]: Simplify 0 into 0 6.750 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.752 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 6.752 * [backup-simplify]: Simplify 0 into 0 6.753 * [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 6.754 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 6.754 * [backup-simplify]: Simplify 0 into 0 6.755 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 6.756 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 6.756 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 6.756 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.756 * [taylor]: Taking taylor expansion of -2.0 in n 6.756 * [backup-simplify]: Simplify -2.0 into -2.0 6.756 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.756 * [taylor]: Taking taylor expansion of PI in n 6.756 * [backup-simplify]: Simplify PI into PI 6.756 * [taylor]: Taking taylor expansion of n in n 6.756 * [backup-simplify]: Simplify 0 into 0 6.756 * [backup-simplify]: Simplify 1 into 1 6.757 * [backup-simplify]: Simplify (/ PI 1) into PI 6.757 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.757 * [taylor]: Taking taylor expansion of -2.0 in n 6.757 * [backup-simplify]: Simplify -2.0 into -2.0 6.757 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.757 * [taylor]: Taking taylor expansion of PI in n 6.757 * [backup-simplify]: Simplify PI into PI 6.757 * [taylor]: Taking taylor expansion of n in n 6.757 * [backup-simplify]: Simplify 0 into 0 6.757 * [backup-simplify]: Simplify 1 into 1 6.757 * [backup-simplify]: Simplify (/ PI 1) into PI 6.758 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.758 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.759 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.760 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 6.760 * [backup-simplify]: Simplify 0 into 0 6.761 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.762 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.762 * [backup-simplify]: Simplify 0 into 0 6.764 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.765 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.765 * [backup-simplify]: Simplify 0 into 0 6.766 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.768 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 6.768 * [backup-simplify]: Simplify 0 into 0 6.769 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.771 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 6.771 * [backup-simplify]: Simplify 0 into 0 6.772 * [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 6.774 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 6.774 * [backup-simplify]: Simplify 0 into 0 6.775 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 6.775 * * * [progress]: simplifying candidates 6.783 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 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2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) 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(exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (- (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) (* (* 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) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 6.795 * * [simplify]: Extracting # 0 : cost 0 6.795 * * [simplify]: Extracting # 1 : cost 0 6.796 * * [simplify]: Extracting # 2 : cost 0 6.797 * * [simplify]: Extracting # 3 : cost 0 6.798 * * [simplify]: Extracting # 4 : cost 0 6.799 * * [simplify]: Extracting # 5 : cost 0 6.800 * * [simplify]: Extracting # 6 : cost 0 6.801 * * [simplify]: Extracting # 7 : cost 0 6.803 * * [simplify]: Extracting # 8 : cost 0 6.804 * * [simplify]: Extracting # 9 : cost 0 6.805 * * [simplify]: Extracting # 10 : cost 0 6.806 * * [simplify]: Extracting # 11 : cost 0 6.807 * * [simplify]: Extracting # 12 : cost 0 6.808 * * [simplify]: Extracting # 13 : cost 0 6.809 * * [simplify]: Extracting # 14 : cost 0 6.810 * * [simplify]: iteration 0 : 326 enodes (cost 3510 ) 6.946 * * [simplify]: Extracting # 0 : cost 0 6.948 * * [simplify]: Extracting # 1 : cost 0 6.950 * * [simplify]: Extracting # 2 : cost 0 6.951 * * [simplify]: Extracting # 3 : cost 0 6.953 * * [simplify]: Extracting # 4 : cost 0 6.960 * * [simplify]: Extracting # 5 : cost 0 6.962 * * [simplify]: iteration 1 : 964 enodes (cost 3242 ) 7.583 * * [simplify]: Extracting # 0 : cost 0 7.588 * * [simplify]: Extracting # 1 : cost 0 7.593 * * [simplify]: Extracting # 2 : cost 0 7.602 * * [simplify]: Extracting # 3 : cost 0 7.612 * * [simplify]: Extracting # 4 : cost 0 7.617 * * [simplify]: Extracting # 5 : cost 0 7.626 * * [simplify]: iteration 2 : 4173 enodes (cost 3132 ) 8.974 * * [simplify]: Extracting # 0 : cost 0 8.982 * * [simplify]: Extracting # 1 : cost 0 8.993 * * [simplify]: Extracting # 2 : cost 0 9.000 * * [simplify]: iteration done: 5000 enodes (cost 3128 ) 9.003 * [simplify]: Simplified to: (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (/ (/ (- 1.0 k) 2.0) 2) (/ (/ (- 1.0 k) 2.0) 2) (/ (/ (- 1.0 k) 2.0) 2) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* 2.0 (* n PI)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (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))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (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)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2))) (pow (* 2.0 (* n PI)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (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)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (sqrt 2))) (pow (* 2.0 (* PI n)) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* n PI) 2.0) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2))) (pow (* 2.0 (* PI n)) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* n PI) 2.0) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* n PI) 2.0) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* 2.0 (* PI n)) (- 1.0 k)) (* (* n PI) 2.0) (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* n PI) 2.0) (/ (- 1.0 k) (* 4 2.0))) (pow (* (* n PI) 2.0) (/ (- 1.0 k) (* 4 2.0))) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (/ (/ (- 1.0 k) 2.0) 2) (/ (/ (- 1.0 k) 2.0) 2) (/ (/ (- 1.0 k) 2.0) 2) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* 2.0 (* n PI)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (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))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (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)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2))) (pow (* 2.0 (* n PI)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (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)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (sqrt 2))) (pow (* 2.0 (* PI n)) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* n PI) 2.0) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2))) (pow (* 2.0 (* PI n)) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* n PI) 2.0) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* n PI) 2.0) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* 2.0 (* PI n)) (- 1.0 k)) (* (* n PI) 2.0) (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* n PI) 2.0) (/ (- 1.0 k) (* 4 2.0))) (pow (* (* n PI) 2.0) (/ (- 1.0 k) (* 4 2.0))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (pow 1.0 3) (* (sqrt k) k)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (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)) (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) (* (* n PI) 2.0) (* (* n PI) 2.0) (log (* (* n PI) 2.0)) (log (* (* n PI) 2.0)) (log (* (* n PI) 2.0)) (exp (* (* 2.0 PI) n)) (pow (* 2.0 (* PI n)) 3) (pow (* 2.0 (* PI n)) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* 2.0 (* PI n)) 3) (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) (* PI n) (+ (+ (* (* 0.03125 (pow k 2)) (* (pow (* 2.0 (* PI n)) 0.25) (pow (log (* 2.0 PI)) 2))) (pow (* 2.0 (* PI n)) 0.25)) (- (+ (* 0.0625 (* (pow k 2) (* (* (pow (* 2.0 (* PI n)) 0.25) (log (* 2.0 PI))) (log n)))) (* (* (pow (log n) 2) (pow (* 2.0 (* PI n)) 0.25)) (* 0.03125 (pow k 2)))) (* (* k (+ (* (pow (* 2.0 (* PI n)) 0.25) (log (* 2.0 PI))) (* (log n) (pow (* 2.0 (* PI n)) 0.25)))) 0.25))) (pow (pow (* 2.0 (* PI n)) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (+ (+ (* (* 0.03125 (pow k 2)) (* (pow (* 2.0 (* PI n)) 0.25) (pow (log (* 2.0 PI)) 2))) (pow (* 2.0 (* PI n)) 0.25)) (- (+ (* 0.0625 (* (pow k 2) (* (* (pow (* 2.0 (* PI n)) 0.25) (log (* 2.0 PI))) (log n)))) (* (* (pow (log n) 2) (pow (* 2.0 (* PI n)) 0.25)) (* 0.03125 (pow k 2)))) (* (* k (+ (* (pow (* 2.0 (* PI n)) 0.25) (log (* 2.0 PI))) (* (log n) (pow (* 2.0 (* PI n)) 0.25)))) 0.25))) (pow (pow (* 2.0 (* PI n)) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (- (* +nan.0 k) (- (* +nan.0 (pow k 2)) +nan.0))) (+ (- (/ +nan.0 k) (/ +nan.0 (pow k 3))) (- (/ +nan.0 (pow k 2)))) (+ (- (/ +nan.0 k) +nan.0) (- (/ +nan.0 (pow k 2)))) (* (* n PI) 2.0) (* (* n PI) 2.0) (* (* n PI) 2.0) 9.007 * * * [progress]: adding candidates to table 10.196 * * [progress]: iteration 3 / 4 10.196 * * * [progress]: picking best candidate 10.230 * * * * [pick]: Picked # 10.231 * * * [progress]: localizing error 10.255 * * * [progress]: generating rewritten candidates 10.255 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 10.288 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1 1) 10.298 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 10.304 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 2 1) 10.328 * * * [progress]: generating series expansions 10.328 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 10.329 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 10.329 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 10.329 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 10.329 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 10.329 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 10.329 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 10.329 * [taylor]: Taking taylor expansion of 0.5 in k 10.329 * [backup-simplify]: Simplify 0.5 into 0.5 10.329 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 10.329 * [taylor]: Taking taylor expansion of 1.0 in k 10.329 * [backup-simplify]: Simplify 1.0 into 1.0 10.329 * [taylor]: Taking taylor expansion of k in k 10.329 * [backup-simplify]: Simplify 0 into 0 10.329 * [backup-simplify]: Simplify 1 into 1 10.329 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 10.329 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 10.329 * [taylor]: Taking taylor expansion of 2.0 in k 10.329 * [backup-simplify]: Simplify 2.0 into 2.0 10.329 * [taylor]: Taking taylor expansion of (* n PI) in k 10.329 * [taylor]: Taking taylor expansion of n in k 10.329 * [backup-simplify]: Simplify n into n 10.329 * [taylor]: Taking taylor expansion of PI in k 10.329 * [backup-simplify]: Simplify PI into PI 10.329 * [backup-simplify]: Simplify (* n PI) into (* n PI) 10.329 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 10.330 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 10.330 * [backup-simplify]: Simplify (- 0) into 0 10.330 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 10.334 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 10.334 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 10.334 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 10.334 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 10.334 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 10.334 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 10.334 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 10.334 * [taylor]: Taking taylor expansion of 0.5 in n 10.334 * [backup-simplify]: Simplify 0.5 into 0.5 10.334 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 10.334 * [taylor]: Taking taylor expansion of 1.0 in n 10.334 * [backup-simplify]: Simplify 1.0 into 1.0 10.334 * [taylor]: Taking taylor expansion of k in n 10.334 * [backup-simplify]: Simplify k into k 10.334 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 10.335 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 10.335 * [taylor]: Taking taylor expansion of 2.0 in n 10.335 * [backup-simplify]: Simplify 2.0 into 2.0 10.335 * [taylor]: Taking taylor expansion of (* n PI) in n 10.335 * [taylor]: Taking taylor expansion of n in n 10.335 * [backup-simplify]: Simplify 0 into 0 10.335 * [backup-simplify]: Simplify 1 into 1 10.335 * [taylor]: Taking taylor expansion of PI in n 10.335 * [backup-simplify]: Simplify PI into PI 10.335 * [backup-simplify]: Simplify (* 0 PI) into 0 10.335 * [backup-simplify]: Simplify (* 2.0 0) into 0 10.336 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.337 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 10.338 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.338 * [backup-simplify]: Simplify (- k) into (- k) 10.338 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 10.338 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 10.339 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.340 * [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)))) 10.341 * [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))))) 10.341 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 10.341 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 10.341 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 10.341 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 10.341 * [taylor]: Taking taylor expansion of 0.5 in n 10.341 * [backup-simplify]: Simplify 0.5 into 0.5 10.341 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 10.341 * [taylor]: Taking taylor expansion of 1.0 in n 10.341 * [backup-simplify]: Simplify 1.0 into 1.0 10.341 * [taylor]: Taking taylor expansion of k in n 10.341 * [backup-simplify]: Simplify k into k 10.341 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 10.341 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 10.341 * [taylor]: Taking taylor expansion of 2.0 in n 10.341 * [backup-simplify]: Simplify 2.0 into 2.0 10.341 * [taylor]: Taking taylor expansion of (* n PI) in n 10.341 * [taylor]: Taking taylor expansion of n in n 10.341 * [backup-simplify]: Simplify 0 into 0 10.341 * [backup-simplify]: Simplify 1 into 1 10.341 * [taylor]: Taking taylor expansion of PI in n 10.341 * [backup-simplify]: Simplify PI into PI 10.341 * [backup-simplify]: Simplify (* 0 PI) into 0 10.342 * [backup-simplify]: Simplify (* 2.0 0) into 0 10.343 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.344 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 10.344 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.344 * [backup-simplify]: Simplify (- k) into (- k) 10.344 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 10.344 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 10.345 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.346 * [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)))) 10.347 * [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))))) 10.347 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 10.347 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 10.347 * [taylor]: Taking taylor expansion of 0.5 in k 10.347 * [backup-simplify]: Simplify 0.5 into 0.5 10.347 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 10.347 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 10.347 * [taylor]: Taking taylor expansion of 1.0 in k 10.347 * [backup-simplify]: Simplify 1.0 into 1.0 10.347 * [taylor]: Taking taylor expansion of k in k 10.347 * [backup-simplify]: Simplify 0 into 0 10.347 * [backup-simplify]: Simplify 1 into 1 10.347 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 10.348 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 10.348 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 10.348 * [taylor]: Taking taylor expansion of 2.0 in k 10.348 * [backup-simplify]: Simplify 2.0 into 2.0 10.348 * [taylor]: Taking taylor expansion of PI in k 10.348 * [backup-simplify]: Simplify PI into PI 10.349 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.350 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.350 * [taylor]: Taking taylor expansion of (log n) in k 10.350 * [taylor]: Taking taylor expansion of n in k 10.350 * [backup-simplify]: Simplify n into n 10.350 * [backup-simplify]: Simplify (log n) into (log n) 10.350 * [backup-simplify]: Simplify (- 0) into 0 10.351 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 10.351 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 10.352 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 10.353 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 10.354 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 10.354 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 10.355 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 10.356 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 10.357 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 10.357 * [backup-simplify]: Simplify (- 0) into 0 10.357 * [backup-simplify]: Simplify (+ 0 0) into 0 10.358 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 10.358 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.359 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 10.360 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 10.360 * [taylor]: Taking taylor expansion of 0 in k 10.360 * [backup-simplify]: Simplify 0 into 0 10.360 * [backup-simplify]: Simplify 0 into 0 10.361 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 10.362 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 10.362 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 10.363 * [backup-simplify]: Simplify (+ 0 0) into 0 10.363 * [backup-simplify]: Simplify (- 1) into -1 10.363 * [backup-simplify]: Simplify (+ 0 -1) into -1 10.365 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 10.367 * [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)))) 10.370 * [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)))))) 10.374 * [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)))))) 10.375 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 10.376 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 10.380 * [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 10.380 * [backup-simplify]: Simplify (- 0) into 0 10.381 * [backup-simplify]: Simplify (+ 0 0) into 0 10.382 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 10.383 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.385 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 10.387 * [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 10.387 * [taylor]: Taking taylor expansion of 0 in k 10.387 * [backup-simplify]: Simplify 0 into 0 10.387 * [backup-simplify]: Simplify 0 into 0 10.387 * [backup-simplify]: Simplify 0 into 0 10.388 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 10.391 * [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 10.393 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 10.393 * [backup-simplify]: Simplify (+ 0 0) into 0 10.393 * [backup-simplify]: Simplify (- 0) into 0 10.393 * [backup-simplify]: Simplify (+ 0 0) into 0 10.394 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 10.396 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 10.398 * [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 (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 10.402 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 10.408 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 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 (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 10.408 * [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)))) 10.408 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 10.408 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 10.408 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 10.408 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 10.408 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 10.408 * [taylor]: Taking taylor expansion of 0.5 in k 10.408 * [backup-simplify]: Simplify 0.5 into 0.5 10.408 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 10.408 * [taylor]: Taking taylor expansion of 1.0 in k 10.408 * [backup-simplify]: Simplify 1.0 into 1.0 10.408 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.408 * [taylor]: Taking taylor expansion of k in k 10.408 * [backup-simplify]: Simplify 0 into 0 10.408 * [backup-simplify]: Simplify 1 into 1 10.409 * [backup-simplify]: Simplify (/ 1 1) into 1 10.409 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 10.409 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 10.409 * [taylor]: Taking taylor expansion of 2.0 in k 10.409 * [backup-simplify]: Simplify 2.0 into 2.0 10.409 * [taylor]: Taking taylor expansion of (/ PI n) in k 10.409 * [taylor]: Taking taylor expansion of PI in k 10.409 * [backup-simplify]: Simplify PI into PI 10.409 * [taylor]: Taking taylor expansion of n in k 10.409 * [backup-simplify]: Simplify n into n 10.409 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 10.409 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 10.409 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 10.409 * [backup-simplify]: Simplify (- 1) into -1 10.409 * [backup-simplify]: Simplify (+ 0 -1) into -1 10.410 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 10.410 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 10.410 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 10.410 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 10.410 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 10.410 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 10.410 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 10.410 * [taylor]: Taking taylor expansion of 0.5 in n 10.410 * [backup-simplify]: Simplify 0.5 into 0.5 10.410 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 10.410 * [taylor]: Taking taylor expansion of 1.0 in n 10.410 * [backup-simplify]: Simplify 1.0 into 1.0 10.410 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.410 * [taylor]: Taking taylor expansion of k in n 10.410 * [backup-simplify]: Simplify k into k 10.410 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.410 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 10.410 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 10.410 * [taylor]: Taking taylor expansion of 2.0 in n 10.410 * [backup-simplify]: Simplify 2.0 into 2.0 10.410 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.410 * [taylor]: Taking taylor expansion of PI in n 10.410 * [backup-simplify]: Simplify PI into PI 10.410 * [taylor]: Taking taylor expansion of n in n 10.410 * [backup-simplify]: Simplify 0 into 0 10.410 * [backup-simplify]: Simplify 1 into 1 10.411 * [backup-simplify]: Simplify (/ PI 1) into PI 10.411 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.412 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.412 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 10.412 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 10.412 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 10.413 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.414 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 10.414 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 10.414 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 10.414 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 10.414 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 10.414 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 10.414 * [taylor]: Taking taylor expansion of 0.5 in n 10.414 * [backup-simplify]: Simplify 0.5 into 0.5 10.414 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 10.414 * [taylor]: Taking taylor expansion of 1.0 in n 10.414 * [backup-simplify]: Simplify 1.0 into 1.0 10.415 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.415 * [taylor]: Taking taylor expansion of k in n 10.415 * [backup-simplify]: Simplify k into k 10.415 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.415 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 10.415 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 10.415 * [taylor]: Taking taylor expansion of 2.0 in n 10.415 * [backup-simplify]: Simplify 2.0 into 2.0 10.415 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.415 * [taylor]: Taking taylor expansion of PI in n 10.415 * [backup-simplify]: Simplify PI into PI 10.415 * [taylor]: Taking taylor expansion of n in n 10.415 * [backup-simplify]: Simplify 0 into 0 10.415 * [backup-simplify]: Simplify 1 into 1 10.415 * [backup-simplify]: Simplify (/ PI 1) into PI 10.415 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.416 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.416 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 10.416 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 10.416 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 10.417 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.418 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 10.419 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 10.419 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 10.419 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 10.419 * [taylor]: Taking taylor expansion of 0.5 in k 10.419 * [backup-simplify]: Simplify 0.5 into 0.5 10.419 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 10.419 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 10.419 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 10.419 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 10.419 * [taylor]: Taking taylor expansion of 2.0 in k 10.419 * [backup-simplify]: Simplify 2.0 into 2.0 10.419 * [taylor]: Taking taylor expansion of PI in k 10.419 * [backup-simplify]: Simplify PI into PI 10.419 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.420 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.420 * [taylor]: Taking taylor expansion of (log n) in k 10.420 * [taylor]: Taking taylor expansion of n in k 10.420 * [backup-simplify]: Simplify n into n 10.420 * [backup-simplify]: Simplify (log n) into (log n) 10.420 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 10.420 * [taylor]: Taking taylor expansion of 1.0 in k 10.420 * [backup-simplify]: Simplify 1.0 into 1.0 10.420 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.420 * [taylor]: Taking taylor expansion of k in k 10.420 * [backup-simplify]: Simplify 0 into 0 10.420 * [backup-simplify]: Simplify 1 into 1 10.421 * [backup-simplify]: Simplify (/ 1 1) into 1 10.421 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 10.421 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 10.421 * [backup-simplify]: Simplify (- 1) into -1 10.422 * [backup-simplify]: Simplify (+ 0 -1) into -1 10.422 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 10.423 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 10.424 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 10.426 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 10.427 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 10.427 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 10.429 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 10.429 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 10.430 * [backup-simplify]: Simplify (- 0) into 0 10.430 * [backup-simplify]: Simplify (+ 0 0) into 0 10.431 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 10.432 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.434 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 10.436 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 10.436 * [taylor]: Taking taylor expansion of 0 in k 10.436 * [backup-simplify]: Simplify 0 into 0 10.436 * [backup-simplify]: Simplify 0 into 0 10.436 * [backup-simplify]: Simplify 0 into 0 10.437 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.438 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 10.441 * [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 10.441 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.441 * [backup-simplify]: Simplify (- 0) into 0 10.441 * [backup-simplify]: Simplify (+ 0 0) into 0 10.442 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 10.443 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.450 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 10.452 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 10.452 * [taylor]: Taking taylor expansion of 0 in k 10.452 * [backup-simplify]: Simplify 0 into 0 10.452 * [backup-simplify]: Simplify 0 into 0 10.452 * [backup-simplify]: Simplify 0 into 0 10.452 * [backup-simplify]: Simplify 0 into 0 10.453 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.453 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 10.457 * [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 10.457 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.457 * [backup-simplify]: Simplify (- 0) into 0 10.457 * [backup-simplify]: Simplify (+ 0 0) into 0 10.458 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 10.459 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.460 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 10.462 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 10.462 * [taylor]: Taking taylor expansion of 0 in k 10.462 * [backup-simplify]: Simplify 0 into 0 10.462 * [backup-simplify]: Simplify 0 into 0 10.463 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 10.463 * [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))) 10.463 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 10.463 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 10.463 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 10.463 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 10.463 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 10.463 * [taylor]: Taking taylor expansion of 0.5 in k 10.463 * [backup-simplify]: Simplify 0.5 into 0.5 10.463 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 10.463 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.463 * [taylor]: Taking taylor expansion of k in k 10.463 * [backup-simplify]: Simplify 0 into 0 10.463 * [backup-simplify]: Simplify 1 into 1 10.464 * [backup-simplify]: Simplify (/ 1 1) into 1 10.464 * [taylor]: Taking taylor expansion of 1.0 in k 10.464 * [backup-simplify]: Simplify 1.0 into 1.0 10.464 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 10.464 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 10.464 * [taylor]: Taking taylor expansion of -2.0 in k 10.464 * [backup-simplify]: Simplify -2.0 into -2.0 10.464 * [taylor]: Taking taylor expansion of (/ PI n) in k 10.464 * [taylor]: Taking taylor expansion of PI in k 10.464 * [backup-simplify]: Simplify PI into PI 10.464 * [taylor]: Taking taylor expansion of n in k 10.464 * [backup-simplify]: Simplify n into n 10.464 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 10.464 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 10.464 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 10.464 * [backup-simplify]: Simplify (+ 1 0) into 1 10.464 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 10.465 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 10.465 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 10.465 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 10.465 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 10.465 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 10.465 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 10.465 * [taylor]: Taking taylor expansion of 0.5 in n 10.465 * [backup-simplify]: Simplify 0.5 into 0.5 10.465 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 10.465 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.465 * [taylor]: Taking taylor expansion of k in n 10.465 * [backup-simplify]: Simplify k into k 10.465 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.465 * [taylor]: Taking taylor expansion of 1.0 in n 10.465 * [backup-simplify]: Simplify 1.0 into 1.0 10.465 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 10.465 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 10.465 * [taylor]: Taking taylor expansion of -2.0 in n 10.465 * [backup-simplify]: Simplify -2.0 into -2.0 10.465 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.465 * [taylor]: Taking taylor expansion of PI in n 10.465 * [backup-simplify]: Simplify PI into PI 10.465 * [taylor]: Taking taylor expansion of n in n 10.465 * [backup-simplify]: Simplify 0 into 0 10.465 * [backup-simplify]: Simplify 1 into 1 10.466 * [backup-simplify]: Simplify (/ PI 1) into PI 10.466 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 10.467 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 10.467 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 10.467 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 10.468 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.469 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 10.471 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 10.471 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 10.471 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 10.471 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 10.471 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 10.471 * [taylor]: Taking taylor expansion of 0.5 in n 10.471 * [backup-simplify]: Simplify 0.5 into 0.5 10.471 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 10.471 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.471 * [taylor]: Taking taylor expansion of k in n 10.471 * [backup-simplify]: Simplify k into k 10.471 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.471 * [taylor]: Taking taylor expansion of 1.0 in n 10.471 * [backup-simplify]: Simplify 1.0 into 1.0 10.471 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 10.471 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 10.472 * [taylor]: Taking taylor expansion of -2.0 in n 10.472 * [backup-simplify]: Simplify -2.0 into -2.0 10.472 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.472 * [taylor]: Taking taylor expansion of PI in n 10.472 * [backup-simplify]: Simplify PI into PI 10.472 * [taylor]: Taking taylor expansion of n in n 10.472 * [backup-simplify]: Simplify 0 into 0 10.472 * [backup-simplify]: Simplify 1 into 1 10.472 * [backup-simplify]: Simplify (/ PI 1) into PI 10.473 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 10.474 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 10.474 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 10.474 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 10.476 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.477 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 10.478 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 10.478 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 10.478 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 10.478 * [taylor]: Taking taylor expansion of 0.5 in k 10.478 * [backup-simplify]: Simplify 0.5 into 0.5 10.478 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 10.478 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 10.478 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.479 * [taylor]: Taking taylor expansion of k in k 10.479 * [backup-simplify]: Simplify 0 into 0 10.479 * [backup-simplify]: Simplify 1 into 1 10.479 * [backup-simplify]: Simplify (/ 1 1) into 1 10.479 * [taylor]: Taking taylor expansion of 1.0 in k 10.479 * [backup-simplify]: Simplify 1.0 into 1.0 10.479 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 10.479 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 10.479 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 10.479 * [taylor]: Taking taylor expansion of -2.0 in k 10.479 * [backup-simplify]: Simplify -2.0 into -2.0 10.479 * [taylor]: Taking taylor expansion of PI in k 10.479 * [backup-simplify]: Simplify PI into PI 10.480 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 10.481 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 10.481 * [taylor]: Taking taylor expansion of (log n) in k 10.481 * [taylor]: Taking taylor expansion of n in k 10.481 * [backup-simplify]: Simplify n into n 10.482 * [backup-simplify]: Simplify (log n) into (log n) 10.482 * [backup-simplify]: Simplify (+ 1 0) into 1 10.482 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 10.484 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 10.485 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 10.486 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 10.488 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 10.489 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 10.490 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 10.491 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 10.493 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 10.493 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 10.493 * [backup-simplify]: Simplify (+ 0 0) into 0 10.494 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 10.495 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.496 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 10.498 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 10.498 * [taylor]: Taking taylor expansion of 0 in k 10.499 * [backup-simplify]: Simplify 0 into 0 10.499 * [backup-simplify]: Simplify 0 into 0 10.499 * [backup-simplify]: Simplify 0 into 0 10.500 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.501 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 10.505 * [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 10.505 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.505 * [backup-simplify]: Simplify (+ 0 0) into 0 10.506 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 10.508 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.509 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 10.512 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 10.512 * [taylor]: Taking taylor expansion of 0 in k 10.512 * [backup-simplify]: Simplify 0 into 0 10.512 * [backup-simplify]: Simplify 0 into 0 10.512 * [backup-simplify]: Simplify 0 into 0 10.512 * [backup-simplify]: Simplify 0 into 0 10.514 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.515 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 10.522 * [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 10.522 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.522 * [backup-simplify]: Simplify (+ 0 0) into 0 10.524 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 10.526 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.528 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 10.531 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 10.531 * [taylor]: Taking taylor expansion of 0 in k 10.531 * [backup-simplify]: Simplify 0 into 0 10.531 * [backup-simplify]: Simplify 0 into 0 10.532 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 10.532 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1 1) 10.532 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 10.533 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 10.533 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 10.533 * [taylor]: Taking taylor expansion of 1.0 in k 10.533 * [backup-simplify]: Simplify 1.0 into 1.0 10.533 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 10.533 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.533 * [taylor]: Taking taylor expansion of k in k 10.533 * [backup-simplify]: Simplify 0 into 0 10.533 * [backup-simplify]: Simplify 1 into 1 10.533 * [backup-simplify]: Simplify (/ 1 1) into 1 10.534 * [backup-simplify]: Simplify (sqrt 0) into 0 10.535 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 10.535 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 10.535 * [taylor]: Taking taylor expansion of 1.0 in k 10.535 * [backup-simplify]: Simplify 1.0 into 1.0 10.535 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 10.535 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.535 * [taylor]: Taking taylor expansion of k in k 10.535 * [backup-simplify]: Simplify 0 into 0 10.535 * [backup-simplify]: Simplify 1 into 1 10.536 * [backup-simplify]: Simplify (/ 1 1) into 1 10.536 * [backup-simplify]: Simplify (sqrt 0) into 0 10.537 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 10.538 * [backup-simplify]: Simplify (* 1.0 0) into 0 10.538 * [backup-simplify]: Simplify 0 into 0 10.540 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 10.540 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.541 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 10.544 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 10.546 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 10.546 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.547 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.551 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 10.553 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 10.554 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.555 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 10.556 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 10.556 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 10.556 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 10.556 * [taylor]: Taking taylor expansion of 1.0 in k 10.556 * [backup-simplify]: Simplify 1.0 into 1.0 10.556 * [taylor]: Taking taylor expansion of (sqrt k) in k 10.556 * [taylor]: Taking taylor expansion of k in k 10.556 * [backup-simplify]: Simplify 0 into 0 10.556 * [backup-simplify]: Simplify 1 into 1 10.556 * [backup-simplify]: Simplify (sqrt 0) into 0 10.558 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 10.558 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 10.558 * [taylor]: Taking taylor expansion of 1.0 in k 10.558 * [backup-simplify]: Simplify 1.0 into 1.0 10.558 * [taylor]: Taking taylor expansion of (sqrt k) in k 10.558 * [taylor]: Taking taylor expansion of k in k 10.558 * [backup-simplify]: Simplify 0 into 0 10.558 * [backup-simplify]: Simplify 1 into 1 10.558 * [backup-simplify]: Simplify (sqrt 0) into 0 10.559 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 10.560 * [backup-simplify]: Simplify (* 1.0 0) into 0 10.560 * [backup-simplify]: Simplify 0 into 0 10.562 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 10.562 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.565 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 10.567 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 10.568 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.572 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 10.573 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 10.573 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.574 * [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)))))))) 10.574 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 10.574 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 10.574 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 10.574 * [taylor]: Taking taylor expansion of 1.0 in k 10.574 * [backup-simplify]: Simplify 1.0 into 1.0 10.574 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 10.574 * [taylor]: Taking taylor expansion of (/ -1 k) in k 10.574 * [taylor]: Taking taylor expansion of -1 in k 10.574 * [backup-simplify]: Simplify -1 into -1 10.574 * [taylor]: Taking taylor expansion of k in k 10.574 * [backup-simplify]: Simplify 0 into 0 10.574 * [backup-simplify]: Simplify 1 into 1 10.575 * [backup-simplify]: Simplify (/ -1 1) into -1 10.575 * [backup-simplify]: Simplify (sqrt 0) into 0 10.576 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 10.576 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 10.576 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 10.576 * [taylor]: Taking taylor expansion of 1.0 in k 10.576 * [backup-simplify]: Simplify 1.0 into 1.0 10.576 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 10.576 * [taylor]: Taking taylor expansion of (/ -1 k) in k 10.576 * [taylor]: Taking taylor expansion of -1 in k 10.576 * [backup-simplify]: Simplify -1 into -1 10.576 * [taylor]: Taking taylor expansion of k in k 10.576 * [backup-simplify]: Simplify 0 into 0 10.576 * [backup-simplify]: Simplify 1 into 1 10.576 * [backup-simplify]: Simplify (/ -1 1) into -1 10.577 * [backup-simplify]: Simplify (sqrt 0) into 0 10.578 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 10.578 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 10.578 * [backup-simplify]: Simplify +nan.0 into +nan.0 10.579 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 10.581 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 10.583 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 10.583 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.584 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.593 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 10.595 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 10.595 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.596 * [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))))) 10.596 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 10.596 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 10.596 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 10.596 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 10.596 * [taylor]: Taking taylor expansion of 1.0 in k 10.596 * [backup-simplify]: Simplify 1.0 into 1.0 10.596 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 10.596 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.596 * [taylor]: Taking taylor expansion of k in k 10.597 * [backup-simplify]: Simplify 0 into 0 10.597 * [backup-simplify]: Simplify 1 into 1 10.597 * [backup-simplify]: Simplify (/ 1 1) into 1 10.597 * [backup-simplify]: Simplify (sqrt 0) into 0 10.598 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 10.598 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 10.598 * [taylor]: Taking taylor expansion of 1.0 in k 10.598 * [backup-simplify]: Simplify 1.0 into 1.0 10.598 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 10.598 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.598 * [taylor]: Taking taylor expansion of k in k 10.598 * [backup-simplify]: Simplify 0 into 0 10.598 * [backup-simplify]: Simplify 1 into 1 10.598 * [backup-simplify]: Simplify (/ 1 1) into 1 10.598 * [backup-simplify]: Simplify (sqrt 0) into 0 10.599 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 10.600 * [backup-simplify]: Simplify (* 1.0 0) into 0 10.600 * [backup-simplify]: Simplify 0 into 0 10.600 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 10.601 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.601 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 10.603 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 10.604 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 10.604 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.605 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.607 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 10.608 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 10.609 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.609 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 10.610 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 10.610 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 10.610 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 10.610 * [taylor]: Taking taylor expansion of 1.0 in k 10.610 * [backup-simplify]: Simplify 1.0 into 1.0 10.610 * [taylor]: Taking taylor expansion of (sqrt k) in k 10.610 * [taylor]: Taking taylor expansion of k in k 10.610 * [backup-simplify]: Simplify 0 into 0 10.610 * [backup-simplify]: Simplify 1 into 1 10.610 * [backup-simplify]: Simplify (sqrt 0) into 0 10.611 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 10.611 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 10.611 * [taylor]: Taking taylor expansion of 1.0 in k 10.611 * [backup-simplify]: Simplify 1.0 into 1.0 10.611 * [taylor]: Taking taylor expansion of (sqrt k) in k 10.611 * [taylor]: Taking taylor expansion of k in k 10.611 * [backup-simplify]: Simplify 0 into 0 10.611 * [backup-simplify]: Simplify 1 into 1 10.611 * [backup-simplify]: Simplify (sqrt 0) into 0 10.612 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 10.612 * [backup-simplify]: Simplify (* 1.0 0) into 0 10.612 * [backup-simplify]: Simplify 0 into 0 10.613 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 10.613 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.615 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 10.616 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 10.617 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.619 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 10.622 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 10.622 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.624 * [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)))))))) 10.624 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 10.624 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 10.624 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 10.624 * [taylor]: Taking taylor expansion of 1.0 in k 10.624 * [backup-simplify]: Simplify 1.0 into 1.0 10.624 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 10.624 * [taylor]: Taking taylor expansion of (/ -1 k) in k 10.624 * [taylor]: Taking taylor expansion of -1 in k 10.624 * [backup-simplify]: Simplify -1 into -1 10.624 * [taylor]: Taking taylor expansion of k in k 10.624 * [backup-simplify]: Simplify 0 into 0 10.624 * [backup-simplify]: Simplify 1 into 1 10.625 * [backup-simplify]: Simplify (/ -1 1) into -1 10.625 * [backup-simplify]: Simplify (sqrt 0) into 0 10.626 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 10.627 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 10.627 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 10.627 * [taylor]: Taking taylor expansion of 1.0 in k 10.627 * [backup-simplify]: Simplify 1.0 into 1.0 10.627 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 10.627 * [taylor]: Taking taylor expansion of (/ -1 k) in k 10.627 * [taylor]: Taking taylor expansion of -1 in k 10.627 * [backup-simplify]: Simplify -1 into -1 10.627 * [taylor]: Taking taylor expansion of k in k 10.627 * [backup-simplify]: Simplify 0 into 0 10.627 * [backup-simplify]: Simplify 1 into 1 10.628 * [backup-simplify]: Simplify (/ -1 1) into -1 10.628 * [backup-simplify]: Simplify (sqrt 0) into 0 10.629 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 10.630 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 10.630 * [backup-simplify]: Simplify +nan.0 into +nan.0 10.631 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 10.634 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 10.637 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 10.637 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.638 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.642 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 10.646 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 10.647 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.648 * [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))))) 10.648 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 2 1) 10.649 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 10.649 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 10.649 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 10.649 * [taylor]: Taking taylor expansion of 2.0 in n 10.649 * [backup-simplify]: Simplify 2.0 into 2.0 10.649 * [taylor]: Taking taylor expansion of (* n PI) in n 10.649 * [taylor]: Taking taylor expansion of n in n 10.649 * [backup-simplify]: Simplify 0 into 0 10.649 * [backup-simplify]: Simplify 1 into 1 10.649 * [taylor]: Taking taylor expansion of PI in n 10.649 * [backup-simplify]: Simplify PI into PI 10.649 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 10.649 * [taylor]: Taking taylor expansion of 2.0 in n 10.649 * [backup-simplify]: Simplify 2.0 into 2.0 10.649 * [taylor]: Taking taylor expansion of (* n PI) in n 10.649 * [taylor]: Taking taylor expansion of n in n 10.649 * [backup-simplify]: Simplify 0 into 0 10.649 * [backup-simplify]: Simplify 1 into 1 10.649 * [taylor]: Taking taylor expansion of PI in n 10.649 * [backup-simplify]: Simplify PI into PI 10.650 * [backup-simplify]: Simplify (* 0 PI) into 0 10.650 * [backup-simplify]: Simplify (* 2.0 0) into 0 10.650 * [backup-simplify]: Simplify 0 into 0 10.652 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.654 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 10.654 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.655 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 10.656 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 10.656 * [backup-simplify]: Simplify 0 into 0 10.658 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 10.659 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 10.659 * [backup-simplify]: Simplify 0 into 0 10.660 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 10.662 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 10.662 * [backup-simplify]: Simplify 0 into 0 10.663 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 10.664 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 10.664 * [backup-simplify]: Simplify 0 into 0 10.665 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 10.666 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 10.666 * [backup-simplify]: Simplify 0 into 0 10.667 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 10.668 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 10.668 * [backup-simplify]: Simplify 0 into 0 10.669 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 10.669 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 10.669 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 10.669 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 10.669 * [taylor]: Taking taylor expansion of 2.0 in n 10.669 * [backup-simplify]: Simplify 2.0 into 2.0 10.669 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.669 * [taylor]: Taking taylor expansion of PI in n 10.669 * [backup-simplify]: Simplify PI into PI 10.669 * [taylor]: Taking taylor expansion of n in n 10.669 * [backup-simplify]: Simplify 0 into 0 10.669 * [backup-simplify]: Simplify 1 into 1 10.670 * [backup-simplify]: Simplify (/ PI 1) into PI 10.670 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 10.670 * [taylor]: Taking taylor expansion of 2.0 in n 10.670 * [backup-simplify]: Simplify 2.0 into 2.0 10.670 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.670 * [taylor]: Taking taylor expansion of PI in n 10.670 * [backup-simplify]: Simplify PI into PI 10.670 * [taylor]: Taking taylor expansion of n in n 10.670 * [backup-simplify]: Simplify 0 into 0 10.670 * [backup-simplify]: Simplify 1 into 1 10.670 * [backup-simplify]: Simplify (/ PI 1) into PI 10.670 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.671 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.671 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 10.672 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 10.672 * [backup-simplify]: Simplify 0 into 0 10.672 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.673 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 10.673 * [backup-simplify]: Simplify 0 into 0 10.673 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.674 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 10.674 * [backup-simplify]: Simplify 0 into 0 10.675 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.676 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 10.676 * [backup-simplify]: Simplify 0 into 0 10.676 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.677 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 10.677 * [backup-simplify]: Simplify 0 into 0 10.678 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.679 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 10.679 * [backup-simplify]: Simplify 0 into 0 10.679 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 10.679 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 10.679 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 10.679 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 10.680 * [taylor]: Taking taylor expansion of -2.0 in n 10.680 * [backup-simplify]: Simplify -2.0 into -2.0 10.680 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.680 * [taylor]: Taking taylor expansion of PI in n 10.680 * [backup-simplify]: Simplify PI into PI 10.680 * [taylor]: Taking taylor expansion of n in n 10.680 * [backup-simplify]: Simplify 0 into 0 10.680 * [backup-simplify]: Simplify 1 into 1 10.680 * [backup-simplify]: Simplify (/ PI 1) into PI 10.680 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 10.680 * [taylor]: Taking taylor expansion of -2.0 in n 10.680 * [backup-simplify]: Simplify -2.0 into -2.0 10.680 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.680 * [taylor]: Taking taylor expansion of PI in n 10.680 * [backup-simplify]: Simplify PI into PI 10.680 * [taylor]: Taking taylor expansion of n in n 10.680 * [backup-simplify]: Simplify 0 into 0 10.680 * [backup-simplify]: Simplify 1 into 1 10.680 * [backup-simplify]: Simplify (/ PI 1) into PI 10.681 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 10.681 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 10.682 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 10.682 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 10.682 * [backup-simplify]: Simplify 0 into 0 10.683 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.683 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 10.683 * [backup-simplify]: Simplify 0 into 0 10.684 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.685 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 10.685 * [backup-simplify]: Simplify 0 into 0 10.685 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.686 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 10.686 * [backup-simplify]: Simplify 0 into 0 10.687 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.687 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 10.688 * [backup-simplify]: Simplify 0 into 0 10.688 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.689 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 10.689 * [backup-simplify]: Simplify 0 into 0 10.690 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 10.690 * * * [progress]: simplifying candidates 10.693 * [simplify]: Simplifying: (* (+ (+ (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)) (- (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) (- (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))) (/ 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(* (* 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) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +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 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 10.699 * * [simplify]: Extracting # 0 : cost 0 10.699 * * [simplify]: Extracting # 1 : cost 0 10.700 * * [simplify]: Extracting # 2 : cost 0 10.700 * * [simplify]: Extracting # 3 : cost 0 10.701 * * [simplify]: Extracting # 4 : cost 0 10.701 * * [simplify]: Extracting # 5 : cost 0 10.702 * * [simplify]: Extracting # 6 : cost 0 10.703 * * [simplify]: Extracting # 7 : cost 0 10.703 * * [simplify]: Extracting # 8 : cost 0 10.704 * * [simplify]: Extracting # 9 : cost 0 10.704 * * [simplify]: Extracting # 10 : cost 0 10.712 * * [simplify]: Extracting # 11 : cost 0 10.713 * * [simplify]: Extracting # 12 : cost 0 10.713 * * [simplify]: Extracting # 13 : cost 0 10.713 * * [simplify]: Extracting # 14 : cost 0 10.713 * * [simplify]: iteration 0 : 234 enodes (cost 1642 ) 10.779 * * [simplify]: Extracting # 0 : cost 0 10.781 * * [simplify]: Extracting # 1 : cost 0 10.783 * * [simplify]: Extracting # 2 : cost 0 10.784 * * [simplify]: Extracting # 3 : cost 0 10.786 * * [simplify]: Extracting # 4 : cost 0 10.788 * * [simplify]: Extracting # 5 : cost 0 10.789 * * [simplify]: iteration 1 : 601 enodes (cost 1507 ) 11.205 * * [simplify]: Extracting # 0 : cost 0 11.208 * * [simplify]: Extracting # 1 : cost 0 11.211 * * [simplify]: Extracting # 2 : cost 0 11.215 * * [simplify]: Extracting # 3 : cost 0 11.223 * * [simplify]: Extracting # 4 : cost 0 11.227 * * [simplify]: iteration 2 : 2709 enodes (cost 1405 ) 12.334 * * [simplify]: Extracting # 0 : cost 0 12.361 * * [simplify]: Extracting # 1 : cost 0 12.370 * * [simplify]: Extracting # 2 : cost 0 12.376 * * [simplify]: Extracting # 3 : cost 0 12.382 * * [simplify]: Extracting # 4 : cost 0 12.388 * * [simplify]: iteration done: 5001 enodes (cost 1401 ) 12.389 * [simplify]: Simplified to: (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 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 (* n PI)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (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))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* 2.0 (* PI n)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 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(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) (* 2.0 (* PI n)) (* 2.0 (* PI n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (sqrt (* n (* 2.0 PI))) (sqrt (* n (* 2.0 PI))) (* (* (cbrt n) (cbrt n)) (* 2.0 PI)) (* (sqrt n) (* 2.0 PI)) (* 2.0 PI) (* PI n) (+ (* (* 0.125 (pow k 2)) (+ (* (pow (log (* 2.0 PI)) 2) (pow (* (* 2.0 PI) n) 0.5)) (* (pow (log n) 2) (pow (* (* 2.0 PI) n) 0.5)))) (- (+ (pow (* (* 2.0 PI) n) 0.5) (* (* 0.25 (* (pow k 2) (log (* 2.0 PI)))) (* (pow (* (* 2.0 PI) n) 0.5) (log n)))) (* 0.5 (* k (+ (* (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.5)) (* (pow (* (* 2.0 PI) n) 0.5) (log n))))))) (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (- (* +nan.0 k) (- (* +nan.0 (pow k 2)) +nan.0))) (+ (- (/ +nan.0 (pow k 2))) (- (/ +nan.0 k) (/ +nan.0 (pow k 3)))) (+ (- (/ +nan.0 k) +nan.0) (- (/ +nan.0 (pow k 2)))) (- (- (* +nan.0 k) (- (* +nan.0 (pow k 2)) +nan.0))) (+ (- (/ +nan.0 (pow k 2))) (- (/ +nan.0 k) (/ +nan.0 (pow k 3)))) (+ (- (/ +nan.0 k) +nan.0) (- (/ +nan.0 (pow k 2)))) (* 2.0 (* PI n)) (* 2.0 (* PI n)) (* 2.0 (* PI n)) 12.390 * * * [progress]: adding candidates to table 13.045 * * [progress]: iteration 4 / 4 13.045 * * * [progress]: picking best candidate 13.100 * * * * [pick]: Picked # 13.100 * * * [progress]: localizing error 13.132 * * * [progress]: generating rewritten candidates 13.132 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 13.154 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 13.189 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 13.206 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 13.291 * * * [progress]: generating series expansions 13.291 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 13.293 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 13.293 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 13.293 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 13.293 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 13.293 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 13.293 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 13.293 * [taylor]: Taking taylor expansion of 0.5 in k 13.293 * [backup-simplify]: Simplify 0.5 into 0.5 13.293 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 13.293 * [taylor]: Taking taylor expansion of 1.0 in k 13.293 * [backup-simplify]: Simplify 1.0 into 1.0 13.293 * [taylor]: Taking taylor expansion of k in k 13.293 * [backup-simplify]: Simplify 0 into 0 13.293 * [backup-simplify]: Simplify 1 into 1 13.293 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 13.293 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 13.293 * [taylor]: Taking taylor expansion of 2.0 in k 13.293 * [backup-simplify]: Simplify 2.0 into 2.0 13.293 * [taylor]: Taking taylor expansion of (* n PI) in k 13.293 * [taylor]: Taking taylor expansion of n in k 13.293 * [backup-simplify]: Simplify n into n 13.293 * [taylor]: Taking taylor expansion of PI in k 13.293 * [backup-simplify]: Simplify PI into PI 13.293 * [backup-simplify]: Simplify (* n PI) into (* n PI) 13.294 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 13.294 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 13.294 * [backup-simplify]: Simplify (- 0) into 0 13.295 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 13.295 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 13.295 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 13.295 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 13.295 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 13.295 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 13.295 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 13.295 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 13.295 * [taylor]: Taking taylor expansion of 0.5 in n 13.295 * [backup-simplify]: Simplify 0.5 into 0.5 13.295 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 13.295 * [taylor]: Taking taylor expansion of 1.0 in n 13.295 * [backup-simplify]: Simplify 1.0 into 1.0 13.295 * [taylor]: Taking taylor expansion of k in n 13.296 * [backup-simplify]: Simplify k into k 13.296 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 13.296 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 13.296 * [taylor]: Taking taylor expansion of 2.0 in n 13.296 * [backup-simplify]: Simplify 2.0 into 2.0 13.296 * [taylor]: Taking taylor expansion of (* n PI) in n 13.296 * [taylor]: Taking taylor expansion of n in n 13.296 * [backup-simplify]: Simplify 0 into 0 13.296 * [backup-simplify]: Simplify 1 into 1 13.296 * [taylor]: Taking taylor expansion of PI in n 13.296 * [backup-simplify]: Simplify PI into PI 13.296 * [backup-simplify]: Simplify (* 0 PI) into 0 13.296 * [backup-simplify]: Simplify (* 2.0 0) into 0 13.297 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.298 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 13.299 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.299 * [backup-simplify]: Simplify (- k) into (- k) 13.299 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 13.299 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 13.300 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.301 * [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)))) 13.301 * [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))))) 13.301 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 13.301 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 13.302 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 13.302 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 13.302 * [taylor]: Taking taylor expansion of 0.5 in n 13.302 * [backup-simplify]: Simplify 0.5 into 0.5 13.302 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 13.302 * [taylor]: Taking taylor expansion of 1.0 in n 13.302 * [backup-simplify]: Simplify 1.0 into 1.0 13.302 * [taylor]: Taking taylor expansion of k in n 13.302 * [backup-simplify]: Simplify k into k 13.302 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 13.302 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 13.302 * [taylor]: Taking taylor expansion of 2.0 in n 13.302 * [backup-simplify]: Simplify 2.0 into 2.0 13.302 * [taylor]: Taking taylor expansion of (* n PI) in n 13.302 * [taylor]: Taking taylor expansion of n in n 13.302 * [backup-simplify]: Simplify 0 into 0 13.302 * [backup-simplify]: Simplify 1 into 1 13.302 * [taylor]: Taking taylor expansion of PI in n 13.302 * [backup-simplify]: Simplify PI into PI 13.302 * [backup-simplify]: Simplify (* 0 PI) into 0 13.302 * [backup-simplify]: Simplify (* 2.0 0) into 0 13.303 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.304 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 13.305 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.305 * [backup-simplify]: Simplify (- k) into (- k) 13.305 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 13.305 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 13.306 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.307 * [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)))) 13.307 * [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))))) 13.308 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 13.308 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 13.308 * [taylor]: Taking taylor expansion of 0.5 in k 13.308 * [backup-simplify]: Simplify 0.5 into 0.5 13.308 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 13.308 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 13.308 * [taylor]: Taking taylor expansion of 1.0 in k 13.308 * [backup-simplify]: Simplify 1.0 into 1.0 13.308 * [taylor]: Taking taylor expansion of k in k 13.308 * [backup-simplify]: Simplify 0 into 0 13.308 * [backup-simplify]: Simplify 1 into 1 13.308 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 13.308 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 13.308 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 13.308 * [taylor]: Taking taylor expansion of 2.0 in k 13.308 * [backup-simplify]: Simplify 2.0 into 2.0 13.308 * [taylor]: Taking taylor expansion of PI in k 13.308 * [backup-simplify]: Simplify PI into PI 13.308 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.309 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.309 * [taylor]: Taking taylor expansion of (log n) in k 13.309 * [taylor]: Taking taylor expansion of n in k 13.309 * [backup-simplify]: Simplify n into n 13.309 * [backup-simplify]: Simplify (log n) into (log n) 13.309 * [backup-simplify]: Simplify (- 0) into 0 13.309 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 13.310 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 13.311 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 13.312 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 13.312 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 13.313 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 13.314 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.314 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 13.315 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 13.316 * [backup-simplify]: Simplify (- 0) into 0 13.316 * [backup-simplify]: Simplify (+ 0 0) into 0 13.316 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 13.317 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.318 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 13.319 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.319 * [taylor]: Taking taylor expansion of 0 in k 13.319 * [backup-simplify]: Simplify 0 into 0 13.319 * [backup-simplify]: Simplify 0 into 0 13.319 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 13.320 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 13.321 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 13.321 * [backup-simplify]: Simplify (+ 0 0) into 0 13.322 * [backup-simplify]: Simplify (- 1) into -1 13.322 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.323 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 13.325 * [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)))) 13.327 * [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)))))) 13.329 * [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)))))) 13.330 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 13.331 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 13.333 * [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 13.333 * [backup-simplify]: Simplify (- 0) into 0 13.333 * [backup-simplify]: Simplify (+ 0 0) into 0 13.334 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 13.335 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.336 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 13.337 * [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 13.337 * [taylor]: Taking taylor expansion of 0 in k 13.337 * [backup-simplify]: Simplify 0 into 0 13.337 * [backup-simplify]: Simplify 0 into 0 13.337 * [backup-simplify]: Simplify 0 into 0 13.338 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.340 * [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 13.341 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 13.341 * [backup-simplify]: Simplify (+ 0 0) into 0 13.342 * [backup-simplify]: Simplify (- 0) into 0 13.342 * [backup-simplify]: Simplify (+ 0 0) into 0 13.343 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 13.345 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 13.347 * [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 (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 13.352 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 13.363 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 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 (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 13.364 * [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)))) 13.364 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 13.364 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 13.364 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 13.364 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 13.364 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 13.364 * [taylor]: Taking taylor expansion of 0.5 in k 13.364 * [backup-simplify]: Simplify 0.5 into 0.5 13.364 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.364 * [taylor]: Taking taylor expansion of 1.0 in k 13.364 * [backup-simplify]: Simplify 1.0 into 1.0 13.364 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.364 * [taylor]: Taking taylor expansion of k in k 13.364 * [backup-simplify]: Simplify 0 into 0 13.364 * [backup-simplify]: Simplify 1 into 1 13.365 * [backup-simplify]: Simplify (/ 1 1) into 1 13.365 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 13.365 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 13.365 * [taylor]: Taking taylor expansion of 2.0 in k 13.365 * [backup-simplify]: Simplify 2.0 into 2.0 13.365 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.365 * [taylor]: Taking taylor expansion of PI in k 13.365 * [backup-simplify]: Simplify PI into PI 13.365 * [taylor]: Taking taylor expansion of n in k 13.365 * [backup-simplify]: Simplify n into n 13.365 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.365 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 13.365 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 13.366 * [backup-simplify]: Simplify (- 1) into -1 13.366 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.367 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 13.367 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 13.367 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 13.367 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 13.367 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 13.367 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 13.367 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 13.367 * [taylor]: Taking taylor expansion of 0.5 in n 13.367 * [backup-simplify]: Simplify 0.5 into 0.5 13.367 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 13.367 * [taylor]: Taking taylor expansion of 1.0 in n 13.367 * [backup-simplify]: Simplify 1.0 into 1.0 13.367 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.367 * [taylor]: Taking taylor expansion of k in n 13.367 * [backup-simplify]: Simplify k into k 13.367 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.368 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 13.368 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.368 * [taylor]: Taking taylor expansion of 2.0 in n 13.368 * [backup-simplify]: Simplify 2.0 into 2.0 13.368 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.368 * [taylor]: Taking taylor expansion of PI in n 13.368 * [backup-simplify]: Simplify PI into PI 13.368 * [taylor]: Taking taylor expansion of n in n 13.368 * [backup-simplify]: Simplify 0 into 0 13.368 * [backup-simplify]: Simplify 1 into 1 13.368 * [backup-simplify]: Simplify (/ PI 1) into PI 13.369 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.370 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.370 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 13.370 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 13.370 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 13.379 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.380 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 13.380 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 13.380 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 13.381 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 13.381 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 13.381 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 13.381 * [taylor]: Taking taylor expansion of 0.5 in n 13.381 * [backup-simplify]: Simplify 0.5 into 0.5 13.381 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 13.381 * [taylor]: Taking taylor expansion of 1.0 in n 13.381 * [backup-simplify]: Simplify 1.0 into 1.0 13.381 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.381 * [taylor]: Taking taylor expansion of k in n 13.381 * [backup-simplify]: Simplify k into k 13.381 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.381 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 13.381 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.381 * [taylor]: Taking taylor expansion of 2.0 in n 13.381 * [backup-simplify]: Simplify 2.0 into 2.0 13.381 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.381 * [taylor]: Taking taylor expansion of PI in n 13.381 * [backup-simplify]: Simplify PI into PI 13.381 * [taylor]: Taking taylor expansion of n in n 13.381 * [backup-simplify]: Simplify 0 into 0 13.381 * [backup-simplify]: Simplify 1 into 1 13.381 * [backup-simplify]: Simplify (/ PI 1) into PI 13.382 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.382 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.382 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 13.382 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 13.382 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 13.384 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.384 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 13.385 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 13.385 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 13.385 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 13.385 * [taylor]: Taking taylor expansion of 0.5 in k 13.385 * [backup-simplify]: Simplify 0.5 into 0.5 13.385 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 13.385 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 13.385 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 13.385 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 13.385 * [taylor]: Taking taylor expansion of 2.0 in k 13.385 * [backup-simplify]: Simplify 2.0 into 2.0 13.386 * [taylor]: Taking taylor expansion of PI in k 13.386 * [backup-simplify]: Simplify PI into PI 13.386 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.386 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.387 * [taylor]: Taking taylor expansion of (log n) in k 13.387 * [taylor]: Taking taylor expansion of n in k 13.387 * [backup-simplify]: Simplify n into n 13.387 * [backup-simplify]: Simplify (log n) into (log n) 13.387 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.387 * [taylor]: Taking taylor expansion of 1.0 in k 13.387 * [backup-simplify]: Simplify 1.0 into 1.0 13.387 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.387 * [taylor]: Taking taylor expansion of k in k 13.387 * [backup-simplify]: Simplify 0 into 0 13.387 * [backup-simplify]: Simplify 1 into 1 13.387 * [backup-simplify]: Simplify (/ 1 1) into 1 13.387 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.388 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 13.388 * [backup-simplify]: Simplify (- 1) into -1 13.388 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.389 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 13.390 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 13.390 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 13.391 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 13.392 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.392 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 13.393 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 13.394 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.394 * [backup-simplify]: Simplify (- 0) into 0 13.394 * [backup-simplify]: Simplify (+ 0 0) into 0 13.394 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 13.395 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.396 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 13.397 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.397 * [taylor]: Taking taylor expansion of 0 in k 13.397 * [backup-simplify]: Simplify 0 into 0 13.397 * [backup-simplify]: Simplify 0 into 0 13.397 * [backup-simplify]: Simplify 0 into 0 13.398 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.399 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.402 * [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 13.402 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.403 * [backup-simplify]: Simplify (- 0) into 0 13.403 * [backup-simplify]: Simplify (+ 0 0) into 0 13.404 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 13.406 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.407 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 13.410 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.410 * [taylor]: Taking taylor expansion of 0 in k 13.410 * [backup-simplify]: Simplify 0 into 0 13.410 * [backup-simplify]: Simplify 0 into 0 13.410 * [backup-simplify]: Simplify 0 into 0 13.410 * [backup-simplify]: Simplify 0 into 0 13.411 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.413 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.417 * [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 13.417 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.417 * [backup-simplify]: Simplify (- 0) into 0 13.418 * [backup-simplify]: Simplify (+ 0 0) into 0 13.419 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 13.420 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.421 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 13.422 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.422 * [taylor]: Taking taylor expansion of 0 in k 13.422 * [backup-simplify]: Simplify 0 into 0 13.422 * [backup-simplify]: Simplify 0 into 0 13.423 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 13.424 * [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))) 13.424 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 13.424 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 13.424 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 13.424 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 13.424 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 13.424 * [taylor]: Taking taylor expansion of 0.5 in k 13.424 * [backup-simplify]: Simplify 0.5 into 0.5 13.424 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.424 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.424 * [taylor]: Taking taylor expansion of k in k 13.424 * [backup-simplify]: Simplify 0 into 0 13.424 * [backup-simplify]: Simplify 1 into 1 13.424 * [backup-simplify]: Simplify (/ 1 1) into 1 13.424 * [taylor]: Taking taylor expansion of 1.0 in k 13.424 * [backup-simplify]: Simplify 1.0 into 1.0 13.424 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 13.424 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 13.424 * [taylor]: Taking taylor expansion of -2.0 in k 13.424 * [backup-simplify]: Simplify -2.0 into -2.0 13.424 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.424 * [taylor]: Taking taylor expansion of PI in k 13.425 * [backup-simplify]: Simplify PI into PI 13.425 * [taylor]: Taking taylor expansion of n in k 13.425 * [backup-simplify]: Simplify n into n 13.425 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.425 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 13.425 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 13.425 * [backup-simplify]: Simplify (+ 1 0) into 1 13.425 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 13.425 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 13.426 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 13.426 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 13.426 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 13.426 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 13.426 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 13.426 * [taylor]: Taking taylor expansion of 0.5 in n 13.426 * [backup-simplify]: Simplify 0.5 into 0.5 13.426 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 13.426 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.426 * [taylor]: Taking taylor expansion of k in n 13.426 * [backup-simplify]: Simplify k into k 13.426 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.426 * [taylor]: Taking taylor expansion of 1.0 in n 13.426 * [backup-simplify]: Simplify 1.0 into 1.0 13.426 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 13.426 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.426 * [taylor]: Taking taylor expansion of -2.0 in n 13.426 * [backup-simplify]: Simplify -2.0 into -2.0 13.426 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.426 * [taylor]: Taking taylor expansion of PI in n 13.426 * [backup-simplify]: Simplify PI into PI 13.426 * [taylor]: Taking taylor expansion of n in n 13.426 * [backup-simplify]: Simplify 0 into 0 13.426 * [backup-simplify]: Simplify 1 into 1 13.426 * [backup-simplify]: Simplify (/ PI 1) into PI 13.427 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.427 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.427 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 13.427 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 13.428 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.429 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 13.430 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 13.430 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 13.430 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 13.430 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 13.430 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 13.430 * [taylor]: Taking taylor expansion of 0.5 in n 13.430 * [backup-simplify]: Simplify 0.5 into 0.5 13.430 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 13.430 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.430 * [taylor]: Taking taylor expansion of k in n 13.430 * [backup-simplify]: Simplify k into k 13.430 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.430 * [taylor]: Taking taylor expansion of 1.0 in n 13.430 * [backup-simplify]: Simplify 1.0 into 1.0 13.430 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 13.430 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.430 * [taylor]: Taking taylor expansion of -2.0 in n 13.430 * [backup-simplify]: Simplify -2.0 into -2.0 13.430 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.430 * [taylor]: Taking taylor expansion of PI in n 13.430 * [backup-simplify]: Simplify PI into PI 13.430 * [taylor]: Taking taylor expansion of n in n 13.430 * [backup-simplify]: Simplify 0 into 0 13.430 * [backup-simplify]: Simplify 1 into 1 13.431 * [backup-simplify]: Simplify (/ PI 1) into PI 13.431 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.432 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.432 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 13.432 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 13.433 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.433 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 13.434 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 13.435 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 13.435 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 13.435 * [taylor]: Taking taylor expansion of 0.5 in k 13.435 * [backup-simplify]: Simplify 0.5 into 0.5 13.435 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 13.435 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.435 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.435 * [taylor]: Taking taylor expansion of k in k 13.435 * [backup-simplify]: Simplify 0 into 0 13.435 * [backup-simplify]: Simplify 1 into 1 13.435 * [backup-simplify]: Simplify (/ 1 1) into 1 13.435 * [taylor]: Taking taylor expansion of 1.0 in k 13.435 * [backup-simplify]: Simplify 1.0 into 1.0 13.435 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 13.435 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 13.435 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 13.435 * [taylor]: Taking taylor expansion of -2.0 in k 13.435 * [backup-simplify]: Simplify -2.0 into -2.0 13.435 * [taylor]: Taking taylor expansion of PI in k 13.435 * [backup-simplify]: Simplify PI into PI 13.435 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.436 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.436 * [taylor]: Taking taylor expansion of (log n) in k 13.436 * [taylor]: Taking taylor expansion of n in k 13.436 * [backup-simplify]: Simplify n into n 13.436 * [backup-simplify]: Simplify (log n) into (log n) 13.437 * [backup-simplify]: Simplify (+ 1 0) into 1 13.437 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.437 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 13.438 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 13.439 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 13.440 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 13.441 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 13.442 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.443 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 13.445 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 13.445 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.446 * [backup-simplify]: Simplify (+ 0 0) into 0 13.446 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 13.448 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.449 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 13.451 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.451 * [taylor]: Taking taylor expansion of 0 in k 13.451 * [backup-simplify]: Simplify 0 into 0 13.451 * [backup-simplify]: Simplify 0 into 0 13.451 * [backup-simplify]: Simplify 0 into 0 13.452 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.454 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.457 * [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 13.458 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.458 * [backup-simplify]: Simplify (+ 0 0) into 0 13.459 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 13.460 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.462 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 13.465 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.465 * [taylor]: Taking taylor expansion of 0 in k 13.465 * [backup-simplify]: Simplify 0 into 0 13.465 * [backup-simplify]: Simplify 0 into 0 13.465 * [backup-simplify]: Simplify 0 into 0 13.465 * [backup-simplify]: Simplify 0 into 0 13.466 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.467 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.474 * [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 13.474 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.475 * [backup-simplify]: Simplify (+ 0 0) into 0 13.476 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 13.477 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.479 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 13.482 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.482 * [taylor]: Taking taylor expansion of 0 in k 13.482 * [backup-simplify]: Simplify 0 into 0 13.482 * [backup-simplify]: Simplify 0 into 0 13.484 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 13.484 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 13.484 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) into (* 1.0 (sqrt (/ 1 k))) 13.484 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 13.484 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 13.484 * [taylor]: Taking taylor expansion of 1.0 in k 13.484 * [backup-simplify]: Simplify 1.0 into 1.0 13.484 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 13.484 * [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 13.485 * [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 13.487 * [backup-simplify]: Simplify (/ 1 1) into 1 13.488 * [backup-simplify]: Simplify (sqrt 0) into 0 13.489 * [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 13.491 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 13.491 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.492 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 13.494 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.495 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 13.495 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.495 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.503 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.504 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 13.505 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.506 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 13.506 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt (/ 1 k)))) (sqrt (sqrt (/ 1 k)))) into (* 1.0 (sqrt k)) 13.506 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 13.506 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 13.506 * [taylor]: Taking taylor expansion of 1.0 in k 13.506 * [backup-simplify]: Simplify 1.0 into 1.0 13.506 * [taylor]: Taking taylor expansion of (sqrt k) in k 13.506 * [taylor]: Taking taylor expansion of k in k 13.506 * [backup-simplify]: Simplify 0 into 0 13.506 * [backup-simplify]: Simplify 1 into 1 13.506 * [backup-simplify]: Simplify (sqrt 0) into 0 13.507 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.507 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 13.507 * [taylor]: Taking taylor expansion of 1.0 in k 13.507 * [backup-simplify]: Simplify 1.0 into 1.0 13.507 * [taylor]: Taking taylor expansion of (sqrt k) in k 13.507 * [taylor]: Taking taylor expansion of k in k 13.507 * [backup-simplify]: Simplify 0 into 0 13.507 * [backup-simplify]: Simplify 1 into 1 13.507 * [backup-simplify]: Simplify (sqrt 0) into 0 13.508 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.508 * [backup-simplify]: Simplify (* 1.0 0) into 0 13.508 * [backup-simplify]: Simplify 0 into 0 13.509 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 13.510 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.511 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.513 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 13.513 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.515 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.516 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 13.517 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.518 * [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)))))))) 13.518 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt (/ 1 (- k))))) (sqrt (sqrt (/ 1 (- k))))) into (/ 1.0 (sqrt (/ -1 k))) 13.518 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 13.518 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 13.518 * [taylor]: Taking taylor expansion of 1.0 in k 13.518 * [backup-simplify]: Simplify 1.0 into 1.0 13.518 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 13.518 * [taylor]: Taking taylor expansion of (/ -1 k) in k 13.518 * [taylor]: Taking taylor expansion of -1 in k 13.518 * [backup-simplify]: Simplify -1 into -1 13.518 * [taylor]: Taking taylor expansion of k in k 13.518 * [backup-simplify]: Simplify 0 into 0 13.518 * [backup-simplify]: Simplify 1 into 1 13.519 * [backup-simplify]: Simplify (/ -1 1) into -1 13.519 * [backup-simplify]: Simplify (sqrt 0) into 0 13.520 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 13.520 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 13.520 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 13.520 * [taylor]: Taking taylor expansion of 1.0 in k 13.520 * [backup-simplify]: Simplify 1.0 into 1.0 13.520 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 13.520 * [taylor]: Taking taylor expansion of (/ -1 k) in k 13.520 * [taylor]: Taking taylor expansion of -1 in k 13.520 * [backup-simplify]: Simplify -1 into -1 13.520 * [taylor]: Taking taylor expansion of k in k 13.520 * [backup-simplify]: Simplify 0 into 0 13.520 * [backup-simplify]: Simplify 1 into 1 13.520 * [backup-simplify]: Simplify (/ -1 1) into -1 13.521 * [backup-simplify]: Simplify (sqrt 0) into 0 13.521 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 13.522 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 13.522 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.522 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 13.524 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.526 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 13.526 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.527 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.530 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.534 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 13.534 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.536 * [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))))) 13.536 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 13.536 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt k))) into (* 1.0 (pow (/ 1 k) 1/4)) 13.536 * [approximate]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in (k) around 0 13.536 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 13.536 * [taylor]: Taking taylor expansion of 1.0 in k 13.536 * [backup-simplify]: Simplify 1.0 into 1.0 13.536 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 13.536 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 13.536 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 13.536 * [taylor]: Taking taylor expansion of 1/4 in k 13.536 * [backup-simplify]: Simplify 1/4 into 1/4 13.537 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 13.537 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.537 * [taylor]: Taking taylor expansion of k in k 13.537 * [backup-simplify]: Simplify 0 into 0 13.537 * [backup-simplify]: Simplify 1 into 1 13.537 * [backup-simplify]: Simplify (/ 1 1) into 1 13.537 * [backup-simplify]: Simplify (log 1) into 0 13.538 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 13.538 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 13.538 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 13.538 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 13.538 * [taylor]: Taking taylor expansion of 1.0 in k 13.538 * [backup-simplify]: Simplify 1.0 into 1.0 13.538 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 13.538 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 13.538 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 13.538 * [taylor]: Taking taylor expansion of 1/4 in k 13.538 * [backup-simplify]: Simplify 1/4 into 1/4 13.538 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 13.539 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.539 * [taylor]: Taking taylor expansion of k in k 13.539 * [backup-simplify]: Simplify 0 into 0 13.539 * [backup-simplify]: Simplify 1 into 1 13.539 * [backup-simplify]: Simplify (/ 1 1) into 1 13.539 * [backup-simplify]: Simplify (log 1) into 0 13.540 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 13.540 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 13.540 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 13.540 * [backup-simplify]: Simplify (* 1.0 (pow k -1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 13.541 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 13.541 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 13.543 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 13.543 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 13.544 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0 13.545 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 13.546 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (pow k -1/4))) into 0 13.546 * [backup-simplify]: Simplify 0 into 0 13.547 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.549 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 13.550 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 13.551 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 13.552 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.553 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (pow k -1/4)))) into 0 13.553 * [backup-simplify]: Simplify 0 into 0 13.554 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.557 * [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 13.558 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 13.558 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0 13.559 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.560 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4))))) into 0 13.560 * [backup-simplify]: Simplify 0 into 0 13.561 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.566 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 13.567 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 13.568 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0 13.569 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.570 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4)))))) into 0 13.570 * [backup-simplify]: Simplify 0 into 0 13.571 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.585 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 13.586 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 13.588 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0 13.591 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.594 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4))))))) into 0 13.594 * [backup-simplify]: Simplify 0 into 0 13.595 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.620 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 13.621 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 13.623 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0 13.626 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.628 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4)))))))) into 0 13.628 * [backup-simplify]: Simplify 0 into 0 13.628 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 13.628 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt (/ 1 k)))) into (* 1.0 (pow k 1/4)) 13.628 * [approximate]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in (k) around 0 13.628 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 13.628 * [taylor]: Taking taylor expansion of 1.0 in k 13.628 * [backup-simplify]: Simplify 1.0 into 1.0 13.628 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 13.628 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 13.628 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 13.628 * [taylor]: Taking taylor expansion of 1/4 in k 13.628 * [backup-simplify]: Simplify 1/4 into 1/4 13.628 * [taylor]: Taking taylor expansion of (log k) in k 13.628 * [taylor]: Taking taylor expansion of k in k 13.628 * [backup-simplify]: Simplify 0 into 0 13.628 * [backup-simplify]: Simplify 1 into 1 13.628 * [backup-simplify]: Simplify (log 1) into 0 13.629 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 13.629 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 13.629 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 13.629 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 13.629 * [taylor]: Taking taylor expansion of 1.0 in k 13.629 * [backup-simplify]: Simplify 1.0 into 1.0 13.629 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 13.629 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 13.629 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 13.629 * [taylor]: Taking taylor expansion of 1/4 in k 13.629 * [backup-simplify]: Simplify 1/4 into 1/4 13.629 * [taylor]: Taking taylor expansion of (log k) in k 13.629 * [taylor]: Taking taylor expansion of k in k 13.629 * [backup-simplify]: Simplify 0 into 0 13.629 * [backup-simplify]: Simplify 1 into 1 13.629 * [backup-simplify]: Simplify (log 1) into 0 13.630 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 13.630 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 13.630 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 13.630 * [backup-simplify]: Simplify (* 1.0 (pow k 1/4)) into (* 1.0 (pow k 1/4)) 13.630 * [backup-simplify]: Simplify (* 1.0 (pow k 1/4)) into (* 1.0 (pow k 1/4)) 13.631 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 13.631 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 13.632 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 13.632 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 13.633 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (pow k 1/4))) into 0 13.633 * [backup-simplify]: Simplify 0 into 0 13.634 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 13.635 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 13.635 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 13.636 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.637 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (pow k 1/4)))) into 0 13.637 * [backup-simplify]: Simplify 0 into 0 13.640 * [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 13.640 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 13.641 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0 13.642 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.643 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))) into 0 13.643 * [backup-simplify]: Simplify 0 into 0 13.654 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 13.654 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 13.657 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0 13.659 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.661 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))) into 0 13.661 * [backup-simplify]: Simplify 0 into 0 13.678 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 13.679 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 13.681 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0 13.685 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.688 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))))) into 0 13.688 * [backup-simplify]: Simplify 0 into 0 13.713 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 13.713 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 13.714 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0 13.718 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.720 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))))) into 0 13.720 * [backup-simplify]: Simplify 0 into 0 13.720 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 13.720 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt (/ 1 (- k))))) into (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) 13.720 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in (k) around 0 13.720 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 13.720 * [taylor]: Taking taylor expansion of 1.0 in k 13.720 * [backup-simplify]: Simplify 1.0 into 1.0 13.720 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 13.720 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 13.720 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 13.720 * [taylor]: Taking taylor expansion of (/ -1 k) in k 13.720 * [taylor]: Taking taylor expansion of -1 in k 13.720 * [backup-simplify]: Simplify -1 into -1 13.720 * [taylor]: Taking taylor expansion of k in k 13.720 * [backup-simplify]: Simplify 0 into 0 13.720 * [backup-simplify]: Simplify 1 into 1 13.720 * [backup-simplify]: Simplify (/ -1 1) into -1 13.721 * [backup-simplify]: Simplify (sqrt 0) into 0 13.722 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 13.722 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 13.722 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 13.723 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 13.724 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.726 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 13.727 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 13.727 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 13.727 * [taylor]: Taking taylor expansion of 1.0 in k 13.727 * [backup-simplify]: Simplify 1.0 into 1.0 13.727 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 13.727 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 13.727 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 13.727 * [taylor]: Taking taylor expansion of (/ -1 k) in k 13.727 * [taylor]: Taking taylor expansion of -1 in k 13.727 * [backup-simplify]: Simplify -1 into -1 13.727 * [taylor]: Taking taylor expansion of k in k 13.727 * [backup-simplify]: Simplify 0 into 0 13.727 * [backup-simplify]: Simplify 1 into 1 13.727 * [backup-simplify]: Simplify (/ -1 1) into -1 13.728 * [backup-simplify]: Simplify (sqrt 0) into 0 13.729 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 13.729 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 13.730 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 13.730 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 13.732 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.734 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 13.735 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 13.741 * [backup-simplify]: Simplify (* 1.0 (sqrt +nan.0)) into (* 1.0 (sqrt +nan.0)) 13.742 * [backup-simplify]: Simplify (* 1.0 (sqrt +nan.0)) into (* 1.0 (sqrt +nan.0)) 13.743 * [backup-simplify]: Simplify (+ (* 1.0 (/ +nan.0 (sqrt +nan.0))) (* 0 (sqrt +nan.0))) into (- (* +nan.0 (/ 1 (sqrt +nan.0)))) 13.745 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (sqrt +nan.0)))) into (- (* +nan.0 (/ 1 (sqrt +nan.0)))) 13.745 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.748 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.751 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 13.757 * [backup-simplify]: Simplify (/ (- (- +nan.0) (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) 13.771 * [backup-simplify]: Simplify (+ (* 1.0 (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))) (+ (* 0 (/ +nan.0 (sqrt +nan.0))) (* 0 (sqrt +nan.0)))) into (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) 13.777 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) into (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) 13.784 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (/ 1 (sqrt +nan.0)))) (/ 1 (- k))) (* 1.0 (sqrt +nan.0)))) into (- (* 1.0 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2))))))))) 13.784 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 13.785 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 13.785 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 13.785 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 13.785 * [taylor]: Taking taylor expansion of 2.0 in n 13.785 * [backup-simplify]: Simplify 2.0 into 2.0 13.785 * [taylor]: Taking taylor expansion of (* n PI) in n 13.785 * [taylor]: Taking taylor expansion of n in n 13.785 * [backup-simplify]: Simplify 0 into 0 13.785 * [backup-simplify]: Simplify 1 into 1 13.785 * [taylor]: Taking taylor expansion of PI in n 13.785 * [backup-simplify]: Simplify PI into PI 13.785 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 13.785 * [taylor]: Taking taylor expansion of 2.0 in n 13.785 * [backup-simplify]: Simplify 2.0 into 2.0 13.785 * [taylor]: Taking taylor expansion of (* n PI) in n 13.785 * [taylor]: Taking taylor expansion of n in n 13.785 * [backup-simplify]: Simplify 0 into 0 13.785 * [backup-simplify]: Simplify 1 into 1 13.785 * [taylor]: Taking taylor expansion of PI in n 13.785 * [backup-simplify]: Simplify PI into PI 13.785 * [backup-simplify]: Simplify (* 0 PI) into 0 13.786 * [backup-simplify]: Simplify (* 2.0 0) into 0 13.786 * [backup-simplify]: Simplify 0 into 0 13.787 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.788 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 13.788 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.789 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.789 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 13.789 * [backup-simplify]: Simplify 0 into 0 13.790 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 13.791 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 13.791 * [backup-simplify]: Simplify 0 into 0 13.791 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.792 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 13.792 * [backup-simplify]: Simplify 0 into 0 13.793 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.794 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 13.794 * [backup-simplify]: Simplify 0 into 0 13.795 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.796 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 13.796 * [backup-simplify]: Simplify 0 into 0 13.797 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 13.798 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 13.798 * [backup-simplify]: Simplify 0 into 0 13.798 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 13.799 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 13.799 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 13.799 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.799 * [taylor]: Taking taylor expansion of 2.0 in n 13.799 * [backup-simplify]: Simplify 2.0 into 2.0 13.799 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.799 * [taylor]: Taking taylor expansion of PI in n 13.799 * [backup-simplify]: Simplify PI into PI 13.799 * [taylor]: Taking taylor expansion of n in n 13.799 * [backup-simplify]: Simplify 0 into 0 13.799 * [backup-simplify]: Simplify 1 into 1 13.799 * [backup-simplify]: Simplify (/ PI 1) into PI 13.799 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.799 * [taylor]: Taking taylor expansion of 2.0 in n 13.799 * [backup-simplify]: Simplify 2.0 into 2.0 13.799 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.799 * [taylor]: Taking taylor expansion of PI in n 13.799 * [backup-simplify]: Simplify PI into PI 13.799 * [taylor]: Taking taylor expansion of n in n 13.799 * [backup-simplify]: Simplify 0 into 0 13.799 * [backup-simplify]: Simplify 1 into 1 13.800 * [backup-simplify]: Simplify (/ PI 1) into PI 13.800 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.800 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.801 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.801 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 13.801 * [backup-simplify]: Simplify 0 into 0 13.802 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.803 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.803 * [backup-simplify]: Simplify 0 into 0 13.803 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.804 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.804 * [backup-simplify]: Simplify 0 into 0 13.805 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.805 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.805 * [backup-simplify]: Simplify 0 into 0 13.806 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.807 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.807 * [backup-simplify]: Simplify 0 into 0 13.808 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.810 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.810 * [backup-simplify]: Simplify 0 into 0 13.811 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 13.811 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 13.811 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 13.811 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.811 * [taylor]: Taking taylor expansion of -2.0 in n 13.811 * [backup-simplify]: Simplify -2.0 into -2.0 13.811 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.811 * [taylor]: Taking taylor expansion of PI in n 13.811 * [backup-simplify]: Simplify PI into PI 13.811 * [taylor]: Taking taylor expansion of n in n 13.811 * [backup-simplify]: Simplify 0 into 0 13.812 * [backup-simplify]: Simplify 1 into 1 13.812 * [backup-simplify]: Simplify (/ PI 1) into PI 13.812 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.812 * [taylor]: Taking taylor expansion of -2.0 in n 13.812 * [backup-simplify]: Simplify -2.0 into -2.0 13.812 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.812 * [taylor]: Taking taylor expansion of PI in n 13.812 * [backup-simplify]: Simplify PI into PI 13.812 * [taylor]: Taking taylor expansion of n in n 13.812 * [backup-simplify]: Simplify 0 into 0 13.812 * [backup-simplify]: Simplify 1 into 1 13.813 * [backup-simplify]: Simplify (/ PI 1) into PI 13.813 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.814 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.815 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.816 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 13.816 * [backup-simplify]: Simplify 0 into 0 13.817 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.818 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.818 * [backup-simplify]: Simplify 0 into 0 13.819 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.820 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.820 * [backup-simplify]: Simplify 0 into 0 13.822 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.823 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.823 * [backup-simplify]: Simplify 0 into 0 13.824 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.826 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.826 * [backup-simplify]: Simplify 0 into 0 13.827 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.829 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.829 * [backup-simplify]: Simplify 0 into 0 13.829 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 13.830 * * * [progress]: simplifying candidates 13.845 * [simplify]: Simplifying: (* (+ (+ (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)) (- (- (log 1.0) (log (sqrt (sqrt k)))) (log (sqrt (sqrt k)))) (- (log (/ 1.0 (sqrt (sqrt k)))) (log (sqrt (sqrt k)))) (log (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (exp (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (* (* (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt k)))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))) (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (- (/ 1.0 (sqrt (sqrt k)))) (- (sqrt (sqrt k))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt 1))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt 1)) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) 1) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt 1))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt 1)) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) 1) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt 1))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt 1)) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt 1))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt 1)) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt 1))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt 1)) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) 1) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt 1)) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) 1) (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) 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(/ (/ 1 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt 1)) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) 1) (/ (/ 1.0 (sqrt (sqrt (sqrt 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(/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt 1)) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) 1) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ 1 1) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ (/ 1 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(sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ 1.0 (cbrt (sqrt (sqrt k)))) (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ 1.0 (sqrt (cbrt (sqrt k)))) (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ 1.0 (sqrt (sqrt (cbrt k)))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt 1))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ 1 1) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) (/ (sqrt (sqrt k)) 1.0) (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt 1))) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ 1.0 1) (/ (sqrt (sqrt k)) (cbrt 1.0)) (/ (sqrt (sqrt k)) (sqrt 1.0)) (/ (sqrt (sqrt k)) 1.0) (* (* 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) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +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))))) (* 1.0 (pow (/ 1 k) 1/4)) (* 1.0 (pow (/ 1 k) 1/4)) (- (* 1.0 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2))))))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 13.881 * * [simplify]: Extracting # 0 : cost 0 13.882 * * [simplify]: Extracting # 1 : cost 0 13.884 * * [simplify]: Extracting # 2 : cost 0 13.885 * * [simplify]: Extracting # 3 : cost 0 13.886 * * [simplify]: Extracting # 4 : cost 0 13.887 * * [simplify]: Extracting # 5 : cost 0 13.888 * * [simplify]: Extracting # 6 : cost 0 13.889 * * [simplify]: Extracting # 7 : cost 0 13.890 * * [simplify]: Extracting # 8 : cost 0 13.891 * * [simplify]: Extracting # 9 : cost 0 13.892 * * [simplify]: Extracting # 10 : cost 0 13.893 * * [simplify]: Extracting # 11 : cost 0 13.894 * * [simplify]: Extracting # 12 : cost 0 13.895 * * [simplify]: Extracting # 13 : cost 0 13.896 * * [simplify]: iteration 0 : 558 enodes (cost 8953 ) 14.224 * * [simplify]: Extracting # 0 : cost 0 14.229 * * [simplify]: Extracting # 1 : cost 0 14.233 * * [simplify]: Extracting # 2 : cost 0 14.237 * * [simplify]: Extracting # 3 : cost 0 14.240 * * [simplify]: Extracting # 4 : cost 0 14.244 * * [simplify]: Extracting # 5 : cost 0 14.247 * * [simplify]: Extracting # 6 : cost 0 14.249 * * [simplify]: iteration 1 : 1422 enodes (cost 7629 ) 14.620 * * [simplify]: Extracting # 0 : cost 0 14.630 * * [simplify]: Extracting # 1 : cost 0 14.645 * * [simplify]: Extracting # 2 : cost 0 14.659 * * [simplify]: Extracting # 3 : cost 0 14.673 * * [simplify]: Extracting # 4 : cost 0 14.694 * * [simplify]: Extracting # 5 : cost 0 14.708 * * [simplify]: iteration done: 5000 enodes (cost 7131 ) 14.715 * [simplify]: Simplified to: (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 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) (* 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(sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt (sqrt k)))) (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (fabs (cbrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (cbrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ 1.0 (cbrt (sqrt (sqrt k)))) (/ 1 (fabs (cbrt (sqrt k)))) (/ 1.0 (sqrt (cbrt (sqrt k)))) (/ 1 (sqrt (fabs (cbrt k)))) (/ 1.0 (sqrt (sqrt (cbrt k)))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) (/ (sqrt (sqrt k)) 1.0) (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ 1.0 (fabs (cbrt (sqrt k)))) (/ 1.0 (sqrt (fabs (cbrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) 1.0 (/ 1.0 (sqrt (sqrt (sqrt k)))) 1.0 (/ 1.0 (sqrt (sqrt (sqrt k)))) 1.0 (/ (sqrt (sqrt k)) (cbrt 1.0)) (/ (sqrt (sqrt k)) (sqrt 1.0)) (/ (sqrt (sqrt k)) 1.0) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (log (* n (* 2.0 PI))) (log (* n (* 2.0 PI))) (log (* n (* 2.0 PI))) (exp (* (* 2.0 PI) n)) (* (pow n 3) (* (pow PI 3) (pow 2.0 3))) (* (pow n 3) (pow (* 2.0 PI) 3)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* n (* 2.0 PI)) 3) (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) (* n PI) (+ (* (* 0.125 (pow k 2)) (+ (* (pow (log (* 2.0 PI)) 2) (pow (* n (* 2.0 PI)) 0.5)) (* (pow (log n) 2) (pow (* n (* 2.0 PI)) 0.5)))) (- (+ (pow (* n (* 2.0 PI)) 0.5) (* (* 0.25 (* (pow k 2) (log (* 2.0 PI)))) (* (log n) (pow (* n (* 2.0 PI)) 0.5)))) (* (* 0.5 k) (+ (* (pow (* n (* 2.0 PI)) 0.5) (log (* 2.0 PI))) (* (log n) (pow (* n (* 2.0 PI)) 0.5)))))) (pow (pow (* n (* 2.0 PI)) 0.5) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (- (* +nan.0 k) (- (* +nan.0 (pow k 2)) +nan.0))) (+ (- (/ +nan.0 (pow k 2))) (- (/ +nan.0 k) (/ +nan.0 (pow k 3)))) (+ (- (/ +nan.0 k) +nan.0) (- (/ +nan.0 (pow k 2)))) (* 1.0 (pow (/ 1 k) 1/4)) (* 1.0 (pow (/ 1 k) 1/4)) (+ (- (* 1.0 (sqrt +nan.0)) (/ +nan.0 (* (sqrt +nan.0) (pow k 2)))) (- (/ +nan.0 (* (sqrt +nan.0) k)) (/ +nan.0 (* (pow (sqrt +nan.0) 3) (pow k 2))))) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (* n (* 2.0 PI)) 14.723 * * * [progress]: adding candidates to table 16.154 * [progress]: [Phase 3 of 3] Extracting. 16.154 * * [regime]: Finding splitpoints for: (# # # # # # # #) 16.162 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 16.162 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # # #) 16.199 * * * * [regimes]: Trying to branch on n from (# # # # # # # #) 16.256 * * * * [regimes]: Trying to branch on k from (# # # # # # # #) 16.334 * * * [regime]: Found split indices: #