46.386 * [progress]: [Phase 1 of 3] Setting up. 0.002 * * * [progress]: [1/2] Preparing points 0.134 * * * [progress]: [2/2] Setting up program. 0.137 * [progress]: [Phase 2 of 3] Improving. 0.137 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.137 * * [simplify]: Extracting # 0 : cost 0 0.137 * * [simplify]: Extracting # 1 : cost 0 0.137 * * [simplify]: Extracting # 2 : cost 0 0.137 * * [simplify]: Extracting # 3 : cost 0 0.137 * * [simplify]: Extracting # 4 : cost 0 0.137 * * [simplify]: Extracting # 5 : cost 0 0.137 * * [simplify]: Extracting # 6 : cost 0 0.137 * * [simplify]: Extracting # 7 : cost 0 0.137 * * [simplify]: iteration 0 : 13 enodes (cost 16 ) 0.170 * * [simplify]: Extracting # 0 : cost 0 0.170 * * [simplify]: Extracting # 1 : cost 0 0.170 * * [simplify]: Extracting # 2 : cost 0 0.170 * * [simplify]: Extracting # 3 : cost 0 0.170 * * [simplify]: Extracting # 4 : cost 0 0.170 * * [simplify]: Extracting # 5 : cost 0 0.170 * * [simplify]: iteration 1 : 29 enodes (cost 16 ) 0.176 * * [simplify]: Extracting # 0 : cost 0 0.176 * * [simplify]: Extracting # 1 : cost 0 0.176 * * [simplify]: Extracting # 2 : cost 0 0.177 * * [simplify]: Extracting # 3 : cost 0 0.177 * * [simplify]: Extracting # 4 : cost 0 0.177 * * [simplify]: iteration 2 : 59 enodes (cost 16 ) 0.203 * * [simplify]: Extracting # 0 : cost 0 0.204 * * [simplify]: Extracting # 1 : cost 0 0.204 * * [simplify]: Extracting # 2 : cost 0 0.204 * * [simplify]: Extracting # 3 : cost 0 0.204 * * [simplify]: Extracting # 4 : cost 0 0.205 * * [simplify]: iteration 3 : 119 enodes (cost 16 ) 0.268 * * [simplify]: Extracting # 0 : cost 0 0.268 * * [simplify]: Extracting # 1 : cost 0 0.269 * * [simplify]: Extracting # 2 : cost 0 0.270 * * [simplify]: Extracting # 3 : cost 0 0.270 * * [simplify]: Extracting # 4 : cost 0 0.271 * * [simplify]: iteration 4 : 313 enodes (cost 16 ) 0.519 * * [simplify]: Extracting # 0 : cost 0 0.521 * * [simplify]: Extracting # 1 : cost 0 0.523 * * [simplify]: Extracting # 2 : cost 0 0.524 * * [simplify]: Extracting # 3 : cost 0 0.525 * * [simplify]: Extracting # 4 : cost 0 0.527 * * [simplify]: iteration 5 : 843 enodes (cost 16 ) 2.006 * * [simplify]: Extracting # 0 : cost 0 2.014 * * [simplify]: Extracting # 1 : cost 0 2.019 * * [simplify]: Extracting # 2 : cost 0 2.025 * * [simplify]: Extracting # 3 : cost 0 2.032 * * [simplify]: Extracting # 4 : cost 0 2.037 * * [simplify]: iteration 6 : 3221 enodes (cost 16 ) 3.644 * * [simplify]: Extracting # 0 : cost 0 3.649 * * [simplify]: Extracting # 1 : cost 0 3.655 * * [simplify]: Extracting # 2 : cost 0 3.664 * * [simplify]: Extracting # 3 : cost 0 3.672 * * [simplify]: Extracting # 4 : cost 0 3.681 * * [simplify]: iteration done: 5001 enodes (cost 16 ) 3.681 * [simplify]: Simplified to: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3.682 * * [progress]: iteration 1 / 4 3.682 * * * [progress]: picking best candidate 3.686 * * * * [pick]: Picked # 3.686 * * * [progress]: localizing error 3.719 * * * [progress]: generating rewritten candidates 3.719 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 3.776 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 3.813 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 3.826 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 3.924 * * * [progress]: generating series expansions 3.924 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 3.925 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 3.925 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 3.925 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.925 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.925 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.925 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.925 * [taylor]: Taking taylor expansion of 0.5 in k 3.925 * [backup-simplify]: Simplify 0.5 into 0.5 3.925 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.925 * [taylor]: Taking taylor expansion of 1.0 in k 3.925 * [backup-simplify]: Simplify 1.0 into 1.0 3.925 * [taylor]: Taking taylor expansion of k in k 3.925 * [backup-simplify]: Simplify 0 into 0 3.925 * [backup-simplify]: Simplify 1 into 1 3.925 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.926 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.926 * [taylor]: Taking taylor expansion of 2.0 in k 3.926 * [backup-simplify]: Simplify 2.0 into 2.0 3.926 * [taylor]: Taking taylor expansion of (* n PI) in k 3.926 * [taylor]: Taking taylor expansion of n in k 3.926 * [backup-simplify]: Simplify n into n 3.926 * [taylor]: Taking taylor expansion of PI in k 3.926 * [backup-simplify]: Simplify PI into PI 3.926 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.926 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 3.926 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 3.927 * [backup-simplify]: Simplify (- 0) into 0 3.927 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.928 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.928 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 3.928 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 3.928 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.928 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.928 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.928 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.928 * [taylor]: Taking taylor expansion of 0.5 in n 3.928 * [backup-simplify]: Simplify 0.5 into 0.5 3.928 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.928 * [taylor]: Taking taylor expansion of 1.0 in n 3.928 * [backup-simplify]: Simplify 1.0 into 1.0 3.928 * [taylor]: Taking taylor expansion of k in n 3.928 * [backup-simplify]: Simplify k into k 3.928 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.928 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.928 * [taylor]: Taking taylor expansion of 2.0 in n 3.928 * [backup-simplify]: Simplify 2.0 into 2.0 3.928 * [taylor]: Taking taylor expansion of (* n PI) in n 3.928 * [taylor]: Taking taylor expansion of n in n 3.928 * [backup-simplify]: Simplify 0 into 0 3.928 * [backup-simplify]: Simplify 1 into 1 3.929 * [taylor]: Taking taylor expansion of PI in n 3.929 * [backup-simplify]: Simplify PI into PI 3.929 * [backup-simplify]: Simplify (* 0 PI) into 0 3.930 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.931 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.933 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.934 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.934 * [backup-simplify]: Simplify (- k) into (- k) 3.934 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.934 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.936 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.937 * [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)))) 3.938 * [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))))) 3.938 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.938 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.938 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.939 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.939 * [taylor]: Taking taylor expansion of 0.5 in n 3.939 * [backup-simplify]: Simplify 0.5 into 0.5 3.939 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.939 * [taylor]: Taking taylor expansion of 1.0 in n 3.939 * [backup-simplify]: Simplify 1.0 into 1.0 3.939 * [taylor]: Taking taylor expansion of k in n 3.939 * [backup-simplify]: Simplify k into k 3.939 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.939 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.939 * [taylor]: Taking taylor expansion of 2.0 in n 3.939 * [backup-simplify]: Simplify 2.0 into 2.0 3.939 * [taylor]: Taking taylor expansion of (* n PI) in n 3.939 * [taylor]: Taking taylor expansion of n in n 3.939 * [backup-simplify]: Simplify 0 into 0 3.939 * [backup-simplify]: Simplify 1 into 1 3.939 * [taylor]: Taking taylor expansion of PI in n 3.939 * [backup-simplify]: Simplify PI into PI 3.940 * [backup-simplify]: Simplify (* 0 PI) into 0 3.940 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.942 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.943 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.944 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.944 * [backup-simplify]: Simplify (- k) into (- k) 3.944 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.945 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.946 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.947 * [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)))) 3.948 * [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))))) 3.949 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 3.949 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 3.949 * [taylor]: Taking taylor expansion of 0.5 in k 3.949 * [backup-simplify]: Simplify 0.5 into 0.5 3.949 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 3.949 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.949 * [taylor]: Taking taylor expansion of 1.0 in k 3.949 * [backup-simplify]: Simplify 1.0 into 1.0 3.949 * [taylor]: Taking taylor expansion of k in k 3.949 * [backup-simplify]: Simplify 0 into 0 3.949 * [backup-simplify]: Simplify 1 into 1 3.949 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 3.949 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.949 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.949 * [taylor]: Taking taylor expansion of 2.0 in k 3.949 * [backup-simplify]: Simplify 2.0 into 2.0 3.949 * [taylor]: Taking taylor expansion of PI in k 3.949 * [backup-simplify]: Simplify PI into PI 3.950 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.951 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.951 * [taylor]: Taking taylor expansion of (log n) in k 3.951 * [taylor]: Taking taylor expansion of n in k 3.951 * [backup-simplify]: Simplify n into n 3.951 * [backup-simplify]: Simplify (log n) into (log n) 3.951 * [backup-simplify]: Simplify (- 0) into 0 3.952 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.953 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 3.954 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 3.955 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 3.957 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 3.958 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 3.959 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.960 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 3.963 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.963 * [backup-simplify]: Simplify (- 0) into 0 3.963 * [backup-simplify]: Simplify (+ 0 0) into 0 3.964 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 3.966 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.967 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 3.969 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.969 * [taylor]: Taking taylor expansion of 0 in k 3.969 * [backup-simplify]: Simplify 0 into 0 3.969 * [backup-simplify]: Simplify 0 into 0 3.970 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.972 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.973 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 3.974 * [backup-simplify]: Simplify (+ 0 0) into 0 3.974 * [backup-simplify]: Simplify (- 1) into -1 3.974 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.976 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 3.978 * [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)))) 3.982 * [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)))))) 3.985 * [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)))))) 3.987 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 3.988 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 3.992 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 3.992 * [backup-simplify]: Simplify (- 0) into 0 3.993 * [backup-simplify]: Simplify (+ 0 0) into 0 3.994 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 3.995 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.997 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.000 * [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 4.000 * [taylor]: Taking taylor expansion of 0 in k 4.000 * [backup-simplify]: Simplify 0 into 0 4.000 * [backup-simplify]: Simplify 0 into 0 4.000 * [backup-simplify]: Simplify 0 into 0 4.001 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.005 * [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 4.007 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.007 * [backup-simplify]: Simplify (+ 0 0) into 0 4.008 * [backup-simplify]: Simplify (- 0) into 0 4.008 * [backup-simplify]: Simplify (+ 0 0) into 0 4.010 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.013 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 4.017 * [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)))))) 4.027 * [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)))))) 4.038 * [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)))))) 4.039 * [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)))) 4.039 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 4.039 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 4.039 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.039 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.039 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 4.040 * [taylor]: Taking taylor expansion of 0.5 in k 4.040 * [backup-simplify]: Simplify 0.5 into 0.5 4.040 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.040 * [taylor]: Taking taylor expansion of 1.0 in k 4.040 * [backup-simplify]: Simplify 1.0 into 1.0 4.040 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.040 * [taylor]: Taking taylor expansion of k in k 4.040 * [backup-simplify]: Simplify 0 into 0 4.040 * [backup-simplify]: Simplify 1 into 1 4.040 * [backup-simplify]: Simplify (/ 1 1) into 1 4.040 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.040 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.040 * [taylor]: Taking taylor expansion of 2.0 in k 4.040 * [backup-simplify]: Simplify 2.0 into 2.0 4.040 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.040 * [taylor]: Taking taylor expansion of PI in k 4.040 * [backup-simplify]: Simplify PI into PI 4.040 * [taylor]: Taking taylor expansion of n in k 4.040 * [backup-simplify]: Simplify n into n 4.041 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.041 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.041 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.041 * [backup-simplify]: Simplify (- 1) into -1 4.042 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.042 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 4.042 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 4.043 * [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))))) 4.043 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 4.043 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.043 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.043 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 4.043 * [taylor]: Taking taylor expansion of 0.5 in n 4.043 * [backup-simplify]: Simplify 0.5 into 0.5 4.043 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.043 * [taylor]: Taking taylor expansion of 1.0 in n 4.043 * [backup-simplify]: Simplify 1.0 into 1.0 4.043 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.043 * [taylor]: Taking taylor expansion of k in n 4.043 * [backup-simplify]: Simplify k into k 4.043 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.043 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.043 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.043 * [taylor]: Taking taylor expansion of 2.0 in n 4.043 * [backup-simplify]: Simplify 2.0 into 2.0 4.043 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.043 * [taylor]: Taking taylor expansion of PI in n 4.043 * [backup-simplify]: Simplify PI into PI 4.043 * [taylor]: Taking taylor expansion of n in n 4.043 * [backup-simplify]: Simplify 0 into 0 4.043 * [backup-simplify]: Simplify 1 into 1 4.044 * [backup-simplify]: Simplify (/ PI 1) into PI 4.045 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.046 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.046 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.046 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.046 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 4.048 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.049 * [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)))) 4.051 * [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))))) 4.051 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 4.051 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.051 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.051 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 4.051 * [taylor]: Taking taylor expansion of 0.5 in n 4.051 * [backup-simplify]: Simplify 0.5 into 0.5 4.051 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.051 * [taylor]: Taking taylor expansion of 1.0 in n 4.051 * [backup-simplify]: Simplify 1.0 into 1.0 4.051 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.051 * [taylor]: Taking taylor expansion of k in n 4.051 * [backup-simplify]: Simplify k into k 4.051 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.051 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.051 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.051 * [taylor]: Taking taylor expansion of 2.0 in n 4.051 * [backup-simplify]: Simplify 2.0 into 2.0 4.051 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.051 * [taylor]: Taking taylor expansion of PI in n 4.051 * [backup-simplify]: Simplify PI into PI 4.051 * [taylor]: Taking taylor expansion of n in n 4.051 * [backup-simplify]: Simplify 0 into 0 4.051 * [backup-simplify]: Simplify 1 into 1 4.052 * [backup-simplify]: Simplify (/ PI 1) into PI 4.053 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.054 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.054 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.054 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.054 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 4.056 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.057 * [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)))) 4.058 * [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))))) 4.059 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 4.059 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 4.059 * [taylor]: Taking taylor expansion of 0.5 in k 4.059 * [backup-simplify]: Simplify 0.5 into 0.5 4.059 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 4.059 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 4.059 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.059 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.059 * [taylor]: Taking taylor expansion of 2.0 in k 4.059 * [backup-simplify]: Simplify 2.0 into 2.0 4.059 * [taylor]: Taking taylor expansion of PI in k 4.059 * [backup-simplify]: Simplify PI into PI 4.060 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.061 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.061 * [taylor]: Taking taylor expansion of (log n) in k 4.061 * [taylor]: Taking taylor expansion of n in k 4.061 * [backup-simplify]: Simplify n into n 4.061 * [backup-simplify]: Simplify (log n) into (log n) 4.061 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.061 * [taylor]: Taking taylor expansion of 1.0 in k 4.061 * [backup-simplify]: Simplify 1.0 into 1.0 4.061 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.061 * [taylor]: Taking taylor expansion of k in k 4.061 * [backup-simplify]: Simplify 0 into 0 4.061 * [backup-simplify]: Simplify 1 into 1 4.061 * [backup-simplify]: Simplify (/ 1 1) into 1 4.061 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.063 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 4.063 * [backup-simplify]: Simplify (- 1) into -1 4.063 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.065 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 4.066 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 4.067 * [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))))) 4.068 * [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))))) 4.069 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.069 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.071 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.071 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.072 * [backup-simplify]: Simplify (- 0) into 0 4.072 * [backup-simplify]: Simplify (+ 0 0) into 0 4.072 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.074 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.075 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 4.077 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.077 * [taylor]: Taking taylor expansion of 0 in k 4.077 * [backup-simplify]: Simplify 0 into 0 4.077 * [backup-simplify]: Simplify 0 into 0 4.077 * [backup-simplify]: Simplify 0 into 0 4.078 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.079 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.082 * [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 4.082 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.082 * [backup-simplify]: Simplify (- 0) into 0 4.083 * [backup-simplify]: Simplify (+ 0 0) into 0 4.084 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 4.085 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.086 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 4.089 * [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 4.089 * [taylor]: Taking taylor expansion of 0 in k 4.089 * [backup-simplify]: Simplify 0 into 0 4.089 * [backup-simplify]: Simplify 0 into 0 4.089 * [backup-simplify]: Simplify 0 into 0 4.089 * [backup-simplify]: Simplify 0 into 0 4.090 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.091 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.097 * [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 4.097 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.098 * [backup-simplify]: Simplify (- 0) into 0 4.098 * [backup-simplify]: Simplify (+ 0 0) into 0 4.099 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 4.100 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.102 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 4.105 * [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 4.105 * [taylor]: Taking taylor expansion of 0 in k 4.105 * [backup-simplify]: Simplify 0 into 0 4.105 * [backup-simplify]: Simplify 0 into 0 4.106 * [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)))) 4.107 * [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))) 4.107 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 4.107 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 4.107 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.107 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.107 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 4.107 * [taylor]: Taking taylor expansion of 0.5 in k 4.107 * [backup-simplify]: Simplify 0.5 into 0.5 4.107 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.107 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.107 * [taylor]: Taking taylor expansion of k in k 4.107 * [backup-simplify]: Simplify 0 into 0 4.107 * [backup-simplify]: Simplify 1 into 1 4.108 * [backup-simplify]: Simplify (/ 1 1) into 1 4.108 * [taylor]: Taking taylor expansion of 1.0 in k 4.108 * [backup-simplify]: Simplify 1.0 into 1.0 4.108 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.108 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.108 * [taylor]: Taking taylor expansion of -2.0 in k 4.108 * [backup-simplify]: Simplify -2.0 into -2.0 4.108 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.108 * [taylor]: Taking taylor expansion of PI in k 4.108 * [backup-simplify]: Simplify PI into PI 4.108 * [taylor]: Taking taylor expansion of n in k 4.108 * [backup-simplify]: Simplify n into n 4.108 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.108 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.108 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.109 * [backup-simplify]: Simplify (+ 1 0) into 1 4.109 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 4.109 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 4.109 * [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)))))) 4.109 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 4.109 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.109 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.109 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 4.110 * [taylor]: Taking taylor expansion of 0.5 in n 4.110 * [backup-simplify]: Simplify 0.5 into 0.5 4.110 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.110 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.110 * [taylor]: Taking taylor expansion of k in n 4.110 * [backup-simplify]: Simplify k into k 4.110 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.110 * [taylor]: Taking taylor expansion of 1.0 in n 4.110 * [backup-simplify]: Simplify 1.0 into 1.0 4.110 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.110 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.110 * [taylor]: Taking taylor expansion of -2.0 in n 4.110 * [backup-simplify]: Simplify -2.0 into -2.0 4.110 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.110 * [taylor]: Taking taylor expansion of PI in n 4.110 * [backup-simplify]: Simplify PI into PI 4.110 * [taylor]: Taking taylor expansion of n in n 4.110 * [backup-simplify]: Simplify 0 into 0 4.110 * [backup-simplify]: Simplify 1 into 1 4.110 * [backup-simplify]: Simplify (/ PI 1) into PI 4.111 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.112 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.112 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.112 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 4.113 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.114 * [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)))) 4.115 * [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))))) 4.115 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 4.115 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.116 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.116 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 4.116 * [taylor]: Taking taylor expansion of 0.5 in n 4.116 * [backup-simplify]: Simplify 0.5 into 0.5 4.116 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.116 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.116 * [taylor]: Taking taylor expansion of k in n 4.116 * [backup-simplify]: Simplify k into k 4.116 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.116 * [taylor]: Taking taylor expansion of 1.0 in n 4.116 * [backup-simplify]: Simplify 1.0 into 1.0 4.116 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.116 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.116 * [taylor]: Taking taylor expansion of -2.0 in n 4.116 * [backup-simplify]: Simplify -2.0 into -2.0 4.116 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.116 * [taylor]: Taking taylor expansion of PI in n 4.116 * [backup-simplify]: Simplify PI into PI 4.116 * [taylor]: Taking taylor expansion of n in n 4.116 * [backup-simplify]: Simplify 0 into 0 4.116 * [backup-simplify]: Simplify 1 into 1 4.117 * [backup-simplify]: Simplify (/ PI 1) into PI 4.117 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.118 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.118 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.118 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 4.119 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.121 * [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)))) 4.122 * [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))))) 4.122 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.122 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.122 * [taylor]: Taking taylor expansion of 0.5 in k 4.122 * [backup-simplify]: Simplify 0.5 into 0.5 4.122 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.122 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.122 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.122 * [taylor]: Taking taylor expansion of k in k 4.122 * [backup-simplify]: Simplify 0 into 0 4.122 * [backup-simplify]: Simplify 1 into 1 4.123 * [backup-simplify]: Simplify (/ 1 1) into 1 4.123 * [taylor]: Taking taylor expansion of 1.0 in k 4.123 * [backup-simplify]: Simplify 1.0 into 1.0 4.123 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.123 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.123 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.123 * [taylor]: Taking taylor expansion of -2.0 in k 4.123 * [backup-simplify]: Simplify -2.0 into -2.0 4.123 * [taylor]: Taking taylor expansion of PI in k 4.123 * [backup-simplify]: Simplify PI into PI 4.124 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.124 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.124 * [taylor]: Taking taylor expansion of (log n) in k 4.124 * [taylor]: Taking taylor expansion of n in k 4.124 * [backup-simplify]: Simplify n into n 4.124 * [backup-simplify]: Simplify (log n) into (log n) 4.125 * [backup-simplify]: Simplify (+ 1 0) into 1 4.125 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.125 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 4.126 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 4.127 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 4.128 * [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))))) 4.129 * [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))))) 4.129 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.130 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.132 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.132 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.132 * [backup-simplify]: Simplify (+ 0 0) into 0 4.132 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 4.133 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.134 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.135 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.136 * [taylor]: Taking taylor expansion of 0 in k 4.136 * [backup-simplify]: Simplify 0 into 0 4.136 * [backup-simplify]: Simplify 0 into 0 4.136 * [backup-simplify]: Simplify 0 into 0 4.136 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.137 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.139 * [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 4.139 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.139 * [backup-simplify]: Simplify (+ 0 0) into 0 4.140 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 4.141 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.143 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 4.145 * [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 4.145 * [taylor]: Taking taylor expansion of 0 in k 4.145 * [backup-simplify]: Simplify 0 into 0 4.145 * [backup-simplify]: Simplify 0 into 0 4.145 * [backup-simplify]: Simplify 0 into 0 4.145 * [backup-simplify]: Simplify 0 into 0 4.147 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.148 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.153 * [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 4.153 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.154 * [backup-simplify]: Simplify (+ 0 0) into 0 4.155 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 4.156 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.157 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 4.159 * [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 4.159 * [taylor]: Taking taylor expansion of 0 in k 4.159 * [backup-simplify]: Simplify 0 into 0 4.159 * [backup-simplify]: Simplify 0 into 0 4.160 * [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)))))) 4.160 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 4.163 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 4.163 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 4.163 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.163 * [taylor]: Taking taylor expansion of 2.0 in n 4.163 * [backup-simplify]: Simplify 2.0 into 2.0 4.163 * [taylor]: Taking taylor expansion of (* n PI) in n 4.163 * [taylor]: Taking taylor expansion of n in n 4.163 * [backup-simplify]: Simplify 0 into 0 4.163 * [backup-simplify]: Simplify 1 into 1 4.163 * [taylor]: Taking taylor expansion of PI in n 4.163 * [backup-simplify]: Simplify PI into PI 4.163 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.163 * [taylor]: Taking taylor expansion of 2.0 in n 4.163 * [backup-simplify]: Simplify 2.0 into 2.0 4.163 * [taylor]: Taking taylor expansion of (* n PI) in n 4.163 * [taylor]: Taking taylor expansion of n in n 4.164 * [backup-simplify]: Simplify 0 into 0 4.164 * [backup-simplify]: Simplify 1 into 1 4.164 * [taylor]: Taking taylor expansion of PI in n 4.164 * [backup-simplify]: Simplify PI into PI 4.164 * [backup-simplify]: Simplify (* 0 PI) into 0 4.164 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.164 * [backup-simplify]: Simplify 0 into 0 4.165 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.166 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.167 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.167 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.168 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.168 * [backup-simplify]: Simplify 0 into 0 4.169 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.169 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.169 * [backup-simplify]: Simplify 0 into 0 4.170 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.171 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 4.171 * [backup-simplify]: Simplify 0 into 0 4.172 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.173 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 4.173 * [backup-simplify]: Simplify 0 into 0 4.174 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.175 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 4.175 * [backup-simplify]: Simplify 0 into 0 4.176 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 4.177 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 4.177 * [backup-simplify]: Simplify 0 into 0 4.177 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 4.178 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 4.178 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 4.178 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.178 * [taylor]: Taking taylor expansion of 2.0 in n 4.178 * [backup-simplify]: Simplify 2.0 into 2.0 4.178 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.178 * [taylor]: Taking taylor expansion of PI in n 4.178 * [backup-simplify]: Simplify PI into PI 4.178 * [taylor]: Taking taylor expansion of n in n 4.178 * [backup-simplify]: Simplify 0 into 0 4.178 * [backup-simplify]: Simplify 1 into 1 4.178 * [backup-simplify]: Simplify (/ PI 1) into PI 4.178 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.178 * [taylor]: Taking taylor expansion of 2.0 in n 4.178 * [backup-simplify]: Simplify 2.0 into 2.0 4.178 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.178 * [taylor]: Taking taylor expansion of PI in n 4.178 * [backup-simplify]: Simplify PI into PI 4.178 * [taylor]: Taking taylor expansion of n in n 4.178 * [backup-simplify]: Simplify 0 into 0 4.178 * [backup-simplify]: Simplify 1 into 1 4.179 * [backup-simplify]: Simplify (/ PI 1) into PI 4.179 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.179 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.180 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.180 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.180 * [backup-simplify]: Simplify 0 into 0 4.181 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.182 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.182 * [backup-simplify]: Simplify 0 into 0 4.182 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.184 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.184 * [backup-simplify]: Simplify 0 into 0 4.184 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.185 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.185 * [backup-simplify]: Simplify 0 into 0 4.186 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.187 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.187 * [backup-simplify]: Simplify 0 into 0 4.187 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.188 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.188 * [backup-simplify]: Simplify 0 into 0 4.189 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 4.189 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 4.189 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 4.189 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.189 * [taylor]: Taking taylor expansion of -2.0 in n 4.189 * [backup-simplify]: Simplify -2.0 into -2.0 4.189 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.189 * [taylor]: Taking taylor expansion of PI in n 4.189 * [backup-simplify]: Simplify PI into PI 4.189 * [taylor]: Taking taylor expansion of n in n 4.189 * [backup-simplify]: Simplify 0 into 0 4.189 * [backup-simplify]: Simplify 1 into 1 4.190 * [backup-simplify]: Simplify (/ PI 1) into PI 4.190 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.190 * [taylor]: Taking taylor expansion of -2.0 in n 4.190 * [backup-simplify]: Simplify -2.0 into -2.0 4.190 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.190 * [taylor]: Taking taylor expansion of PI in n 4.190 * [backup-simplify]: Simplify PI into PI 4.190 * [taylor]: Taking taylor expansion of n in n 4.190 * [backup-simplify]: Simplify 0 into 0 4.190 * [backup-simplify]: Simplify 1 into 1 4.190 * [backup-simplify]: Simplify (/ PI 1) into PI 4.191 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.191 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.191 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.192 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.192 * [backup-simplify]: Simplify 0 into 0 4.193 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.193 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.193 * [backup-simplify]: Simplify 0 into 0 4.194 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.194 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.195 * [backup-simplify]: Simplify 0 into 0 4.195 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.196 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.196 * [backup-simplify]: Simplify 0 into 0 4.197 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.197 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.197 * [backup-simplify]: Simplify 0 into 0 4.198 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.199 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.199 * [backup-simplify]: Simplify 0 into 0 4.200 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 4.200 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 4.200 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 4.200 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 4.200 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.200 * [taylor]: Taking taylor expansion of 1.0 in k 4.200 * [backup-simplify]: Simplify 1.0 into 1.0 4.200 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.200 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.200 * [taylor]: Taking taylor expansion of k in k 4.200 * [backup-simplify]: Simplify 0 into 0 4.200 * [backup-simplify]: Simplify 1 into 1 4.201 * [backup-simplify]: Simplify (/ 1 1) into 1 4.201 * [backup-simplify]: Simplify (sqrt 0) into 0 4.203 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.203 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.203 * [taylor]: Taking taylor expansion of 1.0 in k 4.203 * [backup-simplify]: Simplify 1.0 into 1.0 4.203 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.203 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.203 * [taylor]: Taking taylor expansion of k in k 4.203 * [backup-simplify]: Simplify 0 into 0 4.203 * [backup-simplify]: Simplify 1 into 1 4.203 * [backup-simplify]: Simplify (/ 1 1) into 1 4.204 * [backup-simplify]: Simplify (sqrt 0) into 0 4.205 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.206 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.206 * [backup-simplify]: Simplify 0 into 0 4.207 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.208 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.208 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 4.211 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.213 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.214 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.215 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.217 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.219 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.219 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.220 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 4.220 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 4.220 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 4.220 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.220 * [taylor]: Taking taylor expansion of 1.0 in k 4.220 * [backup-simplify]: Simplify 1.0 into 1.0 4.220 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.220 * [taylor]: Taking taylor expansion of k in k 4.220 * [backup-simplify]: Simplify 0 into 0 4.220 * [backup-simplify]: Simplify 1 into 1 4.221 * [backup-simplify]: Simplify (sqrt 0) into 0 4.221 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.221 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.222 * [taylor]: Taking taylor expansion of 1.0 in k 4.222 * [backup-simplify]: Simplify 1.0 into 1.0 4.222 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.222 * [taylor]: Taking taylor expansion of k in k 4.222 * [backup-simplify]: Simplify 0 into 0 4.222 * [backup-simplify]: Simplify 1 into 1 4.222 * [backup-simplify]: Simplify (sqrt 0) into 0 4.223 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.223 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.223 * [backup-simplify]: Simplify 0 into 0 4.224 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.224 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.226 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.227 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.227 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.230 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.231 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.231 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.232 * [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)))))))) 4.233 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 4.233 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 4.233 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.233 * [taylor]: Taking taylor expansion of 1.0 in k 4.233 * [backup-simplify]: Simplify 1.0 into 1.0 4.233 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.233 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.233 * [taylor]: Taking taylor expansion of -1 in k 4.233 * [backup-simplify]: Simplify -1 into -1 4.233 * [taylor]: Taking taylor expansion of k in k 4.233 * [backup-simplify]: Simplify 0 into 0 4.233 * [backup-simplify]: Simplify 1 into 1 4.233 * [backup-simplify]: Simplify (/ -1 1) into -1 4.234 * [backup-simplify]: Simplify (sqrt 0) into 0 4.234 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.235 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.235 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.235 * [taylor]: Taking taylor expansion of 1.0 in k 4.235 * [backup-simplify]: Simplify 1.0 into 1.0 4.235 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.235 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.235 * [taylor]: Taking taylor expansion of -1 in k 4.235 * [backup-simplify]: Simplify -1 into -1 4.235 * [taylor]: Taking taylor expansion of k in k 4.235 * [backup-simplify]: Simplify 0 into 0 4.235 * [backup-simplify]: Simplify 1 into 1 4.235 * [backup-simplify]: Simplify (/ -1 1) into -1 4.235 * [backup-simplify]: Simplify (sqrt 0) into 0 4.236 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.237 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.237 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.237 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 4.239 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.241 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 4.241 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.241 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.244 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.246 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 4.246 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.247 * [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))))) 4.247 * * * * [progress]: [ 4 / 4 ] generating series at (2) 4.248 * [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))))) 4.248 * [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 4.248 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 4.248 * [taylor]: Taking taylor expansion of 1.0 in n 4.248 * [backup-simplify]: Simplify 1.0 into 1.0 4.248 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 4.248 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 4.248 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.248 * [taylor]: Taking taylor expansion of k in n 4.248 * [backup-simplify]: Simplify k into k 4.248 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.248 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 4.248 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.248 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 4.248 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 4.248 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.248 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.248 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 4.248 * [taylor]: Taking taylor expansion of 0.5 in n 4.248 * [backup-simplify]: Simplify 0.5 into 0.5 4.248 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.248 * [taylor]: Taking taylor expansion of 1.0 in n 4.248 * [backup-simplify]: Simplify 1.0 into 1.0 4.248 * [taylor]: Taking taylor expansion of k in n 4.248 * [backup-simplify]: Simplify k into k 4.248 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.248 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.248 * [taylor]: Taking taylor expansion of 2.0 in n 4.248 * [backup-simplify]: Simplify 2.0 into 2.0 4.248 * [taylor]: Taking taylor expansion of (* n PI) in n 4.248 * [taylor]: Taking taylor expansion of n in n 4.248 * [backup-simplify]: Simplify 0 into 0 4.248 * [backup-simplify]: Simplify 1 into 1 4.248 * [taylor]: Taking taylor expansion of PI in n 4.249 * [backup-simplify]: Simplify PI into PI 4.249 * [backup-simplify]: Simplify (* 0 PI) into 0 4.249 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.250 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.251 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.252 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.252 * [backup-simplify]: Simplify (- k) into (- k) 4.252 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.252 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 4.254 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.255 * [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)))) 4.256 * [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))))) 4.256 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 4.256 * [taylor]: Taking taylor expansion of 1.0 in k 4.256 * [backup-simplify]: Simplify 1.0 into 1.0 4.256 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 4.256 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.256 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.256 * [taylor]: Taking taylor expansion of k in k 4.256 * [backup-simplify]: Simplify 0 into 0 4.256 * [backup-simplify]: Simplify 1 into 1 4.257 * [backup-simplify]: Simplify (/ 1 1) into 1 4.257 * [backup-simplify]: Simplify (sqrt 0) into 0 4.258 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.258 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 4.259 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.259 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.259 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 4.259 * [taylor]: Taking taylor expansion of 0.5 in k 4.259 * [backup-simplify]: Simplify 0.5 into 0.5 4.259 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.259 * [taylor]: Taking taylor expansion of 1.0 in k 4.259 * [backup-simplify]: Simplify 1.0 into 1.0 4.259 * [taylor]: Taking taylor expansion of k in k 4.259 * [backup-simplify]: Simplify 0 into 0 4.259 * [backup-simplify]: Simplify 1 into 1 4.259 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.259 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.259 * [taylor]: Taking taylor expansion of 2.0 in k 4.259 * [backup-simplify]: Simplify 2.0 into 2.0 4.259 * [taylor]: Taking taylor expansion of (* n PI) in k 4.259 * [taylor]: Taking taylor expansion of n in k 4.259 * [backup-simplify]: Simplify n into n 4.259 * [taylor]: Taking taylor expansion of PI in k 4.259 * [backup-simplify]: Simplify PI into PI 4.259 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.259 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.259 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.260 * [backup-simplify]: Simplify (- 0) into 0 4.260 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.261 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 4.261 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 4.261 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 4.261 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 4.261 * [taylor]: Taking taylor expansion of 1.0 in k 4.261 * [backup-simplify]: Simplify 1.0 into 1.0 4.261 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 4.261 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.261 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.261 * [taylor]: Taking taylor expansion of k in k 4.261 * [backup-simplify]: Simplify 0 into 0 4.261 * [backup-simplify]: Simplify 1 into 1 4.262 * [backup-simplify]: Simplify (/ 1 1) into 1 4.262 * [backup-simplify]: Simplify (sqrt 0) into 0 4.264 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.264 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 4.264 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.264 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.264 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 4.264 * [taylor]: Taking taylor expansion of 0.5 in k 4.264 * [backup-simplify]: Simplify 0.5 into 0.5 4.264 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.264 * [taylor]: Taking taylor expansion of 1.0 in k 4.264 * [backup-simplify]: Simplify 1.0 into 1.0 4.264 * [taylor]: Taking taylor expansion of k in k 4.264 * [backup-simplify]: Simplify 0 into 0 4.264 * [backup-simplify]: Simplify 1 into 1 4.264 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.264 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.264 * [taylor]: Taking taylor expansion of 2.0 in k 4.264 * [backup-simplify]: Simplify 2.0 into 2.0 4.264 * [taylor]: Taking taylor expansion of (* n PI) in k 4.264 * [taylor]: Taking taylor expansion of n in k 4.264 * [backup-simplify]: Simplify n into n 4.264 * [taylor]: Taking taylor expansion of PI in k 4.264 * [backup-simplify]: Simplify PI into PI 4.264 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.265 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.265 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.270 * [backup-simplify]: Simplify (- 0) into 0 4.271 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.272 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 4.272 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 4.272 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 4.272 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 4.273 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.273 * [taylor]: Taking taylor expansion of 0 in n 4.273 * [backup-simplify]: Simplify 0 into 0 4.273 * [backup-simplify]: Simplify 0 into 0 4.273 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 4.274 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 4.275 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 4.275 * [backup-simplify]: Simplify (- 1) into -1 4.276 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.277 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 4.278 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 4.279 * [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))) 4.280 * [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))) 4.281 * [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))) 4.281 * [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 4.281 * [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 4.281 * [taylor]: Taking taylor expansion of +nan.0 in n 4.281 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.281 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 4.281 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 4.281 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 4.281 * [taylor]: Taking taylor expansion of 0.5 in n 4.281 * [backup-simplify]: Simplify 0.5 into 0.5 4.281 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 4.281 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 4.281 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.281 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.281 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.281 * [taylor]: Taking taylor expansion of 1.0 in n 4.281 * [backup-simplify]: Simplify 1.0 into 1.0 4.281 * [taylor]: Taking taylor expansion of (log PI) in n 4.281 * [taylor]: Taking taylor expansion of PI in n 4.282 * [backup-simplify]: Simplify PI into PI 4.282 * [backup-simplify]: Simplify (log PI) into (log PI) 4.282 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.283 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.284 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 4.284 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.284 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.284 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.284 * [taylor]: Taking taylor expansion of 1.0 in n 4.284 * [backup-simplify]: Simplify 1.0 into 1.0 4.284 * [taylor]: Taking taylor expansion of (log n) in n 4.284 * [taylor]: Taking taylor expansion of n in n 4.284 * [backup-simplify]: Simplify 0 into 0 4.284 * [backup-simplify]: Simplify 1 into 1 4.284 * [backup-simplify]: Simplify (log 1) into 0 4.284 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.284 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.285 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.285 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.285 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.285 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.285 * [taylor]: Taking taylor expansion of 1.0 in n 4.285 * [backup-simplify]: Simplify 1.0 into 1.0 4.285 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.285 * [taylor]: Taking taylor expansion of 2.0 in n 4.285 * [backup-simplify]: Simplify 2.0 into 2.0 4.285 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.286 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.287 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.287 * [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) 4.288 * [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) 4.289 * [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)) 4.290 * [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))) 4.291 * [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) 4.292 * [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)) 4.293 * [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))) 4.293 * [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))) 4.294 * [backup-simplify]: Simplify 0 into 0 4.294 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 4.295 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 4.296 * [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 4.296 * [backup-simplify]: Simplify (- 0) into 0 4.296 * [backup-simplify]: Simplify (+ 0 0) into 0 4.297 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 4.298 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 4.298 * [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))) 4.299 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 4.301 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.303 * [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)))))))) 4.307 * [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)))))))) 4.307 * [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 4.307 * [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 4.307 * [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 4.307 * [taylor]: Taking taylor expansion of +nan.0 in n 4.307 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.307 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 4.307 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 4.307 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 4.307 * [taylor]: Taking taylor expansion of 0.5 in n 4.307 * [backup-simplify]: Simplify 0.5 into 0.5 4.307 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 4.307 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 4.307 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.307 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.307 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.307 * [taylor]: Taking taylor expansion of 1.0 in n 4.307 * [backup-simplify]: Simplify 1.0 into 1.0 4.307 * [taylor]: Taking taylor expansion of (log PI) in n 4.307 * [taylor]: Taking taylor expansion of PI in n 4.307 * [backup-simplify]: Simplify PI into PI 4.308 * [backup-simplify]: Simplify (log PI) into (log PI) 4.308 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.309 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.309 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 4.309 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.309 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.309 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.309 * [taylor]: Taking taylor expansion of 1.0 in n 4.309 * [backup-simplify]: Simplify 1.0 into 1.0 4.309 * [taylor]: Taking taylor expansion of (log n) in n 4.309 * [taylor]: Taking taylor expansion of n in n 4.309 * [backup-simplify]: Simplify 0 into 0 4.309 * [backup-simplify]: Simplify 1 into 1 4.310 * [backup-simplify]: Simplify (log 1) into 0 4.310 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.310 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.310 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.310 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.310 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.310 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.310 * [taylor]: Taking taylor expansion of 1.0 in n 4.310 * [backup-simplify]: Simplify 1.0 into 1.0 4.310 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.310 * [taylor]: Taking taylor expansion of 2.0 in n 4.310 * [backup-simplify]: Simplify 2.0 into 2.0 4.310 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.311 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.313 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.313 * [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) 4.315 * [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) 4.316 * [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)) 4.317 * [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))) 4.319 * [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) 4.319 * [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 4.319 * [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 4.319 * [taylor]: Taking taylor expansion of +nan.0 in n 4.319 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.319 * [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 4.319 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 4.319 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 4.319 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 4.319 * [taylor]: Taking taylor expansion of 0.5 in n 4.319 * [backup-simplify]: Simplify 0.5 into 0.5 4.319 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 4.319 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 4.320 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.320 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.320 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.320 * [taylor]: Taking taylor expansion of 1.0 in n 4.320 * [backup-simplify]: Simplify 1.0 into 1.0 4.320 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.320 * [taylor]: Taking taylor expansion of 2.0 in n 4.320 * [backup-simplify]: Simplify 2.0 into 2.0 4.320 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.321 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.323 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.323 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 4.323 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.323 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.323 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.323 * [taylor]: Taking taylor expansion of 1.0 in n 4.323 * [backup-simplify]: Simplify 1.0 into 1.0 4.323 * [taylor]: Taking taylor expansion of (log PI) in n 4.323 * [taylor]: Taking taylor expansion of PI in n 4.323 * [backup-simplify]: Simplify PI into PI 4.323 * [backup-simplify]: Simplify (log PI) into (log PI) 4.324 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.326 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.326 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.326 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.326 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.326 * [taylor]: Taking taylor expansion of 1.0 in n 4.326 * [backup-simplify]: Simplify 1.0 into 1.0 4.326 * [taylor]: Taking taylor expansion of (log n) in n 4.326 * [taylor]: Taking taylor expansion of n in n 4.326 * [backup-simplify]: Simplify 0 into 0 4.326 * [backup-simplify]: Simplify 1 into 1 4.327 * [backup-simplify]: Simplify (log 1) into 0 4.327 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.328 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.328 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.328 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 4.330 * [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) 4.331 * [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)) 4.333 * [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))) 4.335 * [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) 4.335 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.335 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.335 * [taylor]: Taking taylor expansion of 2.0 in n 4.335 * [backup-simplify]: Simplify 2.0 into 2.0 4.335 * [taylor]: Taking taylor expansion of (* n PI) in n 4.335 * [taylor]: Taking taylor expansion of n in n 4.335 * [backup-simplify]: Simplify 0 into 0 4.335 * [backup-simplify]: Simplify 1 into 1 4.335 * [taylor]: Taking taylor expansion of PI in n 4.336 * [backup-simplify]: Simplify PI into PI 4.336 * [backup-simplify]: Simplify (* 0 PI) into 0 4.336 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.338 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.340 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.341 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.343 * [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)) 4.344 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.347 * [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)) 4.350 * [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))) 4.352 * [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)))))) 4.358 * [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)))))))) 4.365 * [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)))))))) 4.371 * [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)))))))) 4.373 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 4.374 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 4.376 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 4.377 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 4.378 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.378 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 4.379 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 4.380 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 4.382 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 4.383 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 4.384 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 4.386 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 4.388 * [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 4.390 * [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 4.392 * [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 4.394 * [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 4.395 * [backup-simplify]: Simplify (- 0) into 0 4.395 * [backup-simplify]: Simplify 0 into 0 4.395 * [backup-simplify]: Simplify 0 into 0 4.396 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.397 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 4.400 * [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 4.401 * [backup-simplify]: Simplify (- 0) into 0 4.401 * [backup-simplify]: Simplify (+ 0 0) into 0 4.403 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 4.404 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 4.406 * [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))) 4.407 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.417 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.422 * [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)))))))) 4.434 * [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)))))))) 4.434 * [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 4.434 * [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 4.434 * [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 4.435 * [taylor]: Taking taylor expansion of +nan.0 in n 4.435 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.435 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 4.435 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 4.435 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 4.435 * [taylor]: Taking taylor expansion of 0.5 in n 4.435 * [backup-simplify]: Simplify 0.5 into 0.5 4.435 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 4.435 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 4.435 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.435 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.435 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.435 * [taylor]: Taking taylor expansion of 1.0 in n 4.435 * [backup-simplify]: Simplify 1.0 into 1.0 4.435 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.435 * [taylor]: Taking taylor expansion of 2.0 in n 4.435 * [backup-simplify]: Simplify 2.0 into 2.0 4.436 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.437 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.438 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.438 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 4.438 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.438 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.439 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.439 * [taylor]: Taking taylor expansion of 1.0 in n 4.439 * [backup-simplify]: Simplify 1.0 into 1.0 4.439 * [taylor]: Taking taylor expansion of (log n) in n 4.439 * [taylor]: Taking taylor expansion of n in n 4.439 * [backup-simplify]: Simplify 0 into 0 4.439 * [backup-simplify]: Simplify 1 into 1 4.439 * [backup-simplify]: Simplify (log 1) into 0 4.440 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.440 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.440 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.440 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.440 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.440 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.440 * [taylor]: Taking taylor expansion of 1.0 in n 4.440 * [backup-simplify]: Simplify 1.0 into 1.0 4.440 * [taylor]: Taking taylor expansion of (log PI) in n 4.440 * [taylor]: Taking taylor expansion of PI in n 4.440 * [backup-simplify]: Simplify PI into PI 4.440 * [backup-simplify]: Simplify (log PI) into (log PI) 4.441 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.443 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.444 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 4.445 * [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) 4.447 * [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)) 4.448 * [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))) 4.450 * [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) 4.450 * [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 4.450 * [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 4.450 * [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 4.450 * [taylor]: Taking taylor expansion of +nan.0 in n 4.450 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.450 * [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 4.450 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 4.450 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 4.450 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 4.450 * [taylor]: Taking taylor expansion of 0.5 in n 4.450 * [backup-simplify]: Simplify 0.5 into 0.5 4.450 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 4.450 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 4.450 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.450 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.450 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.450 * [taylor]: Taking taylor expansion of 1.0 in n 4.450 * [backup-simplify]: Simplify 1.0 into 1.0 4.450 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.450 * [taylor]: Taking taylor expansion of 2.0 in n 4.450 * [backup-simplify]: Simplify 2.0 into 2.0 4.451 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.452 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.454 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.454 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 4.454 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.454 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.454 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.454 * [taylor]: Taking taylor expansion of 1.0 in n 4.454 * [backup-simplify]: Simplify 1.0 into 1.0 4.454 * [taylor]: Taking taylor expansion of (log PI) in n 4.454 * [taylor]: Taking taylor expansion of PI in n 4.454 * [backup-simplify]: Simplify PI into PI 4.454 * [backup-simplify]: Simplify (log PI) into (log PI) 4.455 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.457 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.457 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.457 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.457 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.457 * [taylor]: Taking taylor expansion of 1.0 in n 4.457 * [backup-simplify]: Simplify 1.0 into 1.0 4.457 * [taylor]: Taking taylor expansion of (log n) in n 4.458 * [taylor]: Taking taylor expansion of n in n 4.458 * [backup-simplify]: Simplify 0 into 0 4.458 * [backup-simplify]: Simplify 1 into 1 4.458 * [backup-simplify]: Simplify (log 1) into 0 4.459 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.459 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.459 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.460 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 4.461 * [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) 4.462 * [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)) 4.464 * [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))) 4.465 * [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) 4.466 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.466 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.466 * [taylor]: Taking taylor expansion of 2.0 in n 4.466 * [backup-simplify]: Simplify 2.0 into 2.0 4.466 * [taylor]: Taking taylor expansion of (* n PI) in n 4.466 * [taylor]: Taking taylor expansion of n in n 4.466 * [backup-simplify]: Simplify 0 into 0 4.466 * [backup-simplify]: Simplify 1 into 1 4.466 * [taylor]: Taking taylor expansion of PI in n 4.466 * [backup-simplify]: Simplify PI into PI 4.466 * [backup-simplify]: Simplify (* 0 PI) into 0 4.467 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.468 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.470 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.471 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.471 * [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 4.471 * [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 4.471 * [taylor]: Taking taylor expansion of +nan.0 in n 4.471 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.471 * [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 4.471 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 4.471 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 4.471 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 4.471 * [taylor]: Taking taylor expansion of 0.5 in n 4.471 * [backup-simplify]: Simplify 0.5 into 0.5 4.471 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 4.471 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 4.472 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.472 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.472 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.472 * [taylor]: Taking taylor expansion of 1.0 in n 4.472 * [backup-simplify]: Simplify 1.0 into 1.0 4.472 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.472 * [taylor]: Taking taylor expansion of 2.0 in n 4.472 * [backup-simplify]: Simplify 2.0 into 2.0 4.472 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.473 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.475 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.475 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 4.475 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.475 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.475 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.475 * [taylor]: Taking taylor expansion of 1.0 in n 4.475 * [backup-simplify]: Simplify 1.0 into 1.0 4.475 * [taylor]: Taking taylor expansion of (log PI) in n 4.475 * [taylor]: Taking taylor expansion of PI in n 4.475 * [backup-simplify]: Simplify PI into PI 4.475 * [backup-simplify]: Simplify (log PI) into (log PI) 4.476 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.478 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.478 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.478 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.478 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.478 * [taylor]: Taking taylor expansion of 1.0 in n 4.478 * [backup-simplify]: Simplify 1.0 into 1.0 4.478 * [taylor]: Taking taylor expansion of (log n) in n 4.478 * [taylor]: Taking taylor expansion of n in n 4.478 * [backup-simplify]: Simplify 0 into 0 4.478 * [backup-simplify]: Simplify 1 into 1 4.479 * [backup-simplify]: Simplify (log 1) into 0 4.479 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.479 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.479 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.480 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 4.481 * [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) 4.483 * [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)) 4.484 * [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))) 4.486 * [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) 4.486 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 4.486 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.486 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.486 * [taylor]: Taking taylor expansion of 2.0 in n 4.486 * [backup-simplify]: Simplify 2.0 into 2.0 4.486 * [taylor]: Taking taylor expansion of (* n PI) in n 4.486 * [taylor]: Taking taylor expansion of n in n 4.486 * [backup-simplify]: Simplify 0 into 0 4.486 * [backup-simplify]: Simplify 1 into 1 4.486 * [taylor]: Taking taylor expansion of PI in n 4.486 * [backup-simplify]: Simplify PI into PI 4.487 * [backup-simplify]: Simplify (* 0 PI) into 0 4.487 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.489 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.491 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.492 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.494 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.495 * [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)) 4.497 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.500 * [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)) 4.502 * [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))) 4.503 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.505 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.507 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 4.509 * [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)) 4.512 * [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))) 4.515 * [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)))))))) 4.522 * [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)))))))))))) 4.531 * [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)))))))))))) 4.541 * [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)))))))))))))) 4.560 * [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)))))))))))))) 4.577 * [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)))))))))))))) 4.605 * [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)))))))))))))))))))))) 4.606 * [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)))))) 4.607 * [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 4.607 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 4.607 * [taylor]: Taking taylor expansion of 1.0 in n 4.607 * [backup-simplify]: Simplify 1.0 into 1.0 4.607 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 4.607 * [taylor]: Taking taylor expansion of (sqrt k) in n 4.607 * [taylor]: Taking taylor expansion of k in n 4.607 * [backup-simplify]: Simplify k into k 4.607 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 4.607 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 4.607 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 4.607 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.607 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.607 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 4.607 * [taylor]: Taking taylor expansion of 0.5 in n 4.607 * [backup-simplify]: Simplify 0.5 into 0.5 4.607 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.607 * [taylor]: Taking taylor expansion of 1.0 in n 4.607 * [backup-simplify]: Simplify 1.0 into 1.0 4.607 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.607 * [taylor]: Taking taylor expansion of k in n 4.607 * [backup-simplify]: Simplify k into k 4.608 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.608 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.608 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.608 * [taylor]: Taking taylor expansion of 2.0 in n 4.608 * [backup-simplify]: Simplify 2.0 into 2.0 4.608 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.608 * [taylor]: Taking taylor expansion of PI in n 4.608 * [backup-simplify]: Simplify PI into PI 4.608 * [taylor]: Taking taylor expansion of n in n 4.608 * [backup-simplify]: Simplify 0 into 0 4.608 * [backup-simplify]: Simplify 1 into 1 4.608 * [backup-simplify]: Simplify (/ PI 1) into PI 4.609 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.611 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.611 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.611 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.611 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 4.613 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.614 * [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)))) 4.615 * [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))))) 4.615 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 4.615 * [taylor]: Taking taylor expansion of 1.0 in k 4.615 * [backup-simplify]: Simplify 1.0 into 1.0 4.615 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 4.615 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.615 * [taylor]: Taking taylor expansion of k in k 4.615 * [backup-simplify]: Simplify 0 into 0 4.615 * [backup-simplify]: Simplify 1 into 1 4.616 * [backup-simplify]: Simplify (sqrt 0) into 0 4.617 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.617 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 4.617 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.617 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.617 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 4.617 * [taylor]: Taking taylor expansion of 0.5 in k 4.617 * [backup-simplify]: Simplify 0.5 into 0.5 4.617 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.617 * [taylor]: Taking taylor expansion of 1.0 in k 4.617 * [backup-simplify]: Simplify 1.0 into 1.0 4.617 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.617 * [taylor]: Taking taylor expansion of k in k 4.618 * [backup-simplify]: Simplify 0 into 0 4.618 * [backup-simplify]: Simplify 1 into 1 4.618 * [backup-simplify]: Simplify (/ 1 1) into 1 4.618 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.618 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.618 * [taylor]: Taking taylor expansion of 2.0 in k 4.618 * [backup-simplify]: Simplify 2.0 into 2.0 4.618 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.618 * [taylor]: Taking taylor expansion of PI in k 4.618 * [backup-simplify]: Simplify PI into PI 4.618 * [taylor]: Taking taylor expansion of n in k 4.618 * [backup-simplify]: Simplify n into n 4.618 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.618 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.618 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.619 * [backup-simplify]: Simplify (- 1) into -1 4.619 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.620 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 4.620 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 4.620 * [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))))) 4.620 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 4.620 * [taylor]: Taking taylor expansion of 1.0 in k 4.620 * [backup-simplify]: Simplify 1.0 into 1.0 4.620 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 4.620 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.620 * [taylor]: Taking taylor expansion of k in k 4.620 * [backup-simplify]: Simplify 0 into 0 4.620 * [backup-simplify]: Simplify 1 into 1 4.621 * [backup-simplify]: Simplify (sqrt 0) into 0 4.622 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.622 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 4.622 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.622 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.622 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 4.622 * [taylor]: Taking taylor expansion of 0.5 in k 4.622 * [backup-simplify]: Simplify 0.5 into 0.5 4.622 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.622 * [taylor]: Taking taylor expansion of 1.0 in k 4.622 * [backup-simplify]: Simplify 1.0 into 1.0 4.622 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.622 * [taylor]: Taking taylor expansion of k in k 4.622 * [backup-simplify]: Simplify 0 into 0 4.622 * [backup-simplify]: Simplify 1 into 1 4.623 * [backup-simplify]: Simplify (/ 1 1) into 1 4.623 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.623 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.623 * [taylor]: Taking taylor expansion of 2.0 in k 4.623 * [backup-simplify]: Simplify 2.0 into 2.0 4.623 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.623 * [taylor]: Taking taylor expansion of PI in k 4.623 * [backup-simplify]: Simplify PI into PI 4.623 * [taylor]: Taking taylor expansion of n in k 4.623 * [backup-simplify]: Simplify n into n 4.623 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.623 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.623 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.624 * [backup-simplify]: Simplify (- 1) into -1 4.624 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.625 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 4.625 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 4.625 * [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))))) 4.626 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 4.626 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.626 * [taylor]: Taking taylor expansion of 0 in n 4.626 * [backup-simplify]: Simplify 0 into 0 4.626 * [backup-simplify]: Simplify 0 into 0 4.627 * [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))))))) 4.628 * [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))))))) 4.628 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 4.628 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 4.628 * [taylor]: Taking taylor expansion of +nan.0 in n 4.628 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.628 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 4.628 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 4.628 * [taylor]: Taking taylor expansion of 0.5 in n 4.628 * [backup-simplify]: Simplify 0.5 into 0.5 4.628 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 4.628 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.628 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.628 * [taylor]: Taking taylor expansion of 2.0 in n 4.628 * [backup-simplify]: Simplify 2.0 into 2.0 4.628 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.628 * [taylor]: Taking taylor expansion of PI in n 4.628 * [backup-simplify]: Simplify PI into PI 4.628 * [taylor]: Taking taylor expansion of n in n 4.628 * [backup-simplify]: Simplify 0 into 0 4.628 * [backup-simplify]: Simplify 1 into 1 4.629 * [backup-simplify]: Simplify (/ PI 1) into PI 4.629 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.630 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.630 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.630 * [taylor]: Taking taylor expansion of 1.0 in n 4.630 * [backup-simplify]: Simplify 1.0 into 1.0 4.630 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.630 * [taylor]: Taking taylor expansion of k in n 4.631 * [backup-simplify]: Simplify k into k 4.631 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.632 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.632 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.632 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.634 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 4.635 * [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)))) 4.636 * [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))))) 4.638 * [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)))))) 4.639 * [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))))))) 4.641 * [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))))))) 4.641 * [backup-simplify]: Simplify 0 into 0 4.644 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.645 * [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))))))) 4.646 * [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))))))) 4.646 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 4.646 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 4.646 * [taylor]: Taking taylor expansion of +nan.0 in n 4.646 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.646 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 4.646 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 4.647 * [taylor]: Taking taylor expansion of 0.5 in n 4.647 * [backup-simplify]: Simplify 0.5 into 0.5 4.647 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 4.647 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.647 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.647 * [taylor]: Taking taylor expansion of 2.0 in n 4.647 * [backup-simplify]: Simplify 2.0 into 2.0 4.647 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.647 * [taylor]: Taking taylor expansion of PI in n 4.647 * [backup-simplify]: Simplify PI into PI 4.647 * [taylor]: Taking taylor expansion of n in n 4.647 * [backup-simplify]: Simplify 0 into 0 4.647 * [backup-simplify]: Simplify 1 into 1 4.647 * [backup-simplify]: Simplify (/ PI 1) into PI 4.648 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.649 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.649 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.649 * [taylor]: Taking taylor expansion of 1.0 in n 4.649 * [backup-simplify]: Simplify 1.0 into 1.0 4.649 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.649 * [taylor]: Taking taylor expansion of k in n 4.649 * [backup-simplify]: Simplify k into k 4.649 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.651 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.651 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.651 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.652 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 4.654 * [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)))) 4.655 * [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))))) 4.656 * [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)))))) 4.658 * [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))))))) 4.659 * [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))))))) 4.661 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.661 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.661 * [backup-simplify]: Simplify (- 0) into 0 4.662 * [backup-simplify]: Simplify (+ 0 0) into 0 4.662 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.663 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.665 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.666 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.668 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 4.670 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.672 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 4.672 * [backup-simplify]: Simplify (- 0) into 0 4.672 * [backup-simplify]: Simplify 0 into 0 4.672 * [backup-simplify]: Simplify 0 into 0 4.676 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.678 * [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))))))) 4.680 * [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))))))) 4.680 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 4.680 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 4.680 * [taylor]: Taking taylor expansion of +nan.0 in n 4.680 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.680 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 4.680 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 4.680 * [taylor]: Taking taylor expansion of 0.5 in n 4.680 * [backup-simplify]: Simplify 0.5 into 0.5 4.680 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 4.680 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.680 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.680 * [taylor]: Taking taylor expansion of 2.0 in n 4.680 * [backup-simplify]: Simplify 2.0 into 2.0 4.680 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.680 * [taylor]: Taking taylor expansion of PI in n 4.680 * [backup-simplify]: Simplify PI into PI 4.680 * [taylor]: Taking taylor expansion of n in n 4.680 * [backup-simplify]: Simplify 0 into 0 4.680 * [backup-simplify]: Simplify 1 into 1 4.681 * [backup-simplify]: Simplify (/ PI 1) into PI 4.681 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.682 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.682 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.682 * [taylor]: Taking taylor expansion of 1.0 in n 4.683 * [backup-simplify]: Simplify 1.0 into 1.0 4.683 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.683 * [taylor]: Taking taylor expansion of k in n 4.683 * [backup-simplify]: Simplify k into k 4.683 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.684 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.684 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.684 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.686 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 4.687 * [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)))) 4.688 * [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))))) 4.690 * [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)))))) 4.691 * [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))))))) 4.693 * [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))))))) 4.698 * [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)))))))) 4.699 * [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)))) 4.699 * [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 4.699 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 4.699 * [taylor]: Taking taylor expansion of 1.0 in n 4.699 * [backup-simplify]: Simplify 1.0 into 1.0 4.699 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 4.699 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 4.699 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.699 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.699 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 4.699 * [taylor]: Taking taylor expansion of 0.5 in n 4.700 * [backup-simplify]: Simplify 0.5 into 0.5 4.700 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.700 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.700 * [taylor]: Taking taylor expansion of k in n 4.700 * [backup-simplify]: Simplify k into k 4.700 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.700 * [taylor]: Taking taylor expansion of 1.0 in n 4.700 * [backup-simplify]: Simplify 1.0 into 1.0 4.700 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.700 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.700 * [taylor]: Taking taylor expansion of -2.0 in n 4.700 * [backup-simplify]: Simplify -2.0 into -2.0 4.700 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.700 * [taylor]: Taking taylor expansion of PI in n 4.700 * [backup-simplify]: Simplify PI into PI 4.700 * [taylor]: Taking taylor expansion of n in n 4.700 * [backup-simplify]: Simplify 0 into 0 4.700 * [backup-simplify]: Simplify 1 into 1 4.701 * [backup-simplify]: Simplify (/ PI 1) into PI 4.701 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.702 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.702 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.702 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 4.704 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.709 * [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)))) 4.711 * [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))))) 4.711 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 4.711 * [taylor]: Taking taylor expansion of (/ -1 k) in n 4.711 * [taylor]: Taking taylor expansion of -1 in n 4.711 * [backup-simplify]: Simplify -1 into -1 4.711 * [taylor]: Taking taylor expansion of k in n 4.711 * [backup-simplify]: Simplify k into k 4.711 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 4.712 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 4.712 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 4.712 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 4.713 * [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))) 4.713 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 4.713 * [taylor]: Taking taylor expansion of 1.0 in k 4.713 * [backup-simplify]: Simplify 1.0 into 1.0 4.713 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 4.713 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 4.714 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.714 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.714 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 4.714 * [taylor]: Taking taylor expansion of 0.5 in k 4.714 * [backup-simplify]: Simplify 0.5 into 0.5 4.714 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.714 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.714 * [taylor]: Taking taylor expansion of k in k 4.714 * [backup-simplify]: Simplify 0 into 0 4.714 * [backup-simplify]: Simplify 1 into 1 4.714 * [backup-simplify]: Simplify (/ 1 1) into 1 4.714 * [taylor]: Taking taylor expansion of 1.0 in k 4.714 * [backup-simplify]: Simplify 1.0 into 1.0 4.714 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.714 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.714 * [taylor]: Taking taylor expansion of -2.0 in k 4.714 * [backup-simplify]: Simplify -2.0 into -2.0 4.714 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.714 * [taylor]: Taking taylor expansion of PI in k 4.715 * [backup-simplify]: Simplify PI into PI 4.715 * [taylor]: Taking taylor expansion of n in k 4.715 * [backup-simplify]: Simplify n into n 4.715 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.715 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.715 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.715 * [backup-simplify]: Simplify (+ 1 0) into 1 4.716 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 4.716 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 4.716 * [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)))))) 4.716 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.716 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.716 * [taylor]: Taking taylor expansion of -1 in k 4.716 * [backup-simplify]: Simplify -1 into -1 4.716 * [taylor]: Taking taylor expansion of k in k 4.716 * [backup-simplify]: Simplify 0 into 0 4.716 * [backup-simplify]: Simplify 1 into 1 4.717 * [backup-simplify]: Simplify (/ -1 1) into -1 4.717 * [backup-simplify]: Simplify (sqrt 0) into 0 4.719 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.719 * [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))))))) 4.719 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 4.719 * [taylor]: Taking taylor expansion of 1.0 in k 4.719 * [backup-simplify]: Simplify 1.0 into 1.0 4.719 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 4.719 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 4.720 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.720 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.720 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 4.720 * [taylor]: Taking taylor expansion of 0.5 in k 4.720 * [backup-simplify]: Simplify 0.5 into 0.5 4.720 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.720 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.720 * [taylor]: Taking taylor expansion of k in k 4.720 * [backup-simplify]: Simplify 0 into 0 4.720 * [backup-simplify]: Simplify 1 into 1 4.720 * [backup-simplify]: Simplify (/ 1 1) into 1 4.720 * [taylor]: Taking taylor expansion of 1.0 in k 4.720 * [backup-simplify]: Simplify 1.0 into 1.0 4.720 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.720 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.720 * [taylor]: Taking taylor expansion of -2.0 in k 4.720 * [backup-simplify]: Simplify -2.0 into -2.0 4.720 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.721 * [taylor]: Taking taylor expansion of PI in k 4.721 * [backup-simplify]: Simplify PI into PI 4.721 * [taylor]: Taking taylor expansion of n in k 4.721 * [backup-simplify]: Simplify n into n 4.721 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.721 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.721 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.721 * [backup-simplify]: Simplify (+ 1 0) into 1 4.722 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 4.722 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 4.722 * [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)))))) 4.722 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.722 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.722 * [taylor]: Taking taylor expansion of -1 in k 4.722 * [backup-simplify]: Simplify -1 into -1 4.722 * [taylor]: Taking taylor expansion of k in k 4.722 * [backup-simplify]: Simplify 0 into 0 4.722 * [backup-simplify]: Simplify 1 into 1 4.723 * [backup-simplify]: Simplify (/ -1 1) into -1 4.723 * [backup-simplify]: Simplify (sqrt 0) into 0 4.725 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.725 * [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))))))) 4.726 * [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))))))) 4.726 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 4.726 * [taylor]: Taking taylor expansion of +nan.0 in n 4.726 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.726 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 4.726 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 4.726 * [taylor]: Taking taylor expansion of 0.5 in n 4.726 * [backup-simplify]: Simplify 0.5 into 0.5 4.726 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 4.726 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.726 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.726 * [taylor]: Taking taylor expansion of k in n 4.726 * [backup-simplify]: Simplify k into k 4.726 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.726 * [taylor]: Taking taylor expansion of 1.0 in n 4.726 * [backup-simplify]: Simplify 1.0 into 1.0 4.726 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.726 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.726 * [taylor]: Taking taylor expansion of -2.0 in n 4.726 * [backup-simplify]: Simplify -2.0 into -2.0 4.726 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.726 * [taylor]: Taking taylor expansion of PI in n 4.726 * [backup-simplify]: Simplify PI into PI 4.726 * [taylor]: Taking taylor expansion of n in n 4.726 * [backup-simplify]: Simplify 0 into 0 4.726 * [backup-simplify]: Simplify 1 into 1 4.727 * [backup-simplify]: Simplify (/ PI 1) into PI 4.728 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.729 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.729 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.730 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.732 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 4.733 * [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)))) 4.734 * [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))))) 4.735 * [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)))))) 4.737 * [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)))))) 4.738 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 4.741 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.742 * [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)))))))) 4.743 * [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)))))))) 4.743 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 4.743 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 4.743 * [taylor]: Taking taylor expansion of +nan.0 in n 4.743 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.743 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 4.743 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 4.743 * [taylor]: Taking taylor expansion of 0.5 in n 4.743 * [backup-simplify]: Simplify 0.5 into 0.5 4.743 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 4.743 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.743 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.743 * [taylor]: Taking taylor expansion of k in n 4.743 * [backup-simplify]: Simplify k into k 4.743 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.743 * [taylor]: Taking taylor expansion of 1.0 in n 4.743 * [backup-simplify]: Simplify 1.0 into 1.0 4.744 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.744 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.744 * [taylor]: Taking taylor expansion of -2.0 in n 4.744 * [backup-simplify]: Simplify -2.0 into -2.0 4.744 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.744 * [taylor]: Taking taylor expansion of PI in n 4.744 * [backup-simplify]: Simplify PI into PI 4.744 * [taylor]: Taking taylor expansion of n in n 4.744 * [backup-simplify]: Simplify 0 into 0 4.744 * [backup-simplify]: Simplify 1 into 1 4.744 * [backup-simplify]: Simplify (/ PI 1) into PI 4.745 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.746 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.746 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.747 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.748 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 4.749 * [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)))) 4.750 * [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))))) 4.751 * [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)))))) 4.752 * [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))))))) 4.753 * [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))))))) 4.753 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.754 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.755 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.755 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.755 * [backup-simplify]: Simplify (+ 0 0) into 0 4.756 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.757 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.758 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 4.759 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.761 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 4.761 * [backup-simplify]: Simplify 0 into 0 4.761 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.764 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.765 * [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)))))))) 4.765 * [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)))))))) 4.765 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 4.765 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 4.765 * [taylor]: Taking taylor expansion of +nan.0 in n 4.765 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.765 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 4.765 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 4.765 * [taylor]: Taking taylor expansion of 0.5 in n 4.765 * [backup-simplify]: Simplify 0.5 into 0.5 4.765 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 4.765 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.765 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.765 * [taylor]: Taking taylor expansion of k in n 4.765 * [backup-simplify]: Simplify k into k 4.765 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.766 * [taylor]: Taking taylor expansion of 1.0 in n 4.766 * [backup-simplify]: Simplify 1.0 into 1.0 4.766 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.766 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.766 * [taylor]: Taking taylor expansion of -2.0 in n 4.766 * [backup-simplify]: Simplify -2.0 into -2.0 4.766 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.766 * [taylor]: Taking taylor expansion of PI in n 4.766 * [backup-simplify]: Simplify PI into PI 4.766 * [taylor]: Taking taylor expansion of n in n 4.766 * [backup-simplify]: Simplify 0 into 0 4.766 * [backup-simplify]: Simplify 1 into 1 4.766 * [backup-simplify]: Simplify (/ PI 1) into PI 4.766 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.767 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.767 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.768 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.769 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 4.770 * [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)))) 4.770 * [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))))) 4.771 * [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)))))) 4.773 * [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))))))) 4.774 * [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))))))) 4.779 * [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)))))))))))) 4.780 * * * [progress]: simplifying candidates 4.784 * [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))) (* 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k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +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 (* (* (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)))))))))))) 4.790 * * [simplify]: Extracting # 0 : cost 0 4.791 * * [simplify]: Extracting # 1 : cost 0 4.791 * * [simplify]: Extracting # 2 : cost 0 4.792 * * [simplify]: Extracting # 3 : cost 0 4.792 * * [simplify]: Extracting # 4 : cost 0 4.792 * * [simplify]: Extracting # 5 : cost 0 4.793 * * [simplify]: Extracting # 6 : cost 0 4.793 * * [simplify]: Extracting # 7 : cost 0 4.794 * * [simplify]: Extracting # 8 : cost 0 4.794 * * [simplify]: Extracting # 9 : cost 0 4.795 * * [simplify]: Extracting # 10 : cost 0 4.796 * * [simplify]: Extracting # 11 : cost 0 4.796 * * [simplify]: Extracting # 12 : cost 0 4.797 * * [simplify]: Extracting # 13 : cost 0 4.797 * * [simplify]: Extracting # 14 : cost 0 4.798 * * [simplify]: Extracting # 15 : cost 0 4.798 * * [simplify]: Extracting # 16 : cost 0 4.799 * * [simplify]: Extracting # 17 : cost 0 4.799 * * [simplify]: Extracting # 18 : cost 0 4.800 * * [simplify]: Extracting # 19 : cost 0 4.801 * * [simplify]: Extracting # 20 : cost 0 4.801 * * [simplify]: Extracting # 21 : cost 0 4.802 * * [simplify]: Extracting # 22 : cost 0 4.802 * * [simplify]: Extracting # 23 : cost 0 4.803 * * [simplify]: Extracting # 24 : cost 0 4.804 * * [simplify]: Extracting # 25 : cost 0 4.804 * * [simplify]: Extracting # 26 : cost 0 4.805 * * [simplify]: Extracting # 27 : cost 0 4.805 * * [simplify]: Extracting # 28 : cost 0 4.806 * * [simplify]: Extracting # 29 : cost 0 4.806 * * [simplify]: Extracting # 30 : cost 0 4.807 * * [simplify]: Extracting # 31 : cost 0 4.812 * * [simplify]: Extracting # 32 : cost 0 4.812 * * [simplify]: iteration 0 : 361 enodes (cost 2800 ) 4.976 * * [simplify]: Extracting # 0 : cost 0 4.979 * * [simplify]: Extracting # 1 : cost 0 4.981 * * [simplify]: Extracting # 2 : cost 0 4.984 * * [simplify]: Extracting # 3 : cost 0 4.987 * * [simplify]: Extracting # 4 : cost 0 4.989 * * [simplify]: Extracting # 5 : cost 0 4.992 * * [simplify]: iteration 1 : 931 enodes (cost 2635 ) 5.547 * * [simplify]: Extracting # 0 : cost 0 5.551 * * [simplify]: Extracting # 1 : cost 0 5.555 * * [simplify]: Extracting # 2 : cost 0 5.559 * * [simplify]: Extracting # 3 : cost 0 5.567 * * [simplify]: Extracting # 4 : cost 0 5.574 * * [simplify]: Extracting # 5 : cost 0 5.582 * * [simplify]: iteration 2 : 3047 enodes (cost 2471 ) 7.285 * * [simplify]: Extracting # 0 : cost 0 7.291 * * [simplify]: Extracting # 1 : cost 0 7.297 * * [simplify]: Extracting # 2 : cost 0 7.309 * * [simplify]: Extracting # 3 : cost 0 7.320 * * [simplify]: Extracting # 4 : cost 0 7.335 * * [simplify]: iteration done: 5000 enodes (cost 2471 ) 7.336 * [simplify]: Simplified to: (* (log (* (* 2.0 PI) 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)) (* (log (* (* 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) (* (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 (* n PI)) (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))) (* n (* 2.0 PI)) (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))) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (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 (* (* 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)) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (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 (* (* 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))) (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) (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 (* (* 2.0 PI) n) 0.5) (* (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (* 2.0 PI) n) 0.5)) 0.25)) (* (* 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)))))) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (- (- (* +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 (pow k 2)) (/ +nan.0 k)) +nan.0)) (+ (- (* +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 k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))) (+ (* (- (/ (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (pow k 3))) +nan.0) (* +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 (- (/ (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)))))))) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)))) 7.337 * * * [progress]: adding candidates to table 7.937 * * [progress]: iteration 2 / 4 7.937 * * * [progress]: picking best candidate 7.962 * * * * [pick]: Picked # 7.962 * * * [progress]: localizing error 7.997 * * * [progress]: generating rewritten candidates 7.997 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 8.027 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 8.068 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 8.092 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 2 1) 8.143 * * * [progress]: generating series expansions 8.143 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 8.144 * [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))) 8.144 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 8.144 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 8.144 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 8.144 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 8.144 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 8.144 * [taylor]: Taking taylor expansion of 0.25 in k 8.144 * [backup-simplify]: Simplify 0.25 into 0.25 8.145 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.145 * [taylor]: Taking taylor expansion of 1.0 in k 8.145 * [backup-simplify]: Simplify 1.0 into 1.0 8.145 * [taylor]: Taking taylor expansion of k in k 8.145 * [backup-simplify]: Simplify 0 into 0 8.145 * [backup-simplify]: Simplify 1 into 1 8.145 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 8.145 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 8.145 * [taylor]: Taking taylor expansion of 2.0 in k 8.145 * [backup-simplify]: Simplify 2.0 into 2.0 8.145 * [taylor]: Taking taylor expansion of (* n PI) in k 8.145 * [taylor]: Taking taylor expansion of n in k 8.145 * [backup-simplify]: Simplify n into n 8.145 * [taylor]: Taking taylor expansion of PI in k 8.145 * [backup-simplify]: Simplify PI into PI 8.145 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.145 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 8.145 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 8.146 * [backup-simplify]: Simplify (- 0) into 0 8.146 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.147 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 8.147 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 8.147 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 8.147 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 8.147 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.147 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.147 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 8.147 * [taylor]: Taking taylor expansion of 0.25 in n 8.147 * [backup-simplify]: Simplify 0.25 into 0.25 8.147 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.147 * [taylor]: Taking taylor expansion of 1.0 in n 8.147 * [backup-simplify]: Simplify 1.0 into 1.0 8.147 * [taylor]: Taking taylor expansion of k in n 8.147 * [backup-simplify]: Simplify k into k 8.147 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.147 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.147 * [taylor]: Taking taylor expansion of 2.0 in n 8.147 * [backup-simplify]: Simplify 2.0 into 2.0 8.147 * [taylor]: Taking taylor expansion of (* n PI) in n 8.148 * [taylor]: Taking taylor expansion of n in n 8.148 * [backup-simplify]: Simplify 0 into 0 8.148 * [backup-simplify]: Simplify 1 into 1 8.148 * [taylor]: Taking taylor expansion of PI in n 8.148 * [backup-simplify]: Simplify PI into PI 8.148 * [backup-simplify]: Simplify (* 0 PI) into 0 8.149 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.150 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.152 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.153 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.153 * [backup-simplify]: Simplify (- k) into (- k) 8.153 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.153 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 8.155 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.156 * [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)))) 8.157 * [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))))) 8.157 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 8.157 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.157 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.157 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 8.157 * [taylor]: Taking taylor expansion of 0.25 in n 8.157 * [backup-simplify]: Simplify 0.25 into 0.25 8.157 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.157 * [taylor]: Taking taylor expansion of 1.0 in n 8.158 * [backup-simplify]: Simplify 1.0 into 1.0 8.158 * [taylor]: Taking taylor expansion of k in n 8.158 * [backup-simplify]: Simplify k into k 8.158 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.158 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.158 * [taylor]: Taking taylor expansion of 2.0 in n 8.158 * [backup-simplify]: Simplify 2.0 into 2.0 8.158 * [taylor]: Taking taylor expansion of (* n PI) in n 8.158 * [taylor]: Taking taylor expansion of n in n 8.158 * [backup-simplify]: Simplify 0 into 0 8.158 * [backup-simplify]: Simplify 1 into 1 8.158 * [taylor]: Taking taylor expansion of PI in n 8.158 * [backup-simplify]: Simplify PI into PI 8.158 * [backup-simplify]: Simplify (* 0 PI) into 0 8.159 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.160 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.162 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.163 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.163 * [backup-simplify]: Simplify (- k) into (- k) 8.163 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.163 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 8.165 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.166 * [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)))) 8.167 * [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))))) 8.167 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 8.167 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 8.167 * [taylor]: Taking taylor expansion of 0.25 in k 8.167 * [backup-simplify]: Simplify 0.25 into 0.25 8.167 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 8.167 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.167 * [taylor]: Taking taylor expansion of 1.0 in k 8.167 * [backup-simplify]: Simplify 1.0 into 1.0 8.168 * [taylor]: Taking taylor expansion of k in k 8.168 * [backup-simplify]: Simplify 0 into 0 8.168 * [backup-simplify]: Simplify 1 into 1 8.168 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 8.168 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.168 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.168 * [taylor]: Taking taylor expansion of 2.0 in k 8.168 * [backup-simplify]: Simplify 2.0 into 2.0 8.168 * [taylor]: Taking taylor expansion of PI in k 8.168 * [backup-simplify]: Simplify PI into PI 8.168 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.169 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.169 * [taylor]: Taking taylor expansion of (log n) in k 8.169 * [taylor]: Taking taylor expansion of n in k 8.169 * [backup-simplify]: Simplify n into n 8.170 * [backup-simplify]: Simplify (log n) into (log n) 8.170 * [backup-simplify]: Simplify (- 0) into 0 8.170 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.171 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 8.173 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 8.174 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 8.175 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 8.176 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 8.177 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.178 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 8.181 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.181 * [backup-simplify]: Simplify (- 0) into 0 8.181 * [backup-simplify]: Simplify (+ 0 0) into 0 8.182 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 8.183 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.184 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 8.186 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.186 * [taylor]: Taking taylor expansion of 0 in k 8.186 * [backup-simplify]: Simplify 0 into 0 8.187 * [backup-simplify]: Simplify 0 into 0 8.187 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.189 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.190 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 8.190 * [backup-simplify]: Simplify (+ 0 0) into 0 8.191 * [backup-simplify]: Simplify (- 1) into -1 8.191 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.199 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 8.201 * [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)))) 8.204 * [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)))))) 8.207 * [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)))))) 8.209 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 8.210 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 8.213 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.214 * [backup-simplify]: Simplify (- 0) into 0 8.214 * [backup-simplify]: Simplify (+ 0 0) into 0 8.215 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 8.216 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.218 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.221 * [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 8.221 * [taylor]: Taking taylor expansion of 0 in k 8.221 * [backup-simplify]: Simplify 0 into 0 8.221 * [backup-simplify]: Simplify 0 into 0 8.221 * [backup-simplify]: Simplify 0 into 0 8.222 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.226 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.228 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 8.228 * [backup-simplify]: Simplify (+ 0 0) into 0 8.228 * [backup-simplify]: Simplify (- 0) into 0 8.229 * [backup-simplify]: Simplify (+ 0 0) into 0 8.231 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.233 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 8.238 * [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))))) 8.243 * [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))))) 8.255 * [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)))))) 8.256 * [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)))) 8.256 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 8.256 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 8.256 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 8.256 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 8.256 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 8.257 * [taylor]: Taking taylor expansion of 0.25 in k 8.257 * [backup-simplify]: Simplify 0.25 into 0.25 8.257 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.257 * [taylor]: Taking taylor expansion of 1.0 in k 8.257 * [backup-simplify]: Simplify 1.0 into 1.0 8.257 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.257 * [taylor]: Taking taylor expansion of k in k 8.257 * [backup-simplify]: Simplify 0 into 0 8.257 * [backup-simplify]: Simplify 1 into 1 8.257 * [backup-simplify]: Simplify (/ 1 1) into 1 8.257 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 8.257 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 8.257 * [taylor]: Taking taylor expansion of 2.0 in k 8.257 * [backup-simplify]: Simplify 2.0 into 2.0 8.257 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.257 * [taylor]: Taking taylor expansion of PI in k 8.257 * [backup-simplify]: Simplify PI into PI 8.257 * [taylor]: Taking taylor expansion of n in k 8.257 * [backup-simplify]: Simplify n into n 8.257 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.258 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 8.258 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 8.258 * [backup-simplify]: Simplify (- 1) into -1 8.259 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.259 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 8.259 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 8.259 * [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))))) 8.259 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 8.260 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.260 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.260 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 8.260 * [taylor]: Taking taylor expansion of 0.25 in n 8.260 * [backup-simplify]: Simplify 0.25 into 0.25 8.260 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.260 * [taylor]: Taking taylor expansion of 1.0 in n 8.260 * [backup-simplify]: Simplify 1.0 into 1.0 8.260 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.260 * [taylor]: Taking taylor expansion of k in n 8.260 * [backup-simplify]: Simplify k into k 8.260 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.260 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.260 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.260 * [taylor]: Taking taylor expansion of 2.0 in n 8.260 * [backup-simplify]: Simplify 2.0 into 2.0 8.260 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.260 * [taylor]: Taking taylor expansion of PI in n 8.260 * [backup-simplify]: Simplify PI into PI 8.260 * [taylor]: Taking taylor expansion of n in n 8.260 * [backup-simplify]: Simplify 0 into 0 8.260 * [backup-simplify]: Simplify 1 into 1 8.261 * [backup-simplify]: Simplify (/ PI 1) into PI 8.261 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.263 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.263 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.263 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.263 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 8.264 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.266 * [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)))) 8.267 * [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))))) 8.267 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 8.267 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.267 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.267 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 8.267 * [taylor]: Taking taylor expansion of 0.25 in n 8.267 * [backup-simplify]: Simplify 0.25 into 0.25 8.267 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.267 * [taylor]: Taking taylor expansion of 1.0 in n 8.267 * [backup-simplify]: Simplify 1.0 into 1.0 8.267 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.267 * [taylor]: Taking taylor expansion of k in n 8.267 * [backup-simplify]: Simplify k into k 8.267 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.267 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.267 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.267 * [taylor]: Taking taylor expansion of 2.0 in n 8.267 * [backup-simplify]: Simplify 2.0 into 2.0 8.267 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.267 * [taylor]: Taking taylor expansion of PI in n 8.268 * [backup-simplify]: Simplify PI into PI 8.268 * [taylor]: Taking taylor expansion of n in n 8.268 * [backup-simplify]: Simplify 0 into 0 8.268 * [backup-simplify]: Simplify 1 into 1 8.268 * [backup-simplify]: Simplify (/ PI 1) into PI 8.269 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.270 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.270 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.270 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.270 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 8.271 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.273 * [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)))) 8.274 * [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))))) 8.274 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 8.274 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 8.274 * [taylor]: Taking taylor expansion of 0.25 in k 8.274 * [backup-simplify]: Simplify 0.25 into 0.25 8.274 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 8.274 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 8.274 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.274 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.274 * [taylor]: Taking taylor expansion of 2.0 in k 8.274 * [backup-simplify]: Simplify 2.0 into 2.0 8.274 * [taylor]: Taking taylor expansion of PI in k 8.274 * [backup-simplify]: Simplify PI into PI 8.275 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.276 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.276 * [taylor]: Taking taylor expansion of (log n) in k 8.276 * [taylor]: Taking taylor expansion of n in k 8.276 * [backup-simplify]: Simplify n into n 8.276 * [backup-simplify]: Simplify (log n) into (log n) 8.276 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.276 * [taylor]: Taking taylor expansion of 1.0 in k 8.276 * [backup-simplify]: Simplify 1.0 into 1.0 8.276 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.276 * [taylor]: Taking taylor expansion of k in k 8.276 * [backup-simplify]: Simplify 0 into 0 8.276 * [backup-simplify]: Simplify 1 into 1 8.277 * [backup-simplify]: Simplify (/ 1 1) into 1 8.277 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.278 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 8.278 * [backup-simplify]: Simplify (- 1) into -1 8.279 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.280 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 8.281 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 8.282 * [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))))) 8.283 * [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))))) 8.284 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.285 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.287 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.287 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.288 * [backup-simplify]: Simplify (- 0) into 0 8.288 * [backup-simplify]: Simplify (+ 0 0) into 0 8.288 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 8.290 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.291 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 8.293 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.293 * [taylor]: Taking taylor expansion of 0 in k 8.293 * [backup-simplify]: Simplify 0 into 0 8.293 * [backup-simplify]: Simplify 0 into 0 8.293 * [backup-simplify]: Simplify 0 into 0 8.295 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.296 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.299 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.300 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.300 * [backup-simplify]: Simplify (- 0) into 0 8.301 * [backup-simplify]: Simplify (+ 0 0) into 0 8.302 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 8.303 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.305 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 8.308 * [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 8.308 * [taylor]: Taking taylor expansion of 0 in k 8.308 * [backup-simplify]: Simplify 0 into 0 8.308 * [backup-simplify]: Simplify 0 into 0 8.308 * [backup-simplify]: Simplify 0 into 0 8.308 * [backup-simplify]: Simplify 0 into 0 8.309 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.311 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.317 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 8.318 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.318 * [backup-simplify]: Simplify (- 0) into 0 8.318 * [backup-simplify]: Simplify (+ 0 0) into 0 8.320 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 8.321 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.323 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 8.326 * [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 8.326 * [taylor]: Taking taylor expansion of 0 in k 8.326 * [backup-simplify]: Simplify 0 into 0 8.326 * [backup-simplify]: Simplify 0 into 0 8.328 * [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)))) 8.329 * [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))) 8.329 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 8.329 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 8.329 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 8.329 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 8.329 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 8.329 * [taylor]: Taking taylor expansion of 0.25 in k 8.329 * [backup-simplify]: Simplify 0.25 into 0.25 8.329 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.330 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.330 * [taylor]: Taking taylor expansion of k in k 8.330 * [backup-simplify]: Simplify 0 into 0 8.330 * [backup-simplify]: Simplify 1 into 1 8.330 * [backup-simplify]: Simplify (/ 1 1) into 1 8.330 * [taylor]: Taking taylor expansion of 1.0 in k 8.330 * [backup-simplify]: Simplify 1.0 into 1.0 8.330 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 8.330 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 8.330 * [taylor]: Taking taylor expansion of -2.0 in k 8.330 * [backup-simplify]: Simplify -2.0 into -2.0 8.330 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.330 * [taylor]: Taking taylor expansion of PI in k 8.330 * [backup-simplify]: Simplify PI into PI 8.330 * [taylor]: Taking taylor expansion of n in k 8.330 * [backup-simplify]: Simplify n into n 8.330 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.330 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 8.331 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 8.331 * [backup-simplify]: Simplify (+ 1 0) into 1 8.331 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 8.332 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 8.332 * [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)))))) 8.332 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 8.332 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.332 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.332 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 8.332 * [taylor]: Taking taylor expansion of 0.25 in n 8.332 * [backup-simplify]: Simplify 0.25 into 0.25 8.332 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.332 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.332 * [taylor]: Taking taylor expansion of k in n 8.332 * [backup-simplify]: Simplify k into k 8.332 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.332 * [taylor]: Taking taylor expansion of 1.0 in n 8.332 * [backup-simplify]: Simplify 1.0 into 1.0 8.332 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.332 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.332 * [taylor]: Taking taylor expansion of -2.0 in n 8.332 * [backup-simplify]: Simplify -2.0 into -2.0 8.332 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.332 * [taylor]: Taking taylor expansion of PI in n 8.333 * [backup-simplify]: Simplify PI into PI 8.333 * [taylor]: Taking taylor expansion of n in n 8.333 * [backup-simplify]: Simplify 0 into 0 8.333 * [backup-simplify]: Simplify 1 into 1 8.333 * [backup-simplify]: Simplify (/ PI 1) into PI 8.334 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.335 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.335 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.335 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 8.336 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.338 * [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)))) 8.339 * [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))))) 8.339 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 8.339 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.339 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.339 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 8.339 * [taylor]: Taking taylor expansion of 0.25 in n 8.339 * [backup-simplify]: Simplify 0.25 into 0.25 8.339 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.339 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.339 * [taylor]: Taking taylor expansion of k in n 8.339 * [backup-simplify]: Simplify k into k 8.339 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.340 * [taylor]: Taking taylor expansion of 1.0 in n 8.340 * [backup-simplify]: Simplify 1.0 into 1.0 8.340 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.340 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.340 * [taylor]: Taking taylor expansion of -2.0 in n 8.340 * [backup-simplify]: Simplify -2.0 into -2.0 8.340 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.340 * [taylor]: Taking taylor expansion of PI in n 8.340 * [backup-simplify]: Simplify PI into PI 8.340 * [taylor]: Taking taylor expansion of n in n 8.340 * [backup-simplify]: Simplify 0 into 0 8.340 * [backup-simplify]: Simplify 1 into 1 8.341 * [backup-simplify]: Simplify (/ PI 1) into PI 8.341 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.342 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.342 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.342 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 8.344 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.345 * [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)))) 8.346 * [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))))) 8.346 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 8.346 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 8.346 * [taylor]: Taking taylor expansion of 0.25 in k 8.347 * [backup-simplify]: Simplify 0.25 into 0.25 8.347 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 8.347 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.347 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.347 * [taylor]: Taking taylor expansion of k in k 8.347 * [backup-simplify]: Simplify 0 into 0 8.347 * [backup-simplify]: Simplify 1 into 1 8.347 * [backup-simplify]: Simplify (/ 1 1) into 1 8.347 * [taylor]: Taking taylor expansion of 1.0 in k 8.347 * [backup-simplify]: Simplify 1.0 into 1.0 8.347 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 8.347 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 8.347 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 8.347 * [taylor]: Taking taylor expansion of -2.0 in k 8.347 * [backup-simplify]: Simplify -2.0 into -2.0 8.347 * [taylor]: Taking taylor expansion of PI in k 8.347 * [backup-simplify]: Simplify PI into PI 8.348 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.349 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.349 * [taylor]: Taking taylor expansion of (log n) in k 8.349 * [taylor]: Taking taylor expansion of n in k 8.349 * [backup-simplify]: Simplify n into n 8.349 * [backup-simplify]: Simplify (log n) into (log n) 8.350 * [backup-simplify]: Simplify (+ 1 0) into 1 8.350 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.351 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 8.356 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 8.357 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 8.359 * [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))))) 8.360 * [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))))) 8.361 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.362 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 8.363 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 8.364 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.364 * [backup-simplify]: Simplify (+ 0 0) into 0 8.365 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 8.366 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.367 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 8.369 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.369 * [taylor]: Taking taylor expansion of 0 in k 8.369 * [backup-simplify]: Simplify 0 into 0 8.369 * [backup-simplify]: Simplify 0 into 0 8.369 * [backup-simplify]: Simplify 0 into 0 8.371 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.372 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.375 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 8.376 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.376 * [backup-simplify]: Simplify (+ 0 0) into 0 8.377 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 8.378 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.380 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 8.383 * [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 8.383 * [taylor]: Taking taylor expansion of 0 in k 8.383 * [backup-simplify]: Simplify 0 into 0 8.383 * [backup-simplify]: Simplify 0 into 0 8.383 * [backup-simplify]: Simplify 0 into 0 8.383 * [backup-simplify]: Simplify 0 into 0 8.384 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.385 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.392 * [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 8.392 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.393 * [backup-simplify]: Simplify (+ 0 0) into 0 8.394 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 8.395 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.397 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 8.400 * [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 8.400 * [taylor]: Taking taylor expansion of 0 in k 8.400 * [backup-simplify]: Simplify 0 into 0 8.400 * [backup-simplify]: Simplify 0 into 0 8.402 * [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)))))) 8.402 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 8.402 * [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))) 8.402 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 8.403 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 8.403 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 8.403 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 8.403 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 8.403 * [taylor]: Taking taylor expansion of 0.25 in k 8.403 * [backup-simplify]: Simplify 0.25 into 0.25 8.403 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.403 * [taylor]: Taking taylor expansion of 1.0 in k 8.403 * [backup-simplify]: Simplify 1.0 into 1.0 8.403 * [taylor]: Taking taylor expansion of k in k 8.403 * [backup-simplify]: Simplify 0 into 0 8.403 * [backup-simplify]: Simplify 1 into 1 8.403 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 8.403 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 8.403 * [taylor]: Taking taylor expansion of 2.0 in k 8.403 * [backup-simplify]: Simplify 2.0 into 2.0 8.403 * [taylor]: Taking taylor expansion of (* n PI) in k 8.403 * [taylor]: Taking taylor expansion of n in k 8.403 * [backup-simplify]: Simplify n into n 8.403 * [taylor]: Taking taylor expansion of PI in k 8.403 * [backup-simplify]: Simplify PI into PI 8.403 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.403 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 8.403 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 8.404 * [backup-simplify]: Simplify (- 0) into 0 8.404 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.405 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 8.405 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 8.405 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 8.405 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 8.405 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.405 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.405 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 8.405 * [taylor]: Taking taylor expansion of 0.25 in n 8.405 * [backup-simplify]: Simplify 0.25 into 0.25 8.405 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.405 * [taylor]: Taking taylor expansion of 1.0 in n 8.405 * [backup-simplify]: Simplify 1.0 into 1.0 8.405 * [taylor]: Taking taylor expansion of k in n 8.405 * [backup-simplify]: Simplify k into k 8.405 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.405 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.405 * [taylor]: Taking taylor expansion of 2.0 in n 8.405 * [backup-simplify]: Simplify 2.0 into 2.0 8.405 * [taylor]: Taking taylor expansion of (* n PI) in n 8.405 * [taylor]: Taking taylor expansion of n in n 8.405 * [backup-simplify]: Simplify 0 into 0 8.405 * [backup-simplify]: Simplify 1 into 1 8.405 * [taylor]: Taking taylor expansion of PI in n 8.405 * [backup-simplify]: Simplify PI into PI 8.406 * [backup-simplify]: Simplify (* 0 PI) into 0 8.406 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.408 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.410 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.411 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.411 * [backup-simplify]: Simplify (- k) into (- k) 8.411 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.411 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 8.412 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.414 * [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)))) 8.415 * [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))))) 8.415 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 8.415 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.415 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.415 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 8.415 * [taylor]: Taking taylor expansion of 0.25 in n 8.415 * [backup-simplify]: Simplify 0.25 into 0.25 8.415 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.415 * [taylor]: Taking taylor expansion of 1.0 in n 8.415 * [backup-simplify]: Simplify 1.0 into 1.0 8.415 * [taylor]: Taking taylor expansion of k in n 8.415 * [backup-simplify]: Simplify k into k 8.415 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.415 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.415 * [taylor]: Taking taylor expansion of 2.0 in n 8.415 * [backup-simplify]: Simplify 2.0 into 2.0 8.416 * [taylor]: Taking taylor expansion of (* n PI) in n 8.416 * [taylor]: Taking taylor expansion of n in n 8.416 * [backup-simplify]: Simplify 0 into 0 8.416 * [backup-simplify]: Simplify 1 into 1 8.416 * [taylor]: Taking taylor expansion of PI in n 8.416 * [backup-simplify]: Simplify PI into PI 8.416 * [backup-simplify]: Simplify (* 0 PI) into 0 8.417 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.418 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.420 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.421 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.421 * [backup-simplify]: Simplify (- k) into (- k) 8.421 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.421 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 8.423 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.424 * [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)))) 8.425 * [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))))) 8.426 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 8.426 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 8.426 * [taylor]: Taking taylor expansion of 0.25 in k 8.426 * [backup-simplify]: Simplify 0.25 into 0.25 8.426 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 8.426 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.426 * [taylor]: Taking taylor expansion of 1.0 in k 8.426 * [backup-simplify]: Simplify 1.0 into 1.0 8.426 * [taylor]: Taking taylor expansion of k in k 8.426 * [backup-simplify]: Simplify 0 into 0 8.426 * [backup-simplify]: Simplify 1 into 1 8.426 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 8.426 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.426 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.426 * [taylor]: Taking taylor expansion of 2.0 in k 8.426 * [backup-simplify]: Simplify 2.0 into 2.0 8.426 * [taylor]: Taking taylor expansion of PI in k 8.426 * [backup-simplify]: Simplify PI into PI 8.427 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.428 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.428 * [taylor]: Taking taylor expansion of (log n) in k 8.428 * [taylor]: Taking taylor expansion of n in k 8.428 * [backup-simplify]: Simplify n into n 8.428 * [backup-simplify]: Simplify (log n) into (log n) 8.428 * [backup-simplify]: Simplify (- 0) into 0 8.429 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.430 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 8.431 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 8.432 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 8.433 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 8.434 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 8.436 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.437 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 8.439 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.440 * [backup-simplify]: Simplify (- 0) into 0 8.440 * [backup-simplify]: Simplify (+ 0 0) into 0 8.440 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 8.442 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.443 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 8.445 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.445 * [taylor]: Taking taylor expansion of 0 in k 8.445 * [backup-simplify]: Simplify 0 into 0 8.445 * [backup-simplify]: Simplify 0 into 0 8.446 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.448 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.449 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 8.450 * [backup-simplify]: Simplify (+ 0 0) into 0 8.450 * [backup-simplify]: Simplify (- 1) into -1 8.451 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.452 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 8.455 * [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)))) 8.458 * [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)))))) 8.461 * [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)))))) 8.462 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 8.464 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 8.467 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.468 * [backup-simplify]: Simplify (- 0) into 0 8.468 * [backup-simplify]: Simplify (+ 0 0) into 0 8.469 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 8.471 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.472 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.475 * [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 8.475 * [taylor]: Taking taylor expansion of 0 in k 8.475 * [backup-simplify]: Simplify 0 into 0 8.475 * [backup-simplify]: Simplify 0 into 0 8.475 * [backup-simplify]: Simplify 0 into 0 8.476 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.479 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.481 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 8.482 * [backup-simplify]: Simplify (+ 0 0) into 0 8.482 * [backup-simplify]: Simplify (- 0) into 0 8.482 * [backup-simplify]: Simplify (+ 0 0) into 0 8.484 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.487 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 8.491 * [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))))) 8.497 * [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))))) 8.513 * [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)))))) 8.514 * [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)))) 8.514 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 8.514 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 8.514 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 8.514 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 8.514 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 8.514 * [taylor]: Taking taylor expansion of 0.25 in k 8.514 * [backup-simplify]: Simplify 0.25 into 0.25 8.514 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.514 * [taylor]: Taking taylor expansion of 1.0 in k 8.514 * [backup-simplify]: Simplify 1.0 into 1.0 8.514 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.514 * [taylor]: Taking taylor expansion of k in k 8.514 * [backup-simplify]: Simplify 0 into 0 8.514 * [backup-simplify]: Simplify 1 into 1 8.515 * [backup-simplify]: Simplify (/ 1 1) into 1 8.515 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 8.515 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 8.515 * [taylor]: Taking taylor expansion of 2.0 in k 8.515 * [backup-simplify]: Simplify 2.0 into 2.0 8.515 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.515 * [taylor]: Taking taylor expansion of PI in k 8.515 * [backup-simplify]: Simplify PI into PI 8.515 * [taylor]: Taking taylor expansion of n in k 8.515 * [backup-simplify]: Simplify n into n 8.515 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.515 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 8.515 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 8.516 * [backup-simplify]: Simplify (- 1) into -1 8.516 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.516 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 8.517 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 8.517 * [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))))) 8.517 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 8.517 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.517 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.517 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 8.517 * [taylor]: Taking taylor expansion of 0.25 in n 8.517 * [backup-simplify]: Simplify 0.25 into 0.25 8.517 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.517 * [taylor]: Taking taylor expansion of 1.0 in n 8.517 * [backup-simplify]: Simplify 1.0 into 1.0 8.517 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.517 * [taylor]: Taking taylor expansion of k in n 8.517 * [backup-simplify]: Simplify k into k 8.517 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.517 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.517 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.517 * [taylor]: Taking taylor expansion of 2.0 in n 8.517 * [backup-simplify]: Simplify 2.0 into 2.0 8.517 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.517 * [taylor]: Taking taylor expansion of PI in n 8.517 * [backup-simplify]: Simplify PI into PI 8.518 * [taylor]: Taking taylor expansion of n in n 8.518 * [backup-simplify]: Simplify 0 into 0 8.518 * [backup-simplify]: Simplify 1 into 1 8.518 * [backup-simplify]: Simplify (/ PI 1) into PI 8.519 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.520 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.520 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.520 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.520 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 8.521 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.523 * [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)))) 8.524 * [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))))) 8.524 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 8.524 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.524 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.524 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 8.524 * [taylor]: Taking taylor expansion of 0.25 in n 8.524 * [backup-simplify]: Simplify 0.25 into 0.25 8.524 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.524 * [taylor]: Taking taylor expansion of 1.0 in n 8.524 * [backup-simplify]: Simplify 1.0 into 1.0 8.524 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.524 * [taylor]: Taking taylor expansion of k in n 8.524 * [backup-simplify]: Simplify k into k 8.524 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.524 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.524 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.525 * [taylor]: Taking taylor expansion of 2.0 in n 8.525 * [backup-simplify]: Simplify 2.0 into 2.0 8.525 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.525 * [taylor]: Taking taylor expansion of PI in n 8.525 * [backup-simplify]: Simplify PI into PI 8.525 * [taylor]: Taking taylor expansion of n in n 8.525 * [backup-simplify]: Simplify 0 into 0 8.525 * [backup-simplify]: Simplify 1 into 1 8.525 * [backup-simplify]: Simplify (/ PI 1) into PI 8.526 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.527 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.527 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.527 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.527 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 8.529 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.530 * [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)))) 8.531 * [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))))) 8.531 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 8.531 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 8.531 * [taylor]: Taking taylor expansion of 0.25 in k 8.532 * [backup-simplify]: Simplify 0.25 into 0.25 8.532 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 8.532 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 8.532 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.532 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.532 * [taylor]: Taking taylor expansion of 2.0 in k 8.532 * [backup-simplify]: Simplify 2.0 into 2.0 8.532 * [taylor]: Taking taylor expansion of PI in k 8.532 * [backup-simplify]: Simplify PI into PI 8.532 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.533 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.533 * [taylor]: Taking taylor expansion of (log n) in k 8.534 * [taylor]: Taking taylor expansion of n in k 8.534 * [backup-simplify]: Simplify n into n 8.534 * [backup-simplify]: Simplify (log n) into (log n) 8.534 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.534 * [taylor]: Taking taylor expansion of 1.0 in k 8.534 * [backup-simplify]: Simplify 1.0 into 1.0 8.534 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.534 * [taylor]: Taking taylor expansion of k in k 8.534 * [backup-simplify]: Simplify 0 into 0 8.534 * [backup-simplify]: Simplify 1 into 1 8.534 * [backup-simplify]: Simplify (/ 1 1) into 1 8.534 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.536 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 8.536 * [backup-simplify]: Simplify (- 1) into -1 8.536 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.538 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 8.539 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 8.540 * [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))))) 8.541 * [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))))) 8.543 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.543 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.544 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.544 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.545 * [backup-simplify]: Simplify (- 0) into 0 8.545 * [backup-simplify]: Simplify (+ 0 0) into 0 8.545 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 8.547 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.547 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 8.549 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.549 * [taylor]: Taking taylor expansion of 0 in k 8.549 * [backup-simplify]: Simplify 0 into 0 8.549 * [backup-simplify]: Simplify 0 into 0 8.549 * [backup-simplify]: Simplify 0 into 0 8.549 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.550 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.552 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.552 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.552 * [backup-simplify]: Simplify (- 0) into 0 8.552 * [backup-simplify]: Simplify (+ 0 0) into 0 8.553 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 8.554 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.555 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 8.556 * [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 8.557 * [taylor]: Taking taylor expansion of 0 in k 8.557 * [backup-simplify]: Simplify 0 into 0 8.557 * [backup-simplify]: Simplify 0 into 0 8.557 * [backup-simplify]: Simplify 0 into 0 8.557 * [backup-simplify]: Simplify 0 into 0 8.557 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.558 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.561 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 8.562 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.562 * [backup-simplify]: Simplify (- 0) into 0 8.562 * [backup-simplify]: Simplify (+ 0 0) into 0 8.563 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 8.564 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.565 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 8.567 * [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 8.567 * [taylor]: Taking taylor expansion of 0 in k 8.567 * [backup-simplify]: Simplify 0 into 0 8.567 * [backup-simplify]: Simplify 0 into 0 8.568 * [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)))) 8.568 * [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))) 8.568 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 8.568 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 8.568 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 8.568 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 8.568 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 8.568 * [taylor]: Taking taylor expansion of 0.25 in k 8.568 * [backup-simplify]: Simplify 0.25 into 0.25 8.568 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.568 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.569 * [taylor]: Taking taylor expansion of k in k 8.569 * [backup-simplify]: Simplify 0 into 0 8.569 * [backup-simplify]: Simplify 1 into 1 8.569 * [backup-simplify]: Simplify (/ 1 1) into 1 8.569 * [taylor]: Taking taylor expansion of 1.0 in k 8.569 * [backup-simplify]: Simplify 1.0 into 1.0 8.569 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 8.569 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 8.569 * [taylor]: Taking taylor expansion of -2.0 in k 8.569 * [backup-simplify]: Simplify -2.0 into -2.0 8.569 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.569 * [taylor]: Taking taylor expansion of PI in k 8.569 * [backup-simplify]: Simplify PI into PI 8.569 * [taylor]: Taking taylor expansion of n in k 8.569 * [backup-simplify]: Simplify n into n 8.569 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.569 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 8.569 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 8.569 * [backup-simplify]: Simplify (+ 1 0) into 1 8.570 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 8.570 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 8.570 * [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)))))) 8.570 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 8.570 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.570 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.570 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 8.570 * [taylor]: Taking taylor expansion of 0.25 in n 8.570 * [backup-simplify]: Simplify 0.25 into 0.25 8.570 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.570 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.570 * [taylor]: Taking taylor expansion of k in n 8.570 * [backup-simplify]: Simplify k into k 8.570 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.570 * [taylor]: Taking taylor expansion of 1.0 in n 8.570 * [backup-simplify]: Simplify 1.0 into 1.0 8.570 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.570 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.570 * [taylor]: Taking taylor expansion of -2.0 in n 8.570 * [backup-simplify]: Simplify -2.0 into -2.0 8.570 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.570 * [taylor]: Taking taylor expansion of PI in n 8.570 * [backup-simplify]: Simplify PI into PI 8.570 * [taylor]: Taking taylor expansion of n in n 8.570 * [backup-simplify]: Simplify 0 into 0 8.570 * [backup-simplify]: Simplify 1 into 1 8.571 * [backup-simplify]: Simplify (/ PI 1) into PI 8.571 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.572 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.572 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.572 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 8.573 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.574 * [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)))) 8.574 * [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))))) 8.574 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 8.574 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.574 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.574 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 8.574 * [taylor]: Taking taylor expansion of 0.25 in n 8.574 * [backup-simplify]: Simplify 0.25 into 0.25 8.574 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.575 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.575 * [taylor]: Taking taylor expansion of k in n 8.575 * [backup-simplify]: Simplify k into k 8.575 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.575 * [taylor]: Taking taylor expansion of 1.0 in n 8.575 * [backup-simplify]: Simplify 1.0 into 1.0 8.575 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.575 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.575 * [taylor]: Taking taylor expansion of -2.0 in n 8.575 * [backup-simplify]: Simplify -2.0 into -2.0 8.575 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.575 * [taylor]: Taking taylor expansion of PI in n 8.575 * [backup-simplify]: Simplify PI into PI 8.575 * [taylor]: Taking taylor expansion of n in n 8.575 * [backup-simplify]: Simplify 0 into 0 8.575 * [backup-simplify]: Simplify 1 into 1 8.575 * [backup-simplify]: Simplify (/ PI 1) into PI 8.575 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.576 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.576 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.576 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 8.577 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.578 * [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)))) 8.579 * [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))))) 8.579 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 8.579 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 8.579 * [taylor]: Taking taylor expansion of 0.25 in k 8.579 * [backup-simplify]: Simplify 0.25 into 0.25 8.579 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 8.579 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.579 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.579 * [taylor]: Taking taylor expansion of k in k 8.579 * [backup-simplify]: Simplify 0 into 0 8.579 * [backup-simplify]: Simplify 1 into 1 8.580 * [backup-simplify]: Simplify (/ 1 1) into 1 8.580 * [taylor]: Taking taylor expansion of 1.0 in k 8.580 * [backup-simplify]: Simplify 1.0 into 1.0 8.580 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 8.580 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 8.580 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 8.580 * [taylor]: Taking taylor expansion of -2.0 in k 8.580 * [backup-simplify]: Simplify -2.0 into -2.0 8.580 * [taylor]: Taking taylor expansion of PI in k 8.580 * [backup-simplify]: Simplify PI into PI 8.580 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.581 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.581 * [taylor]: Taking taylor expansion of (log n) in k 8.581 * [taylor]: Taking taylor expansion of n in k 8.581 * [backup-simplify]: Simplify n into n 8.581 * [backup-simplify]: Simplify (log n) into (log n) 8.581 * [backup-simplify]: Simplify (+ 1 0) into 1 8.581 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.582 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 8.582 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 8.583 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 8.584 * [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))))) 8.586 * [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))))) 8.587 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.587 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 8.589 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 8.589 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.590 * [backup-simplify]: Simplify (+ 0 0) into 0 8.590 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 8.592 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.593 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 8.595 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.595 * [taylor]: Taking taylor expansion of 0 in k 8.595 * [backup-simplify]: Simplify 0 into 0 8.595 * [backup-simplify]: Simplify 0 into 0 8.595 * [backup-simplify]: Simplify 0 into 0 8.597 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.598 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.602 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 8.602 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.602 * [backup-simplify]: Simplify (+ 0 0) into 0 8.603 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 8.605 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.606 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 8.609 * [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 8.609 * [taylor]: Taking taylor expansion of 0 in k 8.609 * [backup-simplify]: Simplify 0 into 0 8.609 * [backup-simplify]: Simplify 0 into 0 8.609 * [backup-simplify]: Simplify 0 into 0 8.609 * [backup-simplify]: Simplify 0 into 0 8.610 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.611 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.617 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 8.618 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.618 * [backup-simplify]: Simplify (+ 0 0) into 0 8.619 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 8.621 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.623 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 8.626 * [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 8.626 * [taylor]: Taking taylor expansion of 0 in k 8.626 * [backup-simplify]: Simplify 0 into 0 8.626 * [backup-simplify]: Simplify 0 into 0 8.627 * [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)))))) 8.628 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 8.628 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 8.628 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 8.628 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.628 * [taylor]: Taking taylor expansion of 2.0 in n 8.628 * [backup-simplify]: Simplify 2.0 into 2.0 8.628 * [taylor]: Taking taylor expansion of (* n PI) in n 8.628 * [taylor]: Taking taylor expansion of n in n 8.628 * [backup-simplify]: Simplify 0 into 0 8.628 * [backup-simplify]: Simplify 1 into 1 8.628 * [taylor]: Taking taylor expansion of PI in n 8.628 * [backup-simplify]: Simplify PI into PI 8.628 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.629 * [taylor]: Taking taylor expansion of 2.0 in n 8.629 * [backup-simplify]: Simplify 2.0 into 2.0 8.629 * [taylor]: Taking taylor expansion of (* n PI) in n 8.629 * [taylor]: Taking taylor expansion of n in n 8.629 * [backup-simplify]: Simplify 0 into 0 8.629 * [backup-simplify]: Simplify 1 into 1 8.629 * [taylor]: Taking taylor expansion of PI in n 8.629 * [backup-simplify]: Simplify PI into PI 8.629 * [backup-simplify]: Simplify (* 0 PI) into 0 8.630 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.630 * [backup-simplify]: Simplify 0 into 0 8.631 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.633 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.633 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.634 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.635 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 8.635 * [backup-simplify]: Simplify 0 into 0 8.637 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 8.643 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 8.643 * [backup-simplify]: Simplify 0 into 0 8.644 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.646 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 8.646 * [backup-simplify]: Simplify 0 into 0 8.647 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.649 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 8.649 * [backup-simplify]: Simplify 0 into 0 8.651 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.652 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 8.652 * [backup-simplify]: Simplify 0 into 0 8.654 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 8.657 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 8.657 * [backup-simplify]: Simplify 0 into 0 8.657 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 8.658 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 8.658 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 8.658 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.658 * [taylor]: Taking taylor expansion of 2.0 in n 8.658 * [backup-simplify]: Simplify 2.0 into 2.0 8.658 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.658 * [taylor]: Taking taylor expansion of PI in n 8.658 * [backup-simplify]: Simplify PI into PI 8.658 * [taylor]: Taking taylor expansion of n in n 8.658 * [backup-simplify]: Simplify 0 into 0 8.658 * [backup-simplify]: Simplify 1 into 1 8.659 * [backup-simplify]: Simplify (/ PI 1) into PI 8.659 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.659 * [taylor]: Taking taylor expansion of 2.0 in n 8.659 * [backup-simplify]: Simplify 2.0 into 2.0 8.659 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.659 * [taylor]: Taking taylor expansion of PI in n 8.659 * [backup-simplify]: Simplify PI into PI 8.659 * [taylor]: Taking taylor expansion of n in n 8.659 * [backup-simplify]: Simplify 0 into 0 8.659 * [backup-simplify]: Simplify 1 into 1 8.659 * [backup-simplify]: Simplify (/ PI 1) into PI 8.660 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.660 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.661 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.662 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.662 * [backup-simplify]: Simplify 0 into 0 8.663 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.664 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.664 * [backup-simplify]: Simplify 0 into 0 8.665 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.667 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.667 * [backup-simplify]: Simplify 0 into 0 8.667 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.668 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.668 * [backup-simplify]: Simplify 0 into 0 8.669 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.670 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.670 * [backup-simplify]: Simplify 0 into 0 8.671 * [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 8.672 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.672 * [backup-simplify]: Simplify 0 into 0 8.672 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 8.672 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 8.672 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 8.672 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.672 * [taylor]: Taking taylor expansion of -2.0 in n 8.672 * [backup-simplify]: Simplify -2.0 into -2.0 8.673 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.673 * [taylor]: Taking taylor expansion of PI in n 8.673 * [backup-simplify]: Simplify PI into PI 8.673 * [taylor]: Taking taylor expansion of n in n 8.673 * [backup-simplify]: Simplify 0 into 0 8.673 * [backup-simplify]: Simplify 1 into 1 8.673 * [backup-simplify]: Simplify (/ PI 1) into PI 8.673 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.673 * [taylor]: Taking taylor expansion of -2.0 in n 8.673 * [backup-simplify]: Simplify -2.0 into -2.0 8.673 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.673 * [taylor]: Taking taylor expansion of PI in n 8.673 * [backup-simplify]: Simplify PI into PI 8.673 * [taylor]: Taking taylor expansion of n in n 8.673 * [backup-simplify]: Simplify 0 into 0 8.673 * [backup-simplify]: Simplify 1 into 1 8.673 * [backup-simplify]: Simplify (/ PI 1) into PI 8.674 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.674 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.675 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.675 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 8.675 * [backup-simplify]: Simplify 0 into 0 8.676 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.676 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.676 * [backup-simplify]: Simplify 0 into 0 8.677 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.678 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.678 * [backup-simplify]: Simplify 0 into 0 8.678 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.679 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.679 * [backup-simplify]: Simplify 0 into 0 8.680 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.681 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.681 * [backup-simplify]: Simplify 0 into 0 8.681 * [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 8.682 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.682 * [backup-simplify]: Simplify 0 into 0 8.683 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 8.683 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 2 1) 8.683 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 8.683 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 8.683 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.683 * [taylor]: Taking taylor expansion of 2.0 in n 8.683 * [backup-simplify]: Simplify 2.0 into 2.0 8.683 * [taylor]: Taking taylor expansion of (* n PI) in n 8.683 * [taylor]: Taking taylor expansion of n in n 8.683 * [backup-simplify]: Simplify 0 into 0 8.683 * [backup-simplify]: Simplify 1 into 1 8.683 * [taylor]: Taking taylor expansion of PI in n 8.683 * [backup-simplify]: Simplify PI into PI 8.683 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.684 * [taylor]: Taking taylor expansion of 2.0 in n 8.684 * [backup-simplify]: Simplify 2.0 into 2.0 8.684 * [taylor]: Taking taylor expansion of (* n PI) in n 8.684 * [taylor]: Taking taylor expansion of n in n 8.684 * [backup-simplify]: Simplify 0 into 0 8.684 * [backup-simplify]: Simplify 1 into 1 8.684 * [taylor]: Taking taylor expansion of PI in n 8.684 * [backup-simplify]: Simplify PI into PI 8.684 * [backup-simplify]: Simplify (* 0 PI) into 0 8.684 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.684 * [backup-simplify]: Simplify 0 into 0 8.685 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.686 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.687 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.687 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.688 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 8.688 * [backup-simplify]: Simplify 0 into 0 8.689 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 8.690 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 8.690 * [backup-simplify]: Simplify 0 into 0 8.691 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.691 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 8.691 * [backup-simplify]: Simplify 0 into 0 8.692 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.693 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 8.693 * [backup-simplify]: Simplify 0 into 0 8.694 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.695 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 8.695 * [backup-simplify]: Simplify 0 into 0 8.696 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 8.697 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 8.698 * [backup-simplify]: Simplify 0 into 0 8.698 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 8.698 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 8.698 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 8.698 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.698 * [taylor]: Taking taylor expansion of 2.0 in n 8.698 * [backup-simplify]: Simplify 2.0 into 2.0 8.698 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.698 * [taylor]: Taking taylor expansion of PI in n 8.698 * [backup-simplify]: Simplify PI into PI 8.698 * [taylor]: Taking taylor expansion of n in n 8.699 * [backup-simplify]: Simplify 0 into 0 8.699 * [backup-simplify]: Simplify 1 into 1 8.699 * [backup-simplify]: Simplify (/ PI 1) into PI 8.699 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.699 * [taylor]: Taking taylor expansion of 2.0 in n 8.699 * [backup-simplify]: Simplify 2.0 into 2.0 8.699 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.699 * [taylor]: Taking taylor expansion of PI in n 8.699 * [backup-simplify]: Simplify PI into PI 8.699 * [taylor]: Taking taylor expansion of n in n 8.699 * [backup-simplify]: Simplify 0 into 0 8.699 * [backup-simplify]: Simplify 1 into 1 8.699 * [backup-simplify]: Simplify (/ PI 1) into PI 8.700 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.700 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.701 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.701 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.701 * [backup-simplify]: Simplify 0 into 0 8.702 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.703 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.703 * [backup-simplify]: Simplify 0 into 0 8.703 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.704 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.704 * [backup-simplify]: Simplify 0 into 0 8.705 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.705 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.705 * [backup-simplify]: Simplify 0 into 0 8.706 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.707 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.707 * [backup-simplify]: Simplify 0 into 0 8.708 * [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 8.710 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.710 * [backup-simplify]: Simplify 0 into 0 8.711 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 8.711 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 8.711 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 8.711 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.711 * [taylor]: Taking taylor expansion of -2.0 in n 8.711 * [backup-simplify]: Simplify -2.0 into -2.0 8.711 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.711 * [taylor]: Taking taylor expansion of PI in n 8.711 * [backup-simplify]: Simplify PI into PI 8.711 * [taylor]: Taking taylor expansion of n in n 8.711 * [backup-simplify]: Simplify 0 into 0 8.711 * [backup-simplify]: Simplify 1 into 1 8.712 * [backup-simplify]: Simplify (/ PI 1) into PI 8.712 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.712 * [taylor]: Taking taylor expansion of -2.0 in n 8.712 * [backup-simplify]: Simplify -2.0 into -2.0 8.712 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.712 * [taylor]: Taking taylor expansion of PI in n 8.712 * [backup-simplify]: Simplify PI into PI 8.712 * [taylor]: Taking taylor expansion of n in n 8.712 * [backup-simplify]: Simplify 0 into 0 8.712 * [backup-simplify]: Simplify 1 into 1 8.713 * [backup-simplify]: Simplify (/ PI 1) into PI 8.713 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.714 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.715 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.715 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 8.715 * [backup-simplify]: Simplify 0 into 0 8.717 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.718 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.718 * [backup-simplify]: Simplify 0 into 0 8.719 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.720 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.720 * [backup-simplify]: Simplify 0 into 0 8.721 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.723 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.723 * [backup-simplify]: Simplify 0 into 0 8.724 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.725 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.725 * [backup-simplify]: Simplify 0 into 0 8.727 * [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 8.728 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.728 * [backup-simplify]: Simplify 0 into 0 8.729 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 8.729 * * * [progress]: simplifying candidates 8.735 * [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) (/ 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2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (* 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)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 8.744 * * [simplify]: Extracting # 0 : cost 0 8.744 * * [simplify]: Extracting # 1 : cost 0 8.744 * * [simplify]: Extracting # 2 : cost 0 8.745 * * [simplify]: Extracting # 3 : cost 0 8.745 * * [simplify]: Extracting # 4 : cost 0 8.746 * * [simplify]: Extracting # 5 : cost 0 8.746 * * [simplify]: Extracting # 6 : cost 0 8.747 * * [simplify]: Extracting # 7 : cost 0 8.747 * * [simplify]: Extracting # 8 : cost 0 8.748 * * [simplify]: Extracting # 9 : cost 0 8.748 * * [simplify]: Extracting # 10 : cost 0 8.748 * * [simplify]: Extracting # 11 : cost 0 8.749 * * [simplify]: Extracting # 12 : cost 0 8.749 * * [simplify]: iteration 0 : 241 enodes (cost 3252 ) 8.844 * * [simplify]: Extracting # 0 : cost 0 8.846 * * [simplify]: Extracting # 1 : cost 0 8.848 * * [simplify]: Extracting # 2 : cost 0 8.850 * * [simplify]: Extracting # 3 : cost 0 8.852 * * [simplify]: Extracting # 4 : cost 0 8.858 * * [simplify]: Extracting # 5 : cost 0 8.858 * * [simplify]: iteration 1 : 675 enodes (cost 3014 ) 9.362 * * [simplify]: Extracting # 0 : cost 0 9.367 * * [simplify]: Extracting # 1 : cost 0 9.372 * * [simplify]: Extracting # 2 : cost 0 9.383 * * [simplify]: Extracting # 3 : cost 0 9.388 * * [simplify]: Extracting # 4 : cost 0 9.394 * * [simplify]: Extracting # 5 : cost 0 9.399 * * [simplify]: iteration 2 : 2094 enodes (cost 2898 ) 10.279 * * [simplify]: Extracting # 0 : cost 0 10.291 * * [simplify]: Extracting # 1 : cost 0 10.304 * * [simplify]: Extracting # 2 : cost 0 10.326 * * [simplify]: Extracting # 3 : cost 0 10.339 * * [simplify]: Extracting # 4 : cost 0 10.352 * * [simplify]: Extracting # 5 : cost 0 10.365 * * [simplify]: iteration done: 5000 enodes (cost 2852 ) 10.368 * [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) 2.0) (/ (/ (- 1.0 k) 2) 2.0) (/ (/ (- 1.0 k) 2) 2.0) (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 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(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))) (* PI (* 2.0 n)) (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 (* n PI)) (/ (+ (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))) (* PI (* 2.0 n)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* PI (* 2.0 n)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* PI (* 2.0 n)) (- 1.0 k)) (* PI (* 2.0 n)) (pow (* 2.0 (* n PI)) (/ (- 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 (* 2.0 (* PI n)) (/ (/ (- 1.0 k) 2.0) 4)) (pow (* 2.0 (* PI n)) (/ (/ (- 1.0 k) 2.0) 4)) (* (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) 2.0) (/ (/ (- 1.0 k) 2) 2.0) (/ (/ (- 1.0 k) 2) 2.0) (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))) (* PI (* 2.0 n)) (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 (* n PI)) (/ (+ (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))) (* PI (* 2.0 n)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* PI (* 2.0 n)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* PI (* 2.0 n)) (- 1.0 k)) (* PI (* 2.0 n)) (pow (* 2.0 (* n PI)) (/ (- 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 (* 2.0 (* PI n)) (/ (/ (- 1.0 k) 2.0) 4)) (pow (* 2.0 (* PI n)) (/ (/ (- 1.0 k) 2.0) 4)) (* PI (* 2.0 n)) (* PI (* 2.0 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 (* (* 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) (* PI (* 2.0 n)) (* PI (* 2.0 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 (* (* 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) (- (+ (+ (pow (* 2.0 (* PI n)) 0.25) (* (* (* 0.0625 (pow k 2)) (* (log n) (pow (* 2.0 (* PI n)) 0.25))) (log (* 2.0 PI)))) (* (* (* 0.03125 (pow k 2)) (pow (* 2.0 (* PI n)) 0.25)) (+ (pow (log n) 2) (pow (log (* 2.0 PI)) 2)))) (* (* 0.25 k) (* (pow (* 2.0 (* PI n)) 0.25) (log (* 2.0 (* PI n)))))) (pow (pow (* 2.0 (* PI n)) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (+ (pow (* 2.0 (* PI n)) 0.25) (* (* (* 0.0625 (pow k 2)) (* (log n) (pow (* 2.0 (* PI n)) 0.25))) (log (* 2.0 PI)))) (* (* (* 0.03125 (pow k 2)) (pow (* 2.0 (* PI n)) 0.25)) (+ (pow (log n) 2) (pow (log (* 2.0 PI)) 2)))) (* (* 0.25 k) (* (pow (* 2.0 (* PI n)) 0.25) (log (* 2.0 (* PI n)))))) (pow (pow (* 2.0 (* PI n)) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* PI (* 2.0 n)) (* PI (* 2.0 n)) (* PI (* 2.0 n)) (* PI (* 2.0 n)) (* PI (* 2.0 n)) (* PI (* 2.0 n)) 10.370 * * * [progress]: adding candidates to table 11.535 * * [progress]: iteration 3 / 4 11.535 * * * [progress]: picking best candidate 11.575 * * * * [pick]: Picked # 11.575 * * * [progress]: localizing error 11.593 * * * [progress]: generating rewritten candidates 11.593 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 11.617 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1) 11.651 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1) 11.660 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 11.671 * * * [progress]: generating series expansions 11.671 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 11.672 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 11.672 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 11.672 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 11.673 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 11.673 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 11.673 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 11.673 * [taylor]: Taking taylor expansion of 0.5 in k 11.673 * [backup-simplify]: Simplify 0.5 into 0.5 11.673 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 11.673 * [taylor]: Taking taylor expansion of 1.0 in k 11.673 * [backup-simplify]: Simplify 1.0 into 1.0 11.673 * [taylor]: Taking taylor expansion of k in k 11.673 * [backup-simplify]: Simplify 0 into 0 11.673 * [backup-simplify]: Simplify 1 into 1 11.673 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 11.673 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 11.673 * [taylor]: Taking taylor expansion of 2.0 in k 11.673 * [backup-simplify]: Simplify 2.0 into 2.0 11.673 * [taylor]: Taking taylor expansion of (* n PI) in k 11.673 * [taylor]: Taking taylor expansion of n in k 11.673 * [backup-simplify]: Simplify n into n 11.673 * [taylor]: Taking taylor expansion of PI in k 11.673 * [backup-simplify]: Simplify PI into PI 11.673 * [backup-simplify]: Simplify (* n PI) into (* n PI) 11.673 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 11.673 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 11.673 * [backup-simplify]: Simplify (- 0) into 0 11.674 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 11.674 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 11.674 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 11.674 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 11.674 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 11.674 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 11.674 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 11.674 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 11.674 * [taylor]: Taking taylor expansion of 0.5 in n 11.674 * [backup-simplify]: Simplify 0.5 into 0.5 11.674 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 11.674 * [taylor]: Taking taylor expansion of 1.0 in n 11.674 * [backup-simplify]: Simplify 1.0 into 1.0 11.674 * [taylor]: Taking taylor expansion of k in n 11.674 * [backup-simplify]: Simplify k into k 11.674 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 11.674 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 11.674 * [taylor]: Taking taylor expansion of 2.0 in n 11.674 * [backup-simplify]: Simplify 2.0 into 2.0 11.674 * [taylor]: Taking taylor expansion of (* n PI) in n 11.674 * [taylor]: Taking taylor expansion of n in n 11.674 * [backup-simplify]: Simplify 0 into 0 11.674 * [backup-simplify]: Simplify 1 into 1 11.674 * [taylor]: Taking taylor expansion of PI in n 11.674 * [backup-simplify]: Simplify PI into PI 11.675 * [backup-simplify]: Simplify (* 0 PI) into 0 11.675 * [backup-simplify]: Simplify (* 2.0 0) into 0 11.676 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.677 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 11.678 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.678 * [backup-simplify]: Simplify (- k) into (- k) 11.678 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 11.678 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 11.679 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.679 * [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)))) 11.680 * [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))))) 11.680 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 11.680 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 11.680 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 11.680 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 11.680 * [taylor]: Taking taylor expansion of 0.5 in n 11.680 * [backup-simplify]: Simplify 0.5 into 0.5 11.680 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 11.680 * [taylor]: Taking taylor expansion of 1.0 in n 11.680 * [backup-simplify]: Simplify 1.0 into 1.0 11.680 * [taylor]: Taking taylor expansion of k in n 11.680 * [backup-simplify]: Simplify k into k 11.680 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 11.680 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 11.680 * [taylor]: Taking taylor expansion of 2.0 in n 11.680 * [backup-simplify]: Simplify 2.0 into 2.0 11.680 * [taylor]: Taking taylor expansion of (* n PI) in n 11.681 * [taylor]: Taking taylor expansion of n in n 11.681 * [backup-simplify]: Simplify 0 into 0 11.681 * [backup-simplify]: Simplify 1 into 1 11.681 * [taylor]: Taking taylor expansion of PI in n 11.681 * [backup-simplify]: Simplify PI into PI 11.681 * [backup-simplify]: Simplify (* 0 PI) into 0 11.681 * [backup-simplify]: Simplify (* 2.0 0) into 0 11.682 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.683 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 11.684 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.684 * [backup-simplify]: Simplify (- k) into (- k) 11.684 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 11.684 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 11.685 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.686 * [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)))) 11.686 * [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))))) 11.686 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 11.686 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 11.686 * [taylor]: Taking taylor expansion of 0.5 in k 11.687 * [backup-simplify]: Simplify 0.5 into 0.5 11.687 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 11.687 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 11.687 * [taylor]: Taking taylor expansion of 1.0 in k 11.687 * [backup-simplify]: Simplify 1.0 into 1.0 11.687 * [taylor]: Taking taylor expansion of k in k 11.687 * [backup-simplify]: Simplify 0 into 0 11.687 * [backup-simplify]: Simplify 1 into 1 11.687 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 11.687 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 11.687 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 11.687 * [taylor]: Taking taylor expansion of 2.0 in k 11.687 * [backup-simplify]: Simplify 2.0 into 2.0 11.687 * [taylor]: Taking taylor expansion of PI in k 11.687 * [backup-simplify]: Simplify PI into PI 11.687 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.688 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.688 * [taylor]: Taking taylor expansion of (log n) in k 11.688 * [taylor]: Taking taylor expansion of n in k 11.688 * [backup-simplify]: Simplify n into n 11.688 * [backup-simplify]: Simplify (log n) into (log n) 11.688 * [backup-simplify]: Simplify (- 0) into 0 11.688 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 11.689 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 11.690 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 11.690 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 11.691 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 11.692 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 11.692 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.693 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 11.694 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 11.694 * [backup-simplify]: Simplify (- 0) into 0 11.695 * [backup-simplify]: Simplify (+ 0 0) into 0 11.695 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 11.696 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.697 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 11.698 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.698 * [taylor]: Taking taylor expansion of 0 in k 11.698 * [backup-simplify]: Simplify 0 into 0 11.698 * [backup-simplify]: Simplify 0 into 0 11.698 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 11.699 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 11.700 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 11.700 * [backup-simplify]: Simplify (+ 0 0) into 0 11.700 * [backup-simplify]: Simplify (- 1) into -1 11.701 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.702 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 11.703 * [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)))) 11.705 * [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)))))) 11.707 * [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)))))) 11.708 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 11.709 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 11.711 * [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 11.711 * [backup-simplify]: Simplify (- 0) into 0 11.711 * [backup-simplify]: Simplify (+ 0 0) into 0 11.712 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 11.713 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.713 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 11.715 * [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 11.715 * [taylor]: Taking taylor expansion of 0 in k 11.715 * [backup-simplify]: Simplify 0 into 0 11.715 * [backup-simplify]: Simplify 0 into 0 11.715 * [backup-simplify]: Simplify 0 into 0 11.716 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.718 * [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 11.719 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 11.719 * [backup-simplify]: Simplify (+ 0 0) into 0 11.720 * [backup-simplify]: Simplify (- 0) into 0 11.720 * [backup-simplify]: Simplify (+ 0 0) into 0 11.722 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 11.724 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 11.726 * [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)))))) 11.735 * [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)))))) 11.742 * [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)))))) 11.742 * [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)))) 11.742 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 11.742 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 11.742 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 11.742 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 11.742 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 11.742 * [taylor]: Taking taylor expansion of 0.5 in k 11.742 * [backup-simplify]: Simplify 0.5 into 0.5 11.742 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 11.742 * [taylor]: Taking taylor expansion of 1.0 in k 11.742 * [backup-simplify]: Simplify 1.0 into 1.0 11.742 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.742 * [taylor]: Taking taylor expansion of k in k 11.742 * [backup-simplify]: Simplify 0 into 0 11.742 * [backup-simplify]: Simplify 1 into 1 11.743 * [backup-simplify]: Simplify (/ 1 1) into 1 11.743 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 11.743 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 11.743 * [taylor]: Taking taylor expansion of 2.0 in k 11.743 * [backup-simplify]: Simplify 2.0 into 2.0 11.743 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.743 * [taylor]: Taking taylor expansion of PI in k 11.743 * [backup-simplify]: Simplify PI into PI 11.743 * [taylor]: Taking taylor expansion of n in k 11.743 * [backup-simplify]: Simplify n into n 11.743 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.743 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 11.743 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 11.743 * [backup-simplify]: Simplify (- 1) into -1 11.743 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.744 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 11.744 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 11.744 * [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))))) 11.744 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 11.744 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 11.744 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 11.744 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 11.744 * [taylor]: Taking taylor expansion of 0.5 in n 11.744 * [backup-simplify]: Simplify 0.5 into 0.5 11.744 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 11.744 * [taylor]: Taking taylor expansion of 1.0 in n 11.744 * [backup-simplify]: Simplify 1.0 into 1.0 11.744 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.744 * [taylor]: Taking taylor expansion of k in n 11.744 * [backup-simplify]: Simplify k into k 11.744 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.744 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 11.744 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 11.744 * [taylor]: Taking taylor expansion of 2.0 in n 11.744 * [backup-simplify]: Simplify 2.0 into 2.0 11.744 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.744 * [taylor]: Taking taylor expansion of PI in n 11.744 * [backup-simplify]: Simplify PI into PI 11.744 * [taylor]: Taking taylor expansion of n in n 11.744 * [backup-simplify]: Simplify 0 into 0 11.744 * [backup-simplify]: Simplify 1 into 1 11.745 * [backup-simplify]: Simplify (/ PI 1) into PI 11.745 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.746 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.746 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.746 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 11.746 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 11.747 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.748 * [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)))) 11.748 * [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))))) 11.748 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 11.748 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 11.748 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 11.748 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 11.748 * [taylor]: Taking taylor expansion of 0.5 in n 11.748 * [backup-simplify]: Simplify 0.5 into 0.5 11.748 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 11.748 * [taylor]: Taking taylor expansion of 1.0 in n 11.748 * [backup-simplify]: Simplify 1.0 into 1.0 11.748 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.749 * [taylor]: Taking taylor expansion of k in n 11.749 * [backup-simplify]: Simplify k into k 11.749 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.749 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 11.749 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 11.749 * [taylor]: Taking taylor expansion of 2.0 in n 11.749 * [backup-simplify]: Simplify 2.0 into 2.0 11.749 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.749 * [taylor]: Taking taylor expansion of PI in n 11.749 * [backup-simplify]: Simplify PI into PI 11.749 * [taylor]: Taking taylor expansion of n in n 11.749 * [backup-simplify]: Simplify 0 into 0 11.749 * [backup-simplify]: Simplify 1 into 1 11.749 * [backup-simplify]: Simplify (/ PI 1) into PI 11.749 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.750 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.750 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.750 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 11.750 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 11.751 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.752 * [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)))) 11.753 * [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))))) 11.753 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 11.753 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 11.753 * [taylor]: Taking taylor expansion of 0.5 in k 11.753 * [backup-simplify]: Simplify 0.5 into 0.5 11.753 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 11.753 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 11.753 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 11.753 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 11.753 * [taylor]: Taking taylor expansion of 2.0 in k 11.753 * [backup-simplify]: Simplify 2.0 into 2.0 11.753 * [taylor]: Taking taylor expansion of PI in k 11.753 * [backup-simplify]: Simplify PI into PI 11.753 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.754 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.754 * [taylor]: Taking taylor expansion of (log n) in k 11.754 * [taylor]: Taking taylor expansion of n in k 11.754 * [backup-simplify]: Simplify n into n 11.754 * [backup-simplify]: Simplify (log n) into (log n) 11.754 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 11.754 * [taylor]: Taking taylor expansion of 1.0 in k 11.754 * [backup-simplify]: Simplify 1.0 into 1.0 11.754 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.754 * [taylor]: Taking taylor expansion of k in k 11.754 * [backup-simplify]: Simplify 0 into 0 11.754 * [backup-simplify]: Simplify 1 into 1 11.754 * [backup-simplify]: Simplify (/ 1 1) into 1 11.754 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 11.755 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 11.755 * [backup-simplify]: Simplify (- 1) into -1 11.756 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.757 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 11.758 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 11.760 * [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))))) 11.761 * [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))))) 11.762 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.763 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 11.765 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 11.765 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.765 * [backup-simplify]: Simplify (- 0) into 0 11.766 * [backup-simplify]: Simplify (+ 0 0) into 0 11.766 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 11.768 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.769 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 11.771 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.771 * [taylor]: Taking taylor expansion of 0 in k 11.771 * [backup-simplify]: Simplify 0 into 0 11.771 * [backup-simplify]: Simplify 0 into 0 11.771 * [backup-simplify]: Simplify 0 into 0 11.772 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.773 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.776 * [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 11.777 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.777 * [backup-simplify]: Simplify (- 0) into 0 11.778 * [backup-simplify]: Simplify (+ 0 0) into 0 11.778 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 11.780 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.781 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 11.783 * [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 11.784 * [taylor]: Taking taylor expansion of 0 in k 11.784 * [backup-simplify]: Simplify 0 into 0 11.784 * [backup-simplify]: Simplify 0 into 0 11.784 * [backup-simplify]: Simplify 0 into 0 11.784 * [backup-simplify]: Simplify 0 into 0 11.784 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.785 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.789 * [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 11.789 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.789 * [backup-simplify]: Simplify (- 0) into 0 11.789 * [backup-simplify]: Simplify (+ 0 0) into 0 11.790 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 11.791 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.792 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 11.794 * [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 11.794 * [taylor]: Taking taylor expansion of 0 in k 11.794 * [backup-simplify]: Simplify 0 into 0 11.794 * [backup-simplify]: Simplify 0 into 0 11.795 * [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)))) 11.795 * [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))) 11.795 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 11.795 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 11.796 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 11.796 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 11.796 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 11.796 * [taylor]: Taking taylor expansion of 0.5 in k 11.796 * [backup-simplify]: Simplify 0.5 into 0.5 11.796 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 11.796 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.796 * [taylor]: Taking taylor expansion of k in k 11.796 * [backup-simplify]: Simplify 0 into 0 11.796 * [backup-simplify]: Simplify 1 into 1 11.796 * [backup-simplify]: Simplify (/ 1 1) into 1 11.796 * [taylor]: Taking taylor expansion of 1.0 in k 11.796 * [backup-simplify]: Simplify 1.0 into 1.0 11.796 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 11.796 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 11.796 * [taylor]: Taking taylor expansion of -2.0 in k 11.796 * [backup-simplify]: Simplify -2.0 into -2.0 11.796 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.796 * [taylor]: Taking taylor expansion of PI in k 11.796 * [backup-simplify]: Simplify PI into PI 11.796 * [taylor]: Taking taylor expansion of n in k 11.796 * [backup-simplify]: Simplify n into n 11.796 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.796 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 11.796 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 11.797 * [backup-simplify]: Simplify (+ 1 0) into 1 11.797 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 11.797 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 11.797 * [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)))))) 11.797 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 11.797 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 11.797 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 11.797 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 11.797 * [taylor]: Taking taylor expansion of 0.5 in n 11.797 * [backup-simplify]: Simplify 0.5 into 0.5 11.797 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 11.797 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.797 * [taylor]: Taking taylor expansion of k in n 11.797 * [backup-simplify]: Simplify k into k 11.797 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.797 * [taylor]: Taking taylor expansion of 1.0 in n 11.797 * [backup-simplify]: Simplify 1.0 into 1.0 11.797 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 11.797 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 11.797 * [taylor]: Taking taylor expansion of -2.0 in n 11.797 * [backup-simplify]: Simplify -2.0 into -2.0 11.797 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.797 * [taylor]: Taking taylor expansion of PI in n 11.797 * [backup-simplify]: Simplify PI into PI 11.797 * [taylor]: Taking taylor expansion of n in n 11.797 * [backup-simplify]: Simplify 0 into 0 11.798 * [backup-simplify]: Simplify 1 into 1 11.798 * [backup-simplify]: Simplify (/ PI 1) into PI 11.798 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.799 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 11.799 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 11.799 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 11.800 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.801 * [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)))) 11.801 * [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))))) 11.801 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 11.802 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 11.802 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 11.802 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 11.802 * [taylor]: Taking taylor expansion of 0.5 in n 11.802 * [backup-simplify]: Simplify 0.5 into 0.5 11.802 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 11.802 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.802 * [taylor]: Taking taylor expansion of k in n 11.802 * [backup-simplify]: Simplify k into k 11.802 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.802 * [taylor]: Taking taylor expansion of 1.0 in n 11.802 * [backup-simplify]: Simplify 1.0 into 1.0 11.802 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 11.802 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 11.802 * [taylor]: Taking taylor expansion of -2.0 in n 11.802 * [backup-simplify]: Simplify -2.0 into -2.0 11.802 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.802 * [taylor]: Taking taylor expansion of PI in n 11.802 * [backup-simplify]: Simplify PI into PI 11.802 * [taylor]: Taking taylor expansion of n in n 11.802 * [backup-simplify]: Simplify 0 into 0 11.802 * [backup-simplify]: Simplify 1 into 1 11.802 * [backup-simplify]: Simplify (/ PI 1) into PI 11.803 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.803 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 11.803 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 11.803 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 11.804 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.805 * [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)))) 11.806 * [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))))) 11.806 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 11.806 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 11.806 * [taylor]: Taking taylor expansion of 0.5 in k 11.806 * [backup-simplify]: Simplify 0.5 into 0.5 11.806 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 11.806 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 11.806 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.806 * [taylor]: Taking taylor expansion of k in k 11.806 * [backup-simplify]: Simplify 0 into 0 11.806 * [backup-simplify]: Simplify 1 into 1 11.806 * [backup-simplify]: Simplify (/ 1 1) into 1 11.806 * [taylor]: Taking taylor expansion of 1.0 in k 11.806 * [backup-simplify]: Simplify 1.0 into 1.0 11.806 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 11.806 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 11.806 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 11.806 * [taylor]: Taking taylor expansion of -2.0 in k 11.806 * [backup-simplify]: Simplify -2.0 into -2.0 11.806 * [taylor]: Taking taylor expansion of PI in k 11.806 * [backup-simplify]: Simplify PI into PI 11.807 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.808 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 11.808 * [taylor]: Taking taylor expansion of (log n) in k 11.808 * [taylor]: Taking taylor expansion of n in k 11.808 * [backup-simplify]: Simplify n into n 11.808 * [backup-simplify]: Simplify (log n) into (log n) 11.808 * [backup-simplify]: Simplify (+ 1 0) into 1 11.808 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 11.809 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 11.809 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 11.810 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 11.811 * [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))))) 11.812 * [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))))) 11.812 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.813 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 11.814 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 11.814 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.814 * [backup-simplify]: Simplify (+ 0 0) into 0 11.814 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 11.815 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.816 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 11.817 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.817 * [taylor]: Taking taylor expansion of 0 in k 11.817 * [backup-simplify]: Simplify 0 into 0 11.817 * [backup-simplify]: Simplify 0 into 0 11.817 * [backup-simplify]: Simplify 0 into 0 11.818 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.819 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.821 * [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 11.821 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.821 * [backup-simplify]: Simplify (+ 0 0) into 0 11.822 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 11.823 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.824 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 11.825 * [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 11.825 * [taylor]: Taking taylor expansion of 0 in k 11.825 * [backup-simplify]: Simplify 0 into 0 11.825 * [backup-simplify]: Simplify 0 into 0 11.825 * [backup-simplify]: Simplify 0 into 0 11.825 * [backup-simplify]: Simplify 0 into 0 11.826 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.827 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.830 * [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 11.830 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.830 * [backup-simplify]: Simplify (+ 0 0) into 0 11.831 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 11.832 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.833 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 11.840 * [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 11.840 * [taylor]: Taking taylor expansion of 0 in k 11.840 * [backup-simplify]: Simplify 0 into 0 11.840 * [backup-simplify]: Simplify 0 into 0 11.841 * [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)))))) 11.841 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1) 11.842 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 11.842 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 11.842 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 11.842 * [taylor]: Taking taylor expansion of 2.0 in n 11.842 * [backup-simplify]: Simplify 2.0 into 2.0 11.842 * [taylor]: Taking taylor expansion of (* n PI) in n 11.842 * [taylor]: Taking taylor expansion of n in n 11.842 * [backup-simplify]: Simplify 0 into 0 11.842 * [backup-simplify]: Simplify 1 into 1 11.842 * [taylor]: Taking taylor expansion of PI in n 11.842 * [backup-simplify]: Simplify PI into PI 11.842 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 11.842 * [taylor]: Taking taylor expansion of 2.0 in n 11.842 * [backup-simplify]: Simplify 2.0 into 2.0 11.842 * [taylor]: Taking taylor expansion of (* n PI) in n 11.842 * [taylor]: Taking taylor expansion of n in n 11.842 * [backup-simplify]: Simplify 0 into 0 11.842 * [backup-simplify]: Simplify 1 into 1 11.842 * [taylor]: Taking taylor expansion of PI in n 11.842 * [backup-simplify]: Simplify PI into PI 11.842 * [backup-simplify]: Simplify (* 0 PI) into 0 11.843 * [backup-simplify]: Simplify (* 2.0 0) into 0 11.843 * [backup-simplify]: Simplify 0 into 0 11.844 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.845 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 11.845 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.845 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.846 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 11.846 * [backup-simplify]: Simplify 0 into 0 11.847 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 11.847 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 11.847 * [backup-simplify]: Simplify 0 into 0 11.848 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.849 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 11.849 * [backup-simplify]: Simplify 0 into 0 11.850 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.851 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 11.851 * [backup-simplify]: Simplify 0 into 0 11.852 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.853 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 11.853 * [backup-simplify]: Simplify 0 into 0 11.854 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 11.855 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 11.855 * [backup-simplify]: Simplify 0 into 0 11.855 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 11.856 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 11.856 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 11.856 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 11.856 * [taylor]: Taking taylor expansion of 2.0 in n 11.856 * [backup-simplify]: Simplify 2.0 into 2.0 11.856 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.856 * [taylor]: Taking taylor expansion of PI in n 11.856 * [backup-simplify]: Simplify PI into PI 11.856 * [taylor]: Taking taylor expansion of n in n 11.856 * [backup-simplify]: Simplify 0 into 0 11.856 * [backup-simplify]: Simplify 1 into 1 11.856 * [backup-simplify]: Simplify (/ PI 1) into PI 11.856 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 11.856 * [taylor]: Taking taylor expansion of 2.0 in n 11.856 * [backup-simplify]: Simplify 2.0 into 2.0 11.856 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.856 * [taylor]: Taking taylor expansion of PI in n 11.856 * [backup-simplify]: Simplify PI into PI 11.856 * [taylor]: Taking taylor expansion of n in n 11.856 * [backup-simplify]: Simplify 0 into 0 11.857 * [backup-simplify]: Simplify 1 into 1 11.857 * [backup-simplify]: Simplify (/ PI 1) into PI 11.857 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.858 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.858 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.859 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 11.859 * [backup-simplify]: Simplify 0 into 0 11.859 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.860 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.860 * [backup-simplify]: Simplify 0 into 0 11.861 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.861 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.861 * [backup-simplify]: Simplify 0 into 0 11.862 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.863 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.863 * [backup-simplify]: Simplify 0 into 0 11.863 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.864 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.864 * [backup-simplify]: Simplify 0 into 0 11.865 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.866 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.866 * [backup-simplify]: Simplify 0 into 0 11.866 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 11.867 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 11.867 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 11.867 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 11.867 * [taylor]: Taking taylor expansion of -2.0 in n 11.867 * [backup-simplify]: Simplify -2.0 into -2.0 11.867 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.867 * [taylor]: Taking taylor expansion of PI in n 11.867 * [backup-simplify]: Simplify PI into PI 11.867 * [taylor]: Taking taylor expansion of n in n 11.867 * [backup-simplify]: Simplify 0 into 0 11.867 * [backup-simplify]: Simplify 1 into 1 11.867 * [backup-simplify]: Simplify (/ PI 1) into PI 11.867 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 11.867 * [taylor]: Taking taylor expansion of -2.0 in n 11.867 * [backup-simplify]: Simplify -2.0 into -2.0 11.867 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.867 * [taylor]: Taking taylor expansion of PI in n 11.867 * [backup-simplify]: Simplify PI into PI 11.867 * [taylor]: Taking taylor expansion of n in n 11.867 * [backup-simplify]: Simplify 0 into 0 11.867 * [backup-simplify]: Simplify 1 into 1 11.868 * [backup-simplify]: Simplify (/ PI 1) into PI 11.868 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.868 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.869 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.869 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 11.870 * [backup-simplify]: Simplify 0 into 0 11.870 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.871 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.871 * [backup-simplify]: Simplify 0 into 0 11.872 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.873 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.873 * [backup-simplify]: Simplify 0 into 0 11.873 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.874 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.874 * [backup-simplify]: Simplify 0 into 0 11.875 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.876 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.876 * [backup-simplify]: Simplify 0 into 0 11.876 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.877 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.877 * [backup-simplify]: Simplify 0 into 0 11.878 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 11.878 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1) 11.878 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 11.878 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 11.878 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 11.878 * [taylor]: Taking taylor expansion of 1.0 in k 11.878 * [backup-simplify]: Simplify 1.0 into 1.0 11.878 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.878 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.878 * [taylor]: Taking taylor expansion of k in k 11.878 * [backup-simplify]: Simplify 0 into 0 11.878 * [backup-simplify]: Simplify 1 into 1 11.878 * [backup-simplify]: Simplify (/ 1 1) into 1 11.879 * [backup-simplify]: Simplify (sqrt 0) into 0 11.880 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.880 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 11.880 * [taylor]: Taking taylor expansion of 1.0 in k 11.880 * [backup-simplify]: Simplify 1.0 into 1.0 11.880 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.880 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.880 * [taylor]: Taking taylor expansion of k in k 11.880 * [backup-simplify]: Simplify 0 into 0 11.880 * [backup-simplify]: Simplify 1 into 1 11.880 * [backup-simplify]: Simplify (/ 1 1) into 1 11.880 * [backup-simplify]: Simplify (sqrt 0) into 0 11.881 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.881 * [backup-simplify]: Simplify (* 1.0 0) into 0 11.881 * [backup-simplify]: Simplify 0 into 0 11.882 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 11.883 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.883 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 11.885 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.886 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 11.886 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.887 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.889 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.890 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 11.891 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.892 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 11.892 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 11.892 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 11.892 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 11.892 * [taylor]: Taking taylor expansion of 1.0 in k 11.892 * [backup-simplify]: Simplify 1.0 into 1.0 11.892 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.892 * [taylor]: Taking taylor expansion of k in k 11.892 * [backup-simplify]: Simplify 0 into 0 11.892 * [backup-simplify]: Simplify 1 into 1 11.892 * [backup-simplify]: Simplify (sqrt 0) into 0 11.893 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.893 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 11.893 * [taylor]: Taking taylor expansion of 1.0 in k 11.893 * [backup-simplify]: Simplify 1.0 into 1.0 11.893 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.893 * [taylor]: Taking taylor expansion of k in k 11.893 * [backup-simplify]: Simplify 0 into 0 11.893 * [backup-simplify]: Simplify 1 into 1 11.893 * [backup-simplify]: Simplify (sqrt 0) into 0 11.894 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.894 * [backup-simplify]: Simplify (* 1.0 0) into 0 11.894 * [backup-simplify]: Simplify 0 into 0 11.895 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 11.895 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.897 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.898 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 11.899 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.901 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.902 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 11.902 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.903 * [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)))))))) 11.904 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 11.904 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 11.904 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 11.904 * [taylor]: Taking taylor expansion of 1.0 in k 11.904 * [backup-simplify]: Simplify 1.0 into 1.0 11.904 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.904 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.904 * [taylor]: Taking taylor expansion of -1 in k 11.904 * [backup-simplify]: Simplify -1 into -1 11.904 * [taylor]: Taking taylor expansion of k in k 11.904 * [backup-simplify]: Simplify 0 into 0 11.904 * [backup-simplify]: Simplify 1 into 1 11.904 * [backup-simplify]: Simplify (/ -1 1) into -1 11.904 * [backup-simplify]: Simplify (sqrt 0) into 0 11.905 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.905 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 11.905 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 11.905 * [taylor]: Taking taylor expansion of 1.0 in k 11.905 * [backup-simplify]: Simplify 1.0 into 1.0 11.905 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.905 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.906 * [taylor]: Taking taylor expansion of -1 in k 11.906 * [backup-simplify]: Simplify -1 into -1 11.906 * [taylor]: Taking taylor expansion of k in k 11.906 * [backup-simplify]: Simplify 0 into 0 11.906 * [backup-simplify]: Simplify 1 into 1 11.906 * [backup-simplify]: Simplify (/ -1 1) into -1 11.906 * [backup-simplify]: Simplify (sqrt 0) into 0 11.907 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.907 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 11.907 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.908 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 11.910 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.911 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 11.912 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.912 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.914 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.917 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 11.917 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.918 * [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))))) 11.918 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 11.918 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 11.918 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 11.918 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 11.918 * [taylor]: Taking taylor expansion of 1.0 in k 11.918 * [backup-simplify]: Simplify 1.0 into 1.0 11.918 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.918 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.918 * [taylor]: Taking taylor expansion of k in k 11.918 * [backup-simplify]: Simplify 0 into 0 11.918 * [backup-simplify]: Simplify 1 into 1 11.919 * [backup-simplify]: Simplify (/ 1 1) into 1 11.919 * [backup-simplify]: Simplify (sqrt 0) into 0 11.920 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.920 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 11.920 * [taylor]: Taking taylor expansion of 1.0 in k 11.920 * [backup-simplify]: Simplify 1.0 into 1.0 11.920 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.920 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.920 * [taylor]: Taking taylor expansion of k in k 11.920 * [backup-simplify]: Simplify 0 into 0 11.920 * [backup-simplify]: Simplify 1 into 1 11.920 * [backup-simplify]: Simplify (/ 1 1) into 1 11.920 * [backup-simplify]: Simplify (sqrt 0) into 0 11.921 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.921 * [backup-simplify]: Simplify (* 1.0 0) into 0 11.921 * [backup-simplify]: Simplify 0 into 0 11.922 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 11.922 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.923 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 11.925 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.926 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 11.926 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.927 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.935 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.936 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 11.937 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.938 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 11.938 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 11.938 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 11.938 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 11.938 * [taylor]: Taking taylor expansion of 1.0 in k 11.938 * [backup-simplify]: Simplify 1.0 into 1.0 11.938 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.938 * [taylor]: Taking taylor expansion of k in k 11.938 * [backup-simplify]: Simplify 0 into 0 11.938 * [backup-simplify]: Simplify 1 into 1 11.938 * [backup-simplify]: Simplify (sqrt 0) into 0 11.939 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.939 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 11.939 * [taylor]: Taking taylor expansion of 1.0 in k 11.939 * [backup-simplify]: Simplify 1.0 into 1.0 11.939 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.939 * [taylor]: Taking taylor expansion of k in k 11.939 * [backup-simplify]: Simplify 0 into 0 11.939 * [backup-simplify]: Simplify 1 into 1 11.939 * [backup-simplify]: Simplify (sqrt 0) into 0 11.940 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.940 * [backup-simplify]: Simplify (* 1.0 0) into 0 11.940 * [backup-simplify]: Simplify 0 into 0 11.941 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 11.942 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.943 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.944 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 11.945 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.947 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.949 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 11.950 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.951 * [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)))))))) 11.951 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 11.951 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 11.951 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 11.952 * [taylor]: Taking taylor expansion of 1.0 in k 11.952 * [backup-simplify]: Simplify 1.0 into 1.0 11.952 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.952 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.952 * [taylor]: Taking taylor expansion of -1 in k 11.952 * [backup-simplify]: Simplify -1 into -1 11.952 * [taylor]: Taking taylor expansion of k in k 11.952 * [backup-simplify]: Simplify 0 into 0 11.952 * [backup-simplify]: Simplify 1 into 1 11.952 * [backup-simplify]: Simplify (/ -1 1) into -1 11.953 * [backup-simplify]: Simplify (sqrt 0) into 0 11.954 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.954 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 11.954 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 11.954 * [taylor]: Taking taylor expansion of 1.0 in k 11.954 * [backup-simplify]: Simplify 1.0 into 1.0 11.954 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.954 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.954 * [taylor]: Taking taylor expansion of -1 in k 11.954 * [backup-simplify]: Simplify -1 into -1 11.955 * [taylor]: Taking taylor expansion of k in k 11.955 * [backup-simplify]: Simplify 0 into 0 11.955 * [backup-simplify]: Simplify 1 into 1 11.955 * [backup-simplify]: Simplify (/ -1 1) into -1 11.955 * [backup-simplify]: Simplify (sqrt 0) into 0 11.957 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.957 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 11.957 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.958 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 11.962 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.964 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 11.965 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.966 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.970 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.974 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 11.974 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.975 * [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))))) 11.976 * * * [progress]: simplifying candidates 11.978 * [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)) (* (* 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 (/ 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))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (- (+ (* 0.125 (* (pow 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)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +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))))) 11.981 * * [simplify]: Extracting # 0 : cost 0 11.981 * * [simplify]: Extracting # 1 : cost 0 11.981 * * [simplify]: Extracting # 2 : cost 0 11.981 * * [simplify]: Extracting # 3 : cost 0 11.982 * * [simplify]: Extracting # 4 : cost 0 11.982 * * [simplify]: Extracting # 5 : cost 0 11.982 * * [simplify]: Extracting # 6 : cost 0 11.982 * * [simplify]: Extracting # 7 : cost 0 11.983 * * [simplify]: Extracting # 8 : cost 0 11.983 * * [simplify]: Extracting # 9 : cost 0 11.983 * * [simplify]: Extracting # 10 : cost 0 11.984 * * [simplify]: Extracting # 11 : cost 0 11.984 * * [simplify]: Extracting # 12 : cost 0 11.984 * * [simplify]: Extracting # 13 : cost 0 11.984 * * [simplify]: iteration 0 : 234 enodes (cost 1642 ) 12.055 * * [simplify]: Extracting # 0 : cost 0 12.056 * * [simplify]: Extracting # 1 : cost 0 12.057 * * [simplify]: Extracting # 2 : cost 0 12.059 * * [simplify]: Extracting # 3 : cost 0 12.060 * * [simplify]: Extracting # 4 : cost 0 12.062 * * [simplify]: Extracting # 5 : cost 0 12.063 * * [simplify]: iteration 1 : 555 enodes (cost 1507 ) 12.320 * * [simplify]: Extracting # 0 : cost 0 12.323 * * [simplify]: Extracting # 1 : cost 0 12.325 * * [simplify]: Extracting # 2 : cost 0 12.327 * * [simplify]: Extracting # 3 : cost 0 12.329 * * [simplify]: Extracting # 4 : cost 0 12.332 * * [simplify]: iteration 2 : 1707 enodes (cost 1401 ) 13.094 * * [simplify]: Extracting # 0 : cost 0 13.106 * * [simplify]: Extracting # 1 : cost 0 13.121 * * [simplify]: Extracting # 2 : cost 0 13.127 * * [simplify]: Extracting # 3 : cost 0 13.137 * * [simplify]: Extracting # 4 : cost 0 13.150 * * [simplify]: iteration done: 5000 enodes (cost 1380 ) 13.151 * [simplify]: Simplified to: (* (log (* (* 2.0 PI) 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)) (* (log (* (* 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))) (* PI (* 2.0 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))) (* PI (* 2.0 n)) (* PI (* 2.0 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 (* (* 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)) (* PI (* 2.0 n)) (* PI (* 2.0 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 (* (* 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))) (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) (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) (- (+ (+ (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)))) (* (* (* 0.125 (pow k 2)) (pow (* (* 2.0 PI) n) 0.5)) (+ (pow (log (* 2.0 PI)) 2) (pow (log n) 2)))) (* 0.5 (* (* k (pow (* (* 2.0 PI) n) 0.5)) (log (* (* 2.0 PI) 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)))))) (* PI (* 2.0 n)) (* PI (* 2.0 n)) (* PI (* 2.0 n)) (- (+ (* +nan.0 (- k (pow k 2))) +nan.0)) (- (+ (- (/ (/ +nan.0 k) k) (/ +nan.0 k)) (/ +nan.0 (pow k 3)))) (- (- (/ (/ +nan.0 k) k) (- (/ +nan.0 k) +nan.0))) (- (+ (* +nan.0 (- k (pow k 2))) +nan.0)) (- (+ (- (/ (/ +nan.0 k) k) (/ +nan.0 k)) (/ +nan.0 (pow k 3)))) (- (- (/ (/ +nan.0 k) k) (- (/ +nan.0 k) +nan.0))) 13.153 * * * [progress]: adding candidates to table 13.837 * * [progress]: iteration 4 / 4 13.837 * * * [progress]: picking best candidate 13.864 * * * * [pick]: Picked # 13.864 * * * [progress]: localizing error 13.910 * * * [progress]: generating rewritten candidates 13.910 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 13.932 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1) 13.969 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1 1) 13.985 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 2 1) 14.083 * * * [progress]: generating series expansions 14.083 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 14.084 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 14.084 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 14.084 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 14.084 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 14.084 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 14.084 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 14.084 * [taylor]: Taking taylor expansion of 0.5 in k 14.084 * [backup-simplify]: Simplify 0.5 into 0.5 14.084 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 14.085 * [taylor]: Taking taylor expansion of 1.0 in k 14.085 * [backup-simplify]: Simplify 1.0 into 1.0 14.085 * [taylor]: Taking taylor expansion of k in k 14.085 * [backup-simplify]: Simplify 0 into 0 14.085 * [backup-simplify]: Simplify 1 into 1 14.085 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 14.085 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 14.085 * [taylor]: Taking taylor expansion of 2.0 in k 14.085 * [backup-simplify]: Simplify 2.0 into 2.0 14.085 * [taylor]: Taking taylor expansion of (* n PI) in k 14.085 * [taylor]: Taking taylor expansion of n in k 14.085 * [backup-simplify]: Simplify n into n 14.085 * [taylor]: Taking taylor expansion of PI in k 14.085 * [backup-simplify]: Simplify PI into PI 14.085 * [backup-simplify]: Simplify (* n PI) into (* n PI) 14.085 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 14.085 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 14.085 * [backup-simplify]: Simplify (- 0) into 0 14.086 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 14.086 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 14.086 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 14.086 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 14.086 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 14.086 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 14.086 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 14.086 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 14.086 * [taylor]: Taking taylor expansion of 0.5 in n 14.086 * [backup-simplify]: Simplify 0.5 into 0.5 14.086 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 14.086 * [taylor]: Taking taylor expansion of 1.0 in n 14.086 * [backup-simplify]: Simplify 1.0 into 1.0 14.086 * [taylor]: Taking taylor expansion of k in n 14.086 * [backup-simplify]: Simplify k into k 14.086 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 14.086 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 14.086 * [taylor]: Taking taylor expansion of 2.0 in n 14.086 * [backup-simplify]: Simplify 2.0 into 2.0 14.086 * [taylor]: Taking taylor expansion of (* n PI) in n 14.086 * [taylor]: Taking taylor expansion of n in n 14.086 * [backup-simplify]: Simplify 0 into 0 14.086 * [backup-simplify]: Simplify 1 into 1 14.086 * [taylor]: Taking taylor expansion of PI in n 14.086 * [backup-simplify]: Simplify PI into PI 14.087 * [backup-simplify]: Simplify (* 0 PI) into 0 14.087 * [backup-simplify]: Simplify (* 2.0 0) into 0 14.088 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 14.089 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 14.090 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.090 * [backup-simplify]: Simplify (- k) into (- k) 14.090 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 14.090 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 14.091 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.092 * [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)))) 14.092 * [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))))) 14.092 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 14.092 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 14.092 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 14.092 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 14.092 * [taylor]: Taking taylor expansion of 0.5 in n 14.093 * [backup-simplify]: Simplify 0.5 into 0.5 14.093 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 14.093 * [taylor]: Taking taylor expansion of 1.0 in n 14.093 * [backup-simplify]: Simplify 1.0 into 1.0 14.093 * [taylor]: Taking taylor expansion of k in n 14.093 * [backup-simplify]: Simplify k into k 14.093 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 14.093 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 14.093 * [taylor]: Taking taylor expansion of 2.0 in n 14.093 * [backup-simplify]: Simplify 2.0 into 2.0 14.093 * [taylor]: Taking taylor expansion of (* n PI) in n 14.093 * [taylor]: Taking taylor expansion of n in n 14.093 * [backup-simplify]: Simplify 0 into 0 14.093 * [backup-simplify]: Simplify 1 into 1 14.093 * [taylor]: Taking taylor expansion of PI in n 14.093 * [backup-simplify]: Simplify PI into PI 14.093 * [backup-simplify]: Simplify (* 0 PI) into 0 14.093 * [backup-simplify]: Simplify (* 2.0 0) into 0 14.094 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 14.095 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 14.096 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.097 * [backup-simplify]: Simplify (- k) into (- k) 14.097 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 14.097 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 14.098 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.100 * [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)))) 14.101 * [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))))) 14.101 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 14.101 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 14.101 * [taylor]: Taking taylor expansion of 0.5 in k 14.101 * [backup-simplify]: Simplify 0.5 into 0.5 14.101 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 14.101 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 14.101 * [taylor]: Taking taylor expansion of 1.0 in k 14.101 * [backup-simplify]: Simplify 1.0 into 1.0 14.101 * [taylor]: Taking taylor expansion of k in k 14.101 * [backup-simplify]: Simplify 0 into 0 14.101 * [backup-simplify]: Simplify 1 into 1 14.101 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 14.101 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 14.101 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 14.101 * [taylor]: Taking taylor expansion of 2.0 in k 14.102 * [backup-simplify]: Simplify 2.0 into 2.0 14.102 * [taylor]: Taking taylor expansion of PI in k 14.102 * [backup-simplify]: Simplify PI into PI 14.102 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.103 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.103 * [taylor]: Taking taylor expansion of (log n) in k 14.103 * [taylor]: Taking taylor expansion of n in k 14.103 * [backup-simplify]: Simplify n into n 14.103 * [backup-simplify]: Simplify (log n) into (log n) 14.104 * [backup-simplify]: Simplify (- 0) into 0 14.104 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 14.105 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 14.107 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 14.108 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 14.109 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 14.110 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 14.111 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 14.113 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 14.115 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 14.115 * [backup-simplify]: Simplify (- 0) into 0 14.115 * [backup-simplify]: Simplify (+ 0 0) into 0 14.116 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 14.117 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.119 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 14.120 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 14.120 * [taylor]: Taking taylor expansion of 0 in k 14.120 * [backup-simplify]: Simplify 0 into 0 14.120 * [backup-simplify]: Simplify 0 into 0 14.121 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 14.122 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 14.122 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 14.123 * [backup-simplify]: Simplify (+ 0 0) into 0 14.123 * [backup-simplify]: Simplify (- 1) into -1 14.123 * [backup-simplify]: Simplify (+ 0 -1) into -1 14.124 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 14.126 * [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)))) 14.128 * [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)))))) 14.130 * [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)))))) 14.131 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 14.132 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 14.134 * [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 14.135 * [backup-simplify]: Simplify (- 0) into 0 14.135 * [backup-simplify]: Simplify (+ 0 0) into 0 14.136 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 14.137 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.138 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 14.139 * [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 14.139 * [taylor]: Taking taylor expansion of 0 in k 14.139 * [backup-simplify]: Simplify 0 into 0 14.140 * [backup-simplify]: Simplify 0 into 0 14.140 * [backup-simplify]: Simplify 0 into 0 14.140 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 14.143 * [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 14.145 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 14.145 * [backup-simplify]: Simplify (+ 0 0) into 0 14.145 * [backup-simplify]: Simplify (- 0) into 0 14.145 * [backup-simplify]: Simplify (+ 0 0) into 0 14.147 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 14.149 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 14.153 * [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)))))) 14.160 * [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)))))) 14.176 * [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)))))) 14.176 * [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)))) 14.176 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 14.176 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 14.176 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 14.176 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 14.176 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 14.176 * [taylor]: Taking taylor expansion of 0.5 in k 14.176 * [backup-simplify]: Simplify 0.5 into 0.5 14.176 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 14.177 * [taylor]: Taking taylor expansion of 1.0 in k 14.177 * [backup-simplify]: Simplify 1.0 into 1.0 14.177 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.177 * [taylor]: Taking taylor expansion of k in k 14.177 * [backup-simplify]: Simplify 0 into 0 14.177 * [backup-simplify]: Simplify 1 into 1 14.177 * [backup-simplify]: Simplify (/ 1 1) into 1 14.177 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 14.177 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 14.177 * [taylor]: Taking taylor expansion of 2.0 in k 14.177 * [backup-simplify]: Simplify 2.0 into 2.0 14.177 * [taylor]: Taking taylor expansion of (/ PI n) in k 14.177 * [taylor]: Taking taylor expansion of PI in k 14.177 * [backup-simplify]: Simplify PI into PI 14.177 * [taylor]: Taking taylor expansion of n in k 14.177 * [backup-simplify]: Simplify n into n 14.177 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 14.177 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 14.177 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 14.177 * [backup-simplify]: Simplify (- 1) into -1 14.178 * [backup-simplify]: Simplify (+ 0 -1) into -1 14.178 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 14.178 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 14.178 * [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))))) 14.178 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 14.178 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 14.178 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 14.178 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 14.178 * [taylor]: Taking taylor expansion of 0.5 in n 14.178 * [backup-simplify]: Simplify 0.5 into 0.5 14.178 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 14.178 * [taylor]: Taking taylor expansion of 1.0 in n 14.178 * [backup-simplify]: Simplify 1.0 into 1.0 14.178 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.178 * [taylor]: Taking taylor expansion of k in n 14.178 * [backup-simplify]: Simplify k into k 14.178 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.179 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 14.179 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 14.179 * [taylor]: Taking taylor expansion of 2.0 in n 14.179 * [backup-simplify]: Simplify 2.0 into 2.0 14.179 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.179 * [taylor]: Taking taylor expansion of PI in n 14.179 * [backup-simplify]: Simplify PI into PI 14.179 * [taylor]: Taking taylor expansion of n in n 14.179 * [backup-simplify]: Simplify 0 into 0 14.179 * [backup-simplify]: Simplify 1 into 1 14.179 * [backup-simplify]: Simplify (/ PI 1) into PI 14.179 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.180 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.180 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 14.180 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 14.180 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 14.181 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 14.183 * [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)))) 14.183 * [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))))) 14.184 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 14.184 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 14.184 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 14.184 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 14.184 * [taylor]: Taking taylor expansion of 0.5 in n 14.184 * [backup-simplify]: Simplify 0.5 into 0.5 14.184 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 14.184 * [taylor]: Taking taylor expansion of 1.0 in n 14.184 * [backup-simplify]: Simplify 1.0 into 1.0 14.184 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.184 * [taylor]: Taking taylor expansion of k in n 14.184 * [backup-simplify]: Simplify k into k 14.184 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.184 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 14.184 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 14.184 * [taylor]: Taking taylor expansion of 2.0 in n 14.184 * [backup-simplify]: Simplify 2.0 into 2.0 14.184 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.184 * [taylor]: Taking taylor expansion of PI in n 14.184 * [backup-simplify]: Simplify PI into PI 14.184 * [taylor]: Taking taylor expansion of n in n 14.184 * [backup-simplify]: Simplify 0 into 0 14.184 * [backup-simplify]: Simplify 1 into 1 14.185 * [backup-simplify]: Simplify (/ PI 1) into PI 14.185 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.186 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.186 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 14.187 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 14.187 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 14.188 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 14.189 * [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)))) 14.191 * [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))))) 14.191 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 14.191 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 14.191 * [taylor]: Taking taylor expansion of 0.5 in k 14.191 * [backup-simplify]: Simplify 0.5 into 0.5 14.191 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 14.191 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 14.191 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 14.191 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 14.191 * [taylor]: Taking taylor expansion of 2.0 in k 14.191 * [backup-simplify]: Simplify 2.0 into 2.0 14.191 * [taylor]: Taking taylor expansion of PI in k 14.191 * [backup-simplify]: Simplify PI into PI 14.192 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.193 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.193 * [taylor]: Taking taylor expansion of (log n) in k 14.193 * [taylor]: Taking taylor expansion of n in k 14.193 * [backup-simplify]: Simplify n into n 14.193 * [backup-simplify]: Simplify (log n) into (log n) 14.193 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 14.193 * [taylor]: Taking taylor expansion of 1.0 in k 14.193 * [backup-simplify]: Simplify 1.0 into 1.0 14.193 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.193 * [taylor]: Taking taylor expansion of k in k 14.193 * [backup-simplify]: Simplify 0 into 0 14.193 * [backup-simplify]: Simplify 1 into 1 14.194 * [backup-simplify]: Simplify (/ 1 1) into 1 14.194 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 14.195 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 14.195 * [backup-simplify]: Simplify (- 1) into -1 14.196 * [backup-simplify]: Simplify (+ 0 -1) into -1 14.197 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 14.198 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 14.199 * [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))))) 14.201 * [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))))) 14.202 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 14.203 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 14.204 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 14.205 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 14.205 * [backup-simplify]: Simplify (- 0) into 0 14.205 * [backup-simplify]: Simplify (+ 0 0) into 0 14.206 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 14.208 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 14.209 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 14.211 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 14.211 * [taylor]: Taking taylor expansion of 0 in k 14.211 * [backup-simplify]: Simplify 0 into 0 14.211 * [backup-simplify]: Simplify 0 into 0 14.211 * [backup-simplify]: Simplify 0 into 0 14.212 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.213 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 14.217 * [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 14.217 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 14.217 * [backup-simplify]: Simplify (- 0) into 0 14.218 * [backup-simplify]: Simplify (+ 0 0) into 0 14.219 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 14.220 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 14.222 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 14.225 * [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 14.225 * [taylor]: Taking taylor expansion of 0 in k 14.225 * [backup-simplify]: Simplify 0 into 0 14.225 * [backup-simplify]: Simplify 0 into 0 14.225 * [backup-simplify]: Simplify 0 into 0 14.225 * [backup-simplify]: Simplify 0 into 0 14.226 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.227 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 14.231 * [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 14.231 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 14.231 * [backup-simplify]: Simplify (- 0) into 0 14.231 * [backup-simplify]: Simplify (+ 0 0) into 0 14.232 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 14.233 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 14.234 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 14.236 * [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 14.236 * [taylor]: Taking taylor expansion of 0 in k 14.236 * [backup-simplify]: Simplify 0 into 0 14.236 * [backup-simplify]: Simplify 0 into 0 14.237 * [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)))) 14.237 * [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))) 14.237 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 14.238 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 14.238 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 14.238 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 14.238 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 14.238 * [taylor]: Taking taylor expansion of 0.5 in k 14.238 * [backup-simplify]: Simplify 0.5 into 0.5 14.238 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 14.238 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.238 * [taylor]: Taking taylor expansion of k in k 14.238 * [backup-simplify]: Simplify 0 into 0 14.238 * [backup-simplify]: Simplify 1 into 1 14.238 * [backup-simplify]: Simplify (/ 1 1) into 1 14.238 * [taylor]: Taking taylor expansion of 1.0 in k 14.238 * [backup-simplify]: Simplify 1.0 into 1.0 14.238 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 14.238 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 14.238 * [taylor]: Taking taylor expansion of -2.0 in k 14.238 * [backup-simplify]: Simplify -2.0 into -2.0 14.238 * [taylor]: Taking taylor expansion of (/ PI n) in k 14.238 * [taylor]: Taking taylor expansion of PI in k 14.238 * [backup-simplify]: Simplify PI into PI 14.238 * [taylor]: Taking taylor expansion of n in k 14.238 * [backup-simplify]: Simplify n into n 14.238 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 14.238 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 14.238 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 14.239 * [backup-simplify]: Simplify (+ 1 0) into 1 14.239 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 14.239 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 14.239 * [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)))))) 14.239 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 14.239 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 14.239 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 14.239 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 14.239 * [taylor]: Taking taylor expansion of 0.5 in n 14.239 * [backup-simplify]: Simplify 0.5 into 0.5 14.239 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 14.239 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.239 * [taylor]: Taking taylor expansion of k in n 14.239 * [backup-simplify]: Simplify k into k 14.239 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.239 * [taylor]: Taking taylor expansion of 1.0 in n 14.239 * [backup-simplify]: Simplify 1.0 into 1.0 14.239 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 14.239 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 14.239 * [taylor]: Taking taylor expansion of -2.0 in n 14.239 * [backup-simplify]: Simplify -2.0 into -2.0 14.240 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.240 * [taylor]: Taking taylor expansion of PI in n 14.240 * [backup-simplify]: Simplify PI into PI 14.240 * [taylor]: Taking taylor expansion of n in n 14.240 * [backup-simplify]: Simplify 0 into 0 14.240 * [backup-simplify]: Simplify 1 into 1 14.240 * [backup-simplify]: Simplify (/ PI 1) into PI 14.240 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 14.241 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 14.241 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 14.241 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 14.242 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 14.243 * [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)))) 14.244 * [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))))) 14.244 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 14.244 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 14.244 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 14.244 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 14.244 * [taylor]: Taking taylor expansion of 0.5 in n 14.244 * [backup-simplify]: Simplify 0.5 into 0.5 14.244 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 14.244 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.244 * [taylor]: Taking taylor expansion of k in n 14.244 * [backup-simplify]: Simplify k into k 14.244 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.244 * [taylor]: Taking taylor expansion of 1.0 in n 14.244 * [backup-simplify]: Simplify 1.0 into 1.0 14.244 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 14.244 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 14.244 * [taylor]: Taking taylor expansion of -2.0 in n 14.244 * [backup-simplify]: Simplify -2.0 into -2.0 14.244 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.244 * [taylor]: Taking taylor expansion of PI in n 14.244 * [backup-simplify]: Simplify PI into PI 14.244 * [taylor]: Taking taylor expansion of n in n 14.244 * [backup-simplify]: Simplify 0 into 0 14.244 * [backup-simplify]: Simplify 1 into 1 14.245 * [backup-simplify]: Simplify (/ PI 1) into PI 14.245 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 14.246 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 14.246 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 14.246 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 14.247 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 14.247 * [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)))) 14.248 * [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))))) 14.248 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 14.248 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 14.248 * [taylor]: Taking taylor expansion of 0.5 in k 14.248 * [backup-simplify]: Simplify 0.5 into 0.5 14.248 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 14.248 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 14.248 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.248 * [taylor]: Taking taylor expansion of k in k 14.248 * [backup-simplify]: Simplify 0 into 0 14.248 * [backup-simplify]: Simplify 1 into 1 14.249 * [backup-simplify]: Simplify (/ 1 1) into 1 14.249 * [taylor]: Taking taylor expansion of 1.0 in k 14.249 * [backup-simplify]: Simplify 1.0 into 1.0 14.249 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 14.249 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 14.249 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 14.249 * [taylor]: Taking taylor expansion of -2.0 in k 14.249 * [backup-simplify]: Simplify -2.0 into -2.0 14.249 * [taylor]: Taking taylor expansion of PI in k 14.249 * [backup-simplify]: Simplify PI into PI 14.249 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 14.250 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 14.250 * [taylor]: Taking taylor expansion of (log n) in k 14.250 * [taylor]: Taking taylor expansion of n in k 14.250 * [backup-simplify]: Simplify n into n 14.250 * [backup-simplify]: Simplify (log n) into (log n) 14.250 * [backup-simplify]: Simplify (+ 1 0) into 1 14.250 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 14.251 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 14.252 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 14.252 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 14.253 * [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))))) 14.254 * [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))))) 14.255 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 14.255 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 14.256 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 14.256 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 14.257 * [backup-simplify]: Simplify (+ 0 0) into 0 14.257 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 14.258 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 14.259 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 14.260 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 14.260 * [taylor]: Taking taylor expansion of 0 in k 14.260 * [backup-simplify]: Simplify 0 into 0 14.260 * [backup-simplify]: Simplify 0 into 0 14.260 * [backup-simplify]: Simplify 0 into 0 14.261 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.261 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 14.264 * [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 14.264 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 14.264 * [backup-simplify]: Simplify (+ 0 0) into 0 14.265 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 14.267 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 14.268 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 14.271 * [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 14.271 * [taylor]: Taking taylor expansion of 0 in k 14.271 * [backup-simplify]: Simplify 0 into 0 14.271 * [backup-simplify]: Simplify 0 into 0 14.271 * [backup-simplify]: Simplify 0 into 0 14.271 * [backup-simplify]: Simplify 0 into 0 14.272 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.273 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 14.278 * [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 14.278 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 14.278 * [backup-simplify]: Simplify (+ 0 0) into 0 14.279 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 14.280 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 14.281 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 14.284 * [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 14.284 * [taylor]: Taking taylor expansion of 0 in k 14.284 * [backup-simplify]: Simplify 0 into 0 14.284 * [backup-simplify]: Simplify 0 into 0 14.285 * [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)))))) 14.285 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1) 14.285 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) into (* 1.0 (sqrt (/ 1 k))) 14.285 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 14.285 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 14.285 * [taylor]: Taking taylor expansion of 1.0 in k 14.285 * [backup-simplify]: Simplify 1.0 into 1.0 14.285 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 14.285 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.285 * [taylor]: Taking taylor expansion of k in k 14.285 * [backup-simplify]: Simplify 0 into 0 14.285 * [backup-simplify]: Simplify 1 into 1 14.285 * [backup-simplify]: Simplify (/ 1 1) into 1 14.286 * [backup-simplify]: Simplify (sqrt 0) into 0 14.287 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.287 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 14.287 * [taylor]: Taking taylor expansion of 1.0 in k 14.287 * [backup-simplify]: Simplify 1.0 into 1.0 14.287 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 14.287 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.287 * [taylor]: Taking taylor expansion of k in k 14.287 * [backup-simplify]: Simplify 0 into 0 14.287 * [backup-simplify]: Simplify 1 into 1 14.287 * [backup-simplify]: Simplify (/ 1 1) into 1 14.287 * [backup-simplify]: Simplify (sqrt 0) into 0 14.295 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.295 * [backup-simplify]: Simplify (* 1.0 0) into 0 14.295 * [backup-simplify]: Simplify 0 into 0 14.296 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 14.297 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.297 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 14.299 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 14.301 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 14.301 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.301 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.304 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 14.305 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 14.305 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.306 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 14.306 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt (/ 1 k)))) (sqrt (sqrt (/ 1 k)))) into (* 1.0 (sqrt k)) 14.306 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 14.306 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 14.307 * [taylor]: Taking taylor expansion of 1.0 in k 14.307 * [backup-simplify]: Simplify 1.0 into 1.0 14.307 * [taylor]: Taking taylor expansion of (sqrt k) in k 14.307 * [taylor]: Taking taylor expansion of k in k 14.307 * [backup-simplify]: Simplify 0 into 0 14.307 * [backup-simplify]: Simplify 1 into 1 14.307 * [backup-simplify]: Simplify (sqrt 0) into 0 14.308 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.308 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 14.308 * [taylor]: Taking taylor expansion of 1.0 in k 14.308 * [backup-simplify]: Simplify 1.0 into 1.0 14.308 * [taylor]: Taking taylor expansion of (sqrt k) in k 14.308 * [taylor]: Taking taylor expansion of k in k 14.308 * [backup-simplify]: Simplify 0 into 0 14.308 * [backup-simplify]: Simplify 1 into 1 14.309 * [backup-simplify]: Simplify (sqrt 0) into 0 14.310 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.310 * [backup-simplify]: Simplify (* 1.0 0) into 0 14.310 * [backup-simplify]: Simplify 0 into 0 14.312 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 14.312 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.315 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 14.318 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 14.318 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.322 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 14.324 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 14.325 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.326 * [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)))))))) 14.327 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt (/ 1 (- k))))) (sqrt (sqrt (/ 1 (- k))))) into (/ 1.0 (sqrt (/ -1 k))) 14.327 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 14.327 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 14.327 * [taylor]: Taking taylor expansion of 1.0 in k 14.327 * [backup-simplify]: Simplify 1.0 into 1.0 14.327 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 14.327 * [taylor]: Taking taylor expansion of (/ -1 k) in k 14.327 * [taylor]: Taking taylor expansion of -1 in k 14.327 * [backup-simplify]: Simplify -1 into -1 14.327 * [taylor]: Taking taylor expansion of k in k 14.327 * [backup-simplify]: Simplify 0 into 0 14.327 * [backup-simplify]: Simplify 1 into 1 14.328 * [backup-simplify]: Simplify (/ -1 1) into -1 14.328 * [backup-simplify]: Simplify (sqrt 0) into 0 14.329 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 14.330 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 14.330 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 14.330 * [taylor]: Taking taylor expansion of 1.0 in k 14.330 * [backup-simplify]: Simplify 1.0 into 1.0 14.330 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 14.330 * [taylor]: Taking taylor expansion of (/ -1 k) in k 14.330 * [taylor]: Taking taylor expansion of -1 in k 14.330 * [backup-simplify]: Simplify -1 into -1 14.330 * [taylor]: Taking taylor expansion of k in k 14.330 * [backup-simplify]: Simplify 0 into 0 14.330 * [backup-simplify]: Simplify 1 into 1 14.330 * [backup-simplify]: Simplify (/ -1 1) into -1 14.331 * [backup-simplify]: Simplify (sqrt 0) into 0 14.332 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 14.333 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 14.333 * [backup-simplify]: Simplify +nan.0 into +nan.0 14.334 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 14.337 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 14.339 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 14.340 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.341 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.344 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 14.347 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 14.347 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.348 * [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))))) 14.348 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1 1) 14.348 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt k))) into (* 1.0 (pow (/ 1 k) 1/4)) 14.348 * [approximate]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in (k) around 0 14.348 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 14.348 * [taylor]: Taking taylor expansion of 1.0 in k 14.348 * [backup-simplify]: Simplify 1.0 into 1.0 14.348 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 14.348 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 14.348 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 14.348 * [taylor]: Taking taylor expansion of 1/4 in k 14.348 * [backup-simplify]: Simplify 1/4 into 1/4 14.348 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 14.348 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.348 * [taylor]: Taking taylor expansion of k in k 14.348 * [backup-simplify]: Simplify 0 into 0 14.348 * [backup-simplify]: Simplify 1 into 1 14.348 * [backup-simplify]: Simplify (/ 1 1) into 1 14.349 * [backup-simplify]: Simplify (log 1) into 0 14.349 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.349 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 14.349 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 14.349 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 14.349 * [taylor]: Taking taylor expansion of 1.0 in k 14.349 * [backup-simplify]: Simplify 1.0 into 1.0 14.349 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 14.349 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 14.349 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 14.349 * [taylor]: Taking taylor expansion of 1/4 in k 14.349 * [backup-simplify]: Simplify 1/4 into 1/4 14.349 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 14.349 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.349 * [taylor]: Taking taylor expansion of k in k 14.349 * [backup-simplify]: Simplify 0 into 0 14.349 * [backup-simplify]: Simplify 1 into 1 14.350 * [backup-simplify]: Simplify (/ 1 1) into 1 14.350 * [backup-simplify]: Simplify (log 1) into 0 14.350 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.350 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 14.350 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 14.350 * [backup-simplify]: Simplify (* 1.0 (pow k -1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 14.351 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 14.351 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 14.352 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 14.352 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.353 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0 14.353 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 14.354 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (pow k -1/4))) into 0 14.354 * [backup-simplify]: Simplify 0 into 0 14.354 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.356 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 14.356 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.357 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 14.358 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.358 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (pow k -1/4)))) into 0 14.358 * [backup-simplify]: Simplify 0 into 0 14.359 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.362 * [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 14.362 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.363 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0 14.364 * [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 14.365 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4))))) into 0 14.365 * [backup-simplify]: Simplify 0 into 0 14.365 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.376 * [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 14.376 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.378 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0 14.381 * [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 14.383 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4)))))) into 0 14.383 * [backup-simplify]: Simplify 0 into 0 14.384 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.401 * [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 14.402 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.404 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0 14.408 * [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 14.410 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4))))))) into 0 14.410 * [backup-simplify]: Simplify 0 into 0 14.412 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.454 * [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 14.454 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.456 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0 14.460 * [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 14.461 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4)))))))) into 0 14.461 * [backup-simplify]: Simplify 0 into 0 14.461 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 14.462 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt (/ 1 k)))) into (* 1.0 (pow k 1/4)) 14.462 * [approximate]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in (k) around 0 14.462 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 14.462 * [taylor]: Taking taylor expansion of 1.0 in k 14.462 * [backup-simplify]: Simplify 1.0 into 1.0 14.462 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 14.462 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 14.462 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 14.462 * [taylor]: Taking taylor expansion of 1/4 in k 14.462 * [backup-simplify]: Simplify 1/4 into 1/4 14.462 * [taylor]: Taking taylor expansion of (log k) in k 14.462 * [taylor]: Taking taylor expansion of k in k 14.462 * [backup-simplify]: Simplify 0 into 0 14.462 * [backup-simplify]: Simplify 1 into 1 14.462 * [backup-simplify]: Simplify (log 1) into 0 14.462 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 14.462 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 14.462 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 14.463 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 14.463 * [taylor]: Taking taylor expansion of 1.0 in k 14.463 * [backup-simplify]: Simplify 1.0 into 1.0 14.463 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 14.463 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 14.463 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 14.463 * [taylor]: Taking taylor expansion of 1/4 in k 14.463 * [backup-simplify]: Simplify 1/4 into 1/4 14.463 * [taylor]: Taking taylor expansion of (log k) in k 14.463 * [taylor]: Taking taylor expansion of k in k 14.463 * [backup-simplify]: Simplify 0 into 0 14.463 * [backup-simplify]: Simplify 1 into 1 14.463 * [backup-simplify]: Simplify (log 1) into 0 14.463 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 14.463 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 14.463 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 14.464 * [backup-simplify]: Simplify (* 1.0 (pow k 1/4)) into (* 1.0 (pow k 1/4)) 14.464 * [backup-simplify]: Simplify (* 1.0 (pow k 1/4)) into (* 1.0 (pow k 1/4)) 14.464 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 14.465 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 14.465 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 14.466 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 14.466 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (pow k 1/4))) into 0 14.466 * [backup-simplify]: Simplify 0 into 0 14.468 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 14.468 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 14.469 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 14.470 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.470 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (pow k 1/4)))) into 0 14.470 * [backup-simplify]: Simplify 0 into 0 14.473 * [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 14.474 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 14.475 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0 14.476 * [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 14.476 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))) into 0 14.476 * [backup-simplify]: Simplify 0 into 0 14.482 * [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 14.483 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 14.484 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0 14.485 * [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 14.486 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))) into 0 14.486 * [backup-simplify]: Simplify 0 into 0 14.496 * [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 14.496 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 14.497 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0 14.500 * [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 14.502 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))))) into 0 14.502 * [backup-simplify]: Simplify 0 into 0 14.534 * [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 14.535 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 14.537 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0 14.543 * [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 14.546 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))))) into 0 14.546 * [backup-simplify]: Simplify 0 into 0 14.546 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 14.546 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt (/ 1 (- k))))) into (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) 14.546 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in (k) around 0 14.546 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 14.546 * [taylor]: Taking taylor expansion of 1.0 in k 14.547 * [backup-simplify]: Simplify 1.0 into 1.0 14.547 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 14.547 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 14.547 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 14.547 * [taylor]: Taking taylor expansion of (/ -1 k) in k 14.547 * [taylor]: Taking taylor expansion of -1 in k 14.547 * [backup-simplify]: Simplify -1 into -1 14.547 * [taylor]: Taking taylor expansion of k in k 14.547 * [backup-simplify]: Simplify 0 into 0 14.547 * [backup-simplify]: Simplify 1 into 1 14.547 * [backup-simplify]: Simplify (/ -1 1) into -1 14.548 * [backup-simplify]: Simplify (sqrt 0) into 0 14.549 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 14.550 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 14.550 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 14.551 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 14.554 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 14.556 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 14.558 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 14.559 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 14.559 * [taylor]: Taking taylor expansion of 1.0 in k 14.559 * [backup-simplify]: Simplify 1.0 into 1.0 14.559 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 14.559 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 14.559 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 14.559 * [taylor]: Taking taylor expansion of (/ -1 k) in k 14.559 * [taylor]: Taking taylor expansion of -1 in k 14.559 * [backup-simplify]: Simplify -1 into -1 14.559 * [taylor]: Taking taylor expansion of k in k 14.559 * [backup-simplify]: Simplify 0 into 0 14.559 * [backup-simplify]: Simplify 1 into 1 14.559 * [backup-simplify]: Simplify (/ -1 1) into -1 14.560 * [backup-simplify]: Simplify (sqrt 0) into 0 14.561 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 14.561 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 14.562 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 14.563 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 14.575 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 14.578 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 14.580 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 14.581 * [backup-simplify]: Simplify (* 1.0 (sqrt +nan.0)) into (* 1.0 (sqrt +nan.0)) 14.582 * [backup-simplify]: Simplify (* 1.0 (sqrt +nan.0)) into (* 1.0 (sqrt +nan.0)) 14.585 * [backup-simplify]: Simplify (+ (* 1.0 (/ +nan.0 (sqrt +nan.0))) (* 0 (sqrt +nan.0))) into (- (* +nan.0 (/ 1 (sqrt +nan.0)))) 14.587 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (sqrt +nan.0)))) into (- (* +nan.0 (/ 1 (sqrt +nan.0)))) 14.588 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.592 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 14.597 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 14.602 * [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))) 14.617 * [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)))))) 14.625 * [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)))))) 14.638 * [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))))))))) 14.638 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 2 1) 14.638 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 14.638 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 14.639 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 14.639 * [taylor]: Taking taylor expansion of 2.0 in n 14.639 * [backup-simplify]: Simplify 2.0 into 2.0 14.639 * [taylor]: Taking taylor expansion of (* n PI) in n 14.639 * [taylor]: Taking taylor expansion of n in n 14.639 * [backup-simplify]: Simplify 0 into 0 14.639 * [backup-simplify]: Simplify 1 into 1 14.639 * [taylor]: Taking taylor expansion of PI in n 14.639 * [backup-simplify]: Simplify PI into PI 14.639 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 14.639 * [taylor]: Taking taylor expansion of 2.0 in n 14.639 * [backup-simplify]: Simplify 2.0 into 2.0 14.639 * [taylor]: Taking taylor expansion of (* n PI) in n 14.639 * [taylor]: Taking taylor expansion of n in n 14.639 * [backup-simplify]: Simplify 0 into 0 14.639 * [backup-simplify]: Simplify 1 into 1 14.639 * [taylor]: Taking taylor expansion of PI in n 14.639 * [backup-simplify]: Simplify PI into PI 14.640 * [backup-simplify]: Simplify (* 0 PI) into 0 14.640 * [backup-simplify]: Simplify (* 2.0 0) into 0 14.640 * [backup-simplify]: Simplify 0 into 0 14.642 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 14.643 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 14.644 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.645 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 14.646 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 14.646 * [backup-simplify]: Simplify 0 into 0 14.647 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 14.648 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 14.648 * [backup-simplify]: Simplify 0 into 0 14.649 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 14.649 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 14.649 * [backup-simplify]: Simplify 0 into 0 14.650 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 14.651 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 14.651 * [backup-simplify]: Simplify 0 into 0 14.652 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 14.653 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 14.653 * [backup-simplify]: Simplify 0 into 0 14.654 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 14.656 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 14.656 * [backup-simplify]: Simplify 0 into 0 14.656 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 14.656 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 14.656 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 14.656 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 14.656 * [taylor]: Taking taylor expansion of 2.0 in n 14.656 * [backup-simplify]: Simplify 2.0 into 2.0 14.656 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.656 * [taylor]: Taking taylor expansion of PI in n 14.656 * [backup-simplify]: Simplify PI into PI 14.656 * [taylor]: Taking taylor expansion of n in n 14.657 * [backup-simplify]: Simplify 0 into 0 14.657 * [backup-simplify]: Simplify 1 into 1 14.657 * [backup-simplify]: Simplify (/ PI 1) into PI 14.657 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 14.657 * [taylor]: Taking taylor expansion of 2.0 in n 14.657 * [backup-simplify]: Simplify 2.0 into 2.0 14.657 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.657 * [taylor]: Taking taylor expansion of PI in n 14.657 * [backup-simplify]: Simplify PI into PI 14.657 * [taylor]: Taking taylor expansion of n in n 14.657 * [backup-simplify]: Simplify 0 into 0 14.657 * [backup-simplify]: Simplify 1 into 1 14.657 * [backup-simplify]: Simplify (/ PI 1) into PI 14.658 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.658 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.659 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 14.659 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 14.659 * [backup-simplify]: Simplify 0 into 0 14.660 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.660 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 14.660 * [backup-simplify]: Simplify 0 into 0 14.661 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.662 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 14.662 * [backup-simplify]: Simplify 0 into 0 14.662 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.663 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 14.663 * [backup-simplify]: Simplify 0 into 0 14.664 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.665 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 14.665 * [backup-simplify]: Simplify 0 into 0 14.665 * [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 14.666 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 14.666 * [backup-simplify]: Simplify 0 into 0 14.667 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 14.667 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 14.667 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 14.667 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 14.667 * [taylor]: Taking taylor expansion of -2.0 in n 14.667 * [backup-simplify]: Simplify -2.0 into -2.0 14.667 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.667 * [taylor]: Taking taylor expansion of PI in n 14.667 * [backup-simplify]: Simplify PI into PI 14.667 * [taylor]: Taking taylor expansion of n in n 14.667 * [backup-simplify]: Simplify 0 into 0 14.667 * [backup-simplify]: Simplify 1 into 1 14.668 * [backup-simplify]: Simplify (/ PI 1) into PI 14.668 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 14.668 * [taylor]: Taking taylor expansion of -2.0 in n 14.668 * [backup-simplify]: Simplify -2.0 into -2.0 14.668 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.668 * [taylor]: Taking taylor expansion of PI in n 14.668 * [backup-simplify]: Simplify PI into PI 14.668 * [taylor]: Taking taylor expansion of n in n 14.668 * [backup-simplify]: Simplify 0 into 0 14.668 * [backup-simplify]: Simplify 1 into 1 14.668 * [backup-simplify]: Simplify (/ PI 1) into PI 14.668 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 14.669 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 14.669 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 14.670 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 14.670 * [backup-simplify]: Simplify 0 into 0 14.670 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.671 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 14.671 * [backup-simplify]: Simplify 0 into 0 14.672 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.672 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 14.672 * [backup-simplify]: Simplify 0 into 0 14.673 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.674 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 14.674 * [backup-simplify]: Simplify 0 into 0 14.674 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.676 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 14.676 * [backup-simplify]: Simplify 0 into 0 14.676 * [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 14.677 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 14.677 * [backup-simplify]: Simplify 0 into 0 14.678 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 14.678 * * * [progress]: simplifying candidates 14.693 * [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 (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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(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)) 14.732 * * [simplify]: Extracting # 0 : cost 0 14.733 * * [simplify]: Extracting # 1 : cost 0 14.735 * * [simplify]: Extracting # 2 : cost 0 14.737 * * [simplify]: Extracting # 3 : cost 0 14.739 * * [simplify]: Extracting # 4 : cost 0 14.741 * * [simplify]: Extracting # 5 : cost 0 14.743 * * [simplify]: Extracting # 6 : cost 0 14.744 * * [simplify]: Extracting # 7 : cost 0 14.745 * * [simplify]: Extracting # 8 : cost 0 14.746 * * [simplify]: Extracting # 9 : cost 0 14.747 * * [simplify]: Extracting # 10 : cost 0 14.748 * * [simplify]: Extracting # 11 : cost 0 14.749 * * [simplify]: Extracting # 12 : cost 0 14.750 * * [simplify]: Extracting # 13 : cost 0 14.752 * * [simplify]: iteration 0 : 558 enodes (cost 8953 ) 15.034 * * [simplify]: Extracting # 0 : cost 0 15.039 * * [simplify]: Extracting # 1 : cost 0 15.043 * * [simplify]: Extracting # 2 : cost 0 15.047 * * [simplify]: Extracting # 3 : cost 0 15.050 * * [simplify]: Extracting # 4 : cost 0 15.054 * * [simplify]: iteration 1 : 1320 enodes (cost 7629 ) 15.709 * * [simplify]: Extracting # 0 : cost 0 15.714 * * [simplify]: Extracting # 1 : cost 0 15.724 * * [simplify]: Extracting # 2 : cost 0 15.728 * * [simplify]: Extracting # 3 : cost 0 15.731 * * [simplify]: Extracting # 4 : cost 0 15.735 * * [simplify]: Extracting # 5 : cost 0 15.739 * * [simplify]: iteration 2 : 3045 enodes (cost 7052 ) 16.789 * * [simplify]: Extracting # 0 : cost 0 16.796 * * [simplify]: Extracting # 1 : cost 0 16.802 * * [simplify]: Extracting # 2 : cost 0 16.814 * * [simplify]: Extracting # 3 : cost 0 16.820 * * [simplify]: Extracting # 4 : cost 0 16.826 * * [simplify]: iteration done: 5001 enodes (cost 6884 ) 16.831 * [simplify]: Simplified to: (* (log (* (* 2.0 PI) 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)) (* (log (* (* 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))) 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(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 (* 2.0 PI)) 3) (pow (* n (* 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))) (* (pow (* n (* 2.0 PI)) 0.5) (log n)))) (* (* 0.5 k) (+ (* (pow (* n (* 2.0 PI)) 0.5) (log (* 2.0 PI))) (* (pow (* n (* 2.0 PI)) 0.5) (log n)))))) (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 k) (/ +nan.0 (pow k 3))) (/ (- +nan.0) (pow k 2))) (- (- (/ +nan.0 (pow k 2)) (- (/ +nan.0 k) +nan.0))) (* 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)) 16.836 * * * [progress]: adding candidates to table 18.228 * [progress]: [Phase 3 of 3] Extracting. 18.228 * * [regime]: Finding splitpoints for: (# # # # # # #) 18.234 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 18.234 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # #) 18.314 * * * * [regimes]: Trying to branch on n from (# # # # # # #) 18.392 * * * * [regimes]: Trying to branch on k from (# # # # # # #) 18.465 * * * [regime]: Found split indices: #