54.235 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.213 * * * [progress]: [2/2] Setting up program. 0.218 * [progress]: [Phase 2 of 3] Improving. 0.219 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.219 * * [simplify]: Extracting # 0 : cost 0 0.219 * * [simplify]: Extracting # 1 : cost 0 0.219 * * [simplify]: Extracting # 2 : cost 0 0.219 * * [simplify]: Extracting # 3 : cost 0 0.219 * * [simplify]: Extracting # 4 : cost 0 0.219 * * [simplify]: Extracting # 5 : cost 0 0.219 * * [simplify]: Extracting # 6 : cost 0 0.220 * * [simplify]: Extracting # 7 : cost 0 0.220 * * [simplify]: iteration 0 : 13 enodes (cost 16 ) 0.226 * * [simplify]: Extracting # 0 : cost 0 0.226 * * [simplify]: Extracting # 1 : cost 0 0.226 * * [simplify]: Extracting # 2 : cost 0 0.226 * * [simplify]: Extracting # 3 : cost 0 0.226 * * [simplify]: Extracting # 4 : cost 0 0.226 * * [simplify]: Extracting # 5 : cost 0 0.226 * * [simplify]: iteration 1 : 29 enodes (cost 16 ) 0.236 * * [simplify]: Extracting # 0 : cost 0 0.236 * * [simplify]: Extracting # 1 : cost 0 0.236 * * [simplify]: Extracting # 2 : cost 0 0.236 * * [simplify]: Extracting # 3 : cost 0 0.236 * * [simplify]: Extracting # 4 : cost 0 0.236 * * [simplify]: iteration 2 : 59 enodes (cost 16 ) 0.250 * * [simplify]: Extracting # 0 : cost 0 0.250 * * [simplify]: Extracting # 1 : cost 0 0.250 * * [simplify]: Extracting # 2 : cost 0 0.250 * * [simplify]: Extracting # 3 : cost 0 0.250 * * [simplify]: Extracting # 4 : cost 0 0.250 * * [simplify]: iteration 3 : 119 enodes (cost 16 ) 0.299 * * [simplify]: Extracting # 0 : cost 0 0.299 * * [simplify]: Extracting # 1 : cost 0 0.300 * * [simplify]: Extracting # 2 : cost 0 0.300 * * [simplify]: Extracting # 3 : cost 0 0.300 * * [simplify]: Extracting # 4 : cost 0 0.301 * * [simplify]: iteration 4 : 313 enodes (cost 16 ) 0.521 * * [simplify]: Extracting # 0 : cost 0 0.523 * * [simplify]: Extracting # 1 : cost 0 0.525 * * [simplify]: Extracting # 2 : cost 0 0.526 * * [simplify]: Extracting # 3 : cost 0 0.528 * * [simplify]: Extracting # 4 : cost 0 0.530 * * [simplify]: iteration 5 : 843 enodes (cost 16 ) 1.963 * * [simplify]: Extracting # 0 : cost 0 1.970 * * [simplify]: Extracting # 1 : cost 0 1.974 * * [simplify]: Extracting # 2 : cost 0 1.976 * * [simplify]: Extracting # 3 : cost 0 1.979 * * [simplify]: Extracting # 4 : cost 0 1.982 * * [simplify]: iteration 6 : 3221 enodes (cost 16 ) 3.857 * * [simplify]: Extracting # 0 : cost 0 3.866 * * [simplify]: Extracting # 1 : cost 0 3.871 * * [simplify]: Extracting # 2 : cost 0 3.876 * * [simplify]: Extracting # 3 : cost 0 3.880 * * [simplify]: Extracting # 4 : cost 0 3.885 * * [simplify]: iteration done: 5001 enodes (cost 16 ) 3.885 * [simplify]: Simplified to: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3.885 * * [progress]: iteration 1 / 4 3.885 * * * [progress]: picking best candidate 3.888 * * * * [pick]: Picked # 3.888 * * * [progress]: localizing error 3.915 * * * [progress]: generating rewritten candidates 3.915 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 3.953 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 3.959 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 3.978 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 4.066 * * * [progress]: generating series expansions 4.066 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 4.067 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 4.067 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 4.067 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 4.067 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.067 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.067 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 4.067 * [taylor]: Taking taylor expansion of 0.5 in k 4.067 * [backup-simplify]: Simplify 0.5 into 0.5 4.067 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.067 * [taylor]: Taking taylor expansion of 1.0 in k 4.067 * [backup-simplify]: Simplify 1.0 into 1.0 4.067 * [taylor]: Taking taylor expansion of k in k 4.067 * [backup-simplify]: Simplify 0 into 0 4.068 * [backup-simplify]: Simplify 1 into 1 4.068 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.068 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.068 * [taylor]: Taking taylor expansion of 2.0 in k 4.068 * [backup-simplify]: Simplify 2.0 into 2.0 4.068 * [taylor]: Taking taylor expansion of (* n PI) in k 4.068 * [taylor]: Taking taylor expansion of n in k 4.068 * [backup-simplify]: Simplify n into n 4.068 * [taylor]: Taking taylor expansion of PI in k 4.068 * [backup-simplify]: Simplify PI into PI 4.068 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.068 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.068 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.069 * [backup-simplify]: Simplify (- 0) into 0 4.069 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.070 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 4.070 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 4.070 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 4.070 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 4.070 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.070 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.070 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 4.070 * [taylor]: Taking taylor expansion of 0.5 in n 4.070 * [backup-simplify]: Simplify 0.5 into 0.5 4.070 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.070 * [taylor]: Taking taylor expansion of 1.0 in n 4.070 * [backup-simplify]: Simplify 1.0 into 1.0 4.070 * [taylor]: Taking taylor expansion of k in n 4.070 * [backup-simplify]: Simplify k into k 4.070 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.070 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.070 * [taylor]: Taking taylor expansion of 2.0 in n 4.070 * [backup-simplify]: Simplify 2.0 into 2.0 4.070 * [taylor]: Taking taylor expansion of (* n PI) in n 4.071 * [taylor]: Taking taylor expansion of n in n 4.071 * [backup-simplify]: Simplify 0 into 0 4.071 * [backup-simplify]: Simplify 1 into 1 4.071 * [taylor]: Taking taylor expansion of PI in n 4.071 * [backup-simplify]: Simplify PI into PI 4.071 * [backup-simplify]: Simplify (* 0 PI) into 0 4.072 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.073 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.075 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.076 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.076 * [backup-simplify]: Simplify (- k) into (- k) 4.076 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.076 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 4.077 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.077 * [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)))) 4.078 * [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))))) 4.078 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 4.078 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.078 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.078 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 4.078 * [taylor]: Taking taylor expansion of 0.5 in n 4.078 * [backup-simplify]: Simplify 0.5 into 0.5 4.078 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.078 * [taylor]: Taking taylor expansion of 1.0 in n 4.078 * [backup-simplify]: Simplify 1.0 into 1.0 4.078 * [taylor]: Taking taylor expansion of k in n 4.078 * [backup-simplify]: Simplify k into k 4.078 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.078 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.078 * [taylor]: Taking taylor expansion of 2.0 in n 4.078 * [backup-simplify]: Simplify 2.0 into 2.0 4.078 * [taylor]: Taking taylor expansion of (* n PI) in n 4.079 * [taylor]: Taking taylor expansion of n in n 4.079 * [backup-simplify]: Simplify 0 into 0 4.079 * [backup-simplify]: Simplify 1 into 1 4.079 * [taylor]: Taking taylor expansion of PI in n 4.079 * [backup-simplify]: Simplify PI into PI 4.079 * [backup-simplify]: Simplify (* 0 PI) into 0 4.079 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.080 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.081 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.082 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.082 * [backup-simplify]: Simplify (- k) into (- k) 4.082 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.082 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 4.083 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.083 * [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)))) 4.084 * [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))))) 4.084 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 4.084 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 4.084 * [taylor]: Taking taylor expansion of 0.5 in k 4.084 * [backup-simplify]: Simplify 0.5 into 0.5 4.084 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 4.084 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.084 * [taylor]: Taking taylor expansion of 1.0 in k 4.084 * [backup-simplify]: Simplify 1.0 into 1.0 4.084 * [taylor]: Taking taylor expansion of k in k 4.084 * [backup-simplify]: Simplify 0 into 0 4.084 * [backup-simplify]: Simplify 1 into 1 4.084 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 4.084 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.084 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.084 * [taylor]: Taking taylor expansion of 2.0 in k 4.084 * [backup-simplify]: Simplify 2.0 into 2.0 4.084 * [taylor]: Taking taylor expansion of PI in k 4.084 * [backup-simplify]: Simplify PI into PI 4.085 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.085 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.085 * [taylor]: Taking taylor expansion of (log n) in k 4.085 * [taylor]: Taking taylor expansion of n in k 4.085 * [backup-simplify]: Simplify n into n 4.085 * [backup-simplify]: Simplify (log n) into (log n) 4.086 * [backup-simplify]: Simplify (- 0) into 0 4.086 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.087 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 4.087 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 4.088 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 4.089 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 4.089 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 4.090 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.090 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.092 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.092 * [backup-simplify]: Simplify (- 0) into 0 4.092 * [backup-simplify]: Simplify (+ 0 0) into 0 4.092 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 4.093 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.094 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 4.095 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.095 * [taylor]: Taking taylor expansion of 0 in k 4.095 * [backup-simplify]: Simplify 0 into 0 4.095 * [backup-simplify]: Simplify 0 into 0 4.096 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.097 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.098 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.098 * [backup-simplify]: Simplify (+ 0 0) into 0 4.098 * [backup-simplify]: Simplify (- 1) into -1 4.098 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.099 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 4.100 * [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)))) 4.102 * [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)))))) 4.104 * [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)))))) 4.105 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.106 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.107 * [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 4.108 * [backup-simplify]: Simplify (- 0) into 0 4.108 * [backup-simplify]: Simplify (+ 0 0) into 0 4.108 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 4.110 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.110 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.112 * [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 4.112 * [taylor]: Taking taylor expansion of 0 in k 4.112 * [backup-simplify]: Simplify 0 into 0 4.112 * [backup-simplify]: Simplify 0 into 0 4.112 * [backup-simplify]: Simplify 0 into 0 4.113 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.119 * [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 4.120 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.120 * [backup-simplify]: Simplify (+ 0 0) into 0 4.121 * [backup-simplify]: Simplify (- 0) into 0 4.121 * [backup-simplify]: Simplify (+ 0 0) into 0 4.122 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.124 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 4.126 * [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)))))) 4.129 * [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)))))) 4.135 * [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)))))) 4.136 * [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)))) 4.137 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 4.137 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 4.137 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.137 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.137 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 4.137 * [taylor]: Taking taylor expansion of 0.5 in k 4.137 * [backup-simplify]: Simplify 0.5 into 0.5 4.137 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.137 * [taylor]: Taking taylor expansion of 1.0 in k 4.137 * [backup-simplify]: Simplify 1.0 into 1.0 4.137 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.137 * [taylor]: Taking taylor expansion of k in k 4.137 * [backup-simplify]: Simplify 0 into 0 4.137 * [backup-simplify]: Simplify 1 into 1 4.137 * [backup-simplify]: Simplify (/ 1 1) into 1 4.137 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.137 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.138 * [taylor]: Taking taylor expansion of 2.0 in k 4.138 * [backup-simplify]: Simplify 2.0 into 2.0 4.138 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.138 * [taylor]: Taking taylor expansion of PI in k 4.138 * [backup-simplify]: Simplify PI into PI 4.138 * [taylor]: Taking taylor expansion of n in k 4.138 * [backup-simplify]: Simplify n into n 4.138 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.138 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.138 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.138 * [backup-simplify]: Simplify (- 1) into -1 4.139 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.139 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 4.140 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 4.140 * [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))))) 4.140 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 4.140 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.140 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.140 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 4.140 * [taylor]: Taking taylor expansion of 0.5 in n 4.140 * [backup-simplify]: Simplify 0.5 into 0.5 4.140 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.140 * [taylor]: Taking taylor expansion of 1.0 in n 4.140 * [backup-simplify]: Simplify 1.0 into 1.0 4.140 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.140 * [taylor]: Taking taylor expansion of k in n 4.140 * [backup-simplify]: Simplify k into k 4.140 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.140 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.140 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.140 * [taylor]: Taking taylor expansion of 2.0 in n 4.141 * [backup-simplify]: Simplify 2.0 into 2.0 4.141 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.141 * [taylor]: Taking taylor expansion of PI in n 4.141 * [backup-simplify]: Simplify PI into PI 4.141 * [taylor]: Taking taylor expansion of n in n 4.141 * [backup-simplify]: Simplify 0 into 0 4.141 * [backup-simplify]: Simplify 1 into 1 4.141 * [backup-simplify]: Simplify (/ PI 1) into PI 4.142 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.143 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.143 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.143 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.143 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 4.145 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.146 * [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)))) 4.147 * [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))))) 4.147 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 4.147 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.147 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.147 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 4.147 * [taylor]: Taking taylor expansion of 0.5 in n 4.147 * [backup-simplify]: Simplify 0.5 into 0.5 4.148 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.148 * [taylor]: Taking taylor expansion of 1.0 in n 4.148 * [backup-simplify]: Simplify 1.0 into 1.0 4.148 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.148 * [taylor]: Taking taylor expansion of k in n 4.148 * [backup-simplify]: Simplify k into k 4.148 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.148 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.148 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.148 * [taylor]: Taking taylor expansion of 2.0 in n 4.148 * [backup-simplify]: Simplify 2.0 into 2.0 4.148 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.148 * [taylor]: Taking taylor expansion of PI in n 4.148 * [backup-simplify]: Simplify PI into PI 4.148 * [taylor]: Taking taylor expansion of n in n 4.148 * [backup-simplify]: Simplify 0 into 0 4.148 * [backup-simplify]: Simplify 1 into 1 4.148 * [backup-simplify]: Simplify (/ PI 1) into PI 4.149 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.150 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.150 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.150 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.150 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 4.152 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.153 * [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)))) 4.154 * [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))))) 4.155 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 4.155 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 4.155 * [taylor]: Taking taylor expansion of 0.5 in k 4.155 * [backup-simplify]: Simplify 0.5 into 0.5 4.155 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 4.155 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 4.155 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.155 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.155 * [taylor]: Taking taylor expansion of 2.0 in k 4.155 * [backup-simplify]: Simplify 2.0 into 2.0 4.155 * [taylor]: Taking taylor expansion of PI in k 4.155 * [backup-simplify]: Simplify PI into PI 4.155 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.157 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.157 * [taylor]: Taking taylor expansion of (log n) in k 4.157 * [taylor]: Taking taylor expansion of n in k 4.157 * [backup-simplify]: Simplify n into n 4.157 * [backup-simplify]: Simplify (log n) into (log n) 4.157 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.157 * [taylor]: Taking taylor expansion of 1.0 in k 4.157 * [backup-simplify]: Simplify 1.0 into 1.0 4.157 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.157 * [taylor]: Taking taylor expansion of k in k 4.157 * [backup-simplify]: Simplify 0 into 0 4.157 * [backup-simplify]: Simplify 1 into 1 4.157 * [backup-simplify]: Simplify (/ 1 1) into 1 4.157 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.159 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 4.159 * [backup-simplify]: Simplify (- 1) into -1 4.160 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.161 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 4.162 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 4.163 * [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))))) 4.165 * [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))))) 4.166 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.166 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.168 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.169 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.169 * [backup-simplify]: Simplify (- 0) into 0 4.169 * [backup-simplify]: Simplify (+ 0 0) into 0 4.170 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.171 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.173 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 4.175 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.175 * [taylor]: Taking taylor expansion of 0 in k 4.175 * [backup-simplify]: Simplify 0 into 0 4.175 * [backup-simplify]: Simplify 0 into 0 4.175 * [backup-simplify]: Simplify 0 into 0 4.176 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.177 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.181 * [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 4.181 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.181 * [backup-simplify]: Simplify (- 0) into 0 4.182 * [backup-simplify]: Simplify (+ 0 0) into 0 4.183 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 4.184 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.186 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 4.189 * [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 4.189 * [taylor]: Taking taylor expansion of 0 in k 4.189 * [backup-simplify]: Simplify 0 into 0 4.189 * [backup-simplify]: Simplify 0 into 0 4.189 * [backup-simplify]: Simplify 0 into 0 4.189 * [backup-simplify]: Simplify 0 into 0 4.190 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.191 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.198 * [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 4.198 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.198 * [backup-simplify]: Simplify (- 0) into 0 4.199 * [backup-simplify]: Simplify (+ 0 0) into 0 4.200 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 4.202 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.204 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 4.206 * [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 4.207 * [taylor]: Taking taylor expansion of 0 in k 4.207 * [backup-simplify]: Simplify 0 into 0 4.207 * [backup-simplify]: Simplify 0 into 0 4.208 * [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)))) 4.209 * [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))) 4.209 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 4.209 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 4.209 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.209 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.209 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 4.209 * [taylor]: Taking taylor expansion of 0.5 in k 4.209 * [backup-simplify]: Simplify 0.5 into 0.5 4.209 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.209 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.209 * [taylor]: Taking taylor expansion of k in k 4.209 * [backup-simplify]: Simplify 0 into 0 4.209 * [backup-simplify]: Simplify 1 into 1 4.210 * [backup-simplify]: Simplify (/ 1 1) into 1 4.210 * [taylor]: Taking taylor expansion of 1.0 in k 4.210 * [backup-simplify]: Simplify 1.0 into 1.0 4.210 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.210 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.210 * [taylor]: Taking taylor expansion of -2.0 in k 4.210 * [backup-simplify]: Simplify -2.0 into -2.0 4.210 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.210 * [taylor]: Taking taylor expansion of PI in k 4.210 * [backup-simplify]: Simplify PI into PI 4.210 * [taylor]: Taking taylor expansion of n in k 4.210 * [backup-simplify]: Simplify n into n 4.210 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.210 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.211 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.211 * [backup-simplify]: Simplify (+ 1 0) into 1 4.211 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 4.212 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 4.212 * [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)))))) 4.212 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 4.212 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.212 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.212 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 4.212 * [taylor]: Taking taylor expansion of 0.5 in n 4.212 * [backup-simplify]: Simplify 0.5 into 0.5 4.212 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.212 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.212 * [taylor]: Taking taylor expansion of k in n 4.212 * [backup-simplify]: Simplify k into k 4.212 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.212 * [taylor]: Taking taylor expansion of 1.0 in n 4.212 * [backup-simplify]: Simplify 1.0 into 1.0 4.212 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.212 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.212 * [taylor]: Taking taylor expansion of -2.0 in n 4.213 * [backup-simplify]: Simplify -2.0 into -2.0 4.213 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.213 * [taylor]: Taking taylor expansion of PI in n 4.213 * [backup-simplify]: Simplify PI into PI 4.213 * [taylor]: Taking taylor expansion of n in n 4.213 * [backup-simplify]: Simplify 0 into 0 4.213 * [backup-simplify]: Simplify 1 into 1 4.213 * [backup-simplify]: Simplify (/ PI 1) into PI 4.214 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.215 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.215 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.215 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 4.217 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.218 * [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)))) 4.219 * [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))))) 4.219 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 4.219 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.219 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.219 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 4.219 * [taylor]: Taking taylor expansion of 0.5 in n 4.219 * [backup-simplify]: Simplify 0.5 into 0.5 4.219 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.219 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.219 * [taylor]: Taking taylor expansion of k in n 4.219 * [backup-simplify]: Simplify k into k 4.219 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.219 * [taylor]: Taking taylor expansion of 1.0 in n 4.219 * [backup-simplify]: Simplify 1.0 into 1.0 4.220 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.220 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.220 * [taylor]: Taking taylor expansion of -2.0 in n 4.220 * [backup-simplify]: Simplify -2.0 into -2.0 4.220 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.220 * [taylor]: Taking taylor expansion of PI in n 4.220 * [backup-simplify]: Simplify PI into PI 4.220 * [taylor]: Taking taylor expansion of n in n 4.220 * [backup-simplify]: Simplify 0 into 0 4.220 * [backup-simplify]: Simplify 1 into 1 4.221 * [backup-simplify]: Simplify (/ PI 1) into PI 4.221 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.222 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.222 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.223 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 4.224 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.226 * [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)))) 4.227 * [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))))) 4.227 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.227 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.227 * [taylor]: Taking taylor expansion of 0.5 in k 4.227 * [backup-simplify]: Simplify 0.5 into 0.5 4.227 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.227 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.227 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.227 * [taylor]: Taking taylor expansion of k in k 4.227 * [backup-simplify]: Simplify 0 into 0 4.227 * [backup-simplify]: Simplify 1 into 1 4.228 * [backup-simplify]: Simplify (/ 1 1) into 1 4.228 * [taylor]: Taking taylor expansion of 1.0 in k 4.228 * [backup-simplify]: Simplify 1.0 into 1.0 4.228 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.228 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.228 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.228 * [taylor]: Taking taylor expansion of -2.0 in k 4.228 * [backup-simplify]: Simplify -2.0 into -2.0 4.228 * [taylor]: Taking taylor expansion of PI in k 4.228 * [backup-simplify]: Simplify PI into PI 4.229 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.230 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.230 * [taylor]: Taking taylor expansion of (log n) in k 4.230 * [taylor]: Taking taylor expansion of n in k 4.230 * [backup-simplify]: Simplify n into n 4.230 * [backup-simplify]: Simplify (log n) into (log n) 4.230 * [backup-simplify]: Simplify (+ 1 0) into 1 4.230 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.231 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 4.233 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 4.234 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 4.235 * [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))))) 4.236 * [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))))) 4.237 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.238 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.240 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.240 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.241 * [backup-simplify]: Simplify (+ 0 0) into 0 4.241 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 4.243 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.244 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.246 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.246 * [taylor]: Taking taylor expansion of 0 in k 4.246 * [backup-simplify]: Simplify 0 into 0 4.246 * [backup-simplify]: Simplify 0 into 0 4.246 * [backup-simplify]: Simplify 0 into 0 4.247 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.248 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.252 * [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 4.252 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.253 * [backup-simplify]: Simplify (+ 0 0) into 0 4.253 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 4.255 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.256 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 4.259 * [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 4.259 * [taylor]: Taking taylor expansion of 0 in k 4.259 * [backup-simplify]: Simplify 0 into 0 4.259 * [backup-simplify]: Simplify 0 into 0 4.259 * [backup-simplify]: Simplify 0 into 0 4.259 * [backup-simplify]: Simplify 0 into 0 4.260 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.266 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.272 * [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 4.273 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.273 * [backup-simplify]: Simplify (+ 0 0) into 0 4.274 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 4.276 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.278 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 4.281 * [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 4.281 * [taylor]: Taking taylor expansion of 0 in k 4.281 * [backup-simplify]: Simplify 0 into 0 4.281 * [backup-simplify]: Simplify 0 into 0 4.283 * [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)))))) 4.283 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 4.283 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 4.283 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 4.283 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.283 * [taylor]: Taking taylor expansion of 1.0 in k 4.283 * [backup-simplify]: Simplify 1.0 into 1.0 4.283 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.283 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.283 * [taylor]: Taking taylor expansion of k in k 4.283 * [backup-simplify]: Simplify 0 into 0 4.283 * [backup-simplify]: Simplify 1 into 1 4.284 * [backup-simplify]: Simplify (/ 1 1) into 1 4.284 * [backup-simplify]: Simplify (sqrt 0) into 0 4.286 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.286 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.286 * [taylor]: Taking taylor expansion of 1.0 in k 4.286 * [backup-simplify]: Simplify 1.0 into 1.0 4.286 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.286 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.286 * [taylor]: Taking taylor expansion of k in k 4.286 * [backup-simplify]: Simplify 0 into 0 4.286 * [backup-simplify]: Simplify 1 into 1 4.286 * [backup-simplify]: Simplify (/ 1 1) into 1 4.287 * [backup-simplify]: Simplify (sqrt 0) into 0 4.288 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.288 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.288 * [backup-simplify]: Simplify 0 into 0 4.289 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.289 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.289 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 4.291 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.292 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.292 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.293 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.295 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.296 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.297 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.297 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 4.297 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 4.297 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 4.297 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.298 * [taylor]: Taking taylor expansion of 1.0 in k 4.298 * [backup-simplify]: Simplify 1.0 into 1.0 4.298 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.298 * [taylor]: Taking taylor expansion of k in k 4.298 * [backup-simplify]: Simplify 0 into 0 4.298 * [backup-simplify]: Simplify 1 into 1 4.298 * [backup-simplify]: Simplify (sqrt 0) into 0 4.299 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.299 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.299 * [taylor]: Taking taylor expansion of 1.0 in k 4.299 * [backup-simplify]: Simplify 1.0 into 1.0 4.299 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.299 * [taylor]: Taking taylor expansion of k in k 4.299 * [backup-simplify]: Simplify 0 into 0 4.299 * [backup-simplify]: Simplify 1 into 1 4.299 * [backup-simplify]: Simplify (sqrt 0) into 0 4.300 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.300 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.300 * [backup-simplify]: Simplify 0 into 0 4.301 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.301 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.303 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.304 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.304 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.306 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.308 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.308 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.309 * [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)))))))) 4.309 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 4.309 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 4.309 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.309 * [taylor]: Taking taylor expansion of 1.0 in k 4.309 * [backup-simplify]: Simplify 1.0 into 1.0 4.309 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.309 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.309 * [taylor]: Taking taylor expansion of -1 in k 4.310 * [backup-simplify]: Simplify -1 into -1 4.310 * [taylor]: Taking taylor expansion of k in k 4.310 * [backup-simplify]: Simplify 0 into 0 4.310 * [backup-simplify]: Simplify 1 into 1 4.310 * [backup-simplify]: Simplify (/ -1 1) into -1 4.310 * [backup-simplify]: Simplify (sqrt 0) into 0 4.311 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.311 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.311 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.311 * [taylor]: Taking taylor expansion of 1.0 in k 4.311 * [backup-simplify]: Simplify 1.0 into 1.0 4.311 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.311 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.311 * [taylor]: Taking taylor expansion of -1 in k 4.311 * [backup-simplify]: Simplify -1 into -1 4.311 * [taylor]: Taking taylor expansion of k in k 4.311 * [backup-simplify]: Simplify 0 into 0 4.311 * [backup-simplify]: Simplify 1 into 1 4.312 * [backup-simplify]: Simplify (/ -1 1) into -1 4.312 * [backup-simplify]: Simplify (sqrt 0) into 0 4.313 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.313 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.313 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.313 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 4.315 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.318 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 4.318 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.319 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.323 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.327 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 4.328 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.329 * [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))))) 4.329 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 4.330 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 4.330 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 4.330 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.330 * [taylor]: Taking taylor expansion of 2.0 in n 4.330 * [backup-simplify]: Simplify 2.0 into 2.0 4.330 * [taylor]: Taking taylor expansion of (* n PI) in n 4.330 * [taylor]: Taking taylor expansion of n in n 4.330 * [backup-simplify]: Simplify 0 into 0 4.330 * [backup-simplify]: Simplify 1 into 1 4.330 * [taylor]: Taking taylor expansion of PI in n 4.330 * [backup-simplify]: Simplify PI into PI 4.330 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.330 * [taylor]: Taking taylor expansion of 2.0 in n 4.330 * [backup-simplify]: Simplify 2.0 into 2.0 4.330 * [taylor]: Taking taylor expansion of (* n PI) in n 4.330 * [taylor]: Taking taylor expansion of n in n 4.330 * [backup-simplify]: Simplify 0 into 0 4.330 * [backup-simplify]: Simplify 1 into 1 4.330 * [taylor]: Taking taylor expansion of PI in n 4.330 * [backup-simplify]: Simplify PI into PI 4.331 * [backup-simplify]: Simplify (* 0 PI) into 0 4.331 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.331 * [backup-simplify]: Simplify 0 into 0 4.333 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.334 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.335 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.336 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.337 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.337 * [backup-simplify]: Simplify 0 into 0 4.338 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.339 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.339 * [backup-simplify]: Simplify 0 into 0 4.341 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.342 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 4.342 * [backup-simplify]: Simplify 0 into 0 4.344 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.345 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 4.345 * [backup-simplify]: Simplify 0 into 0 4.347 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.349 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 4.349 * [backup-simplify]: Simplify 0 into 0 4.351 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 4.353 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 4.353 * [backup-simplify]: Simplify 0 into 0 4.353 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 4.354 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 4.354 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 4.354 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.354 * [taylor]: Taking taylor expansion of 2.0 in n 4.354 * [backup-simplify]: Simplify 2.0 into 2.0 4.354 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.354 * [taylor]: Taking taylor expansion of PI in n 4.354 * [backup-simplify]: Simplify PI into PI 4.354 * [taylor]: Taking taylor expansion of n in n 4.354 * [backup-simplify]: Simplify 0 into 0 4.354 * [backup-simplify]: Simplify 1 into 1 4.354 * [backup-simplify]: Simplify (/ PI 1) into PI 4.355 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.355 * [taylor]: Taking taylor expansion of 2.0 in n 4.355 * [backup-simplify]: Simplify 2.0 into 2.0 4.355 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.355 * [taylor]: Taking taylor expansion of PI in n 4.355 * [backup-simplify]: Simplify PI into PI 4.355 * [taylor]: Taking taylor expansion of n in n 4.355 * [backup-simplify]: Simplify 0 into 0 4.355 * [backup-simplify]: Simplify 1 into 1 4.355 * [backup-simplify]: Simplify (/ PI 1) into PI 4.356 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.356 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.357 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.358 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.358 * [backup-simplify]: Simplify 0 into 0 4.359 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.360 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.360 * [backup-simplify]: Simplify 0 into 0 4.361 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.362 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.362 * [backup-simplify]: Simplify 0 into 0 4.364 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.365 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.365 * [backup-simplify]: Simplify 0 into 0 4.366 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.367 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.368 * [backup-simplify]: Simplify 0 into 0 4.368 * [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 4.369 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.369 * [backup-simplify]: Simplify 0 into 0 4.370 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 4.370 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 4.370 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 4.370 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.370 * [taylor]: Taking taylor expansion of -2.0 in n 4.370 * [backup-simplify]: Simplify -2.0 into -2.0 4.370 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.370 * [taylor]: Taking taylor expansion of PI in n 4.370 * [backup-simplify]: Simplify PI into PI 4.370 * [taylor]: Taking taylor expansion of n in n 4.370 * [backup-simplify]: Simplify 0 into 0 4.370 * [backup-simplify]: Simplify 1 into 1 4.371 * [backup-simplify]: Simplify (/ PI 1) into PI 4.371 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.371 * [taylor]: Taking taylor expansion of -2.0 in n 4.371 * [backup-simplify]: Simplify -2.0 into -2.0 4.371 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.371 * [taylor]: Taking taylor expansion of PI in n 4.371 * [backup-simplify]: Simplify PI into PI 4.371 * [taylor]: Taking taylor expansion of n in n 4.371 * [backup-simplify]: Simplify 0 into 0 4.371 * [backup-simplify]: Simplify 1 into 1 4.371 * [backup-simplify]: Simplify (/ PI 1) into PI 4.372 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.372 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.372 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.373 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.373 * [backup-simplify]: Simplify 0 into 0 4.373 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.374 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.374 * [backup-simplify]: Simplify 0 into 0 4.375 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.376 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.376 * [backup-simplify]: Simplify 0 into 0 4.376 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.377 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.377 * [backup-simplify]: Simplify 0 into 0 4.378 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.379 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.379 * [backup-simplify]: Simplify 0 into 0 4.379 * [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 4.380 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.380 * [backup-simplify]: Simplify 0 into 0 4.380 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 4.380 * * * * [progress]: [ 4 / 4 ] generating series at (2) 4.381 * [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))))) 4.381 * [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 4.381 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 4.381 * [taylor]: Taking taylor expansion of 1.0 in n 4.381 * [backup-simplify]: Simplify 1.0 into 1.0 4.381 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 4.381 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 4.381 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.381 * [taylor]: Taking taylor expansion of k in n 4.381 * [backup-simplify]: Simplify k into k 4.381 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.382 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 4.382 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.382 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 4.382 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 4.382 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.382 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.382 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 4.382 * [taylor]: Taking taylor expansion of 0.5 in n 4.382 * [backup-simplify]: Simplify 0.5 into 0.5 4.382 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.382 * [taylor]: Taking taylor expansion of 1.0 in n 4.382 * [backup-simplify]: Simplify 1.0 into 1.0 4.382 * [taylor]: Taking taylor expansion of k in n 4.382 * [backup-simplify]: Simplify k into k 4.382 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.382 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.382 * [taylor]: Taking taylor expansion of 2.0 in n 4.382 * [backup-simplify]: Simplify 2.0 into 2.0 4.382 * [taylor]: Taking taylor expansion of (* n PI) in n 4.382 * [taylor]: Taking taylor expansion of n in n 4.382 * [backup-simplify]: Simplify 0 into 0 4.382 * [backup-simplify]: Simplify 1 into 1 4.382 * [taylor]: Taking taylor expansion of PI in n 4.382 * [backup-simplify]: Simplify PI into PI 4.382 * [backup-simplify]: Simplify (* 0 PI) into 0 4.386 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.387 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.388 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.389 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.389 * [backup-simplify]: Simplify (- k) into (- k) 4.389 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.389 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 4.390 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.391 * [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)))) 4.391 * [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))))) 4.392 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 4.392 * [taylor]: Taking taylor expansion of 1.0 in k 4.392 * [backup-simplify]: Simplify 1.0 into 1.0 4.392 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 4.392 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.392 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.392 * [taylor]: Taking taylor expansion of k in k 4.392 * [backup-simplify]: Simplify 0 into 0 4.392 * [backup-simplify]: Simplify 1 into 1 4.392 * [backup-simplify]: Simplify (/ 1 1) into 1 4.392 * [backup-simplify]: Simplify (sqrt 0) into 0 4.393 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.393 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 4.393 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.393 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.393 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 4.393 * [taylor]: Taking taylor expansion of 0.5 in k 4.393 * [backup-simplify]: Simplify 0.5 into 0.5 4.393 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.393 * [taylor]: Taking taylor expansion of 1.0 in k 4.393 * [backup-simplify]: Simplify 1.0 into 1.0 4.393 * [taylor]: Taking taylor expansion of k in k 4.393 * [backup-simplify]: Simplify 0 into 0 4.393 * [backup-simplify]: Simplify 1 into 1 4.393 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.393 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.393 * [taylor]: Taking taylor expansion of 2.0 in k 4.393 * [backup-simplify]: Simplify 2.0 into 2.0 4.393 * [taylor]: Taking taylor expansion of (* n PI) in k 4.393 * [taylor]: Taking taylor expansion of n in k 4.393 * [backup-simplify]: Simplify n into n 4.393 * [taylor]: Taking taylor expansion of PI in k 4.393 * [backup-simplify]: Simplify PI into PI 4.393 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.394 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.394 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.394 * [backup-simplify]: Simplify (- 0) into 0 4.394 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.394 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 4.394 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 4.395 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 4.395 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 4.395 * [taylor]: Taking taylor expansion of 1.0 in k 4.395 * [backup-simplify]: Simplify 1.0 into 1.0 4.395 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 4.395 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.395 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.395 * [taylor]: Taking taylor expansion of k in k 4.395 * [backup-simplify]: Simplify 0 into 0 4.395 * [backup-simplify]: Simplify 1 into 1 4.395 * [backup-simplify]: Simplify (/ 1 1) into 1 4.395 * [backup-simplify]: Simplify (sqrt 0) into 0 4.396 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.396 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 4.396 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.396 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.396 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 4.396 * [taylor]: Taking taylor expansion of 0.5 in k 4.396 * [backup-simplify]: Simplify 0.5 into 0.5 4.396 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.396 * [taylor]: Taking taylor expansion of 1.0 in k 4.396 * [backup-simplify]: Simplify 1.0 into 1.0 4.396 * [taylor]: Taking taylor expansion of k in k 4.396 * [backup-simplify]: Simplify 0 into 0 4.396 * [backup-simplify]: Simplify 1 into 1 4.396 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.396 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.396 * [taylor]: Taking taylor expansion of 2.0 in k 4.396 * [backup-simplify]: Simplify 2.0 into 2.0 4.396 * [taylor]: Taking taylor expansion of (* n PI) in k 4.396 * [taylor]: Taking taylor expansion of n in k 4.396 * [backup-simplify]: Simplify n into n 4.396 * [taylor]: Taking taylor expansion of PI in k 4.396 * [backup-simplify]: Simplify PI into PI 4.396 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.396 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.396 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.397 * [backup-simplify]: Simplify (- 0) into 0 4.397 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.397 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 4.397 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 4.397 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 4.398 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 4.398 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.398 * [taylor]: Taking taylor expansion of 0 in n 4.398 * [backup-simplify]: Simplify 0 into 0 4.398 * [backup-simplify]: Simplify 0 into 0 4.398 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 4.399 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 4.399 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 4.399 * [backup-simplify]: Simplify (- 1) into -1 4.400 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.401 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 4.401 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 4.401 * [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))) 4.402 * [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))) 4.404 * [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))) 4.404 * [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 4.404 * [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 4.404 * [taylor]: Taking taylor expansion of +nan.0 in n 4.404 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.404 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 4.404 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 4.404 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 4.404 * [taylor]: Taking taylor expansion of 0.5 in n 4.404 * [backup-simplify]: Simplify 0.5 into 0.5 4.404 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 4.404 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 4.404 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.404 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.404 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.404 * [taylor]: Taking taylor expansion of 1.0 in n 4.404 * [backup-simplify]: Simplify 1.0 into 1.0 4.404 * [taylor]: Taking taylor expansion of (log PI) in n 4.404 * [taylor]: Taking taylor expansion of PI in n 4.404 * [backup-simplify]: Simplify PI into PI 4.404 * [backup-simplify]: Simplify (log PI) into (log PI) 4.405 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.406 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.406 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 4.406 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.406 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.406 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.406 * [taylor]: Taking taylor expansion of 1.0 in n 4.406 * [backup-simplify]: Simplify 1.0 into 1.0 4.406 * [taylor]: Taking taylor expansion of (log n) in n 4.406 * [taylor]: Taking taylor expansion of n in n 4.406 * [backup-simplify]: Simplify 0 into 0 4.406 * [backup-simplify]: Simplify 1 into 1 4.406 * [backup-simplify]: Simplify (log 1) into 0 4.407 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.407 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.407 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.407 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.407 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.407 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.407 * [taylor]: Taking taylor expansion of 1.0 in n 4.407 * [backup-simplify]: Simplify 1.0 into 1.0 4.407 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.407 * [taylor]: Taking taylor expansion of 2.0 in n 4.407 * [backup-simplify]: Simplify 2.0 into 2.0 4.407 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.409 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.410 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.411 * [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) 4.412 * [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) 4.413 * [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)) 4.415 * [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))) 4.416 * [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) 4.418 * [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)) 4.419 * [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))) 4.420 * [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))) 4.420 * [backup-simplify]: Simplify 0 into 0 4.421 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 4.422 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 4.424 * [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 4.424 * [backup-simplify]: Simplify (- 0) into 0 4.425 * [backup-simplify]: Simplify (+ 0 0) into 0 4.426 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 4.427 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 4.428 * [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))) 4.429 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 4.432 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.435 * [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)))))))) 4.441 * [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)))))))) 4.441 * [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 4.441 * [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 4.441 * [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 4.441 * [taylor]: Taking taylor expansion of +nan.0 in n 4.441 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.441 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 4.441 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 4.441 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 4.441 * [taylor]: Taking taylor expansion of 0.5 in n 4.441 * [backup-simplify]: Simplify 0.5 into 0.5 4.441 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 4.441 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 4.441 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.441 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.441 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.441 * [taylor]: Taking taylor expansion of 1.0 in n 4.441 * [backup-simplify]: Simplify 1.0 into 1.0 4.441 * [taylor]: Taking taylor expansion of (log PI) in n 4.442 * [taylor]: Taking taylor expansion of PI in n 4.442 * [backup-simplify]: Simplify PI into PI 4.442 * [backup-simplify]: Simplify (log PI) into (log PI) 4.443 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.445 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.445 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 4.445 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.445 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.445 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.445 * [taylor]: Taking taylor expansion of 1.0 in n 4.445 * [backup-simplify]: Simplify 1.0 into 1.0 4.445 * [taylor]: Taking taylor expansion of (log n) in n 4.445 * [taylor]: Taking taylor expansion of n in n 4.445 * [backup-simplify]: Simplify 0 into 0 4.445 * [backup-simplify]: Simplify 1 into 1 4.445 * [backup-simplify]: Simplify (log 1) into 0 4.446 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.446 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.446 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.446 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.446 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.446 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.446 * [taylor]: Taking taylor expansion of 1.0 in n 4.446 * [backup-simplify]: Simplify 1.0 into 1.0 4.446 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.446 * [taylor]: Taking taylor expansion of 2.0 in n 4.446 * [backup-simplify]: Simplify 2.0 into 2.0 4.447 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.448 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.449 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.450 * [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) 4.451 * [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) 4.452 * [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)) 4.454 * [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))) 4.455 * [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) 4.455 * [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 4.456 * [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 4.456 * [taylor]: Taking taylor expansion of +nan.0 in n 4.456 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.456 * [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 4.456 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 4.456 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 4.456 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 4.456 * [taylor]: Taking taylor expansion of 0.5 in n 4.456 * [backup-simplify]: Simplify 0.5 into 0.5 4.456 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 4.456 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 4.456 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.456 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.456 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.456 * [taylor]: Taking taylor expansion of 1.0 in n 4.456 * [backup-simplify]: Simplify 1.0 into 1.0 4.456 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.456 * [taylor]: Taking taylor expansion of 2.0 in n 4.456 * [backup-simplify]: Simplify 2.0 into 2.0 4.457 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.458 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.459 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.459 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 4.459 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.459 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.459 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.459 * [taylor]: Taking taylor expansion of 1.0 in n 4.459 * [backup-simplify]: Simplify 1.0 into 1.0 4.459 * [taylor]: Taking taylor expansion of (log PI) in n 4.459 * [taylor]: Taking taylor expansion of PI in n 4.459 * [backup-simplify]: Simplify PI into PI 4.460 * [backup-simplify]: Simplify (log PI) into (log PI) 4.461 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.463 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.463 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.463 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.463 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.463 * [taylor]: Taking taylor expansion of 1.0 in n 4.463 * [backup-simplify]: Simplify 1.0 into 1.0 4.463 * [taylor]: Taking taylor expansion of (log n) in n 4.463 * [taylor]: Taking taylor expansion of n in n 4.463 * [backup-simplify]: Simplify 0 into 0 4.463 * [backup-simplify]: Simplify 1 into 1 4.463 * [backup-simplify]: Simplify (log 1) into 0 4.464 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.464 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.464 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.465 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 4.466 * [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) 4.467 * [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)) 4.469 * [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))) 4.471 * [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) 4.471 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.471 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.471 * [taylor]: Taking taylor expansion of 2.0 in n 4.471 * [backup-simplify]: Simplify 2.0 into 2.0 4.471 * [taylor]: Taking taylor expansion of (* n PI) in n 4.471 * [taylor]: Taking taylor expansion of n in n 4.471 * [backup-simplify]: Simplify 0 into 0 4.471 * [backup-simplify]: Simplify 1 into 1 4.471 * [taylor]: Taking taylor expansion of PI in n 4.471 * [backup-simplify]: Simplify PI into PI 4.471 * [backup-simplify]: Simplify (* 0 PI) into 0 4.472 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.473 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.475 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.476 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.478 * [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)) 4.480 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.483 * [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)) 4.485 * [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))) 4.488 * [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)))))) 4.494 * [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)))))))) 4.500 * [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)))))))) 4.505 * [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)))))))) 4.506 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 4.506 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 4.507 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 4.508 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 4.508 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.509 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 4.509 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 4.510 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 4.510 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 4.511 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 4.512 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 4.513 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 4.514 * [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 4.515 * [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 4.516 * [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 4.521 * [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 4.522 * [backup-simplify]: Simplify (- 0) into 0 4.522 * [backup-simplify]: Simplify 0 into 0 4.522 * [backup-simplify]: Simplify 0 into 0 4.522 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.523 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 4.525 * [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 4.525 * [backup-simplify]: Simplify (- 0) into 0 4.525 * [backup-simplify]: Simplify (+ 0 0) into 0 4.526 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 4.527 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 4.528 * [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))) 4.529 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.531 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.537 * [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)))))))) 4.548 * [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)))))))) 4.548 * [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 4.548 * [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 4.548 * [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 4.548 * [taylor]: Taking taylor expansion of +nan.0 in n 4.548 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.548 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 4.548 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 4.548 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 4.548 * [taylor]: Taking taylor expansion of 0.5 in n 4.548 * [backup-simplify]: Simplify 0.5 into 0.5 4.548 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 4.548 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 4.548 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.548 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.548 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.548 * [taylor]: Taking taylor expansion of 1.0 in n 4.548 * [backup-simplify]: Simplify 1.0 into 1.0 4.548 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.548 * [taylor]: Taking taylor expansion of 2.0 in n 4.548 * [backup-simplify]: Simplify 2.0 into 2.0 4.549 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.549 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.550 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.550 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 4.550 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.550 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.550 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.550 * [taylor]: Taking taylor expansion of 1.0 in n 4.550 * [backup-simplify]: Simplify 1.0 into 1.0 4.550 * [taylor]: Taking taylor expansion of (log n) in n 4.550 * [taylor]: Taking taylor expansion of n in n 4.550 * [backup-simplify]: Simplify 0 into 0 4.550 * [backup-simplify]: Simplify 1 into 1 4.550 * [backup-simplify]: Simplify (log 1) into 0 4.551 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.551 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.551 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.551 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.551 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.551 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.551 * [taylor]: Taking taylor expansion of 1.0 in n 4.551 * [backup-simplify]: Simplify 1.0 into 1.0 4.551 * [taylor]: Taking taylor expansion of (log PI) in n 4.551 * [taylor]: Taking taylor expansion of PI in n 4.551 * [backup-simplify]: Simplify PI into PI 4.551 * [backup-simplify]: Simplify (log PI) into (log PI) 4.552 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.553 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.553 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 4.554 * [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) 4.555 * [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)) 4.556 * [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))) 4.556 * [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) 4.557 * [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 4.557 * [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 4.557 * [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 4.557 * [taylor]: Taking taylor expansion of +nan.0 in n 4.557 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.557 * [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 4.557 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 4.557 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 4.557 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 4.557 * [taylor]: Taking taylor expansion of 0.5 in n 4.557 * [backup-simplify]: Simplify 0.5 into 0.5 4.557 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 4.557 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 4.557 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.557 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.557 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.557 * [taylor]: Taking taylor expansion of 1.0 in n 4.557 * [backup-simplify]: Simplify 1.0 into 1.0 4.557 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.557 * [taylor]: Taking taylor expansion of 2.0 in n 4.557 * [backup-simplify]: Simplify 2.0 into 2.0 4.557 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.558 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.559 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.559 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 4.559 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.559 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.559 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.559 * [taylor]: Taking taylor expansion of 1.0 in n 4.559 * [backup-simplify]: Simplify 1.0 into 1.0 4.559 * [taylor]: Taking taylor expansion of (log PI) in n 4.559 * [taylor]: Taking taylor expansion of PI in n 4.559 * [backup-simplify]: Simplify PI into PI 4.559 * [backup-simplify]: Simplify (log PI) into (log PI) 4.560 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.561 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.561 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.561 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.561 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.561 * [taylor]: Taking taylor expansion of 1.0 in n 4.561 * [backup-simplify]: Simplify 1.0 into 1.0 4.561 * [taylor]: Taking taylor expansion of (log n) in n 4.561 * [taylor]: Taking taylor expansion of n in n 4.561 * [backup-simplify]: Simplify 0 into 0 4.561 * [backup-simplify]: Simplify 1 into 1 4.561 * [backup-simplify]: Simplify (log 1) into 0 4.561 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.561 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.561 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.562 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 4.563 * [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) 4.563 * [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)) 4.564 * [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))) 4.565 * [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) 4.565 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.565 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.565 * [taylor]: Taking taylor expansion of 2.0 in n 4.565 * [backup-simplify]: Simplify 2.0 into 2.0 4.565 * [taylor]: Taking taylor expansion of (* n PI) in n 4.565 * [taylor]: Taking taylor expansion of n in n 4.565 * [backup-simplify]: Simplify 0 into 0 4.565 * [backup-simplify]: Simplify 1 into 1 4.565 * [taylor]: Taking taylor expansion of PI in n 4.565 * [backup-simplify]: Simplify PI into PI 4.566 * [backup-simplify]: Simplify (* 0 PI) into 0 4.566 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.567 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.568 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.569 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.569 * [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 4.569 * [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 4.569 * [taylor]: Taking taylor expansion of +nan.0 in n 4.569 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.569 * [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 4.569 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 4.569 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 4.569 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 4.569 * [taylor]: Taking taylor expansion of 0.5 in n 4.569 * [backup-simplify]: Simplify 0.5 into 0.5 4.569 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 4.569 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 4.569 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.569 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.569 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.569 * [taylor]: Taking taylor expansion of 1.0 in n 4.569 * [backup-simplify]: Simplify 1.0 into 1.0 4.569 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.569 * [taylor]: Taking taylor expansion of 2.0 in n 4.569 * [backup-simplify]: Simplify 2.0 into 2.0 4.569 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.570 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.571 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.571 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 4.571 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.571 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.571 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.571 * [taylor]: Taking taylor expansion of 1.0 in n 4.571 * [backup-simplify]: Simplify 1.0 into 1.0 4.571 * [taylor]: Taking taylor expansion of (log PI) in n 4.571 * [taylor]: Taking taylor expansion of PI in n 4.571 * [backup-simplify]: Simplify PI into PI 4.571 * [backup-simplify]: Simplify (log PI) into (log PI) 4.572 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.573 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.573 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.573 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.573 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.573 * [taylor]: Taking taylor expansion of 1.0 in n 4.573 * [backup-simplify]: Simplify 1.0 into 1.0 4.573 * [taylor]: Taking taylor expansion of (log n) in n 4.573 * [taylor]: Taking taylor expansion of n in n 4.573 * [backup-simplify]: Simplify 0 into 0 4.573 * [backup-simplify]: Simplify 1 into 1 4.573 * [backup-simplify]: Simplify (log 1) into 0 4.573 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.574 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.574 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.574 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 4.575 * [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) 4.576 * [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)) 4.576 * [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))) 4.577 * [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) 4.577 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 4.577 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.577 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.577 * [taylor]: Taking taylor expansion of 2.0 in n 4.577 * [backup-simplify]: Simplify 2.0 into 2.0 4.577 * [taylor]: Taking taylor expansion of (* n PI) in n 4.578 * [taylor]: Taking taylor expansion of n in n 4.578 * [backup-simplify]: Simplify 0 into 0 4.578 * [backup-simplify]: Simplify 1 into 1 4.578 * [taylor]: Taking taylor expansion of PI in n 4.578 * [backup-simplify]: Simplify PI into PI 4.578 * [backup-simplify]: Simplify (* 0 PI) into 0 4.578 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.579 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.580 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.581 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.583 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.585 * [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)) 4.586 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.588 * [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)) 4.591 * [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))) 4.592 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.593 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.594 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 4.596 * [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)) 4.597 * [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))) 4.599 * [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)))))))) 4.606 * [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)))))))))))) 4.614 * [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)))))))))))) 4.636 * [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)))))))))))))) 4.655 * [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)))))))))))))) 4.670 * [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)))))))))))))) 4.686 * [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)))))))))))))))))))))) 4.687 * [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)))))) 4.687 * [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 4.687 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 4.687 * [taylor]: Taking taylor expansion of 1.0 in n 4.687 * [backup-simplify]: Simplify 1.0 into 1.0 4.687 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 4.687 * [taylor]: Taking taylor expansion of (sqrt k) in n 4.687 * [taylor]: Taking taylor expansion of k in n 4.687 * [backup-simplify]: Simplify k into k 4.687 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 4.687 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 4.687 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 4.687 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.687 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.687 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 4.687 * [taylor]: Taking taylor expansion of 0.5 in n 4.687 * [backup-simplify]: Simplify 0.5 into 0.5 4.687 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.687 * [taylor]: Taking taylor expansion of 1.0 in n 4.687 * [backup-simplify]: Simplify 1.0 into 1.0 4.687 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.687 * [taylor]: Taking taylor expansion of k in n 4.687 * [backup-simplify]: Simplify k into k 4.687 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.687 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.688 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.688 * [taylor]: Taking taylor expansion of 2.0 in n 4.688 * [backup-simplify]: Simplify 2.0 into 2.0 4.688 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.688 * [taylor]: Taking taylor expansion of PI in n 4.688 * [backup-simplify]: Simplify PI into PI 4.688 * [taylor]: Taking taylor expansion of n in n 4.688 * [backup-simplify]: Simplify 0 into 0 4.688 * [backup-simplify]: Simplify 1 into 1 4.688 * [backup-simplify]: Simplify (/ PI 1) into PI 4.688 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.689 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.689 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.689 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.689 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 4.690 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.691 * [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)))) 4.692 * [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))))) 4.692 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 4.692 * [taylor]: Taking taylor expansion of 1.0 in k 4.692 * [backup-simplify]: Simplify 1.0 into 1.0 4.692 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 4.692 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.692 * [taylor]: Taking taylor expansion of k in k 4.692 * [backup-simplify]: Simplify 0 into 0 4.692 * [backup-simplify]: Simplify 1 into 1 4.692 * [backup-simplify]: Simplify (sqrt 0) into 0 4.693 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.693 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 4.693 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.693 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.693 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 4.693 * [taylor]: Taking taylor expansion of 0.5 in k 4.693 * [backup-simplify]: Simplify 0.5 into 0.5 4.693 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.693 * [taylor]: Taking taylor expansion of 1.0 in k 4.693 * [backup-simplify]: Simplify 1.0 into 1.0 4.693 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.693 * [taylor]: Taking taylor expansion of k in k 4.693 * [backup-simplify]: Simplify 0 into 0 4.693 * [backup-simplify]: Simplify 1 into 1 4.694 * [backup-simplify]: Simplify (/ 1 1) into 1 4.694 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.694 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.694 * [taylor]: Taking taylor expansion of 2.0 in k 4.694 * [backup-simplify]: Simplify 2.0 into 2.0 4.694 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.694 * [taylor]: Taking taylor expansion of PI in k 4.694 * [backup-simplify]: Simplify PI into PI 4.694 * [taylor]: Taking taylor expansion of n in k 4.694 * [backup-simplify]: Simplify n into n 4.694 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.694 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.694 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.694 * [backup-simplify]: Simplify (- 1) into -1 4.694 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.695 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 4.695 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 4.695 * [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))))) 4.695 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 4.695 * [taylor]: Taking taylor expansion of 1.0 in k 4.695 * [backup-simplify]: Simplify 1.0 into 1.0 4.695 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 4.695 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.695 * [taylor]: Taking taylor expansion of k in k 4.695 * [backup-simplify]: Simplify 0 into 0 4.695 * [backup-simplify]: Simplify 1 into 1 4.695 * [backup-simplify]: Simplify (sqrt 0) into 0 4.696 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.696 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 4.696 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.696 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.696 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 4.696 * [taylor]: Taking taylor expansion of 0.5 in k 4.696 * [backup-simplify]: Simplify 0.5 into 0.5 4.696 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.696 * [taylor]: Taking taylor expansion of 1.0 in k 4.696 * [backup-simplify]: Simplify 1.0 into 1.0 4.696 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.696 * [taylor]: Taking taylor expansion of k in k 4.697 * [backup-simplify]: Simplify 0 into 0 4.697 * [backup-simplify]: Simplify 1 into 1 4.697 * [backup-simplify]: Simplify (/ 1 1) into 1 4.697 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.697 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.697 * [taylor]: Taking taylor expansion of 2.0 in k 4.697 * [backup-simplify]: Simplify 2.0 into 2.0 4.697 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.697 * [taylor]: Taking taylor expansion of PI in k 4.697 * [backup-simplify]: Simplify PI into PI 4.697 * [taylor]: Taking taylor expansion of n in k 4.697 * [backup-simplify]: Simplify n into n 4.697 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.697 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.697 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.697 * [backup-simplify]: Simplify (- 1) into -1 4.698 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.698 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 4.698 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 4.698 * [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))))) 4.698 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 4.699 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.699 * [taylor]: Taking taylor expansion of 0 in n 4.699 * [backup-simplify]: Simplify 0 into 0 4.699 * [backup-simplify]: Simplify 0 into 0 4.699 * [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))))))) 4.700 * [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))))))) 4.700 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 4.700 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 4.700 * [taylor]: Taking taylor expansion of +nan.0 in n 4.700 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.700 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 4.700 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 4.700 * [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 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 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)) 4.703 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.703 * [taylor]: Taking taylor expansion of 1.0 in n 4.703 * [backup-simplify]: Simplify 1.0 into 1.0 4.703 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.703 * [taylor]: Taking taylor expansion of k in n 4.703 * [backup-simplify]: Simplify k into k 4.703 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.704 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.704 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.705 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.706 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 4.707 * [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)))) 4.708 * [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))))) 4.710 * [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)))))) 4.711 * [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))))))) 4.712 * [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))))))) 4.712 * [backup-simplify]: Simplify 0 into 0 4.715 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.716 * [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))))))) 4.717 * [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))))))) 4.717 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 4.717 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 4.717 * [taylor]: Taking taylor expansion of +nan.0 in n 4.717 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.717 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 4.717 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 4.717 * [taylor]: Taking taylor expansion of 0.5 in n 4.717 * [backup-simplify]: Simplify 0.5 into 0.5 4.717 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 4.717 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.717 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.717 * [taylor]: Taking taylor expansion of 2.0 in n 4.717 * [backup-simplify]: Simplify 2.0 into 2.0 4.717 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.717 * [taylor]: Taking taylor expansion of PI in n 4.717 * [backup-simplify]: Simplify PI into PI 4.717 * [taylor]: Taking taylor expansion of n in n 4.717 * [backup-simplify]: Simplify 0 into 0 4.717 * [backup-simplify]: Simplify 1 into 1 4.717 * [backup-simplify]: Simplify (/ PI 1) into PI 4.718 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.718 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.718 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.718 * [taylor]: Taking taylor expansion of 1.0 in n 4.718 * [backup-simplify]: Simplify 1.0 into 1.0 4.718 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.718 * [taylor]: Taking taylor expansion of k in n 4.718 * [backup-simplify]: Simplify k into k 4.719 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.719 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.719 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.720 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.720 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 4.721 * [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)))) 4.722 * [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))))) 4.722 * [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)))))) 4.723 * [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))))))) 4.724 * [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))))))) 4.725 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.725 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.725 * [backup-simplify]: Simplify (- 0) into 0 4.725 * [backup-simplify]: Simplify (+ 0 0) into 0 4.726 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.726 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.727 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.728 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.729 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 4.730 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.731 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 4.732 * [backup-simplify]: Simplify (- 0) into 0 4.732 * [backup-simplify]: Simplify 0 into 0 4.732 * [backup-simplify]: Simplify 0 into 0 4.734 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.735 * [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))))))) 4.736 * [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))))))) 4.736 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 4.736 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 4.736 * [taylor]: Taking taylor expansion of +nan.0 in n 4.736 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.736 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 4.736 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 4.736 * [taylor]: Taking taylor expansion of 0.5 in n 4.736 * [backup-simplify]: Simplify 0.5 into 0.5 4.736 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 4.736 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.736 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.736 * [taylor]: Taking taylor expansion of 2.0 in n 4.736 * [backup-simplify]: Simplify 2.0 into 2.0 4.736 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.736 * [taylor]: Taking taylor expansion of PI in n 4.736 * [backup-simplify]: Simplify PI into PI 4.736 * [taylor]: Taking taylor expansion of n in n 4.736 * [backup-simplify]: Simplify 0 into 0 4.736 * [backup-simplify]: Simplify 1 into 1 4.736 * [backup-simplify]: Simplify (/ PI 1) into PI 4.737 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.737 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.737 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.737 * [taylor]: Taking taylor expansion of 1.0 in n 4.737 * [backup-simplify]: Simplify 1.0 into 1.0 4.737 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.737 * [taylor]: Taking taylor expansion of k in n 4.737 * [backup-simplify]: Simplify k into k 4.737 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.738 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.738 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.738 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.740 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 4.741 * [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)))) 4.741 * [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))))) 4.747 * [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)))))) 4.749 * [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))))))) 4.750 * [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))))))) 4.755 * [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)))))))) 4.756 * [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)))) 4.756 * [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 4.756 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 4.756 * [taylor]: Taking taylor expansion of 1.0 in n 4.756 * [backup-simplify]: Simplify 1.0 into 1.0 4.756 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 4.756 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 4.756 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.756 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.756 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 4.756 * [taylor]: Taking taylor expansion of 0.5 in n 4.756 * [backup-simplify]: Simplify 0.5 into 0.5 4.756 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.756 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.756 * [taylor]: Taking taylor expansion of k in n 4.756 * [backup-simplify]: Simplify k into k 4.756 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.756 * [taylor]: Taking taylor expansion of 1.0 in n 4.756 * [backup-simplify]: Simplify 1.0 into 1.0 4.757 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.757 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.757 * [taylor]: Taking taylor expansion of -2.0 in n 4.757 * [backup-simplify]: Simplify -2.0 into -2.0 4.757 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.757 * [taylor]: Taking taylor expansion of PI in n 4.757 * [backup-simplify]: Simplify PI into PI 4.757 * [taylor]: Taking taylor expansion of n in n 4.757 * [backup-simplify]: Simplify 0 into 0 4.757 * [backup-simplify]: Simplify 1 into 1 4.757 * [backup-simplify]: Simplify (/ PI 1) into PI 4.758 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.759 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.759 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.759 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 4.760 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.762 * [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)))) 4.763 * [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))))) 4.763 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 4.763 * [taylor]: Taking taylor expansion of (/ -1 k) in n 4.763 * [taylor]: Taking taylor expansion of -1 in n 4.763 * [backup-simplify]: Simplify -1 into -1 4.763 * [taylor]: Taking taylor expansion of k in n 4.763 * [backup-simplify]: Simplify k into k 4.763 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 4.763 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 4.764 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 4.764 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 4.765 * [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))) 4.765 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 4.765 * [taylor]: Taking taylor expansion of 1.0 in k 4.765 * [backup-simplify]: Simplify 1.0 into 1.0 4.765 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 4.765 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 4.765 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.765 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.765 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 4.765 * [taylor]: Taking taylor expansion of 0.5 in k 4.766 * [backup-simplify]: Simplify 0.5 into 0.5 4.766 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.766 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.766 * [taylor]: Taking taylor expansion of k in k 4.766 * [backup-simplify]: Simplify 0 into 0 4.766 * [backup-simplify]: Simplify 1 into 1 4.766 * [backup-simplify]: Simplify (/ 1 1) into 1 4.766 * [taylor]: Taking taylor expansion of 1.0 in k 4.766 * [backup-simplify]: Simplify 1.0 into 1.0 4.766 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.766 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.766 * [taylor]: Taking taylor expansion of -2.0 in k 4.766 * [backup-simplify]: Simplify -2.0 into -2.0 4.766 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.766 * [taylor]: Taking taylor expansion of PI in k 4.767 * [backup-simplify]: Simplify PI into PI 4.767 * [taylor]: Taking taylor expansion of n in k 4.767 * [backup-simplify]: Simplify n into n 4.767 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.767 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.767 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.767 * [backup-simplify]: Simplify (+ 1 0) into 1 4.768 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 4.768 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 4.768 * [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)))))) 4.768 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.768 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.768 * [taylor]: Taking taylor expansion of -1 in k 4.768 * [backup-simplify]: Simplify -1 into -1 4.768 * [taylor]: Taking taylor expansion of k in k 4.768 * [backup-simplify]: Simplify 0 into 0 4.768 * [backup-simplify]: Simplify 1 into 1 4.769 * [backup-simplify]: Simplify (/ -1 1) into -1 4.769 * [backup-simplify]: Simplify (sqrt 0) into 0 4.771 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.771 * [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))))))) 4.771 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 4.771 * [taylor]: Taking taylor expansion of 1.0 in k 4.771 * [backup-simplify]: Simplify 1.0 into 1.0 4.771 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 4.771 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 4.771 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.771 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.771 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 4.772 * [taylor]: Taking taylor expansion of 0.5 in k 4.772 * [backup-simplify]: Simplify 0.5 into 0.5 4.772 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.772 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.772 * [taylor]: Taking taylor expansion of k in k 4.772 * [backup-simplify]: Simplify 0 into 0 4.772 * [backup-simplify]: Simplify 1 into 1 4.772 * [backup-simplify]: Simplify (/ 1 1) into 1 4.772 * [taylor]: Taking taylor expansion of 1.0 in k 4.772 * [backup-simplify]: Simplify 1.0 into 1.0 4.772 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.772 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.772 * [taylor]: Taking taylor expansion of -2.0 in k 4.772 * [backup-simplify]: Simplify -2.0 into -2.0 4.772 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.772 * [taylor]: Taking taylor expansion of PI in k 4.772 * [backup-simplify]: Simplify PI into PI 4.772 * [taylor]: Taking taylor expansion of n in k 4.772 * [backup-simplify]: Simplify n into n 4.773 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.773 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.773 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.773 * [backup-simplify]: Simplify (+ 1 0) into 1 4.774 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 4.774 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 4.774 * [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)))))) 4.774 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.774 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.774 * [taylor]: Taking taylor expansion of -1 in k 4.774 * [backup-simplify]: Simplify -1 into -1 4.774 * [taylor]: Taking taylor expansion of k in k 4.774 * [backup-simplify]: Simplify 0 into 0 4.774 * [backup-simplify]: Simplify 1 into 1 4.775 * [backup-simplify]: Simplify (/ -1 1) into -1 4.775 * [backup-simplify]: Simplify (sqrt 0) into 0 4.777 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.777 * [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))))))) 4.778 * [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))))))) 4.778 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 4.778 * [taylor]: Taking taylor expansion of +nan.0 in n 4.778 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.778 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 4.778 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 4.778 * [taylor]: Taking taylor expansion of 0.5 in n 4.778 * [backup-simplify]: Simplify 0.5 into 0.5 4.778 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 4.778 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.778 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.778 * [taylor]: Taking taylor expansion of k in n 4.778 * [backup-simplify]: Simplify k into k 4.778 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.778 * [taylor]: Taking taylor expansion of 1.0 in n 4.778 * [backup-simplify]: Simplify 1.0 into 1.0 4.778 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.779 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.779 * [taylor]: Taking taylor expansion of -2.0 in n 4.779 * [backup-simplify]: Simplify -2.0 into -2.0 4.779 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.779 * [taylor]: Taking taylor expansion of PI in n 4.779 * [backup-simplify]: Simplify PI into PI 4.779 * [taylor]: Taking taylor expansion of n in n 4.779 * [backup-simplify]: Simplify 0 into 0 4.779 * [backup-simplify]: Simplify 1 into 1 4.779 * [backup-simplify]: Simplify (/ PI 1) into PI 4.780 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.781 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.781 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.783 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.784 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 4.785 * [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)))) 4.786 * [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))))) 4.788 * [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)))))) 4.789 * [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)))))) 4.790 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 4.793 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.794 * [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)))))))) 4.795 * [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)))))))) 4.795 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 4.795 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 4.795 * [taylor]: Taking taylor expansion of +nan.0 in n 4.795 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.795 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 4.795 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 4.795 * [taylor]: Taking taylor expansion of 0.5 in n 4.795 * [backup-simplify]: Simplify 0.5 into 0.5 4.796 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 4.796 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.796 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.796 * [taylor]: Taking taylor expansion of k in n 4.796 * [backup-simplify]: Simplify k into k 4.796 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.796 * [taylor]: Taking taylor expansion of 1.0 in n 4.796 * [backup-simplify]: Simplify 1.0 into 1.0 4.796 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.796 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.796 * [taylor]: Taking taylor expansion of -2.0 in n 4.796 * [backup-simplify]: Simplify -2.0 into -2.0 4.796 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.796 * [taylor]: Taking taylor expansion of PI in n 4.796 * [backup-simplify]: Simplify PI into PI 4.796 * [taylor]: Taking taylor expansion of n in n 4.796 * [backup-simplify]: Simplify 0 into 0 4.796 * [backup-simplify]: Simplify 1 into 1 4.797 * [backup-simplify]: Simplify (/ PI 1) into PI 4.797 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.798 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.798 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.800 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.801 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 4.802 * [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)))) 4.804 * [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))))) 4.806 * [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)))))) 4.807 * [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))))))) 4.809 * [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))))))) 4.810 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.811 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.813 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.813 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.813 * [backup-simplify]: Simplify (+ 0 0) into 0 4.815 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.816 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.818 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 4.820 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.822 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 4.822 * [backup-simplify]: Simplify 0 into 0 4.823 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.827 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.829 * [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)))))))) 4.830 * [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)))))))) 4.830 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 4.830 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 4.830 * [taylor]: Taking taylor expansion of +nan.0 in n 4.830 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.830 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 4.830 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 4.830 * [taylor]: Taking taylor expansion of 0.5 in n 4.830 * [backup-simplify]: Simplify 0.5 into 0.5 4.830 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 4.831 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.831 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.831 * [taylor]: Taking taylor expansion of k in n 4.831 * [backup-simplify]: Simplify k into k 4.831 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.831 * [taylor]: Taking taylor expansion of 1.0 in n 4.831 * [backup-simplify]: Simplify 1.0 into 1.0 4.831 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.831 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.831 * [taylor]: Taking taylor expansion of -2.0 in n 4.831 * [backup-simplify]: Simplify -2.0 into -2.0 4.831 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.831 * [taylor]: Taking taylor expansion of PI in n 4.831 * [backup-simplify]: Simplify PI into PI 4.831 * [taylor]: Taking taylor expansion of n in n 4.831 * [backup-simplify]: Simplify 0 into 0 4.831 * [backup-simplify]: Simplify 1 into 1 4.832 * [backup-simplify]: Simplify (/ PI 1) into PI 4.832 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.834 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.834 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.835 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.837 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 4.838 * [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)))) 4.839 * [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))))) 4.841 * [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)))))) 4.842 * [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))))))) 4.843 * [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))))))) 4.848 * [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)))))))))))) 4.849 * * * [progress]: simplifying candidates 4.853 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (+ (- (log 1.0) (log (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (+ (log (/ 1.0 (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) 1) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 4.863 * * [simplify]: Extracting # 0 : cost 0 4.863 * * [simplify]: Extracting # 1 : cost 0 4.864 * * [simplify]: Extracting # 2 : cost 0 4.865 * * [simplify]: Extracting # 3 : cost 0 4.866 * * [simplify]: Extracting # 4 : cost 0 4.866 * * [simplify]: Extracting # 5 : cost 0 4.867 * * [simplify]: Extracting # 6 : cost 0 4.868 * * [simplify]: Extracting # 7 : cost 0 4.869 * * [simplify]: Extracting # 8 : cost 0 4.870 * * [simplify]: Extracting # 9 : cost 0 4.871 * * [simplify]: Extracting # 10 : cost 0 4.873 * * [simplify]: Extracting # 11 : cost 0 4.874 * * [simplify]: Extracting # 12 : cost 0 4.875 * * [simplify]: Extracting # 13 : cost 0 4.876 * * [simplify]: Extracting # 14 : cost 0 4.877 * * [simplify]: Extracting # 15 : cost 0 4.878 * * [simplify]: Extracting # 16 : cost 0 4.879 * * [simplify]: Extracting # 17 : cost 0 4.880 * * [simplify]: Extracting # 18 : cost 0 4.882 * * [simplify]: Extracting # 19 : cost 0 4.883 * * [simplify]: Extracting # 20 : cost 0 4.884 * * [simplify]: Extracting # 21 : cost 0 4.885 * * [simplify]: Extracting # 22 : cost 0 4.886 * * [simplify]: Extracting # 23 : cost 0 4.888 * * [simplify]: Extracting # 24 : cost 0 4.889 * * [simplify]: Extracting # 25 : cost 0 4.890 * * [simplify]: Extracting # 26 : cost 0 4.901 * * [simplify]: Extracting # 27 : cost 0 4.903 * * [simplify]: Extracting # 28 : cost 0 4.904 * * [simplify]: Extracting # 29 : cost 0 4.905 * * [simplify]: Extracting # 30 : cost 0 4.906 * * [simplify]: Extracting # 31 : cost 0 4.907 * * [simplify]: Extracting # 32 : cost 0 4.909 * * [simplify]: Extracting # 33 : cost 0 4.910 * * [simplify]: iteration 0 : 361 enodes (cost 2800 ) 5.090 * * [simplify]: Extracting # 0 : cost 0 5.091 * * [simplify]: Extracting # 1 : cost 0 5.093 * * [simplify]: Extracting # 2 : cost 0 5.094 * * [simplify]: Extracting # 3 : cost 0 5.096 * * [simplify]: Extracting # 4 : cost 0 5.097 * * [simplify]: Extracting # 5 : cost 0 5.098 * * [simplify]: Extracting # 6 : cost 0 5.100 * * [simplify]: iteration 1 : 931 enodes (cost 2635 ) 5.617 * * [simplify]: Extracting # 0 : cost 0 5.621 * * [simplify]: Extracting # 1 : cost 0 5.625 * * [simplify]: Extracting # 2 : cost 0 5.629 * * [simplify]: Extracting # 3 : cost 0 5.634 * * [simplify]: Extracting # 4 : cost 0 5.642 * * [simplify]: Extracting # 5 : cost 0 5.650 * * [simplify]: iteration 2 : 3051 enodes (cost 2471 ) 7.217 * * [simplify]: Extracting # 0 : cost 0 7.224 * * [simplify]: Extracting # 1 : cost 0 7.230 * * [simplify]: Extracting # 2 : cost 0 7.236 * * [simplify]: Extracting # 3 : cost 0 7.253 * * [simplify]: Extracting # 4 : cost 0 7.265 * * [simplify]: iteration done: 5001 enodes (cost 2471 ) 7.267 * [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 (* PI (* 2.0 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 (* PI (* 2.0 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 (* PI (* 2.0 n)) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* PI (* 2.0 n)) (/ (/ (- 1.0 k) 2.0) 2)) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (/ (pow 1.0 3) k) (sqrt k)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (* PI (* 2.0 n)) (* PI (* 2.0 n)) (log (* PI (* 2.0 n))) (log (* PI (* 2.0 n))) (log (* PI (* 2.0 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)) (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))) (- (+ (+ (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)) (* (* 0.125 (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))))) (* (* 0.5 k) (+ (* (pow (* (* 2.0 PI) n) 0.5) (log n)) (* (pow (* (* 2.0 PI) n) 0.5) (log (* 2.0 PI)))))) (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (pow (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)) (* PI (* 2.0 n)) (* PI (* 2.0 n)) (* PI (* 2.0 n)) (+ (+ (- (* +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))))) (+ (* (- +nan.0) (/ (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (pow k 3))) (* +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)))) 7.269 * * * [progress]: adding candidates to table 7.940 * * [progress]: iteration 2 / 4 7.940 * * * [progress]: picking best candidate 7.996 * * * * [pick]: Picked # 7.996 * * * [progress]: localizing error 8.022 * * * [progress]: generating rewritten candidates 8.022 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 8.072 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 8.132 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 8.145 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 8.183 * * * [progress]: generating series expansions 8.183 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 8.184 * [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))) 8.184 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 8.184 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 8.184 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 8.184 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 8.184 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 8.184 * [taylor]: Taking taylor expansion of 0.25 in k 8.184 * [backup-simplify]: Simplify 0.25 into 0.25 8.184 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.184 * [taylor]: Taking taylor expansion of 1.0 in k 8.184 * [backup-simplify]: Simplify 1.0 into 1.0 8.184 * [taylor]: Taking taylor expansion of k in k 8.184 * [backup-simplify]: Simplify 0 into 0 8.184 * [backup-simplify]: Simplify 1 into 1 8.184 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 8.184 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 8.184 * [taylor]: Taking taylor expansion of 2.0 in k 8.184 * [backup-simplify]: Simplify 2.0 into 2.0 8.184 * [taylor]: Taking taylor expansion of (* n PI) in k 8.184 * [taylor]: Taking taylor expansion of n in k 8.184 * [backup-simplify]: Simplify n into n 8.184 * [taylor]: Taking taylor expansion of PI in k 8.185 * [backup-simplify]: Simplify PI into PI 8.185 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.185 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 8.185 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 8.185 * [backup-simplify]: Simplify (- 0) into 0 8.185 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.186 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 8.186 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 8.186 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 8.186 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 8.186 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.186 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.186 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 8.186 * [taylor]: Taking taylor expansion of 0.25 in n 8.186 * [backup-simplify]: Simplify 0.25 into 0.25 8.186 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.186 * [taylor]: Taking taylor expansion of 1.0 in n 8.186 * [backup-simplify]: Simplify 1.0 into 1.0 8.186 * [taylor]: Taking taylor expansion of k in n 8.186 * [backup-simplify]: Simplify k into k 8.186 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.186 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.186 * [taylor]: Taking taylor expansion of 2.0 in n 8.186 * [backup-simplify]: Simplify 2.0 into 2.0 8.186 * [taylor]: Taking taylor expansion of (* n PI) in n 8.186 * [taylor]: Taking taylor expansion of n in n 8.186 * [backup-simplify]: Simplify 0 into 0 8.186 * [backup-simplify]: Simplify 1 into 1 8.186 * [taylor]: Taking taylor expansion of PI in n 8.186 * [backup-simplify]: Simplify PI into PI 8.186 * [backup-simplify]: Simplify (* 0 PI) into 0 8.187 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.188 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.189 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.189 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.189 * [backup-simplify]: Simplify (- k) into (- k) 8.189 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.189 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 8.190 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.191 * [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)))) 8.192 * [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))))) 8.192 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 8.192 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.192 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.192 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 8.192 * [taylor]: Taking taylor expansion of 0.25 in n 8.192 * [backup-simplify]: Simplify 0.25 into 0.25 8.192 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.192 * [taylor]: Taking taylor expansion of 1.0 in n 8.192 * [backup-simplify]: Simplify 1.0 into 1.0 8.192 * [taylor]: Taking taylor expansion of k in n 8.192 * [backup-simplify]: Simplify k into k 8.192 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.192 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.192 * [taylor]: Taking taylor expansion of 2.0 in n 8.192 * [backup-simplify]: Simplify 2.0 into 2.0 8.192 * [taylor]: Taking taylor expansion of (* n PI) in n 8.192 * [taylor]: Taking taylor expansion of n in n 8.192 * [backup-simplify]: Simplify 0 into 0 8.192 * [backup-simplify]: Simplify 1 into 1 8.192 * [taylor]: Taking taylor expansion of PI in n 8.192 * [backup-simplify]: Simplify PI into PI 8.193 * [backup-simplify]: Simplify (* 0 PI) into 0 8.193 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.195 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.196 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.197 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.198 * [backup-simplify]: Simplify (- k) into (- k) 8.198 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.198 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 8.199 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.200 * [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)))) 8.202 * [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))))) 8.202 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 8.202 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 8.202 * [taylor]: Taking taylor expansion of 0.25 in k 8.202 * [backup-simplify]: Simplify 0.25 into 0.25 8.202 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 8.202 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.202 * [taylor]: Taking taylor expansion of 1.0 in k 8.202 * [backup-simplify]: Simplify 1.0 into 1.0 8.202 * [taylor]: Taking taylor expansion of k in k 8.202 * [backup-simplify]: Simplify 0 into 0 8.202 * [backup-simplify]: Simplify 1 into 1 8.202 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 8.202 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.202 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.202 * [taylor]: Taking taylor expansion of 2.0 in k 8.202 * [backup-simplify]: Simplify 2.0 into 2.0 8.202 * [taylor]: Taking taylor expansion of PI in k 8.203 * [backup-simplify]: Simplify PI into PI 8.203 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.204 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.204 * [taylor]: Taking taylor expansion of (log n) in k 8.204 * [taylor]: Taking taylor expansion of n in k 8.204 * [backup-simplify]: Simplify n into n 8.204 * [backup-simplify]: Simplify (log n) into (log n) 8.205 * [backup-simplify]: Simplify (- 0) into 0 8.205 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.206 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 8.208 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 8.209 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 8.210 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 8.212 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 8.212 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.213 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 8.214 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.214 * [backup-simplify]: Simplify (- 0) into 0 8.215 * [backup-simplify]: Simplify (+ 0 0) into 0 8.215 * [backup-simplify]: Simplify (+ (* 0.25 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)) 8.217 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 8.218 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.218 * [taylor]: Taking taylor expansion of 0 in k 8.218 * [backup-simplify]: Simplify 0 into 0 8.218 * [backup-simplify]: Simplify 0 into 0 8.218 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.219 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.220 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 8.220 * [backup-simplify]: Simplify (+ 0 0) into 0 8.220 * [backup-simplify]: Simplify (- 1) into -1 8.221 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.222 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 8.223 * [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)))) 8.232 * [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)))))) 8.235 * [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)))))) 8.237 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 8.238 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 8.241 * [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 8.242 * [backup-simplify]: Simplify (- 0) into 0 8.242 * [backup-simplify]: Simplify (+ 0 0) into 0 8.243 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 8.244 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.246 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.248 * [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 8.248 * [taylor]: Taking taylor expansion of 0 in k 8.248 * [backup-simplify]: Simplify 0 into 0 8.248 * [backup-simplify]: Simplify 0 into 0 8.248 * [backup-simplify]: Simplify 0 into 0 8.249 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.252 * [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 8.254 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 8.255 * [backup-simplify]: Simplify (+ 0 0) into 0 8.255 * [backup-simplify]: Simplify (- 0) into 0 8.255 * [backup-simplify]: Simplify (+ 0 0) into 0 8.257 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.259 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 8.263 * [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))))) 8.268 * [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))))) 8.279 * [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)))))) 8.280 * [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)))) 8.280 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 8.280 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 8.280 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 8.280 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 8.280 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 8.280 * [taylor]: Taking taylor expansion of 0.25 in k 8.280 * [backup-simplify]: Simplify 0.25 into 0.25 8.280 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.280 * [taylor]: Taking taylor expansion of 1.0 in k 8.280 * [backup-simplify]: Simplify 1.0 into 1.0 8.280 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.280 * [taylor]: Taking taylor expansion of k in k 8.280 * [backup-simplify]: Simplify 0 into 0 8.280 * [backup-simplify]: Simplify 1 into 1 8.281 * [backup-simplify]: Simplify (/ 1 1) into 1 8.281 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 8.281 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 8.281 * [taylor]: Taking taylor expansion of 2.0 in k 8.281 * [backup-simplify]: Simplify 2.0 into 2.0 8.281 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.281 * [taylor]: Taking taylor expansion of PI in k 8.281 * [backup-simplify]: Simplify PI into PI 8.281 * [taylor]: Taking taylor expansion of n in k 8.281 * [backup-simplify]: Simplify n into n 8.281 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.281 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 8.281 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 8.282 * [backup-simplify]: Simplify (- 1) into -1 8.282 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.282 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 8.283 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 8.283 * [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))))) 8.283 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 8.283 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.283 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.283 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 8.283 * [taylor]: Taking taylor expansion of 0.25 in n 8.283 * [backup-simplify]: Simplify 0.25 into 0.25 8.283 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.283 * [taylor]: Taking taylor expansion of 1.0 in n 8.283 * [backup-simplify]: Simplify 1.0 into 1.0 8.283 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.283 * [taylor]: Taking taylor expansion of k in n 8.283 * [backup-simplify]: Simplify k into k 8.283 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.283 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.283 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.283 * [taylor]: Taking taylor expansion of 2.0 in n 8.283 * [backup-simplify]: Simplify 2.0 into 2.0 8.283 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.284 * [taylor]: Taking taylor expansion of PI in n 8.284 * [backup-simplify]: Simplify PI into PI 8.284 * [taylor]: Taking taylor expansion of n in n 8.284 * [backup-simplify]: Simplify 0 into 0 8.284 * [backup-simplify]: Simplify 1 into 1 8.284 * [backup-simplify]: Simplify (/ PI 1) into PI 8.285 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.286 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.286 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.286 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.286 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 8.287 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.289 * [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)))) 8.290 * [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))))) 8.290 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 8.290 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.290 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.290 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 8.290 * [taylor]: Taking taylor expansion of 0.25 in n 8.290 * [backup-simplify]: Simplify 0.25 into 0.25 8.290 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.290 * [taylor]: Taking taylor expansion of 1.0 in n 8.290 * [backup-simplify]: Simplify 1.0 into 1.0 8.290 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.290 * [taylor]: Taking taylor expansion of k in n 8.290 * [backup-simplify]: Simplify k into k 8.290 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.290 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.290 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.291 * [taylor]: Taking taylor expansion of 2.0 in n 8.291 * [backup-simplify]: Simplify 2.0 into 2.0 8.291 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.291 * [taylor]: Taking taylor expansion of PI in n 8.291 * [backup-simplify]: Simplify PI into PI 8.291 * [taylor]: Taking taylor expansion of n in n 8.291 * [backup-simplify]: Simplify 0 into 0 8.291 * [backup-simplify]: Simplify 1 into 1 8.291 * [backup-simplify]: Simplify (/ PI 1) into PI 8.292 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.293 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.293 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.293 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.293 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 8.294 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.296 * [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)))) 8.297 * [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))))) 8.297 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 8.297 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 8.297 * [taylor]: Taking taylor expansion of 0.25 in k 8.297 * [backup-simplify]: Simplify 0.25 into 0.25 8.298 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 8.298 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 8.298 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.298 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.298 * [taylor]: Taking taylor expansion of 2.0 in k 8.298 * [backup-simplify]: Simplify 2.0 into 2.0 8.298 * [taylor]: Taking taylor expansion of PI in k 8.298 * [backup-simplify]: Simplify PI into PI 8.298 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.299 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.299 * [taylor]: Taking taylor expansion of (log n) in k 8.299 * [taylor]: Taking taylor expansion of n in k 8.299 * [backup-simplify]: Simplify n into n 8.299 * [backup-simplify]: Simplify (log n) into (log n) 8.299 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.299 * [taylor]: Taking taylor expansion of 1.0 in k 8.299 * [backup-simplify]: Simplify 1.0 into 1.0 8.299 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.300 * [taylor]: Taking taylor expansion of k in k 8.300 * [backup-simplify]: Simplify 0 into 0 8.300 * [backup-simplify]: Simplify 1 into 1 8.300 * [backup-simplify]: Simplify (/ 1 1) into 1 8.300 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.301 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 8.301 * [backup-simplify]: Simplify (- 1) into -1 8.302 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.303 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 8.304 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 8.306 * [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))))) 8.307 * [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))))) 8.308 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.309 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.310 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.311 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.311 * [backup-simplify]: Simplify (- 0) into 0 8.312 * [backup-simplify]: Simplify (+ 0 0) into 0 8.312 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 8.314 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.315 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 8.317 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.317 * [taylor]: Taking taylor expansion of 0 in k 8.317 * [backup-simplify]: Simplify 0 into 0 8.317 * [backup-simplify]: Simplify 0 into 0 8.317 * [backup-simplify]: Simplify 0 into 0 8.318 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.319 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.323 * [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 8.323 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.324 * [backup-simplify]: Simplify (- 0) into 0 8.324 * [backup-simplify]: Simplify (+ 0 0) into 0 8.325 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 8.327 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.328 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 8.331 * [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 8.331 * [taylor]: Taking taylor expansion of 0 in k 8.331 * [backup-simplify]: Simplify 0 into 0 8.331 * [backup-simplify]: Simplify 0 into 0 8.331 * [backup-simplify]: Simplify 0 into 0 8.331 * [backup-simplify]: Simplify 0 into 0 8.332 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.334 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.340 * [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 8.340 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.341 * [backup-simplify]: Simplify (- 0) into 0 8.341 * [backup-simplify]: Simplify (+ 0 0) into 0 8.342 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 8.344 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.346 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 8.349 * [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 8.349 * [taylor]: Taking taylor expansion of 0 in k 8.349 * [backup-simplify]: Simplify 0 into 0 8.349 * [backup-simplify]: Simplify 0 into 0 8.351 * [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)))) 8.351 * [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))) 8.351 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 8.351 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 8.352 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 8.352 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 8.352 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 8.352 * [taylor]: Taking taylor expansion of 0.25 in k 8.352 * [backup-simplify]: Simplify 0.25 into 0.25 8.352 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.352 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.352 * [taylor]: Taking taylor expansion of k in k 8.352 * [backup-simplify]: Simplify 0 into 0 8.352 * [backup-simplify]: Simplify 1 into 1 8.352 * [backup-simplify]: Simplify (/ 1 1) into 1 8.352 * [taylor]: Taking taylor expansion of 1.0 in k 8.352 * [backup-simplify]: Simplify 1.0 into 1.0 8.352 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 8.352 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 8.352 * [taylor]: Taking taylor expansion of -2.0 in k 8.352 * [backup-simplify]: Simplify -2.0 into -2.0 8.352 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.353 * [taylor]: Taking taylor expansion of PI in k 8.353 * [backup-simplify]: Simplify PI into PI 8.353 * [taylor]: Taking taylor expansion of n in k 8.353 * [backup-simplify]: Simplify n into n 8.353 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.353 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 8.353 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 8.353 * [backup-simplify]: Simplify (+ 1 0) into 1 8.354 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 8.354 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 8.354 * [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)))))) 8.354 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 8.354 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.354 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.354 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 8.354 * [taylor]: Taking taylor expansion of 0.25 in n 8.354 * [backup-simplify]: Simplify 0.25 into 0.25 8.354 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.354 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.354 * [taylor]: Taking taylor expansion of k in n 8.355 * [backup-simplify]: Simplify k into k 8.355 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.355 * [taylor]: Taking taylor expansion of 1.0 in n 8.355 * [backup-simplify]: Simplify 1.0 into 1.0 8.355 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.355 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.355 * [taylor]: Taking taylor expansion of -2.0 in n 8.355 * [backup-simplify]: Simplify -2.0 into -2.0 8.355 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.355 * [taylor]: Taking taylor expansion of PI in n 8.355 * [backup-simplify]: Simplify PI into PI 8.355 * [taylor]: Taking taylor expansion of n in n 8.355 * [backup-simplify]: Simplify 0 into 0 8.355 * [backup-simplify]: Simplify 1 into 1 8.355 * [backup-simplify]: Simplify (/ PI 1) into PI 8.356 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.356 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.356 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.357 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 8.357 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.358 * [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)))) 8.359 * [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))))) 8.359 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 8.359 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.359 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.359 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 8.359 * [taylor]: Taking taylor expansion of 0.25 in n 8.359 * [backup-simplify]: Simplify 0.25 into 0.25 8.359 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.359 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.359 * [taylor]: Taking taylor expansion of k in n 8.359 * [backup-simplify]: Simplify k into k 8.359 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.359 * [taylor]: Taking taylor expansion of 1.0 in n 8.359 * [backup-simplify]: Simplify 1.0 into 1.0 8.359 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.359 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.359 * [taylor]: Taking taylor expansion of -2.0 in n 8.359 * [backup-simplify]: Simplify -2.0 into -2.0 8.359 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.359 * [taylor]: Taking taylor expansion of PI in n 8.359 * [backup-simplify]: Simplify PI into PI 8.359 * [taylor]: Taking taylor expansion of n in n 8.359 * [backup-simplify]: Simplify 0 into 0 8.359 * [backup-simplify]: Simplify 1 into 1 8.360 * [backup-simplify]: Simplify (/ PI 1) into PI 8.360 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.361 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.361 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.361 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 8.362 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.362 * [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)))) 8.363 * [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))))) 8.363 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 8.363 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 8.363 * [taylor]: Taking taylor expansion of 0.25 in k 8.363 * [backup-simplify]: Simplify 0.25 into 0.25 8.363 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 8.363 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.363 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.363 * [taylor]: Taking taylor expansion of k in k 8.363 * [backup-simplify]: Simplify 0 into 0 8.363 * [backup-simplify]: Simplify 1 into 1 8.364 * [backup-simplify]: Simplify (/ 1 1) into 1 8.364 * [taylor]: Taking taylor expansion of 1.0 in k 8.364 * [backup-simplify]: Simplify 1.0 into 1.0 8.364 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 8.364 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 8.364 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 8.364 * [taylor]: Taking taylor expansion of -2.0 in k 8.364 * [backup-simplify]: Simplify -2.0 into -2.0 8.364 * [taylor]: Taking taylor expansion of PI in k 8.364 * [backup-simplify]: Simplify PI into PI 8.364 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.365 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.365 * [taylor]: Taking taylor expansion of (log n) in k 8.365 * [taylor]: Taking taylor expansion of n in k 8.365 * [backup-simplify]: Simplify n into n 8.365 * [backup-simplify]: Simplify (log n) into (log n) 8.365 * [backup-simplify]: Simplify (+ 1 0) into 1 8.365 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.366 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 8.366 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 8.367 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 8.368 * [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))))) 8.375 * [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))))) 8.377 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.378 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 8.379 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 8.380 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.380 * [backup-simplify]: Simplify (+ 0 0) into 0 8.381 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 8.382 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.383 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 8.385 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.385 * [taylor]: Taking taylor expansion of 0 in k 8.385 * [backup-simplify]: Simplify 0 into 0 8.386 * [backup-simplify]: Simplify 0 into 0 8.386 * [backup-simplify]: Simplify 0 into 0 8.387 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.388 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.391 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 8.392 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.392 * [backup-simplify]: Simplify (+ 0 0) into 0 8.393 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 8.394 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.396 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 8.399 * [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 8.399 * [taylor]: Taking taylor expansion of 0 in k 8.399 * [backup-simplify]: Simplify 0 into 0 8.399 * [backup-simplify]: Simplify 0 into 0 8.399 * [backup-simplify]: Simplify 0 into 0 8.399 * [backup-simplify]: Simplify 0 into 0 8.400 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.401 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.407 * [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 8.408 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.408 * [backup-simplify]: Simplify (+ 0 0) into 0 8.410 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 8.411 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.413 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 8.416 * [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 8.416 * [taylor]: Taking taylor expansion of 0 in k 8.417 * [backup-simplify]: Simplify 0 into 0 8.417 * [backup-simplify]: Simplify 0 into 0 8.418 * [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)))))) 8.418 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 8.419 * [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))) 8.419 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 8.419 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 8.419 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 8.419 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 8.419 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 8.419 * [taylor]: Taking taylor expansion of 0.25 in k 8.419 * [backup-simplify]: Simplify 0.25 into 0.25 8.419 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.419 * [taylor]: Taking taylor expansion of 1.0 in k 8.419 * [backup-simplify]: Simplify 1.0 into 1.0 8.419 * [taylor]: Taking taylor expansion of k in k 8.419 * [backup-simplify]: Simplify 0 into 0 8.419 * [backup-simplify]: Simplify 1 into 1 8.419 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 8.419 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 8.419 * [taylor]: Taking taylor expansion of 2.0 in k 8.420 * [backup-simplify]: Simplify 2.0 into 2.0 8.420 * [taylor]: Taking taylor expansion of (* n PI) in k 8.420 * [taylor]: Taking taylor expansion of n in k 8.420 * [backup-simplify]: Simplify n into n 8.420 * [taylor]: Taking taylor expansion of PI in k 8.420 * [backup-simplify]: Simplify PI into PI 8.420 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.420 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 8.420 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 8.420 * [backup-simplify]: Simplify (- 0) into 0 8.421 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.421 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 8.421 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 8.422 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 8.422 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 8.422 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.422 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.422 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 8.422 * [taylor]: Taking taylor expansion of 0.25 in n 8.422 * [backup-simplify]: Simplify 0.25 into 0.25 8.422 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.422 * [taylor]: Taking taylor expansion of 1.0 in n 8.422 * [backup-simplify]: Simplify 1.0 into 1.0 8.422 * [taylor]: Taking taylor expansion of k in n 8.422 * [backup-simplify]: Simplify k into k 8.422 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.422 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.422 * [taylor]: Taking taylor expansion of 2.0 in n 8.422 * [backup-simplify]: Simplify 2.0 into 2.0 8.422 * [taylor]: Taking taylor expansion of (* n PI) in n 8.422 * [taylor]: Taking taylor expansion of n in n 8.422 * [backup-simplify]: Simplify 0 into 0 8.422 * [backup-simplify]: Simplify 1 into 1 8.422 * [taylor]: Taking taylor expansion of PI in n 8.422 * [backup-simplify]: Simplify PI into PI 8.423 * [backup-simplify]: Simplify (* 0 PI) into 0 8.423 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.425 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.426 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.427 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.428 * [backup-simplify]: Simplify (- k) into (- k) 8.428 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.428 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 8.429 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.430 * [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)))) 8.432 * [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))))) 8.432 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 8.432 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.432 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.432 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 8.432 * [taylor]: Taking taylor expansion of 0.25 in n 8.432 * [backup-simplify]: Simplify 0.25 into 0.25 8.432 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.432 * [taylor]: Taking taylor expansion of 1.0 in n 8.432 * [backup-simplify]: Simplify 1.0 into 1.0 8.432 * [taylor]: Taking taylor expansion of k in n 8.432 * [backup-simplify]: Simplify k into k 8.432 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.432 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.432 * [taylor]: Taking taylor expansion of 2.0 in n 8.432 * [backup-simplify]: Simplify 2.0 into 2.0 8.432 * [taylor]: Taking taylor expansion of (* n PI) in n 8.432 * [taylor]: Taking taylor expansion of n in n 8.432 * [backup-simplify]: Simplify 0 into 0 8.432 * [backup-simplify]: Simplify 1 into 1 8.432 * [taylor]: Taking taylor expansion of PI in n 8.432 * [backup-simplify]: Simplify PI into PI 8.433 * [backup-simplify]: Simplify (* 0 PI) into 0 8.433 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.435 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.437 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.438 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.438 * [backup-simplify]: Simplify (- k) into (- k) 8.438 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.438 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 8.440 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.441 * [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)))) 8.442 * [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))))) 8.442 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 8.442 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 8.442 * [taylor]: Taking taylor expansion of 0.25 in k 8.442 * [backup-simplify]: Simplify 0.25 into 0.25 8.442 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 8.442 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.442 * [taylor]: Taking taylor expansion of 1.0 in k 8.442 * [backup-simplify]: Simplify 1.0 into 1.0 8.442 * [taylor]: Taking taylor expansion of k in k 8.442 * [backup-simplify]: Simplify 0 into 0 8.442 * [backup-simplify]: Simplify 1 into 1 8.442 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 8.442 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.443 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.443 * [taylor]: Taking taylor expansion of 2.0 in k 8.443 * [backup-simplify]: Simplify 2.0 into 2.0 8.443 * [taylor]: Taking taylor expansion of PI in k 8.443 * [backup-simplify]: Simplify PI into PI 8.443 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.444 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.444 * [taylor]: Taking taylor expansion of (log n) in k 8.444 * [taylor]: Taking taylor expansion of n in k 8.444 * [backup-simplify]: Simplify n into n 8.444 * [backup-simplify]: Simplify (log n) into (log n) 8.445 * [backup-simplify]: Simplify (- 0) into 0 8.445 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.446 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 8.448 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 8.449 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 8.450 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 8.451 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 8.452 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.453 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 8.455 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.455 * [backup-simplify]: Simplify (- 0) into 0 8.456 * [backup-simplify]: Simplify (+ 0 0) into 0 8.457 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 8.458 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.459 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 8.461 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.461 * [taylor]: Taking taylor expansion of 0 in k 8.462 * [backup-simplify]: Simplify 0 into 0 8.462 * [backup-simplify]: Simplify 0 into 0 8.462 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.464 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.465 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 8.465 * [backup-simplify]: Simplify (+ 0 0) into 0 8.466 * [backup-simplify]: Simplify (- 1) into -1 8.466 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.468 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 8.470 * [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)))) 8.473 * [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)))))) 8.477 * [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)))))) 8.478 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 8.479 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 8.483 * [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 8.483 * [backup-simplify]: Simplify (- 0) into 0 8.484 * [backup-simplify]: Simplify (+ 0 0) into 0 8.485 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 8.487 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.488 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.491 * [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 8.491 * [taylor]: Taking taylor expansion of 0 in k 8.491 * [backup-simplify]: Simplify 0 into 0 8.491 * [backup-simplify]: Simplify 0 into 0 8.491 * [backup-simplify]: Simplify 0 into 0 8.492 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.496 * [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 8.498 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 8.498 * [backup-simplify]: Simplify (+ 0 0) into 0 8.498 * [backup-simplify]: Simplify (- 0) into 0 8.499 * [backup-simplify]: Simplify (+ 0 0) into 0 8.501 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.503 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 8.508 * [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))))) 8.514 * [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))))) 8.524 * [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)))))) 8.525 * [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)))) 8.525 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 8.525 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 8.525 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 8.525 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 8.525 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 8.525 * [taylor]: Taking taylor expansion of 0.25 in k 8.525 * [backup-simplify]: Simplify 0.25 into 0.25 8.525 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.525 * [taylor]: Taking taylor expansion of 1.0 in k 8.525 * [backup-simplify]: Simplify 1.0 into 1.0 8.525 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.525 * [taylor]: Taking taylor expansion of k in k 8.525 * [backup-simplify]: Simplify 0 into 0 8.525 * [backup-simplify]: Simplify 1 into 1 8.526 * [backup-simplify]: Simplify (/ 1 1) into 1 8.526 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 8.526 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 8.526 * [taylor]: Taking taylor expansion of 2.0 in k 8.526 * [backup-simplify]: Simplify 2.0 into 2.0 8.526 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.526 * [taylor]: Taking taylor expansion of PI in k 8.526 * [backup-simplify]: Simplify PI into PI 8.526 * [taylor]: Taking taylor expansion of n in k 8.526 * [backup-simplify]: Simplify n into n 8.526 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.526 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 8.526 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 8.534 * [backup-simplify]: Simplify (- 1) into -1 8.535 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.535 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 8.535 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 8.536 * [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))))) 8.536 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 8.536 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.536 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.536 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 8.536 * [taylor]: Taking taylor expansion of 0.25 in n 8.536 * [backup-simplify]: Simplify 0.25 into 0.25 8.536 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.536 * [taylor]: Taking taylor expansion of 1.0 in n 8.536 * [backup-simplify]: Simplify 1.0 into 1.0 8.536 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.536 * [taylor]: Taking taylor expansion of k in n 8.536 * [backup-simplify]: Simplify k into k 8.536 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.536 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.536 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.536 * [taylor]: Taking taylor expansion of 2.0 in n 8.536 * [backup-simplify]: Simplify 2.0 into 2.0 8.536 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.536 * [taylor]: Taking taylor expansion of PI in n 8.536 * [backup-simplify]: Simplify PI into PI 8.537 * [taylor]: Taking taylor expansion of n in n 8.537 * [backup-simplify]: Simplify 0 into 0 8.537 * [backup-simplify]: Simplify 1 into 1 8.537 * [backup-simplify]: Simplify (/ PI 1) into PI 8.538 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.539 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.539 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.539 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.539 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 8.541 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.542 * [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)))) 8.543 * [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 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 8.543 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.543 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.543 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 8.543 * [taylor]: Taking taylor expansion of 0.25 in n 8.543 * [backup-simplify]: Simplify 0.25 into 0.25 8.543 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.543 * [taylor]: Taking taylor expansion of 1.0 in n 8.543 * [backup-simplify]: Simplify 1.0 into 1.0 8.543 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.543 * [taylor]: Taking taylor expansion of k in n 8.543 * [backup-simplify]: Simplify k into k 8.544 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.544 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.544 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.544 * [taylor]: Taking taylor expansion of 2.0 in n 8.544 * [backup-simplify]: Simplify 2.0 into 2.0 8.544 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.544 * [taylor]: Taking taylor expansion of PI in n 8.544 * [backup-simplify]: Simplify PI into PI 8.544 * [taylor]: Taking taylor expansion of n in n 8.544 * [backup-simplify]: Simplify 0 into 0 8.544 * [backup-simplify]: Simplify 1 into 1 8.544 * [backup-simplify]: Simplify (/ PI 1) into PI 8.545 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.546 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.546 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.546 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.546 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 8.548 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.549 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 8.550 * [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))))) 8.550 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 8.550 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 8.550 * [taylor]: Taking taylor expansion of 0.25 in k 8.550 * [backup-simplify]: Simplify 0.25 into 0.25 8.551 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 8.551 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 8.551 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.551 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.551 * [taylor]: Taking taylor expansion of 2.0 in k 8.551 * [backup-simplify]: Simplify 2.0 into 2.0 8.551 * [taylor]: Taking taylor expansion of PI in k 8.551 * [backup-simplify]: Simplify PI into PI 8.551 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.552 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.552 * [taylor]: Taking taylor expansion of (log n) in k 8.553 * [taylor]: Taking taylor expansion of n in k 8.553 * [backup-simplify]: Simplify n into n 8.553 * [backup-simplify]: Simplify (log n) into (log n) 8.553 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.553 * [taylor]: Taking taylor expansion of 1.0 in k 8.553 * [backup-simplify]: Simplify 1.0 into 1.0 8.553 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.553 * [taylor]: Taking taylor expansion of k in k 8.553 * [backup-simplify]: Simplify 0 into 0 8.553 * [backup-simplify]: Simplify 1 into 1 8.553 * [backup-simplify]: Simplify (/ 1 1) into 1 8.553 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.554 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 8.555 * [backup-simplify]: Simplify (- 1) into -1 8.555 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.556 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 8.557 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 8.557 * [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))))) 8.558 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.559 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.559 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.560 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.560 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.560 * [backup-simplify]: Simplify (- 0) into 0 8.561 * [backup-simplify]: Simplify (+ 0 0) into 0 8.561 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 8.562 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.563 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 8.564 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.564 * [taylor]: Taking taylor expansion of 0 in k 8.564 * [backup-simplify]: Simplify 0 into 0 8.564 * [backup-simplify]: Simplify 0 into 0 8.564 * [backup-simplify]: Simplify 0 into 0 8.564 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.565 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.567 * [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 8.567 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.568 * [backup-simplify]: Simplify (- 0) into 0 8.568 * [backup-simplify]: Simplify (+ 0 0) into 0 8.568 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 8.569 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.570 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 8.571 * [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 8.572 * [taylor]: Taking taylor expansion of 0 in k 8.572 * [backup-simplify]: Simplify 0 into 0 8.572 * [backup-simplify]: Simplify 0 into 0 8.572 * [backup-simplify]: Simplify 0 into 0 8.572 * [backup-simplify]: Simplify 0 into 0 8.572 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.573 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.577 * [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 8.577 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.577 * [backup-simplify]: Simplify (- 0) into 0 8.577 * [backup-simplify]: Simplify (+ 0 0) into 0 8.578 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 8.579 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.580 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 8.582 * [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 8.582 * [taylor]: Taking taylor expansion of 0 in k 8.582 * [backup-simplify]: Simplify 0 into 0 8.582 * [backup-simplify]: Simplify 0 into 0 8.582 * [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)))) 8.583 * [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))) 8.583 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 8.583 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 8.583 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 8.583 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 8.583 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 8.583 * [taylor]: Taking taylor expansion of 0.25 in k 8.583 * [backup-simplify]: Simplify 0.25 into 0.25 8.583 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.583 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.583 * [taylor]: Taking taylor expansion of k in k 8.583 * [backup-simplify]: Simplify 0 into 0 8.583 * [backup-simplify]: Simplify 1 into 1 8.584 * [backup-simplify]: Simplify (/ 1 1) into 1 8.584 * [taylor]: Taking taylor expansion of 1.0 in k 8.584 * [backup-simplify]: Simplify 1.0 into 1.0 8.584 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 8.584 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 8.584 * [taylor]: Taking taylor expansion of -2.0 in k 8.584 * [backup-simplify]: Simplify -2.0 into -2.0 8.584 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.584 * [taylor]: Taking taylor expansion of PI in k 8.584 * [backup-simplify]: Simplify PI into PI 8.584 * [taylor]: Taking taylor expansion of n in k 8.584 * [backup-simplify]: Simplify n into n 8.584 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.584 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 8.584 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 8.585 * [backup-simplify]: Simplify (+ 1 0) into 1 8.585 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 8.585 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 8.585 * [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)))))) 8.585 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 8.585 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.585 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.586 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 8.586 * [taylor]: Taking taylor expansion of 0.25 in n 8.586 * [backup-simplify]: Simplify 0.25 into 0.25 8.586 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.586 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.586 * [taylor]: Taking taylor expansion of k in n 8.586 * [backup-simplify]: Simplify k into k 8.586 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.586 * [taylor]: Taking taylor expansion of 1.0 in n 8.586 * [backup-simplify]: Simplify 1.0 into 1.0 8.586 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.586 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.586 * [taylor]: Taking taylor expansion of -2.0 in n 8.586 * [backup-simplify]: Simplify -2.0 into -2.0 8.586 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.586 * [taylor]: Taking taylor expansion of PI in n 8.586 * [backup-simplify]: Simplify PI into PI 8.586 * [taylor]: Taking taylor expansion of n in n 8.586 * [backup-simplify]: Simplify 0 into 0 8.586 * [backup-simplify]: Simplify 1 into 1 8.587 * [backup-simplify]: Simplify (/ PI 1) into PI 8.587 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.588 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.588 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.589 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 8.590 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.591 * [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)))) 8.592 * [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))))) 8.593 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 8.593 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.593 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.593 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 8.593 * [taylor]: Taking taylor expansion of 0.25 in n 8.593 * [backup-simplify]: Simplify 0.25 into 0.25 8.593 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.593 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.593 * [taylor]: Taking taylor expansion of k in n 8.593 * [backup-simplify]: Simplify k into k 8.593 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.593 * [taylor]: Taking taylor expansion of 1.0 in n 8.593 * [backup-simplify]: Simplify 1.0 into 1.0 8.593 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.593 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.593 * [taylor]: Taking taylor expansion of -2.0 in n 8.593 * [backup-simplify]: Simplify -2.0 into -2.0 8.593 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.593 * [taylor]: Taking taylor expansion of PI in n 8.593 * [backup-simplify]: Simplify PI into PI 8.593 * [taylor]: Taking taylor expansion of n in n 8.593 * [backup-simplify]: Simplify 0 into 0 8.593 * [backup-simplify]: Simplify 1 into 1 8.594 * [backup-simplify]: Simplify (/ PI 1) into PI 8.594 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.595 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.595 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.596 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 8.597 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.598 * [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)))) 8.599 * [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))))) 8.600 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 8.600 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 8.600 * [taylor]: Taking taylor expansion of 0.25 in k 8.600 * [backup-simplify]: Simplify 0.25 into 0.25 8.600 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 8.600 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.600 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.600 * [taylor]: Taking taylor expansion of k in k 8.600 * [backup-simplify]: Simplify 0 into 0 8.600 * [backup-simplify]: Simplify 1 into 1 8.600 * [backup-simplify]: Simplify (/ 1 1) into 1 8.600 * [taylor]: Taking taylor expansion of 1.0 in k 8.600 * [backup-simplify]: Simplify 1.0 into 1.0 8.600 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 8.600 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 8.600 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 8.601 * [taylor]: Taking taylor expansion of -2.0 in k 8.601 * [backup-simplify]: Simplify -2.0 into -2.0 8.601 * [taylor]: Taking taylor expansion of PI in k 8.601 * [backup-simplify]: Simplify PI into PI 8.601 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.602 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.602 * [taylor]: Taking taylor expansion of (log n) in k 8.602 * [taylor]: Taking taylor expansion of n in k 8.602 * [backup-simplify]: Simplify n into n 8.602 * [backup-simplify]: Simplify (log n) into (log n) 8.603 * [backup-simplify]: Simplify (+ 1 0) into 1 8.603 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.604 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 8.605 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 8.606 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 8.607 * [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))))) 8.609 * [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))))) 8.610 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.610 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 8.612 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 8.612 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.613 * [backup-simplify]: Simplify (+ 0 0) into 0 8.613 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 8.615 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.616 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 8.617 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.617 * [taylor]: Taking taylor expansion of 0 in k 8.617 * [backup-simplify]: Simplify 0 into 0 8.617 * [backup-simplify]: Simplify 0 into 0 8.617 * [backup-simplify]: Simplify 0 into 0 8.618 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.618 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.620 * [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 8.620 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.621 * [backup-simplify]: Simplify (+ 0 0) into 0 8.621 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 8.622 * [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 (- (log (* -2.0 PI)) (log n))))) into 0 8.625 * [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 8.625 * [taylor]: Taking taylor expansion of 0 in k 8.625 * [backup-simplify]: Simplify 0 into 0 8.625 * [backup-simplify]: Simplify 0 into 0 8.625 * [backup-simplify]: Simplify 0 into 0 8.625 * [backup-simplify]: Simplify 0 into 0 8.625 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.626 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.629 * [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 8.629 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.630 * [backup-simplify]: Simplify (+ 0 0) into 0 8.630 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 8.631 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.632 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 8.634 * [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 8.634 * [taylor]: Taking taylor expansion of 0 in k 8.634 * [backup-simplify]: Simplify 0 into 0 8.634 * [backup-simplify]: Simplify 0 into 0 8.635 * [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)))))) 8.635 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 8.635 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 8.635 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 8.635 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 8.635 * [taylor]: Taking taylor expansion of 1.0 in k 8.635 * [backup-simplify]: Simplify 1.0 into 1.0 8.635 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.635 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.635 * [taylor]: Taking taylor expansion of k in k 8.635 * [backup-simplify]: Simplify 0 into 0 8.635 * [backup-simplify]: Simplify 1 into 1 8.636 * [backup-simplify]: Simplify (/ 1 1) into 1 8.636 * [backup-simplify]: Simplify (sqrt 0) into 0 8.637 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.637 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 8.637 * [taylor]: Taking taylor expansion of 1.0 in k 8.637 * [backup-simplify]: Simplify 1.0 into 1.0 8.637 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.637 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.637 * [taylor]: Taking taylor expansion of k in k 8.637 * [backup-simplify]: Simplify 0 into 0 8.637 * [backup-simplify]: Simplify 1 into 1 8.637 * [backup-simplify]: Simplify (/ 1 1) into 1 8.637 * [backup-simplify]: Simplify (sqrt 0) into 0 8.638 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.638 * [backup-simplify]: Simplify (* 1.0 0) into 0 8.638 * [backup-simplify]: Simplify 0 into 0 8.639 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 8.640 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.640 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 8.642 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.648 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 8.649 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.649 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.652 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.653 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 8.653 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.654 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 8.654 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 8.654 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 8.654 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 8.654 * [taylor]: Taking taylor expansion of 1.0 in k 8.654 * [backup-simplify]: Simplify 1.0 into 1.0 8.654 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.654 * [taylor]: Taking taylor expansion of k in k 8.654 * [backup-simplify]: Simplify 0 into 0 8.654 * [backup-simplify]: Simplify 1 into 1 8.654 * [backup-simplify]: Simplify (sqrt 0) into 0 8.655 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.655 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 8.655 * [taylor]: Taking taylor expansion of 1.0 in k 8.655 * [backup-simplify]: Simplify 1.0 into 1.0 8.655 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.655 * [taylor]: Taking taylor expansion of k in k 8.655 * [backup-simplify]: Simplify 0 into 0 8.655 * [backup-simplify]: Simplify 1 into 1 8.656 * [backup-simplify]: Simplify (sqrt 0) into 0 8.657 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.657 * [backup-simplify]: Simplify (* 1.0 0) into 0 8.657 * [backup-simplify]: Simplify 0 into 0 8.659 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 8.659 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.662 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.664 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 8.664 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.668 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.671 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 8.671 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.673 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 8.673 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 8.673 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 8.673 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 8.673 * [taylor]: Taking taylor expansion of 1.0 in k 8.673 * [backup-simplify]: Simplify 1.0 into 1.0 8.673 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.673 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.673 * [taylor]: Taking taylor expansion of -1 in k 8.673 * [backup-simplify]: Simplify -1 into -1 8.673 * [taylor]: Taking taylor expansion of k in k 8.673 * [backup-simplify]: Simplify 0 into 0 8.673 * [backup-simplify]: Simplify 1 into 1 8.674 * [backup-simplify]: Simplify (/ -1 1) into -1 8.674 * [backup-simplify]: Simplify (sqrt 0) into 0 8.675 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.676 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 8.676 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 8.676 * [taylor]: Taking taylor expansion of 1.0 in k 8.676 * [backup-simplify]: Simplify 1.0 into 1.0 8.676 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.676 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.676 * [taylor]: Taking taylor expansion of -1 in k 8.676 * [backup-simplify]: Simplify -1 into -1 8.676 * [taylor]: Taking taylor expansion of k in k 8.676 * [backup-simplify]: Simplify 0 into 0 8.676 * [backup-simplify]: Simplify 1 into 1 8.677 * [backup-simplify]: Simplify (/ -1 1) into -1 8.677 * [backup-simplify]: Simplify (sqrt 0) into 0 8.678 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.679 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 8.679 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.679 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 8.683 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.685 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 8.686 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.687 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.691 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.695 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 8.695 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.697 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 8.697 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 8.697 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 8.697 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 8.697 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.697 * [taylor]: Taking taylor expansion of 2.0 in n 8.697 * [backup-simplify]: Simplify 2.0 into 2.0 8.697 * [taylor]: Taking taylor expansion of (* n PI) in n 8.698 * [taylor]: Taking taylor expansion of n in n 8.698 * [backup-simplify]: Simplify 0 into 0 8.698 * [backup-simplify]: Simplify 1 into 1 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 (* 2.0 (* n PI)) 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 (* n PI) in n 8.698 * [taylor]: Taking taylor expansion of n in n 8.698 * [backup-simplify]: Simplify 0 into 0 8.698 * [backup-simplify]: Simplify 1 into 1 8.698 * [taylor]: Taking taylor expansion of PI in n 8.698 * [backup-simplify]: Simplify PI into PI 8.698 * [backup-simplify]: Simplify (* 0 PI) into 0 8.699 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.699 * [backup-simplify]: Simplify 0 into 0 8.700 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.702 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.702 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.703 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.705 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 8.705 * [backup-simplify]: Simplify 0 into 0 8.706 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 8.707 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 8.707 * [backup-simplify]: Simplify 0 into 0 8.708 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.710 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 8.710 * [backup-simplify]: Simplify 0 into 0 8.711 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.713 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 8.713 * [backup-simplify]: Simplify 0 into 0 8.714 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.716 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 8.716 * [backup-simplify]: Simplify 0 into 0 8.718 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 8.720 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 8.720 * [backup-simplify]: Simplify 0 into 0 8.721 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 8.721 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 8.721 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 8.721 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.721 * [taylor]: Taking taylor expansion of 2.0 in n 8.721 * [backup-simplify]: Simplify 2.0 into 2.0 8.721 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.721 * [taylor]: Taking taylor expansion of PI in n 8.721 * [backup-simplify]: Simplify PI into PI 8.721 * [taylor]: Taking taylor expansion of n in n 8.721 * [backup-simplify]: Simplify 0 into 0 8.722 * [backup-simplify]: Simplify 1 into 1 8.722 * [backup-simplify]: Simplify (/ PI 1) into PI 8.722 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.722 * [taylor]: Taking taylor expansion of 2.0 in n 8.722 * [backup-simplify]: Simplify 2.0 into 2.0 8.722 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.722 * [taylor]: Taking taylor expansion of PI in n 8.722 * [backup-simplify]: Simplify PI into PI 8.722 * [taylor]: Taking taylor expansion of n in n 8.722 * [backup-simplify]: Simplify 0 into 0 8.722 * [backup-simplify]: Simplify 1 into 1 8.723 * [backup-simplify]: Simplify (/ PI 1) into PI 8.723 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.724 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.725 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.725 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.725 * [backup-simplify]: Simplify 0 into 0 8.726 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.727 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.727 * [backup-simplify]: Simplify 0 into 0 8.729 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.730 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.730 * [backup-simplify]: Simplify 0 into 0 8.731 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.732 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.733 * [backup-simplify]: Simplify 0 into 0 8.734 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.735 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.735 * [backup-simplify]: Simplify 0 into 0 8.736 * [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 8.738 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.738 * [backup-simplify]: Simplify 0 into 0 8.739 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 8.740 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 8.740 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 8.740 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.740 * [taylor]: Taking taylor expansion of -2.0 in n 8.740 * [backup-simplify]: Simplify -2.0 into -2.0 8.740 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.740 * [taylor]: Taking taylor expansion of PI in n 8.740 * [backup-simplify]: Simplify PI into PI 8.740 * [taylor]: Taking taylor expansion of n in n 8.740 * [backup-simplify]: Simplify 0 into 0 8.740 * [backup-simplify]: Simplify 1 into 1 8.740 * [backup-simplify]: Simplify (/ PI 1) into PI 8.740 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.740 * [taylor]: Taking taylor expansion of -2.0 in n 8.740 * [backup-simplify]: Simplify -2.0 into -2.0 8.741 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.741 * [taylor]: Taking taylor expansion of PI in n 8.741 * [backup-simplify]: Simplify PI into PI 8.741 * [taylor]: Taking taylor expansion of n in n 8.741 * [backup-simplify]: Simplify 0 into 0 8.741 * [backup-simplify]: Simplify 1 into 1 8.741 * [backup-simplify]: Simplify (/ PI 1) into PI 8.742 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.742 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.743 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.744 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 8.744 * [backup-simplify]: Simplify 0 into 0 8.745 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.746 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.746 * [backup-simplify]: Simplify 0 into 0 8.747 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.748 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.748 * [backup-simplify]: Simplify 0 into 0 8.749 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.751 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.751 * [backup-simplify]: Simplify 0 into 0 8.752 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.754 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.754 * [backup-simplify]: Simplify 0 into 0 8.755 * [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 8.757 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.757 * [backup-simplify]: Simplify 0 into 0 8.757 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 8.757 * * * [progress]: simplifying candidates 8.764 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ 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2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 8.775 * * [simplify]: Extracting # 0 : cost 0 8.775 * * [simplify]: Extracting # 1 : cost 0 8.776 * * [simplify]: Extracting # 2 : cost 0 8.776 * * [simplify]: Extracting # 3 : cost 0 8.777 * * [simplify]: Extracting # 4 : cost 0 8.777 * * [simplify]: Extracting # 5 : cost 0 8.778 * * [simplify]: Extracting # 6 : cost 0 8.778 * * [simplify]: Extracting # 7 : cost 0 8.779 * * [simplify]: Extracting # 8 : cost 0 8.779 * * [simplify]: Extracting # 9 : cost 0 8.780 * * [simplify]: Extracting # 10 : cost 0 8.780 * * [simplify]: Extracting # 11 : cost 0 8.781 * * [simplify]: Extracting # 12 : cost 0 8.782 * * [simplify]: Extracting # 13 : cost 0 8.788 * * [simplify]: Extracting # 14 : cost 0 8.789 * * [simplify]: iteration 0 : 326 enodes (cost 3510 ) 8.936 * * [simplify]: Extracting # 0 : cost 0 8.937 * * [simplify]: Extracting # 1 : cost 0 8.938 * * [simplify]: Extracting # 2 : cost 0 8.939 * * [simplify]: Extracting # 3 : cost 0 8.941 * * [simplify]: Extracting # 4 : cost 0 8.942 * * [simplify]: Extracting # 5 : cost 0 8.943 * * [simplify]: iteration 1 : 839 enodes (cost 3234 ) 9.474 * * [simplify]: Extracting # 0 : cost 0 9.480 * * [simplify]: Extracting # 1 : cost 0 9.487 * * [simplify]: Extracting # 2 : cost 0 9.494 * * [simplify]: Extracting # 3 : cost 0 9.501 * * [simplify]: Extracting # 4 : cost 0 9.507 * * [simplify]: Extracting # 5 : cost 0 9.513 * * [simplify]: iteration 2 : 2444 enodes (cost 3128 ) 10.473 * * [simplify]: Extracting # 0 : cost 0 10.485 * * [simplify]: Extracting # 1 : cost 0 10.499 * * [simplify]: Extracting # 2 : cost 0 10.506 * * [simplify]: Extracting # 3 : cost 0 10.514 * * [simplify]: Extracting # 4 : cost 0 10.525 * * [simplify]: iteration done: 5000 enodes (cost 3080 ) 10.527 * [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 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(- 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))) (* 2.0 (* PI 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 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2))) (pow (* 2.0 (* PI n)) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* 2.0 (* PI n)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* 2.0 (* PI n)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* 2.0 (* PI n)) (- 1.0 k)) (* 2.0 (* PI 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 (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (pow 1.0 3) (* (sqrt k) k)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (* 2.0 (* PI n)) (* 2.0 (* PI n)) (log (* 2.0 (* PI n))) (log (* 2.0 (* PI n))) (log (* 2.0 (* PI n))) (exp (* (* 2.0 PI) n)) (pow (* 2.0 (* PI n)) 3) (pow (* 2.0 (* PI n)) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* 2.0 (* PI n)) 3) (sqrt (* (* 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 (* 2.0 PI)) (* (pow (* 2.0 (* PI n)) 0.25) (log n))))) (* (* (* 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 (* 2.0 PI)) (* (pow (* 2.0 (* PI n)) 0.25) (log n))))) (* (* (* 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)))))) (- (+ (* +nan.0 (- k (* k k))) +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)) (* 2.0 (* PI n)) (* 2.0 (* PI n)) (* 2.0 (* PI n)) 10.529 * * * [progress]: adding candidates to table 11.660 * * [progress]: iteration 3 / 4 11.660 * * * [progress]: picking best candidate 11.688 * * * * [pick]: Picked # 11.689 * * * [progress]: localizing error 11.737 * * * [progress]: generating rewritten candidates 11.737 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1) 11.760 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 11.815 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 11.828 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1 2) 11.866 * * * [progress]: generating series expansions 11.866 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1) 11.867 * [backup-simplify]: Simplify (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 11.867 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 11.867 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 11.867 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 11.867 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 11.867 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 11.867 * [taylor]: Taking taylor expansion of 0.5 in k 11.867 * [backup-simplify]: Simplify 0.5 into 0.5 11.867 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 11.867 * [taylor]: Taking taylor expansion of 1.0 in k 11.867 * [backup-simplify]: Simplify 1.0 into 1.0 11.867 * [taylor]: Taking taylor expansion of k in k 11.867 * [backup-simplify]: Simplify 0 into 0 11.867 * [backup-simplify]: Simplify 1 into 1 11.867 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 11.867 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 11.867 * [taylor]: Taking taylor expansion of 2.0 in k 11.867 * [backup-simplify]: Simplify 2.0 into 2.0 11.867 * [taylor]: Taking taylor expansion of (* n PI) in k 11.867 * [taylor]: Taking taylor expansion of n in k 11.868 * [backup-simplify]: Simplify n into n 11.868 * [taylor]: Taking taylor expansion of PI in k 11.868 * [backup-simplify]: Simplify PI into PI 11.868 * [backup-simplify]: Simplify (* n PI) into (* n PI) 11.868 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 11.868 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 11.869 * [backup-simplify]: Simplify (- 0) into 0 11.869 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 11.870 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 11.870 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 11.870 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 11.870 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 11.870 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 11.870 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 11.870 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 11.870 * [taylor]: Taking taylor expansion of 0.5 in n 11.870 * [backup-simplify]: Simplify 0.5 into 0.5 11.870 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 11.870 * [taylor]: Taking taylor expansion of 1.0 in n 11.870 * [backup-simplify]: Simplify 1.0 into 1.0 11.870 * [taylor]: Taking taylor expansion of k in n 11.870 * [backup-simplify]: Simplify k into k 11.870 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 11.870 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 11.870 * [taylor]: Taking taylor expansion of 2.0 in n 11.870 * [backup-simplify]: Simplify 2.0 into 2.0 11.870 * [taylor]: Taking taylor expansion of (* n PI) in n 11.870 * [taylor]: Taking taylor expansion of n in n 11.870 * [backup-simplify]: Simplify 0 into 0 11.870 * [backup-simplify]: Simplify 1 into 1 11.870 * [taylor]: Taking taylor expansion of PI in n 11.871 * [backup-simplify]: Simplify PI into PI 11.871 * [backup-simplify]: Simplify (* 0 PI) into 0 11.872 * [backup-simplify]: Simplify (* 2.0 0) into 0 11.873 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.875 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 11.876 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.876 * [backup-simplify]: Simplify (- k) into (- k) 11.876 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 11.876 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 11.878 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.879 * [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)))) 11.881 * [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))))) 11.881 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 11.881 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 11.881 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 11.881 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 11.881 * [taylor]: Taking taylor expansion of 0.5 in n 11.881 * [backup-simplify]: Simplify 0.5 into 0.5 11.881 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 11.881 * [taylor]: Taking taylor expansion of 1.0 in n 11.881 * [backup-simplify]: Simplify 1.0 into 1.0 11.881 * [taylor]: Taking taylor expansion of k in n 11.881 * [backup-simplify]: Simplify k into k 11.881 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 11.881 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 11.881 * [taylor]: Taking taylor expansion of 2.0 in n 11.881 * [backup-simplify]: Simplify 2.0 into 2.0 11.881 * [taylor]: Taking taylor expansion of (* n PI) in n 11.881 * [taylor]: Taking taylor expansion of n in n 11.881 * [backup-simplify]: Simplify 0 into 0 11.882 * [backup-simplify]: Simplify 1 into 1 11.882 * [taylor]: Taking taylor expansion of PI in n 11.882 * [backup-simplify]: Simplify PI into PI 11.882 * [backup-simplify]: Simplify (* 0 PI) into 0 11.882 * [backup-simplify]: Simplify (* 2.0 0) into 0 11.884 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.886 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 11.887 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.888 * [backup-simplify]: Simplify (- k) into (- k) 11.888 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 11.888 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 11.889 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.890 * [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)))) 11.892 * [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))))) 11.892 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 11.892 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 11.892 * [taylor]: Taking taylor expansion of 0.5 in k 11.892 * [backup-simplify]: Simplify 0.5 into 0.5 11.892 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 11.892 * [taylor]: Taking taylor expansion of (- 1.0 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 k in k 11.892 * [backup-simplify]: Simplify 0 into 0 11.892 * [backup-simplify]: Simplify 1 into 1 11.892 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 11.892 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 11.892 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 11.892 * [taylor]: Taking taylor expansion of 2.0 in k 11.892 * [backup-simplify]: Simplify 2.0 into 2.0 11.892 * [taylor]: Taking taylor expansion of PI in k 11.892 * [backup-simplify]: Simplify PI into PI 11.893 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.894 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.894 * [taylor]: Taking taylor expansion of (log n) in k 11.894 * [taylor]: Taking taylor expansion of n in k 11.894 * [backup-simplify]: Simplify n into n 11.894 * [backup-simplify]: Simplify (log n) into (log n) 11.895 * [backup-simplify]: Simplify (- 0) into 0 11.895 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 11.896 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 11.897 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 11.899 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 11.900 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 11.901 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 11.902 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.903 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 11.905 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 11.905 * [backup-simplify]: Simplify (- 0) into 0 11.905 * [backup-simplify]: Simplify (+ 0 0) into 0 11.906 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 11.908 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.909 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 11.911 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.911 * [taylor]: Taking taylor expansion of 0 in k 11.911 * [backup-simplify]: Simplify 0 into 0 11.911 * [backup-simplify]: Simplify 0 into 0 11.912 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 11.914 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 11.915 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 11.915 * [backup-simplify]: Simplify (+ 0 0) into 0 11.915 * [backup-simplify]: Simplify (- 1) into -1 11.916 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.917 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 11.919 * [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)))) 11.923 * [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)))))) 11.926 * [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)))))) 11.927 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 11.928 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 11.932 * [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 11.932 * [backup-simplify]: Simplify (- 0) into 0 11.933 * [backup-simplify]: Simplify (+ 0 0) into 0 11.933 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 11.935 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.936 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 11.939 * [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 11.939 * [taylor]: Taking taylor expansion of 0 in k 11.939 * [backup-simplify]: Simplify 0 into 0 11.939 * [backup-simplify]: Simplify 0 into 0 11.939 * [backup-simplify]: Simplify 0 into 0 11.940 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.944 * [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 11.946 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 11.946 * [backup-simplify]: Simplify (+ 0 0) into 0 11.947 * [backup-simplify]: Simplify (- 0) into 0 11.947 * [backup-simplify]: Simplify (+ 0 0) into 0 11.949 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 11.952 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 11.956 * [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)))))) 11.962 * [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)))))) 11.973 * [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)))))) 11.974 * [backup-simplify]: Simplify (pow (* 2.0 (* (/ 1 n) PI)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 11.974 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 11.974 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 11.974 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 11.974 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 11.974 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 11.974 * [taylor]: Taking taylor expansion of 0.5 in k 11.974 * [backup-simplify]: Simplify 0.5 into 0.5 11.974 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 11.974 * [taylor]: Taking taylor expansion of 1.0 in k 11.974 * [backup-simplify]: Simplify 1.0 into 1.0 11.974 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.974 * [taylor]: Taking taylor expansion of k in k 11.974 * [backup-simplify]: Simplify 0 into 0 11.974 * [backup-simplify]: Simplify 1 into 1 11.975 * [backup-simplify]: Simplify (/ 1 1) into 1 11.975 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 11.975 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 11.975 * [taylor]: Taking taylor expansion of 2.0 in k 11.975 * [backup-simplify]: Simplify 2.0 into 2.0 11.975 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.975 * [taylor]: Taking taylor expansion of PI in k 11.975 * [backup-simplify]: Simplify PI into PI 11.975 * [taylor]: Taking taylor expansion of n in k 11.975 * [backup-simplify]: Simplify n into n 11.975 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.975 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 11.975 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 11.976 * [backup-simplify]: Simplify (- 1) into -1 11.976 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.976 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 11.977 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 11.977 * [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))))) 11.977 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 11.977 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 11.977 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 11.977 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 11.977 * [taylor]: Taking taylor expansion of 0.5 in n 11.977 * [backup-simplify]: Simplify 0.5 into 0.5 11.977 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 11.977 * [taylor]: Taking taylor expansion of 1.0 in n 11.977 * [backup-simplify]: Simplify 1.0 into 1.0 11.977 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.977 * [taylor]: Taking taylor expansion of k in n 11.977 * [backup-simplify]: Simplify k into k 11.977 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.977 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 11.978 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 11.978 * [taylor]: Taking taylor expansion of 2.0 in n 11.978 * [backup-simplify]: Simplify 2.0 into 2.0 11.978 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.978 * [taylor]: Taking taylor expansion of PI in n 11.978 * [backup-simplify]: Simplify PI into PI 11.978 * [taylor]: Taking taylor expansion of n in n 11.978 * [backup-simplify]: Simplify 0 into 0 11.978 * [backup-simplify]: Simplify 1 into 1 11.978 * [backup-simplify]: Simplify (/ PI 1) into PI 11.979 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.980 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.980 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.980 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 11.980 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 11.982 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.983 * [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)))) 11.992 * [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))))) 11.992 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 11.993 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 11.993 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 11.993 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 11.993 * [taylor]: Taking taylor expansion of 0.5 in n 11.993 * [backup-simplify]: Simplify 0.5 into 0.5 11.993 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 11.993 * [taylor]: Taking taylor expansion of 1.0 in n 11.993 * [backup-simplify]: Simplify 1.0 into 1.0 11.993 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.993 * [taylor]: Taking taylor expansion of k in n 11.993 * [backup-simplify]: Simplify k into k 11.993 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.993 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 11.993 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 11.993 * [taylor]: Taking taylor expansion of 2.0 in n 11.993 * [backup-simplify]: Simplify 2.0 into 2.0 11.993 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.993 * [taylor]: Taking taylor expansion of PI in n 11.993 * [backup-simplify]: Simplify PI into PI 11.993 * [taylor]: Taking taylor expansion of n in n 11.993 * [backup-simplify]: Simplify 0 into 0 11.993 * [backup-simplify]: Simplify 1 into 1 11.994 * [backup-simplify]: Simplify (/ PI 1) into PI 11.995 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.996 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.996 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.996 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 11.996 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 11.997 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.998 * [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)))) 11.999 * [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))))) 11.999 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 11.999 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 11.999 * [taylor]: Taking taylor expansion of 0.5 in k 11.999 * [backup-simplify]: Simplify 0.5 into 0.5 11.999 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 11.999 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 11.999 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 11.999 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 11.999 * [taylor]: Taking taylor expansion of 2.0 in k 11.999 * [backup-simplify]: Simplify 2.0 into 2.0 11.999 * [taylor]: Taking taylor expansion of PI in k 11.999 * [backup-simplify]: Simplify PI into PI 11.999 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.000 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.000 * [taylor]: Taking taylor expansion of (log n) in k 12.000 * [taylor]: Taking taylor expansion of n in k 12.000 * [backup-simplify]: Simplify n into n 12.000 * [backup-simplify]: Simplify (log n) into (log n) 12.000 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.000 * [taylor]: Taking taylor expansion of 1.0 in k 12.000 * [backup-simplify]: Simplify 1.0 into 1.0 12.000 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.000 * [taylor]: Taking taylor expansion of k in k 12.000 * [backup-simplify]: Simplify 0 into 0 12.000 * [backup-simplify]: Simplify 1 into 1 12.000 * [backup-simplify]: Simplify (/ 1 1) into 1 12.000 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.001 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 12.001 * [backup-simplify]: Simplify (- 1) into -1 12.002 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.002 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 12.003 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 12.004 * [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))))) 12.004 * [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))))) 12.005 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.005 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.006 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.007 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.007 * [backup-simplify]: Simplify (- 0) into 0 12.007 * [backup-simplify]: Simplify (+ 0 0) into 0 12.007 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 12.008 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.009 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 12.011 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.011 * [taylor]: Taking taylor expansion of 0 in k 12.011 * [backup-simplify]: Simplify 0 into 0 12.011 * [backup-simplify]: Simplify 0 into 0 12.011 * [backup-simplify]: Simplify 0 into 0 12.012 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.012 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.014 * [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 12.015 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.015 * [backup-simplify]: Simplify (- 0) into 0 12.015 * [backup-simplify]: Simplify (+ 0 0) into 0 12.016 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 12.017 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.018 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 12.019 * [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 12.019 * [taylor]: Taking taylor expansion of 0 in k 12.019 * [backup-simplify]: Simplify 0 into 0 12.019 * [backup-simplify]: Simplify 0 into 0 12.019 * [backup-simplify]: Simplify 0 into 0 12.019 * [backup-simplify]: Simplify 0 into 0 12.020 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.021 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.024 * [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 12.024 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.024 * [backup-simplify]: Simplify (- 0) into 0 12.025 * [backup-simplify]: Simplify (+ 0 0) into 0 12.025 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 12.026 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.027 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 12.029 * [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 12.029 * [taylor]: Taking taylor expansion of 0 in k 12.029 * [backup-simplify]: Simplify 0 into 0 12.029 * [backup-simplify]: Simplify 0 into 0 12.030 * [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)))) 12.030 * [backup-simplify]: Simplify (pow (* 2.0 (* (/ 1 (- n)) PI)) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 12.030 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 12.030 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 12.030 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 12.030 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 12.030 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 12.030 * [taylor]: Taking taylor expansion of 0.5 in k 12.030 * [backup-simplify]: Simplify 0.5 into 0.5 12.030 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.030 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.030 * [taylor]: Taking taylor expansion of k in k 12.030 * [backup-simplify]: Simplify 0 into 0 12.030 * [backup-simplify]: Simplify 1 into 1 12.031 * [backup-simplify]: Simplify (/ 1 1) into 1 12.031 * [taylor]: Taking taylor expansion of 1.0 in k 12.031 * [backup-simplify]: Simplify 1.0 into 1.0 12.031 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 12.031 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 12.031 * [taylor]: Taking taylor expansion of -2.0 in k 12.031 * [backup-simplify]: Simplify -2.0 into -2.0 12.031 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.031 * [taylor]: Taking taylor expansion of PI in k 12.031 * [backup-simplify]: Simplify PI into PI 12.031 * [taylor]: Taking taylor expansion of n in k 12.031 * [backup-simplify]: Simplify n into n 12.031 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.031 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 12.031 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 12.031 * [backup-simplify]: Simplify (+ 1 0) into 1 12.032 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 12.032 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 12.032 * [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)))))) 12.032 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 12.032 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.032 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.032 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 12.032 * [taylor]: Taking taylor expansion of 0.5 in n 12.032 * [backup-simplify]: Simplify 0.5 into 0.5 12.032 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.032 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.032 * [taylor]: Taking taylor expansion of k in n 12.032 * [backup-simplify]: Simplify k into k 12.032 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.032 * [taylor]: Taking taylor expansion of 1.0 in n 12.032 * [backup-simplify]: Simplify 1.0 into 1.0 12.032 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.032 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.032 * [taylor]: Taking taylor expansion of -2.0 in n 12.032 * [backup-simplify]: Simplify -2.0 into -2.0 12.032 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.032 * [taylor]: Taking taylor expansion of PI in n 12.032 * [backup-simplify]: Simplify PI into PI 12.032 * [taylor]: Taking taylor expansion of n in n 12.032 * [backup-simplify]: Simplify 0 into 0 12.032 * [backup-simplify]: Simplify 1 into 1 12.033 * [backup-simplify]: Simplify (/ PI 1) into PI 12.033 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.034 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.034 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.034 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 12.035 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.035 * [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)))) 12.036 * [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))))) 12.036 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 12.036 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.036 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.036 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 12.036 * [taylor]: Taking taylor expansion of 0.5 in n 12.036 * [backup-simplify]: Simplify 0.5 into 0.5 12.036 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.036 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.036 * [taylor]: Taking taylor expansion of k in n 12.036 * [backup-simplify]: Simplify k into k 12.036 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.036 * [taylor]: Taking taylor expansion of 1.0 in n 12.036 * [backup-simplify]: Simplify 1.0 into 1.0 12.036 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.036 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.036 * [taylor]: Taking taylor expansion of -2.0 in n 12.036 * [backup-simplify]: Simplify -2.0 into -2.0 12.036 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.036 * [taylor]: Taking taylor expansion of PI in n 12.036 * [backup-simplify]: Simplify PI into PI 12.036 * [taylor]: Taking taylor expansion of n in n 12.036 * [backup-simplify]: Simplify 0 into 0 12.037 * [backup-simplify]: Simplify 1 into 1 12.037 * [backup-simplify]: Simplify (/ PI 1) into PI 12.037 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.038 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.038 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.038 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 12.039 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.039 * [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)))) 12.040 * [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))))) 12.040 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 12.040 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 12.040 * [taylor]: Taking taylor expansion of 0.5 in k 12.040 * [backup-simplify]: Simplify 0.5 into 0.5 12.040 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 12.040 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.040 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.041 * [taylor]: Taking taylor expansion of k in k 12.041 * [backup-simplify]: Simplify 0 into 0 12.041 * [backup-simplify]: Simplify 1 into 1 12.041 * [backup-simplify]: Simplify (/ 1 1) into 1 12.041 * [taylor]: Taking taylor expansion of 1.0 in k 12.041 * [backup-simplify]: Simplify 1.0 into 1.0 12.041 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 12.041 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 12.041 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 12.041 * [taylor]: Taking taylor expansion of -2.0 in k 12.041 * [backup-simplify]: Simplify -2.0 into -2.0 12.041 * [taylor]: Taking taylor expansion of PI in k 12.041 * [backup-simplify]: Simplify PI into PI 12.041 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.042 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.042 * [taylor]: Taking taylor expansion of (log n) in k 12.042 * [taylor]: Taking taylor expansion of n in k 12.042 * [backup-simplify]: Simplify n into n 12.042 * [backup-simplify]: Simplify (log n) into (log n) 12.042 * [backup-simplify]: Simplify (+ 1 0) into 1 12.042 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.043 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 12.044 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 12.045 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 12.046 * [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))))) 12.047 * [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))))) 12.049 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.050 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 12.051 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 12.052 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.052 * [backup-simplify]: Simplify (+ 0 0) into 0 12.053 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 12.054 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.055 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 12.057 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.057 * [taylor]: Taking taylor expansion of 0 in k 12.057 * [backup-simplify]: Simplify 0 into 0 12.057 * [backup-simplify]: Simplify 0 into 0 12.057 * [backup-simplify]: Simplify 0 into 0 12.058 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.059 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.063 * [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 12.063 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.064 * [backup-simplify]: Simplify (+ 0 0) into 0 12.065 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 12.066 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.068 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 12.070 * [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 12.070 * [taylor]: Taking taylor expansion of 0 in k 12.070 * [backup-simplify]: Simplify 0 into 0 12.070 * [backup-simplify]: Simplify 0 into 0 12.070 * [backup-simplify]: Simplify 0 into 0 12.070 * [backup-simplify]: Simplify 0 into 0 12.072 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.073 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.079 * [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 12.079 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.080 * [backup-simplify]: Simplify (+ 0 0) into 0 12.081 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 12.082 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.084 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 12.087 * [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 12.087 * [taylor]: Taking taylor expansion of 0 in k 12.087 * [backup-simplify]: Simplify 0 into 0 12.087 * [backup-simplify]: Simplify 0 into 0 12.089 * [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)))))) 12.089 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 12.090 * [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))) 12.090 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 12.090 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 12.090 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 12.090 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 12.090 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 12.090 * [taylor]: Taking taylor expansion of 0.25 in k 12.090 * [backup-simplify]: Simplify 0.25 into 0.25 12.090 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.090 * [taylor]: Taking taylor expansion of 1.0 in k 12.090 * [backup-simplify]: Simplify 1.0 into 1.0 12.090 * [taylor]: Taking taylor expansion of k in k 12.090 * [backup-simplify]: Simplify 0 into 0 12.090 * [backup-simplify]: Simplify 1 into 1 12.090 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 12.090 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 12.090 * [taylor]: Taking taylor expansion of 2.0 in k 12.090 * [backup-simplify]: Simplify 2.0 into 2.0 12.090 * [taylor]: Taking taylor expansion of (* n PI) in k 12.090 * [taylor]: Taking taylor expansion of n in k 12.090 * [backup-simplify]: Simplify n into n 12.090 * [taylor]: Taking taylor expansion of PI in k 12.090 * [backup-simplify]: Simplify PI into PI 12.090 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.090 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 12.090 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 12.091 * [backup-simplify]: Simplify (- 0) into 0 12.091 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.092 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 12.092 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 12.092 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 12.092 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 12.092 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.092 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.092 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 12.092 * [taylor]: Taking taylor expansion of 0.25 in n 12.092 * [backup-simplify]: Simplify 0.25 into 0.25 12.092 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.092 * [taylor]: Taking taylor expansion of 1.0 in n 12.092 * [backup-simplify]: Simplify 1.0 into 1.0 12.092 * [taylor]: Taking taylor expansion of k in n 12.092 * [backup-simplify]: Simplify k into k 12.092 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.092 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.093 * [taylor]: Taking taylor expansion of 2.0 in n 12.093 * [backup-simplify]: Simplify 2.0 into 2.0 12.093 * [taylor]: Taking taylor expansion of (* n PI) in n 12.093 * [taylor]: Taking taylor expansion of n in n 12.093 * [backup-simplify]: Simplify 0 into 0 12.093 * [backup-simplify]: Simplify 1 into 1 12.093 * [taylor]: Taking taylor expansion of PI in n 12.093 * [backup-simplify]: Simplify PI into PI 12.093 * [backup-simplify]: Simplify (* 0 PI) into 0 12.094 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.095 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.097 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.098 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.098 * [backup-simplify]: Simplify (- k) into (- k) 12.098 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.098 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 12.100 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.101 * [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)))) 12.102 * [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))))) 12.102 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 12.102 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.102 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.102 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 12.102 * [taylor]: Taking taylor expansion of 0.25 in n 12.102 * [backup-simplify]: Simplify 0.25 into 0.25 12.102 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.102 * [taylor]: Taking taylor expansion of 1.0 in n 12.102 * [backup-simplify]: Simplify 1.0 into 1.0 12.102 * [taylor]: Taking taylor expansion of k in n 12.102 * [backup-simplify]: Simplify k into k 12.102 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.102 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.103 * [taylor]: Taking taylor expansion of 2.0 in n 12.103 * [backup-simplify]: Simplify 2.0 into 2.0 12.103 * [taylor]: Taking taylor expansion of (* n PI) in n 12.103 * [taylor]: Taking taylor expansion of n in n 12.103 * [backup-simplify]: Simplify 0 into 0 12.103 * [backup-simplify]: Simplify 1 into 1 12.103 * [taylor]: Taking taylor expansion of PI in n 12.103 * [backup-simplify]: Simplify PI into PI 12.103 * [backup-simplify]: Simplify (* 0 PI) into 0 12.104 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.105 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.107 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.108 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.108 * [backup-simplify]: Simplify (- k) into (- k) 12.108 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.108 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 12.109 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.111 * [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)))) 12.119 * [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))))) 12.119 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 12.119 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 12.119 * [taylor]: Taking taylor expansion of 0.25 in k 12.119 * [backup-simplify]: Simplify 0.25 into 0.25 12.119 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 12.119 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.119 * [taylor]: Taking taylor expansion of 1.0 in k 12.119 * [backup-simplify]: Simplify 1.0 into 1.0 12.119 * [taylor]: Taking taylor expansion of k in k 12.119 * [backup-simplify]: Simplify 0 into 0 12.119 * [backup-simplify]: Simplify 1 into 1 12.119 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 12.120 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.120 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.120 * [taylor]: Taking taylor expansion of 2.0 in k 12.120 * [backup-simplify]: Simplify 2.0 into 2.0 12.120 * [taylor]: Taking taylor expansion of PI in k 12.120 * [backup-simplify]: Simplify PI into PI 12.120 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.121 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.121 * [taylor]: Taking taylor expansion of (log n) in k 12.121 * [taylor]: Taking taylor expansion of n in k 12.121 * [backup-simplify]: Simplify n into n 12.121 * [backup-simplify]: Simplify (log n) into (log n) 12.122 * [backup-simplify]: Simplify (- 0) into 0 12.122 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.123 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 12.124 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 12.126 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 12.127 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 12.128 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 12.129 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.130 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 12.132 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.132 * [backup-simplify]: Simplify (- 0) into 0 12.133 * [backup-simplify]: Simplify (+ 0 0) into 0 12.133 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 12.135 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.136 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 12.138 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.138 * [taylor]: Taking taylor expansion of 0 in k 12.138 * [backup-simplify]: Simplify 0 into 0 12.138 * [backup-simplify]: Simplify 0 into 0 12.139 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.141 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.142 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 12.142 * [backup-simplify]: Simplify (+ 0 0) into 0 12.143 * [backup-simplify]: Simplify (- 1) into -1 12.143 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.144 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 12.146 * [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)))) 12.148 * [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)))))) 12.149 * [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)))))) 12.150 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.151 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 12.153 * [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 12.153 * [backup-simplify]: Simplify (- 0) into 0 12.153 * [backup-simplify]: Simplify (+ 0 0) into 0 12.154 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 12.155 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.156 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.157 * [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 12.157 * [taylor]: Taking taylor expansion of 0 in k 12.157 * [backup-simplify]: Simplify 0 into 0 12.157 * [backup-simplify]: Simplify 0 into 0 12.157 * [backup-simplify]: Simplify 0 into 0 12.158 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.160 * [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 12.162 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 12.162 * [backup-simplify]: Simplify (+ 0 0) into 0 12.162 * [backup-simplify]: Simplify (- 0) into 0 12.162 * [backup-simplify]: Simplify (+ 0 0) into 0 12.164 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.165 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 12.168 * [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))))) 12.171 * [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))))) 12.177 * [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)))))) 12.178 * [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)))) 12.178 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 12.178 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 12.178 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 12.178 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 12.178 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 12.178 * [taylor]: Taking taylor expansion of 0.25 in k 12.178 * [backup-simplify]: Simplify 0.25 into 0.25 12.178 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.178 * [taylor]: Taking taylor expansion of 1.0 in k 12.178 * [backup-simplify]: Simplify 1.0 into 1.0 12.178 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.178 * [taylor]: Taking taylor expansion of k in k 12.178 * [backup-simplify]: Simplify 0 into 0 12.178 * [backup-simplify]: Simplify 1 into 1 12.178 * [backup-simplify]: Simplify (/ 1 1) into 1 12.178 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 12.178 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 12.178 * [taylor]: Taking taylor expansion of 2.0 in k 12.179 * [backup-simplify]: Simplify 2.0 into 2.0 12.179 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.179 * [taylor]: Taking taylor expansion of PI in k 12.179 * [backup-simplify]: Simplify PI into PI 12.179 * [taylor]: Taking taylor expansion of n in k 12.179 * [backup-simplify]: Simplify n into n 12.179 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.179 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 12.179 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 12.179 * [backup-simplify]: Simplify (- 1) into -1 12.179 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.180 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 12.180 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 12.180 * [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))))) 12.180 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 12.180 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.180 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.180 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 12.180 * [taylor]: Taking taylor expansion of 0.25 in n 12.180 * [backup-simplify]: Simplify 0.25 into 0.25 12.180 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.180 * [taylor]: Taking taylor expansion of 1.0 in n 12.180 * [backup-simplify]: Simplify 1.0 into 1.0 12.180 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.180 * [taylor]: Taking taylor expansion of k in n 12.181 * [backup-simplify]: Simplify k into k 12.181 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.181 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.181 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.181 * [taylor]: Taking taylor expansion of 2.0 in n 12.181 * [backup-simplify]: Simplify 2.0 into 2.0 12.181 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.181 * [taylor]: Taking taylor expansion of PI in n 12.181 * [backup-simplify]: Simplify PI into PI 12.181 * [taylor]: Taking taylor expansion of n in n 12.181 * [backup-simplify]: Simplify 0 into 0 12.181 * [backup-simplify]: Simplify 1 into 1 12.181 * [backup-simplify]: Simplify (/ PI 1) into PI 12.182 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.183 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.183 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.183 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.183 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 12.185 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.186 * [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)))) 12.187 * [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))))) 12.187 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 12.187 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.187 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.187 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 12.187 * [taylor]: Taking taylor expansion of 0.25 in n 12.187 * [backup-simplify]: Simplify 0.25 into 0.25 12.187 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.187 * [taylor]: Taking taylor expansion of 1.0 in n 12.187 * [backup-simplify]: Simplify 1.0 into 1.0 12.187 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.187 * [taylor]: Taking taylor expansion of k in n 12.187 * [backup-simplify]: Simplify k into k 12.187 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.187 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.188 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.188 * [taylor]: Taking taylor expansion of 2.0 in n 12.188 * [backup-simplify]: Simplify 2.0 into 2.0 12.188 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.188 * [taylor]: Taking taylor expansion of PI in n 12.188 * [backup-simplify]: Simplify PI into PI 12.188 * [taylor]: Taking taylor expansion of n in n 12.188 * [backup-simplify]: Simplify 0 into 0 12.188 * [backup-simplify]: Simplify 1 into 1 12.188 * [backup-simplify]: Simplify (/ PI 1) into PI 12.189 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.190 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.190 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.190 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.190 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 12.192 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.193 * [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)))) 12.194 * [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))))) 12.194 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 12.194 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 12.195 * [taylor]: Taking taylor expansion of 0.25 in k 12.195 * [backup-simplify]: Simplify 0.25 into 0.25 12.195 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 12.195 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 12.195 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.195 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.195 * [taylor]: Taking taylor expansion of 2.0 in k 12.195 * [backup-simplify]: Simplify 2.0 into 2.0 12.195 * [taylor]: Taking taylor expansion of PI in k 12.195 * [backup-simplify]: Simplify PI into PI 12.195 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.196 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.197 * [taylor]: Taking taylor expansion of (log n) in k 12.197 * [taylor]: Taking taylor expansion of n in k 12.197 * [backup-simplify]: Simplify n into n 12.197 * [backup-simplify]: Simplify (log n) into (log n) 12.197 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.197 * [taylor]: Taking taylor expansion of 1.0 in k 12.197 * [backup-simplify]: Simplify 1.0 into 1.0 12.197 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.197 * [taylor]: Taking taylor expansion of k in k 12.197 * [backup-simplify]: Simplify 0 into 0 12.197 * [backup-simplify]: Simplify 1 into 1 12.197 * [backup-simplify]: Simplify (/ 1 1) into 1 12.197 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.198 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 12.199 * [backup-simplify]: Simplify (- 1) into -1 12.199 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.200 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 12.201 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 12.203 * [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))))) 12.204 * [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))))) 12.205 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.206 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.208 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.208 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.209 * [backup-simplify]: Simplify (- 0) into 0 12.209 * [backup-simplify]: Simplify (+ 0 0) into 0 12.210 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 12.212 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.213 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 12.215 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.215 * [taylor]: Taking taylor expansion of 0 in k 12.215 * [backup-simplify]: Simplify 0 into 0 12.215 * [backup-simplify]: Simplify 0 into 0 12.215 * [backup-simplify]: Simplify 0 into 0 12.216 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.217 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.221 * [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 12.221 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.222 * [backup-simplify]: Simplify (- 0) into 0 12.222 * [backup-simplify]: Simplify (+ 0 0) into 0 12.223 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 12.225 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.226 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 12.229 * [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 12.229 * [taylor]: Taking taylor expansion of 0 in k 12.229 * [backup-simplify]: Simplify 0 into 0 12.230 * [backup-simplify]: Simplify 0 into 0 12.230 * [backup-simplify]: Simplify 0 into 0 12.230 * [backup-simplify]: Simplify 0 into 0 12.231 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.232 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.238 * [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 12.238 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.239 * [backup-simplify]: Simplify (- 0) into 0 12.239 * [backup-simplify]: Simplify (+ 0 0) into 0 12.241 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 12.242 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.244 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 12.257 * [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 12.257 * [taylor]: Taking taylor expansion of 0 in k 12.257 * [backup-simplify]: Simplify 0 into 0 12.257 * [backup-simplify]: Simplify 0 into 0 12.258 * [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)))) 12.259 * [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))) 12.259 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 12.259 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 12.260 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 12.260 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 12.260 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 12.260 * [taylor]: Taking taylor expansion of 0.25 in k 12.260 * [backup-simplify]: Simplify 0.25 into 0.25 12.260 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.260 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.260 * [taylor]: Taking taylor expansion of k in k 12.260 * [backup-simplify]: Simplify 0 into 0 12.260 * [backup-simplify]: Simplify 1 into 1 12.261 * [backup-simplify]: Simplify (/ 1 1) into 1 12.261 * [taylor]: Taking taylor expansion of 1.0 in k 12.261 * [backup-simplify]: Simplify 1.0 into 1.0 12.261 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 12.261 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 12.261 * [taylor]: Taking taylor expansion of -2.0 in k 12.261 * [backup-simplify]: Simplify -2.0 into -2.0 12.261 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.261 * [taylor]: Taking taylor expansion of PI in k 12.261 * [backup-simplify]: Simplify PI into PI 12.261 * [taylor]: Taking taylor expansion of n in k 12.261 * [backup-simplify]: Simplify n into n 12.261 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.261 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 12.261 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 12.262 * [backup-simplify]: Simplify (+ 1 0) into 1 12.262 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 12.262 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 12.263 * [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)))))) 12.263 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 12.263 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.263 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.263 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 12.263 * [taylor]: Taking taylor expansion of 0.25 in n 12.263 * [backup-simplify]: Simplify 0.25 into 0.25 12.263 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.263 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.263 * [taylor]: Taking taylor expansion of k in n 12.263 * [backup-simplify]: Simplify k into k 12.263 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.263 * [taylor]: Taking taylor expansion of 1.0 in n 12.263 * [backup-simplify]: Simplify 1.0 into 1.0 12.263 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.263 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.263 * [taylor]: Taking taylor expansion of -2.0 in n 12.263 * [backup-simplify]: Simplify -2.0 into -2.0 12.263 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.263 * [taylor]: Taking taylor expansion of PI in n 12.263 * [backup-simplify]: Simplify PI into PI 12.264 * [taylor]: Taking taylor expansion of n in n 12.264 * [backup-simplify]: Simplify 0 into 0 12.264 * [backup-simplify]: Simplify 1 into 1 12.264 * [backup-simplify]: Simplify (/ PI 1) into PI 12.265 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.266 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.266 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.266 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 12.268 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.269 * [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)))) 12.270 * [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))))) 12.270 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 12.270 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.270 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.270 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 12.270 * [taylor]: Taking taylor expansion of 0.25 in n 12.270 * [backup-simplify]: Simplify 0.25 into 0.25 12.270 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.271 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.271 * [taylor]: Taking taylor expansion of k in n 12.271 * [backup-simplify]: Simplify k into k 12.271 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.271 * [taylor]: Taking taylor expansion of 1.0 in n 12.271 * [backup-simplify]: Simplify 1.0 into 1.0 12.271 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.271 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.271 * [taylor]: Taking taylor expansion of -2.0 in n 12.271 * [backup-simplify]: Simplify -2.0 into -2.0 12.271 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.271 * [taylor]: Taking taylor expansion of PI in n 12.271 * [backup-simplify]: Simplify PI into PI 12.271 * [taylor]: Taking taylor expansion of n in n 12.271 * [backup-simplify]: Simplify 0 into 0 12.271 * [backup-simplify]: Simplify 1 into 1 12.272 * [backup-simplify]: Simplify (/ PI 1) into PI 12.272 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.273 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.273 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.273 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 12.275 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.276 * [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)))) 12.277 * [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))))) 12.277 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 12.277 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 12.277 * [taylor]: Taking taylor expansion of 0.25 in k 12.277 * [backup-simplify]: Simplify 0.25 into 0.25 12.277 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 12.277 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.277 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.277 * [taylor]: Taking taylor expansion of k in k 12.277 * [backup-simplify]: Simplify 0 into 0 12.277 * [backup-simplify]: Simplify 1 into 1 12.278 * [backup-simplify]: Simplify (/ 1 1) into 1 12.278 * [taylor]: Taking taylor expansion of 1.0 in k 12.278 * [backup-simplify]: Simplify 1.0 into 1.0 12.278 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 12.278 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 12.278 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 12.278 * [taylor]: Taking taylor expansion of -2.0 in k 12.278 * [backup-simplify]: Simplify -2.0 into -2.0 12.278 * [taylor]: Taking taylor expansion of PI in k 12.278 * [backup-simplify]: Simplify PI into PI 12.278 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.279 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.279 * [taylor]: Taking taylor expansion of (log n) in k 12.279 * [taylor]: Taking taylor expansion of n in k 12.280 * [backup-simplify]: Simplify n into n 12.280 * [backup-simplify]: Simplify (log n) into (log n) 12.280 * [backup-simplify]: Simplify (+ 1 0) into 1 12.280 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.281 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 12.282 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 12.283 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 12.284 * [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))))) 12.285 * [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))))) 12.286 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.287 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 12.289 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 12.289 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.290 * [backup-simplify]: Simplify (+ 0 0) into 0 12.290 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 12.291 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.293 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 12.295 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.295 * [taylor]: Taking taylor expansion of 0 in k 12.295 * [backup-simplify]: Simplify 0 into 0 12.295 * [backup-simplify]: Simplify 0 into 0 12.295 * [backup-simplify]: Simplify 0 into 0 12.296 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.297 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.300 * [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 12.300 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.300 * [backup-simplify]: Simplify (+ 0 0) into 0 12.301 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 12.302 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.303 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 12.304 * [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 12.304 * [taylor]: Taking taylor expansion of 0 in k 12.304 * [backup-simplify]: Simplify 0 into 0 12.304 * [backup-simplify]: Simplify 0 into 0 12.304 * [backup-simplify]: Simplify 0 into 0 12.304 * [backup-simplify]: Simplify 0 into 0 12.305 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.306 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.309 * [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 12.309 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.309 * [backup-simplify]: Simplify (+ 0 0) into 0 12.310 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 12.311 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.312 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 12.314 * [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 12.314 * [taylor]: Taking taylor expansion of 0 in k 12.314 * [backup-simplify]: Simplify 0 into 0 12.314 * [backup-simplify]: Simplify 0 into 0 12.315 * [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)))))) 12.315 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 12.315 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 12.315 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 12.315 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 12.315 * [taylor]: Taking taylor expansion of 1.0 in k 12.315 * [backup-simplify]: Simplify 1.0 into 1.0 12.315 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 12.315 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.315 * [taylor]: Taking taylor expansion of k in k 12.315 * [backup-simplify]: Simplify 0 into 0 12.315 * [backup-simplify]: Simplify 1 into 1 12.315 * [backup-simplify]: Simplify (/ 1 1) into 1 12.316 * [backup-simplify]: Simplify (sqrt 0) into 0 12.317 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.317 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 12.317 * [taylor]: Taking taylor expansion of 1.0 in k 12.317 * [backup-simplify]: Simplify 1.0 into 1.0 12.317 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 12.317 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.317 * [taylor]: Taking taylor expansion of k in k 12.317 * [backup-simplify]: Simplify 0 into 0 12.317 * [backup-simplify]: Simplify 1 into 1 12.317 * [backup-simplify]: Simplify (/ 1 1) into 1 12.317 * [backup-simplify]: Simplify (sqrt 0) into 0 12.318 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.318 * [backup-simplify]: Simplify (* 1.0 0) into 0 12.318 * [backup-simplify]: Simplify 0 into 0 12.319 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 12.319 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.320 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 12.321 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.323 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 12.323 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.323 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.325 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.327 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 12.327 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.328 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 12.328 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 12.328 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 12.328 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 12.328 * [taylor]: Taking taylor expansion of 1.0 in k 12.328 * [backup-simplify]: Simplify 1.0 into 1.0 12.328 * [taylor]: Taking taylor expansion of (sqrt k) in k 12.328 * [taylor]: Taking taylor expansion of k in k 12.328 * [backup-simplify]: Simplify 0 into 0 12.328 * [backup-simplify]: Simplify 1 into 1 12.328 * [backup-simplify]: Simplify (sqrt 0) into 0 12.329 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.329 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 12.329 * [taylor]: Taking taylor expansion of 1.0 in k 12.329 * [backup-simplify]: Simplify 1.0 into 1.0 12.329 * [taylor]: Taking taylor expansion of (sqrt k) in k 12.329 * [taylor]: Taking taylor expansion of k in k 12.329 * [backup-simplify]: Simplify 0 into 0 12.329 * [backup-simplify]: Simplify 1 into 1 12.329 * [backup-simplify]: Simplify (sqrt 0) into 0 12.330 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.331 * [backup-simplify]: Simplify (* 1.0 0) into 0 12.331 * [backup-simplify]: Simplify 0 into 0 12.331 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 12.332 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.335 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.337 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 12.337 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.341 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.343 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 12.344 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.345 * [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)))))))) 12.345 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 12.345 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 12.345 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 12.345 * [taylor]: Taking taylor expansion of 1.0 in k 12.345 * [backup-simplify]: Simplify 1.0 into 1.0 12.345 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.345 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.345 * [taylor]: Taking taylor expansion of -1 in k 12.345 * [backup-simplify]: Simplify -1 into -1 12.345 * [taylor]: Taking taylor expansion of k in k 12.345 * [backup-simplify]: Simplify 0 into 0 12.345 * [backup-simplify]: Simplify 1 into 1 12.345 * [backup-simplify]: Simplify (/ -1 1) into -1 12.346 * [backup-simplify]: Simplify (sqrt 0) into 0 12.346 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.347 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 12.347 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 12.347 * [taylor]: Taking taylor expansion of 1.0 in k 12.347 * [backup-simplify]: Simplify 1.0 into 1.0 12.347 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.347 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.347 * [taylor]: Taking taylor expansion of -1 in k 12.347 * [backup-simplify]: Simplify -1 into -1 12.347 * [taylor]: Taking taylor expansion of k in k 12.347 * [backup-simplify]: Simplify 0 into 0 12.347 * [backup-simplify]: Simplify 1 into 1 12.347 * [backup-simplify]: Simplify (/ -1 1) into -1 12.347 * [backup-simplify]: Simplify (sqrt 0) into 0 12.348 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.348 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 12.348 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.349 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 12.350 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.352 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 12.352 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.353 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.355 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.357 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 12.358 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.358 * [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))))) 12.358 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1 2) 12.359 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.359 * [approximate]: Taking taylor expansion of (* n PI) in (n) around 0 12.359 * [taylor]: Taking taylor expansion of (* n PI) in n 12.359 * [taylor]: Taking taylor expansion of n in n 12.359 * [backup-simplify]: Simplify 0 into 0 12.359 * [backup-simplify]: Simplify 1 into 1 12.359 * [taylor]: Taking taylor expansion of PI in n 12.359 * [backup-simplify]: Simplify PI into PI 12.359 * [taylor]: Taking taylor expansion of (* n PI) in n 12.359 * [taylor]: Taking taylor expansion of n in n 12.359 * [backup-simplify]: Simplify 0 into 0 12.359 * [backup-simplify]: Simplify 1 into 1 12.359 * [taylor]: Taking taylor expansion of PI in n 12.359 * [backup-simplify]: Simplify PI into PI 12.359 * [backup-simplify]: Simplify (* 0 PI) into 0 12.359 * [backup-simplify]: Simplify 0 into 0 12.360 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.360 * [backup-simplify]: Simplify PI into PI 12.361 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.361 * [backup-simplify]: Simplify 0 into 0 12.362 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.362 * [backup-simplify]: Simplify 0 into 0 12.362 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 12.362 * [backup-simplify]: Simplify 0 into 0 12.363 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 12.363 * [backup-simplify]: Simplify 0 into 0 12.370 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 12.371 * [backup-simplify]: Simplify 0 into 0 12.372 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 12.372 * [backup-simplify]: Simplify 0 into 0 12.372 * [backup-simplify]: Simplify (* PI n) into (* n PI) 12.372 * [backup-simplify]: Simplify (* (/ 1 n) PI) into (/ PI n) 12.372 * [approximate]: Taking taylor expansion of (/ PI n) in (n) around 0 12.372 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.372 * [taylor]: Taking taylor expansion of PI in n 12.372 * [backup-simplify]: Simplify PI into PI 12.372 * [taylor]: Taking taylor expansion of n in n 12.372 * [backup-simplify]: Simplify 0 into 0 12.372 * [backup-simplify]: Simplify 1 into 1 12.373 * [backup-simplify]: Simplify (/ PI 1) into PI 12.373 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.373 * [taylor]: Taking taylor expansion of PI in n 12.373 * [backup-simplify]: Simplify PI into PI 12.373 * [taylor]: Taking taylor expansion of n in n 12.373 * [backup-simplify]: Simplify 0 into 0 12.373 * [backup-simplify]: Simplify 1 into 1 12.373 * [backup-simplify]: Simplify (/ PI 1) into PI 12.373 * [backup-simplify]: Simplify PI into PI 12.374 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.374 * [backup-simplify]: Simplify 0 into 0 12.374 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.374 * [backup-simplify]: Simplify 0 into 0 12.375 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.375 * [backup-simplify]: Simplify 0 into 0 12.375 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.375 * [backup-simplify]: Simplify 0 into 0 12.376 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.376 * [backup-simplify]: Simplify 0 into 0 12.377 * [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 12.377 * [backup-simplify]: Simplify 0 into 0 12.377 * [backup-simplify]: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI) 12.377 * [backup-simplify]: Simplify (* (/ 1 (- n)) PI) into (* -1 (/ PI n)) 12.377 * [approximate]: Taking taylor expansion of (* -1 (/ PI n)) in (n) around 0 12.377 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 12.377 * [taylor]: Taking taylor expansion of -1 in n 12.377 * [backup-simplify]: Simplify -1 into -1 12.377 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.377 * [taylor]: Taking taylor expansion of PI in n 12.377 * [backup-simplify]: Simplify PI into PI 12.377 * [taylor]: Taking taylor expansion of n in n 12.377 * [backup-simplify]: Simplify 0 into 0 12.377 * [backup-simplify]: Simplify 1 into 1 12.377 * [backup-simplify]: Simplify (/ PI 1) into PI 12.377 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 12.377 * [taylor]: Taking taylor expansion of -1 in n 12.377 * [backup-simplify]: Simplify -1 into -1 12.378 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.378 * [taylor]: Taking taylor expansion of PI in n 12.378 * [backup-simplify]: Simplify PI into PI 12.378 * [taylor]: Taking taylor expansion of n in n 12.378 * [backup-simplify]: Simplify 0 into 0 12.378 * [backup-simplify]: Simplify 1 into 1 12.378 * [backup-simplify]: Simplify (/ PI 1) into PI 12.378 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 12.379 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 12.379 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.380 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0 12.380 * [backup-simplify]: Simplify 0 into 0 12.380 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.381 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 12.381 * [backup-simplify]: Simplify 0 into 0 12.381 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.382 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.382 * [backup-simplify]: Simplify 0 into 0 12.383 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.383 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 12.383 * [backup-simplify]: Simplify 0 into 0 12.385 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.386 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 12.386 * [backup-simplify]: Simplify 0 into 0 12.387 * [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 12.389 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 12.389 * [backup-simplify]: Simplify 0 into 0 12.390 * [backup-simplify]: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) 12.390 * * * [progress]: simplifying candidates 12.395 * [simplify]: Simplifying: (* (+ (log 2.0) (+ (log n) (log PI))) (/ (- 1.0 k) 2.0)) (* (+ (log 2.0) (log (* n PI))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* n PI))) (/ (- 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 (* n PI)) (/ 1.0 2.0)) (pow (* 2.0 (* n PI)) (/ k 2.0)) (pow (* 2.0 (* n PI)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* 2.0 (* n PI)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) 1)) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ 1 1)) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ 1 1)) (pow (* 2.0 (* n PI)) 1) (pow (* 2.0 (* n PI)) (- 1.0 k)) (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)) (log (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (exp (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (+ (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) 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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) (* n PI) (+ (log n) (log PI)) (log (* n PI)) (exp (* n PI)) (* (* (* n n) n) (* (* PI PI) PI)) (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI)) (* (* (* n PI) (* n PI)) (* n PI)) (sqrt (* n PI)) (sqrt (* n PI)) (* (sqrt n) (sqrt PI)) (* (sqrt n) (sqrt PI)) (* n (* (cbrt PI) (cbrt PI))) (* n (sqrt PI)) (* n 1) (* (cbrt n) PI) (* (sqrt n) PI) (* n PI) (- (+ (* 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)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* n PI) (* n PI) (* n PI) 12.405 * * [simplify]: Extracting # 0 : cost 0 12.406 * * [simplify]: Extracting # 1 : cost 0 12.407 * * [simplify]: Extracting # 2 : cost 0 12.408 * * [simplify]: Extracting # 3 : cost 0 12.409 * * [simplify]: Extracting # 4 : cost 0 12.410 * * [simplify]: Extracting # 5 : cost 0 12.412 * * [simplify]: Extracting # 6 : cost 0 12.413 * * [simplify]: Extracting # 7 : cost 0 12.414 * * [simplify]: Extracting # 8 : cost 0 12.415 * * [simplify]: Extracting # 9 : cost 0 12.417 * * [simplify]: Extracting # 10 : cost 0 12.418 * * [simplify]: Extracting # 11 : cost 0 12.419 * * [simplify]: Extracting # 12 : cost 0 12.420 * * [simplify]: Extracting # 13 : cost 0 12.422 * * [simplify]: iteration 0 : 390 enodes (cost 2642 ) 12.589 * * [simplify]: Extracting # 0 : cost 0 12.591 * * [simplify]: Extracting # 1 : cost 0 12.593 * * [simplify]: Extracting # 2 : cost 0 12.596 * * [simplify]: Extracting # 3 : cost 0 12.599 * * [simplify]: Extracting # 4 : cost 0 12.602 * * [simplify]: Extracting # 5 : cost 0 12.604 * * [simplify]: Extracting # 6 : cost 0 12.607 * * [simplify]: iteration 1 : 997 enodes (cost 2438 ) 13.130 * * [simplify]: Extracting # 0 : cost 0 13.137 * * [simplify]: Extracting # 1 : cost 0 13.144 * * [simplify]: Extracting # 2 : cost 0 13.151 * * [simplify]: Extracting # 3 : cost 0 13.158 * * [simplify]: Extracting # 4 : cost 0 13.164 * * [simplify]: Extracting # 5 : cost 0 13.168 * * [simplify]: iteration 2 : 2716 enodes (cost 2342 ) 14.133 * * [simplify]: Extracting # 0 : cost 0 14.145 * * [simplify]: Extracting # 1 : cost 0 14.159 * * [simplify]: Extracting # 2 : cost 0 14.183 * * [simplify]: Extracting # 3 : cost 0 14.192 * * [simplify]: Extracting # 4 : cost 0 14.199 * * [simplify]: iteration done: 5002 enodes (cost 2342 ) 14.200 * [simplify]: Simplified to: (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* 2.0 (* n PI)) (/ 1.0 2.0)) (pow (* 2.0 (* n PI)) (/ k 2.0)) (pow (* 2.0 (* n PI)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* 2.0 (* n PI)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ (* (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 (* n PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (sqrt (- 1.0 k))) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0))) (* 2.0 (* n PI)) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* 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(* n PI)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (sqrt 2))) (pow (* 2.0 (* n PI)) (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 (* n PI)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* 2.0 (* n PI)) (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 k) (sqrt 1.0)) (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 (* n PI)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* 2.0 (* n PI)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* 2.0 (* n PI)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* 2.0 (* n PI)) (- 1.0 k)) (* 2.0 (* n PI)) (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 (* n PI)) (/ (/ (- 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 (* n PI)) (/ (/ (- 1.0 k) 2.0) 4)) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 4)) (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) (* n PI) (log (* n PI)) (log (* n PI)) (exp (* n PI)) (pow (* n PI) 3) (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI)) (pow (* n PI) 3) (sqrt (* n PI)) (sqrt (* n PI)) (* (sqrt n) (sqrt PI)) (* (sqrt n) (sqrt PI)) (* n (* (cbrt PI) (cbrt PI))) (* n (sqrt PI)) n (* (cbrt n) PI) (* (sqrt n) PI) (* n PI) (+ (* (* 0.125 (pow k 2)) (+ (* (pow (* 2.0 (* n PI)) 0.5) (pow (log (* 2.0 PI)) 2)) (* (pow (log n) 2) (pow (* 2.0 (* n PI)) 0.5)))) (- (+ (pow (* 2.0 (* n PI)) 0.5) (* (* (* 0.25 (pow k 2)) (* (pow (* 2.0 (* n PI)) 0.5) (log n))) (log (* 2.0 PI)))) (* (* 0.5 k) (+ (* (pow (* 2.0 (* n PI)) 0.5) (log (* 2.0 PI))) (* (pow (* 2.0 (* n PI)) 0.5) (log n)))))) (pow (pow (* 2.0 (* n PI)) 0.5) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* (* (pow (* 2.0 (* n PI)) 0.25) (pow (log (* 2.0 PI)) 2)) (* 0.03125 (pow k 2))) (+ (+ (pow (* 2.0 (* n PI)) 0.25) (* (* (pow (* 2.0 (* n PI)) 0.25) (pow (log n) 2)) (* 0.03125 (pow k 2)))) (* (* (* (pow k 2) (log (* 2.0 PI))) (* (pow (* 2.0 (* n PI)) 0.25) (log n))) 0.0625))) (* (* 0.25 k) (+ (* (pow (* 2.0 (* n PI)) 0.25) (log n)) (* (log (* 2.0 PI)) (pow (* 2.0 (* n PI)) 0.25))))) (pow (pow (* 2.0 (* n PI)) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (- (* +nan.0 k) (- (* +nan.0 (pow k 2)) +nan.0))) (+ (/ (- +nan.0) (pow k 2)) (- (/ +nan.0 k) (/ +nan.0 (pow k 3)))) (+ (- (/ +nan.0 k) +nan.0) (/ (- +nan.0) (pow k 2))) (* n PI) (* n PI) (* n PI) 14.202 * * * [progress]: adding candidates to table 15.344 * * [progress]: iteration 4 / 4 15.344 * * * [progress]: picking best candidate 15.370 * * * * [pick]: Picked # 15.370 * * * [progress]: localizing error 15.413 * * * [progress]: generating rewritten candidates 15.413 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 2) 15.430 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 15.465 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 15.477 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 2 1) 15.506 * * * [progress]: generating series expansions 15.506 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 2) 15.506 * [backup-simplify]: Simplify (pow (* n PI) (/ (- 1.0 k) 2.0)) into (pow (* n PI) (* 0.5 (- 1.0 k))) 15.506 * [approximate]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in (n k) around 0 15.506 * [taylor]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in k 15.506 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* n PI)))) in k 15.506 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* n PI))) in k 15.506 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 15.506 * [taylor]: Taking taylor expansion of 0.5 in k 15.507 * [backup-simplify]: Simplify 0.5 into 0.5 15.507 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 15.507 * [taylor]: Taking taylor expansion of 1.0 in k 15.507 * [backup-simplify]: Simplify 1.0 into 1.0 15.507 * [taylor]: Taking taylor expansion of k in k 15.507 * [backup-simplify]: Simplify 0 into 0 15.507 * [backup-simplify]: Simplify 1 into 1 15.507 * [taylor]: Taking taylor expansion of (log (* n PI)) in k 15.507 * [taylor]: Taking taylor expansion of (* n PI) in k 15.507 * [taylor]: Taking taylor expansion of n in k 15.507 * [backup-simplify]: Simplify n into n 15.507 * [taylor]: Taking taylor expansion of PI in k 15.507 * [backup-simplify]: Simplify PI into PI 15.507 * [backup-simplify]: Simplify (* n PI) into (* n PI) 15.507 * [backup-simplify]: Simplify (log (* n PI)) into (log (* n PI)) 15.511 * [backup-simplify]: Simplify (- 0) into 0 15.511 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 15.511 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 15.511 * [backup-simplify]: Simplify (* 0.5 (log (* n PI))) into (* 0.5 (log (* n PI))) 15.512 * [backup-simplify]: Simplify (exp (* 0.5 (log (* n PI)))) into (pow (* n PI) 0.5) 15.512 * [taylor]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in n 15.512 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* n PI)))) in n 15.512 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* n PI))) in n 15.512 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 15.512 * [taylor]: Taking taylor expansion of 0.5 in n 15.512 * [backup-simplify]: Simplify 0.5 into 0.5 15.512 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 15.512 * [taylor]: Taking taylor expansion of 1.0 in n 15.512 * [backup-simplify]: Simplify 1.0 into 1.0 15.512 * [taylor]: Taking taylor expansion of k in n 15.512 * [backup-simplify]: Simplify k into k 15.512 * [taylor]: Taking taylor expansion of (log (* n PI)) in n 15.512 * [taylor]: Taking taylor expansion of (* n PI) in n 15.512 * [taylor]: Taking taylor expansion of n in n 15.512 * [backup-simplify]: Simplify 0 into 0 15.512 * [backup-simplify]: Simplify 1 into 1 15.512 * [taylor]: Taking taylor expansion of PI in n 15.512 * [backup-simplify]: Simplify PI into PI 15.512 * [backup-simplify]: Simplify (* 0 PI) into 0 15.513 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 15.513 * [backup-simplify]: Simplify (log PI) into (log PI) 15.514 * [backup-simplify]: Simplify (- k) into (- k) 15.514 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 15.514 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 15.514 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log n) (log PI)) 15.515 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log n) (log PI))) into (* 0.5 (* (- 1.0 k) (+ (log n) (log PI)))) 15.515 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log n) (log PI))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log n) (log PI))))) 15.515 * [taylor]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in n 15.515 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* n PI)))) in n 15.515 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* n PI))) in n 15.515 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 15.515 * [taylor]: Taking taylor expansion of 0.5 in n 15.515 * [backup-simplify]: Simplify 0.5 into 0.5 15.515 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 15.515 * [taylor]: Taking taylor expansion of 1.0 in n 15.515 * [backup-simplify]: Simplify 1.0 into 1.0 15.515 * [taylor]: Taking taylor expansion of k in n 15.515 * [backup-simplify]: Simplify k into k 15.515 * [taylor]: Taking taylor expansion of (log (* n PI)) in n 15.515 * [taylor]: Taking taylor expansion of (* n PI) in n 15.515 * [taylor]: Taking taylor expansion of n in n 15.515 * [backup-simplify]: Simplify 0 into 0 15.515 * [backup-simplify]: Simplify 1 into 1 15.515 * [taylor]: Taking taylor expansion of PI in n 15.515 * [backup-simplify]: Simplify PI into PI 15.516 * [backup-simplify]: Simplify (* 0 PI) into 0 15.516 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 15.517 * [backup-simplify]: Simplify (log PI) into (log PI) 15.517 * [backup-simplify]: Simplify (- k) into (- k) 15.517 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 15.517 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 15.517 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log n) (log PI)) 15.518 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log n) (log PI))) into (* 0.5 (* (- 1.0 k) (+ (log n) (log PI)))) 15.518 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log n) (log PI))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log n) (log PI))))) 15.518 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log n) (log PI))))) in k 15.518 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log n) (log PI)))) in k 15.518 * [taylor]: Taking taylor expansion of 0.5 in k 15.518 * [backup-simplify]: Simplify 0.5 into 0.5 15.518 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log n) (log PI))) in k 15.518 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 15.518 * [taylor]: Taking taylor expansion of 1.0 in k 15.518 * [backup-simplify]: Simplify 1.0 into 1.0 15.518 * [taylor]: Taking taylor expansion of k in k 15.518 * [backup-simplify]: Simplify 0 into 0 15.518 * [backup-simplify]: Simplify 1 into 1 15.518 * [taylor]: Taking taylor expansion of (+ (log n) (log PI)) in k 15.518 * [taylor]: Taking taylor expansion of (log n) in k 15.518 * [taylor]: Taking taylor expansion of n in k 15.518 * [backup-simplify]: Simplify n into n 15.519 * [backup-simplify]: Simplify (log n) into (log n) 15.519 * [taylor]: Taking taylor expansion of (log PI) in k 15.519 * [taylor]: Taking taylor expansion of PI in k 15.519 * [backup-simplify]: Simplify PI into PI 15.519 * [backup-simplify]: Simplify (log PI) into (log PI) 15.519 * [backup-simplify]: Simplify (- 0) into 0 15.519 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 15.520 * [backup-simplify]: Simplify (+ (log n) (log PI)) into (+ (log n) (log PI)) 15.520 * [backup-simplify]: Simplify (* 1.0 (+ (log n) (log PI))) into (* 1.0 (+ (log n) (log PI))) 15.520 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log n) (log PI)))) into (* 0.5 (+ (log n) (log PI))) 15.521 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log n) (log PI)))) into (exp (* 0.5 (+ (log n) (log PI)))) 15.521 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log n) (log PI)))) into (exp (* 0.5 (+ (log n) (log PI)))) 15.522 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 15.523 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 15.523 * [backup-simplify]: Simplify (- 0) into 0 15.523 * [backup-simplify]: Simplify (+ 0 0) into 0 15.523 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 15.524 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log n) (log PI)) 15.524 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log n) (log PI)))) into 0 15.525 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log n) (log PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 15.525 * [taylor]: Taking taylor expansion of 0 in k 15.525 * [backup-simplify]: Simplify 0 into 0 15.525 * [backup-simplify]: Simplify 0 into 0 15.526 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 15.526 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 15.527 * [backup-simplify]: Simplify (+ 0 0) into 0 15.527 * [backup-simplify]: Simplify (- 1) into -1 15.527 * [backup-simplify]: Simplify (+ 0 -1) into -1 15.528 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log n) (log PI)))) into (- (+ (log PI) (log n))) 15.528 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log PI) (log n)))) (* 0 (* 1.0 (+ (log n) (log PI))))) into (- (+ (* 0.5 (log n)) (* 0.5 (log PI)))) 15.530 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log n) (log PI)))) (+ (* (/ (pow (- (+ (* 0.5 (log n)) (* 0.5 (log PI)))) 1) 1)))) into (* -1 (* (exp (* 0.5 (+ (log n) (log PI)))) (+ (* 0.5 (log n)) (* 0.5 (log PI))))) 15.531 * [backup-simplify]: Simplify (* -1 (* (exp (* 0.5 (+ (log n) (log PI)))) (+ (* 0.5 (log n)) (* 0.5 (log PI))))) into (* -1 (* (exp (* 0.5 (+ (log n) (log PI)))) (+ (* 0.5 (log n)) (* 0.5 (log PI))))) 15.532 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 15.535 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 15.535 * [backup-simplify]: Simplify (- 0) into 0 15.536 * [backup-simplify]: Simplify (+ 0 0) into 0 15.537 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 15.537 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log n) (log PI)) 15.539 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log PI))))) into 0 15.541 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log n) (log PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 15.541 * [taylor]: Taking taylor expansion of 0 in k 15.541 * [backup-simplify]: Simplify 0 into 0 15.541 * [backup-simplify]: Simplify 0 into 0 15.541 * [backup-simplify]: Simplify 0 into 0 15.543 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 15.546 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 15.547 * [backup-simplify]: Simplify (+ 0 0) into 0 15.547 * [backup-simplify]: Simplify (- 0) into 0 15.548 * [backup-simplify]: Simplify (+ 0 0) into 0 15.549 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log n) (log PI))))) into 0 15.549 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log PI) (log n)))) (* 0 (* 1.0 (+ (log n) (log PI)))))) into 0 15.551 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log n) (log PI)))) (+ (* (/ (pow (- (+ (* 0.5 (log n)) (* 0.5 (log PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.125 (pow (log PI) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log n) (log PI))))) (exp (* 0.5 (+ (log n) (log PI))))) 15.553 * [backup-simplify]: Simplify (* (+ (* 0.125 (pow (log PI) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log n) (log PI))))) (exp (* 0.5 (+ (log n) (log PI))))) into (* (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log PI) 2)) (* 0.25 (* (log n) (log PI))))) (exp (* 0.5 (+ (log n) (log PI))))) 15.557 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log PI) 2)) (* 0.25 (* (log n) (log PI))))) (exp (* 0.5 (+ (log n) (log PI))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 0.5 (+ (log n) (log PI)))) (+ (* 0.5 (log n)) (* 0.5 (log PI))))) (* k 1)) (exp (* 0.5 (+ (log n) (log PI)))))) into (- (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log n) (log PI)))) (pow (log PI) 2)))) (+ (exp (* 0.5 (+ (log n) (log PI)))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log n) (log PI)))) (pow (log n) 2)))) (* 0.25 (* (pow k 2) (* (exp (* 0.5 (+ (log n) (log PI)))) (* (log n) (log PI)))))))) (+ (* 0.5 (* k (* (exp (* 0.5 (+ (log n) (log PI)))) (log PI)))) (* 0.5 (* k (* (exp (* 0.5 (+ (log n) (log PI)))) (log n)))))) 15.557 * [backup-simplify]: Simplify (pow (* (/ 1 n) PI) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) 15.557 * [approximate]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 15.557 * [taylor]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in k 15.557 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) in k 15.557 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n))) in k 15.557 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 15.557 * [taylor]: Taking taylor expansion of 0.5 in k 15.557 * [backup-simplify]: Simplify 0.5 into 0.5 15.557 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 15.557 * [taylor]: Taking taylor expansion of 1.0 in k 15.557 * [backup-simplify]: Simplify 1.0 into 1.0 15.557 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.557 * [taylor]: Taking taylor expansion of k in k 15.557 * [backup-simplify]: Simplify 0 into 0 15.557 * [backup-simplify]: Simplify 1 into 1 15.558 * [backup-simplify]: Simplify (/ 1 1) into 1 15.558 * [taylor]: Taking taylor expansion of (log (/ PI n)) in k 15.558 * [taylor]: Taking taylor expansion of (/ PI n) in k 15.558 * [taylor]: Taking taylor expansion of PI in k 15.558 * [backup-simplify]: Simplify PI into PI 15.558 * [taylor]: Taking taylor expansion of n in k 15.558 * [backup-simplify]: Simplify n into n 15.558 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 15.558 * [backup-simplify]: Simplify (log (/ PI n)) into (log (/ PI n)) 15.558 * [backup-simplify]: Simplify (- 1) into -1 15.558 * [backup-simplify]: Simplify (+ 0 -1) into -1 15.559 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 15.559 * [backup-simplify]: Simplify (* -0.5 (log (/ PI n))) into (* -0.5 (log (/ PI n))) 15.559 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) into (exp (* 0.5 (* (log (/ PI n)) (- 1.0 (/ 1 k))))) 15.559 * [taylor]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in n 15.559 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) in n 15.559 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n))) in n 15.559 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 15.559 * [taylor]: Taking taylor expansion of 0.5 in n 15.559 * [backup-simplify]: Simplify 0.5 into 0.5 15.559 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 15.559 * [taylor]: Taking taylor expansion of 1.0 in n 15.559 * [backup-simplify]: Simplify 1.0 into 1.0 15.559 * [taylor]: Taking taylor expansion of (/ 1 k) in n 15.559 * [taylor]: Taking taylor expansion of k in n 15.559 * [backup-simplify]: Simplify k into k 15.559 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 15.559 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n 15.559 * [taylor]: Taking taylor expansion of (/ PI n) in n 15.559 * [taylor]: Taking taylor expansion of PI in n 15.559 * [backup-simplify]: Simplify PI into PI 15.559 * [taylor]: Taking taylor expansion of n in n 15.559 * [backup-simplify]: Simplify 0 into 0 15.559 * [backup-simplify]: Simplify 1 into 1 15.560 * [backup-simplify]: Simplify (/ PI 1) into PI 15.560 * [backup-simplify]: Simplify (log PI) into (log PI) 15.560 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 15.560 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 15.560 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 15.561 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 15.561 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log PI) (log n))) into (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k)))) 15.562 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) 15.562 * [taylor]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in n 15.562 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) in n 15.562 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n))) in n 15.562 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 15.562 * [taylor]: Taking taylor expansion of 0.5 in n 15.562 * [backup-simplify]: Simplify 0.5 into 0.5 15.562 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 15.562 * [taylor]: Taking taylor expansion of 1.0 in n 15.562 * [backup-simplify]: Simplify 1.0 into 1.0 15.562 * [taylor]: Taking taylor expansion of (/ 1 k) in n 15.562 * [taylor]: Taking taylor expansion of k in n 15.562 * [backup-simplify]: Simplify k into k 15.562 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 15.562 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n 15.562 * [taylor]: Taking taylor expansion of (/ PI n) in n 15.562 * [taylor]: Taking taylor expansion of PI in n 15.562 * [backup-simplify]: Simplify PI into PI 15.562 * [taylor]: Taking taylor expansion of n in n 15.562 * [backup-simplify]: Simplify 0 into 0 15.562 * [backup-simplify]: Simplify 1 into 1 15.562 * [backup-simplify]: Simplify (/ PI 1) into PI 15.563 * [backup-simplify]: Simplify (log PI) into (log PI) 15.563 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 15.563 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 15.563 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 15.564 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 15.564 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log PI) (log n))) into (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k)))) 15.564 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) 15.564 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) in k 15.564 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k)))) in k 15.564 * [taylor]: Taking taylor expansion of 0.5 in k 15.565 * [backup-simplify]: Simplify 0.5 into 0.5 15.565 * [taylor]: Taking taylor expansion of (* (- (log PI) (log n)) (- 1.0 (/ 1 k))) in k 15.565 * [taylor]: Taking taylor expansion of (- (log PI) (log n)) in k 15.565 * [taylor]: Taking taylor expansion of (log PI) in k 15.565 * [taylor]: Taking taylor expansion of PI in k 15.565 * [backup-simplify]: Simplify PI into PI 15.565 * [backup-simplify]: Simplify (log PI) into (log PI) 15.565 * [taylor]: Taking taylor expansion of (log n) in k 15.565 * [taylor]: Taking taylor expansion of n in k 15.565 * [backup-simplify]: Simplify n into n 15.565 * [backup-simplify]: Simplify (log n) into (log n) 15.565 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 15.565 * [taylor]: Taking taylor expansion of 1.0 in k 15.565 * [backup-simplify]: Simplify 1.0 into 1.0 15.565 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.565 * [taylor]: Taking taylor expansion of k in k 15.565 * [backup-simplify]: Simplify 0 into 0 15.565 * [backup-simplify]: Simplify 1 into 1 15.565 * [backup-simplify]: Simplify (/ 1 1) into 1 15.565 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 15.566 * [backup-simplify]: Simplify (+ (log PI) (- (log n))) into (- (log PI) (log n)) 15.566 * [backup-simplify]: Simplify (- 1) into -1 15.566 * [backup-simplify]: Simplify (+ 0 -1) into -1 15.567 * [backup-simplify]: Simplify (* (- (log PI) (log n)) -1) into (* -1 (- (log PI) (log n))) 15.567 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log PI) (log n)))) into (* -0.5 (- (log PI) (log n))) 15.567 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) 15.568 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) 15.568 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 15.569 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 15.570 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 15.570 * [backup-simplify]: Simplify (- 0) into 0 15.570 * [backup-simplify]: Simplify (+ 0 0) into 0 15.570 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 15.571 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 15.571 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log PI) (log n)))) into 0 15.572 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 15.572 * [taylor]: Taking taylor expansion of 0 in k 15.572 * [backup-simplify]: Simplify 0 into 0 15.572 * [backup-simplify]: Simplify 0 into 0 15.572 * [backup-simplify]: Simplify 0 into 0 15.573 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.574 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 15.575 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 15.575 * [backup-simplify]: Simplify (- 0) into 0 15.575 * [backup-simplify]: Simplify (+ 0 0) into 0 15.576 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 15.576 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 15.577 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log PI) (log n))))) into 0 15.578 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 15.578 * [taylor]: Taking taylor expansion of 0 in k 15.578 * [backup-simplify]: Simplify 0 into 0 15.578 * [backup-simplify]: Simplify 0 into 0 15.578 * [backup-simplify]: Simplify 0 into 0 15.578 * [backup-simplify]: Simplify 0 into 0 15.579 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.582 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 15.582 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 15.582 * [backup-simplify]: Simplify (- 0) into 0 15.582 * [backup-simplify]: Simplify (+ 0 0) into 0 15.583 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 15.584 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 15.585 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log PI) (log n)))))) into 0 15.586 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log 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 15.586 * [taylor]: Taking taylor expansion of 0 in k 15.586 * [backup-simplify]: Simplify 0 into 0 15.586 * [backup-simplify]: Simplify 0 into 0 15.586 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log PI) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- 1.0 k) (- (log PI) (log (/ 1 n)))))) 15.587 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) PI) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 15.587 * [approximate]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 15.587 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 15.587 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) in k 15.587 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n)))) in k 15.587 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 15.587 * [taylor]: Taking taylor expansion of 0.5 in k 15.587 * [backup-simplify]: Simplify 0.5 into 0.5 15.587 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 15.587 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.587 * [taylor]: Taking taylor expansion of k in k 15.587 * [backup-simplify]: Simplify 0 into 0 15.587 * [backup-simplify]: Simplify 1 into 1 15.587 * [backup-simplify]: Simplify (/ 1 1) into 1 15.587 * [taylor]: Taking taylor expansion of 1.0 in k 15.587 * [backup-simplify]: Simplify 1.0 into 1.0 15.587 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in k 15.587 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in k 15.587 * [taylor]: Taking taylor expansion of -1 in k 15.587 * [backup-simplify]: Simplify -1 into -1 15.587 * [taylor]: Taking taylor expansion of (/ PI n) in k 15.587 * [taylor]: Taking taylor expansion of PI in k 15.587 * [backup-simplify]: Simplify PI into PI 15.587 * [taylor]: Taking taylor expansion of n in k 15.587 * [backup-simplify]: Simplify n into n 15.587 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 15.587 * [backup-simplify]: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n)) 15.588 * [backup-simplify]: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n))) 15.588 * [backup-simplify]: Simplify (+ 1 0) into 1 15.588 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 15.588 * [backup-simplify]: Simplify (* 0.5 (log (* -1 (/ PI n)))) into (* 0.5 (log (* -1 (/ PI n)))) 15.588 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -1 (/ PI n)))))) 15.588 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 15.588 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) in n 15.588 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n)))) in n 15.588 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 15.588 * [taylor]: Taking taylor expansion of 0.5 in n 15.588 * [backup-simplify]: Simplify 0.5 into 0.5 15.589 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 15.589 * [taylor]: Taking taylor expansion of (/ 1 k) in n 15.589 * [taylor]: Taking taylor expansion of k in n 15.589 * [backup-simplify]: Simplify k into k 15.589 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 15.589 * [taylor]: Taking taylor expansion of 1.0 in n 15.589 * [backup-simplify]: Simplify 1.0 into 1.0 15.589 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n 15.589 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 15.589 * [taylor]: Taking taylor expansion of -1 in n 15.589 * [backup-simplify]: Simplify -1 into -1 15.589 * [taylor]: Taking taylor expansion of (/ PI n) in n 15.589 * [taylor]: Taking taylor expansion of PI in n 15.589 * [backup-simplify]: Simplify PI into PI 15.589 * [taylor]: Taking taylor expansion of n in n 15.589 * [backup-simplify]: Simplify 0 into 0 15.589 * [backup-simplify]: Simplify 1 into 1 15.589 * [backup-simplify]: Simplify (/ PI 1) into PI 15.589 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 15.590 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI)) 15.590 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 15.590 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 15.591 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 15.592 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -1 PI)) (log n))) into (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))) 15.593 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 15.593 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 15.593 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) in n 15.593 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n)))) in n 15.593 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 15.593 * [taylor]: Taking taylor expansion of 0.5 in n 15.593 * [backup-simplify]: Simplify 0.5 into 0.5 15.593 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 15.593 * [taylor]: Taking taylor expansion of (/ 1 k) in n 15.593 * [taylor]: Taking taylor expansion of k in n 15.593 * [backup-simplify]: Simplify k into k 15.593 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 15.593 * [taylor]: Taking taylor expansion of 1.0 in n 15.593 * [backup-simplify]: Simplify 1.0 into 1.0 15.593 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n 15.593 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 15.593 * [taylor]: Taking taylor expansion of -1 in n 15.593 * [backup-simplify]: Simplify -1 into -1 15.593 * [taylor]: Taking taylor expansion of (/ PI n) in n 15.593 * [taylor]: Taking taylor expansion of PI in n 15.593 * [backup-simplify]: Simplify PI into PI 15.593 * [taylor]: Taking taylor expansion of n in n 15.593 * [backup-simplify]: Simplify 0 into 0 15.593 * [backup-simplify]: Simplify 1 into 1 15.594 * [backup-simplify]: Simplify (/ PI 1) into PI 15.594 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 15.595 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI)) 15.595 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 15.595 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 15.596 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 15.596 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -1 PI)) (log n))) into (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))) 15.597 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 15.597 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 15.597 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 15.597 * [taylor]: Taking taylor expansion of 0.5 in k 15.597 * [backup-simplify]: Simplify 0.5 into 0.5 15.597 * [taylor]: Taking taylor expansion of (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 15.597 * [taylor]: Taking taylor expansion of (- (log (* -1 PI)) (log n)) in k 15.597 * [taylor]: Taking taylor expansion of (log (* -1 PI)) in k 15.597 * [taylor]: Taking taylor expansion of (* -1 PI) in k 15.597 * [taylor]: Taking taylor expansion of -1 in k 15.597 * [backup-simplify]: Simplify -1 into -1 15.598 * [taylor]: Taking taylor expansion of PI in k 15.598 * [backup-simplify]: Simplify PI into PI 15.598 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 15.598 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI)) 15.599 * [taylor]: Taking taylor expansion of (log n) in k 15.599 * [taylor]: Taking taylor expansion of n in k 15.599 * [backup-simplify]: Simplify n into n 15.599 * [backup-simplify]: Simplify (log n) into (log n) 15.599 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 15.599 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.599 * [taylor]: Taking taylor expansion of k in k 15.599 * [backup-simplify]: Simplify 0 into 0 15.599 * [backup-simplify]: Simplify 1 into 1 15.599 * [backup-simplify]: Simplify (/ 1 1) into 1 15.599 * [taylor]: Taking taylor expansion of 1.0 in k 15.599 * [backup-simplify]: Simplify 1.0 into 1.0 15.599 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 15.600 * [backup-simplify]: Simplify (+ (log (* -1 PI)) (- (log n))) into (- (log (* -1 PI)) (log n)) 15.600 * [backup-simplify]: Simplify (+ 1 0) into 1 15.601 * [backup-simplify]: Simplify (* (- (log (* -1 PI)) (log n)) 1) into (- (log (* -1 PI)) (log n)) 15.601 * [backup-simplify]: Simplify (* 0.5 (- (log (* -1 PI)) (log n))) into (* 0.5 (- (log (* -1 PI)) (log n))) 15.602 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 15.603 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 15.604 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 15.604 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0 15.605 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -1 PI) 1)))) 1) into 0 15.605 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 15.606 * [backup-simplify]: Simplify (+ 0 0) into 0 15.606 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 15.607 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 15.608 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -1 PI)) (log n)))) into 0 15.610 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 15.610 * [taylor]: Taking taylor expansion of 0 in k 15.610 * [backup-simplify]: Simplify 0 into 0 15.610 * [backup-simplify]: Simplify 0 into 0 15.610 * [backup-simplify]: Simplify 0 into 0 15.611 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.612 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 15.623 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -1 PI) 1)))) 2) into 0 15.624 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 15.625 * [backup-simplify]: Simplify (+ 0 0) into 0 15.626 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 15.627 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 15.628 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n))))) into 0 15.630 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 15.630 * [taylor]: Taking taylor expansion of 0 in k 15.630 * [backup-simplify]: Simplify 0 into 0 15.630 * [backup-simplify]: Simplify 0 into 0 15.630 * [backup-simplify]: Simplify 0 into 0 15.630 * [backup-simplify]: Simplify 0 into 0 15.630 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.631 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 15.634 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -1 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -1 PI) 1)))) 6) into 0 15.634 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 15.635 * [backup-simplify]: Simplify (+ 0 0) into 0 15.636 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 15.637 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 15.638 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n)))))) into 0 15.639 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 15.639 * [taylor]: Taking taylor expansion of 0 in k 15.639 * [backup-simplify]: Simplify 0 into 0 15.640 * [backup-simplify]: Simplify 0 into 0 15.640 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -1 PI)) (log (/ -1 n)))))) 15.640 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 15.641 * [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))) 15.641 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 15.641 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 15.641 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 15.641 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 15.641 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 15.641 * [taylor]: Taking taylor expansion of 0.25 in k 15.641 * [backup-simplify]: Simplify 0.25 into 0.25 15.641 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 15.641 * [taylor]: Taking taylor expansion of 1.0 in k 15.641 * [backup-simplify]: Simplify 1.0 into 1.0 15.641 * [taylor]: Taking taylor expansion of k in k 15.641 * [backup-simplify]: Simplify 0 into 0 15.641 * [backup-simplify]: Simplify 1 into 1 15.641 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 15.641 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 15.642 * [taylor]: Taking taylor expansion of 2.0 in k 15.642 * [backup-simplify]: Simplify 2.0 into 2.0 15.642 * [taylor]: Taking taylor expansion of (* n PI) in k 15.642 * [taylor]: Taking taylor expansion of n in k 15.642 * [backup-simplify]: Simplify n into n 15.642 * [taylor]: Taking taylor expansion of PI in k 15.642 * [backup-simplify]: Simplify PI into PI 15.642 * [backup-simplify]: Simplify (* n PI) into (* n PI) 15.642 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 15.642 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 15.642 * [backup-simplify]: Simplify (- 0) into 0 15.642 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 15.643 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 15.643 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 15.643 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 15.643 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 15.643 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 15.643 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 15.643 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 15.643 * [taylor]: Taking taylor expansion of 0.25 in n 15.643 * [backup-simplify]: Simplify 0.25 into 0.25 15.643 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 15.643 * [taylor]: Taking taylor expansion of 1.0 in n 15.643 * [backup-simplify]: Simplify 1.0 into 1.0 15.643 * [taylor]: Taking taylor expansion of k in n 15.643 * [backup-simplify]: Simplify k into k 15.643 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 15.643 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 15.643 * [taylor]: Taking taylor expansion of 2.0 in n 15.643 * [backup-simplify]: Simplify 2.0 into 2.0 15.643 * [taylor]: Taking taylor expansion of (* n PI) in n 15.643 * [taylor]: Taking taylor expansion of n in n 15.643 * [backup-simplify]: Simplify 0 into 0 15.643 * [backup-simplify]: Simplify 1 into 1 15.643 * [taylor]: Taking taylor expansion of PI in n 15.643 * [backup-simplify]: Simplify PI into PI 15.643 * [backup-simplify]: Simplify (* 0 PI) into 0 15.644 * [backup-simplify]: Simplify (* 2.0 0) into 0 15.645 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 15.646 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 15.646 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 15.646 * [backup-simplify]: Simplify (- k) into (- k) 15.646 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 15.646 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 15.647 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 15.648 * [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)))) 15.649 * [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))))) 15.649 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 15.649 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 15.649 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 15.649 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 15.649 * [taylor]: Taking taylor expansion of 0.25 in n 15.649 * [backup-simplify]: Simplify 0.25 into 0.25 15.649 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 15.649 * [taylor]: Taking taylor expansion of 1.0 in n 15.649 * [backup-simplify]: Simplify 1.0 into 1.0 15.649 * [taylor]: Taking taylor expansion of k in n 15.649 * [backup-simplify]: Simplify k into k 15.649 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 15.649 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 15.649 * [taylor]: Taking taylor expansion of 2.0 in n 15.649 * [backup-simplify]: Simplify 2.0 into 2.0 15.649 * [taylor]: Taking taylor expansion of (* n PI) in n 15.649 * [taylor]: Taking taylor expansion of n in n 15.649 * [backup-simplify]: Simplify 0 into 0 15.649 * [backup-simplify]: Simplify 1 into 1 15.649 * [taylor]: Taking taylor expansion of PI in n 15.649 * [backup-simplify]: Simplify PI into PI 15.650 * [backup-simplify]: Simplify (* 0 PI) into 0 15.650 * [backup-simplify]: Simplify (* 2.0 0) into 0 15.651 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 15.652 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 15.653 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 15.653 * [backup-simplify]: Simplify (- k) into (- k) 15.653 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 15.653 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 15.654 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 15.656 * [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)))) 15.657 * [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))))) 15.657 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 15.657 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 15.657 * [taylor]: Taking taylor expansion of 0.25 in k 15.657 * [backup-simplify]: Simplify 0.25 into 0.25 15.657 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 15.657 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 15.657 * [taylor]: Taking taylor expansion of 1.0 in k 15.657 * [backup-simplify]: Simplify 1.0 into 1.0 15.657 * [taylor]: Taking taylor expansion of k in k 15.657 * [backup-simplify]: Simplify 0 into 0 15.657 * [backup-simplify]: Simplify 1 into 1 15.657 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 15.657 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 15.657 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 15.657 * [taylor]: Taking taylor expansion of 2.0 in k 15.657 * [backup-simplify]: Simplify 2.0 into 2.0 15.657 * [taylor]: Taking taylor expansion of PI in k 15.657 * [backup-simplify]: Simplify PI into PI 15.658 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 15.659 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 15.659 * [taylor]: Taking taylor expansion of (log n) in k 15.659 * [taylor]: Taking taylor expansion of n in k 15.659 * [backup-simplify]: Simplify n into n 15.659 * [backup-simplify]: Simplify (log n) into (log n) 15.659 * [backup-simplify]: Simplify (- 0) into 0 15.660 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 15.661 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 15.662 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 15.663 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 15.664 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 15.665 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 15.666 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 15.667 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 15.668 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 15.669 * [backup-simplify]: Simplify (- 0) into 0 15.669 * [backup-simplify]: Simplify (+ 0 0) into 0 15.669 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 15.671 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 15.672 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 15.673 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 15.673 * [taylor]: Taking taylor expansion of 0 in k 15.674 * [backup-simplify]: Simplify 0 into 0 15.674 * [backup-simplify]: Simplify 0 into 0 15.674 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 15.676 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 15.677 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 15.677 * [backup-simplify]: Simplify (+ 0 0) into 0 15.677 * [backup-simplify]: Simplify (- 1) into -1 15.678 * [backup-simplify]: Simplify (+ 0 -1) into -1 15.679 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 15.681 * [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)))) 15.684 * [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)))))) 15.687 * [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)))))) 15.688 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 15.689 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 15.693 * [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 15.693 * [backup-simplify]: Simplify (- 0) into 0 15.694 * [backup-simplify]: Simplify (+ 0 0) into 0 15.694 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 15.696 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 15.697 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 15.700 * [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 15.700 * [taylor]: Taking taylor expansion of 0 in k 15.700 * [backup-simplify]: Simplify 0 into 0 15.700 * [backup-simplify]: Simplify 0 into 0 15.700 * [backup-simplify]: Simplify 0 into 0 15.701 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 15.705 * [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 15.707 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 15.707 * [backup-simplify]: Simplify (+ 0 0) into 0 15.708 * [backup-simplify]: Simplify (- 0) into 0 15.708 * [backup-simplify]: Simplify (+ 0 0) into 0 15.710 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 15.713 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 15.717 * [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))))) 15.721 * [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))))) 15.727 * [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)))))) 15.728 * [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)))) 15.728 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 15.728 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 15.728 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 15.728 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 15.728 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 15.728 * [taylor]: Taking taylor expansion of 0.25 in k 15.728 * [backup-simplify]: Simplify 0.25 into 0.25 15.728 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 15.728 * [taylor]: Taking taylor expansion of 1.0 in k 15.728 * [backup-simplify]: Simplify 1.0 into 1.0 15.728 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.728 * [taylor]: Taking taylor expansion of k in k 15.728 * [backup-simplify]: Simplify 0 into 0 15.728 * [backup-simplify]: Simplify 1 into 1 15.728 * [backup-simplify]: Simplify (/ 1 1) into 1 15.728 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 15.728 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 15.728 * [taylor]: Taking taylor expansion of 2.0 in k 15.728 * [backup-simplify]: Simplify 2.0 into 2.0 15.728 * [taylor]: Taking taylor expansion of (/ PI n) in k 15.728 * [taylor]: Taking taylor expansion of PI in k 15.728 * [backup-simplify]: Simplify PI into PI 15.729 * [taylor]: Taking taylor expansion of n in k 15.729 * [backup-simplify]: Simplify n into n 15.729 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 15.729 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 15.729 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 15.729 * [backup-simplify]: Simplify (- 1) into -1 15.729 * [backup-simplify]: Simplify (+ 0 -1) into -1 15.729 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 15.730 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 15.730 * [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))))) 15.730 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 15.730 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 15.730 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 15.730 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 15.730 * [taylor]: Taking taylor expansion of 0.25 in n 15.730 * [backup-simplify]: Simplify 0.25 into 0.25 15.730 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 15.730 * [taylor]: Taking taylor expansion of 1.0 in n 15.730 * [backup-simplify]: Simplify 1.0 into 1.0 15.730 * [taylor]: Taking taylor expansion of (/ 1 k) in n 15.730 * [taylor]: Taking taylor expansion of k in n 15.730 * [backup-simplify]: Simplify k into k 15.730 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 15.730 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 15.730 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 15.730 * [taylor]: Taking taylor expansion of 2.0 in n 15.730 * [backup-simplify]: Simplify 2.0 into 2.0 15.730 * [taylor]: Taking taylor expansion of (/ PI n) in n 15.730 * [taylor]: Taking taylor expansion of PI in n 15.730 * [backup-simplify]: Simplify PI into PI 15.730 * [taylor]: Taking taylor expansion of n in n 15.730 * [backup-simplify]: Simplify 0 into 0 15.730 * [backup-simplify]: Simplify 1 into 1 15.731 * [backup-simplify]: Simplify (/ PI 1) into PI 15.731 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 15.731 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 15.732 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 15.732 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 15.732 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 15.733 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 15.733 * [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)))) 15.734 * [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))))) 15.734 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 15.734 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 15.734 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 15.734 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 15.734 * [taylor]: Taking taylor expansion of 0.25 in n 15.734 * [backup-simplify]: Simplify 0.25 into 0.25 15.734 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 15.734 * [taylor]: Taking taylor expansion of 1.0 in n 15.734 * [backup-simplify]: Simplify 1.0 into 1.0 15.734 * [taylor]: Taking taylor expansion of (/ 1 k) in n 15.734 * [taylor]: Taking taylor expansion of k in n 15.734 * [backup-simplify]: Simplify k into k 15.734 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 15.735 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 15.735 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 15.735 * [taylor]: Taking taylor expansion of 2.0 in n 15.735 * [backup-simplify]: Simplify 2.0 into 2.0 15.735 * [taylor]: Taking taylor expansion of (/ PI n) in n 15.735 * [taylor]: Taking taylor expansion of PI in n 15.735 * [backup-simplify]: Simplify PI into PI 15.735 * [taylor]: Taking taylor expansion of n in n 15.735 * [backup-simplify]: Simplify 0 into 0 15.735 * [backup-simplify]: Simplify 1 into 1 15.735 * [backup-simplify]: Simplify (/ PI 1) into PI 15.735 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 15.736 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 15.736 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 15.736 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 15.736 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 15.737 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 15.738 * [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)))) 15.739 * [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))))) 15.739 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 15.739 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 15.739 * [taylor]: Taking taylor expansion of 0.25 in k 15.739 * [backup-simplify]: Simplify 0.25 into 0.25 15.739 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 15.739 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 15.739 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 15.739 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 15.739 * [taylor]: Taking taylor expansion of 2.0 in k 15.739 * [backup-simplify]: Simplify 2.0 into 2.0 15.739 * [taylor]: Taking taylor expansion of PI in k 15.739 * [backup-simplify]: Simplify PI into PI 15.739 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 15.746 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 15.746 * [taylor]: Taking taylor expansion of (log n) in k 15.747 * [taylor]: Taking taylor expansion of n in k 15.747 * [backup-simplify]: Simplify n into n 15.747 * [backup-simplify]: Simplify (log n) into (log n) 15.747 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 15.747 * [taylor]: Taking taylor expansion of 1.0 in k 15.747 * [backup-simplify]: Simplify 1.0 into 1.0 15.747 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.747 * [taylor]: Taking taylor expansion of k in k 15.747 * [backup-simplify]: Simplify 0 into 0 15.747 * [backup-simplify]: Simplify 1 into 1 15.747 * [backup-simplify]: Simplify (/ 1 1) into 1 15.747 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 15.748 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 15.749 * [backup-simplify]: Simplify (- 1) into -1 15.749 * [backup-simplify]: Simplify (+ 0 -1) into -1 15.750 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 15.751 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 15.753 * [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))))) 15.754 * [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))))) 15.755 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 15.756 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 15.757 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 15.757 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 15.758 * [backup-simplify]: Simplify (- 0) into 0 15.758 * [backup-simplify]: Simplify (+ 0 0) into 0 15.759 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 15.760 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 15.761 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 15.763 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 15.763 * [taylor]: Taking taylor expansion of 0 in k 15.763 * [backup-simplify]: Simplify 0 into 0 15.763 * [backup-simplify]: Simplify 0 into 0 15.763 * [backup-simplify]: Simplify 0 into 0 15.764 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.765 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 15.768 * [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 15.768 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 15.769 * [backup-simplify]: Simplify (- 0) into 0 15.769 * [backup-simplify]: Simplify (+ 0 0) into 0 15.770 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 15.771 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 15.773 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 15.775 * [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 15.775 * [taylor]: Taking taylor expansion of 0 in k 15.775 * [backup-simplify]: Simplify 0 into 0 15.775 * [backup-simplify]: Simplify 0 into 0 15.775 * [backup-simplify]: Simplify 0 into 0 15.775 * [backup-simplify]: Simplify 0 into 0 15.776 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.777 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 15.780 * [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 15.780 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 15.781 * [backup-simplify]: Simplify (- 0) into 0 15.781 * [backup-simplify]: Simplify (+ 0 0) into 0 15.782 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 15.783 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 15.784 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 15.785 * [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 15.786 * [taylor]: Taking taylor expansion of 0 in k 15.786 * [backup-simplify]: Simplify 0 into 0 15.786 * [backup-simplify]: Simplify 0 into 0 15.786 * [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)))) 15.787 * [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))) 15.787 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 15.787 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 15.787 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 15.787 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 15.787 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 15.787 * [taylor]: Taking taylor expansion of 0.25 in k 15.787 * [backup-simplify]: Simplify 0.25 into 0.25 15.787 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 15.787 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.787 * [taylor]: Taking taylor expansion of k in k 15.787 * [backup-simplify]: Simplify 0 into 0 15.787 * [backup-simplify]: Simplify 1 into 1 15.788 * [backup-simplify]: Simplify (/ 1 1) into 1 15.788 * [taylor]: Taking taylor expansion of 1.0 in k 15.788 * [backup-simplify]: Simplify 1.0 into 1.0 15.788 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 15.788 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 15.788 * [taylor]: Taking taylor expansion of -2.0 in k 15.788 * [backup-simplify]: Simplify -2.0 into -2.0 15.788 * [taylor]: Taking taylor expansion of (/ PI n) in k 15.788 * [taylor]: Taking taylor expansion of PI in k 15.788 * [backup-simplify]: Simplify PI into PI 15.788 * [taylor]: Taking taylor expansion of n in k 15.788 * [backup-simplify]: Simplify n into n 15.788 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 15.788 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 15.788 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 15.788 * [backup-simplify]: Simplify (+ 1 0) into 1 15.789 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 15.789 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 15.789 * [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)))))) 15.789 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 15.789 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 15.789 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 15.789 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 15.789 * [taylor]: Taking taylor expansion of 0.25 in n 15.789 * [backup-simplify]: Simplify 0.25 into 0.25 15.789 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 15.789 * [taylor]: Taking taylor expansion of (/ 1 k) in n 15.789 * [taylor]: Taking taylor expansion of k in n 15.789 * [backup-simplify]: Simplify k into k 15.789 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 15.789 * [taylor]: Taking taylor expansion of 1.0 in n 15.789 * [backup-simplify]: Simplify 1.0 into 1.0 15.789 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 15.789 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 15.789 * [taylor]: Taking taylor expansion of -2.0 in n 15.789 * [backup-simplify]: Simplify -2.0 into -2.0 15.789 * [taylor]: Taking taylor expansion of (/ PI n) in n 15.789 * [taylor]: Taking taylor expansion of PI in n 15.789 * [backup-simplify]: Simplify PI into PI 15.789 * [taylor]: Taking taylor expansion of n in n 15.789 * [backup-simplify]: Simplify 0 into 0 15.789 * [backup-simplify]: Simplify 1 into 1 15.790 * [backup-simplify]: Simplify (/ PI 1) into PI 15.790 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 15.791 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 15.791 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 15.791 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 15.792 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 15.792 * [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)))) 15.793 * [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))))) 15.793 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 15.793 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 15.793 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 15.793 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 15.793 * [taylor]: Taking taylor expansion of 0.25 in n 15.793 * [backup-simplify]: Simplify 0.25 into 0.25 15.793 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 15.793 * [taylor]: Taking taylor expansion of (/ 1 k) in n 15.793 * [taylor]: Taking taylor expansion of k in n 15.793 * [backup-simplify]: Simplify k into k 15.794 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 15.794 * [taylor]: Taking taylor expansion of 1.0 in n 15.794 * [backup-simplify]: Simplify 1.0 into 1.0 15.794 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 15.794 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 15.794 * [taylor]: Taking taylor expansion of -2.0 in n 15.794 * [backup-simplify]: Simplify -2.0 into -2.0 15.794 * [taylor]: Taking taylor expansion of (/ PI n) in n 15.794 * [taylor]: Taking taylor expansion of PI in n 15.794 * [backup-simplify]: Simplify PI into PI 15.794 * [taylor]: Taking taylor expansion of n in n 15.794 * [backup-simplify]: Simplify 0 into 0 15.794 * [backup-simplify]: Simplify 1 into 1 15.794 * [backup-simplify]: Simplify (/ PI 1) into PI 15.794 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 15.795 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 15.795 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 15.795 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 15.796 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 15.797 * [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)))) 15.798 * [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))))) 15.798 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 15.798 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 15.798 * [taylor]: Taking taylor expansion of 0.25 in k 15.798 * [backup-simplify]: Simplify 0.25 into 0.25 15.798 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 15.798 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 15.798 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.798 * [taylor]: Taking taylor expansion of k in k 15.798 * [backup-simplify]: Simplify 0 into 0 15.798 * [backup-simplify]: Simplify 1 into 1 15.798 * [backup-simplify]: Simplify (/ 1 1) into 1 15.798 * [taylor]: Taking taylor expansion of 1.0 in k 15.798 * [backup-simplify]: Simplify 1.0 into 1.0 15.798 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 15.798 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 15.798 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 15.798 * [taylor]: Taking taylor expansion of -2.0 in k 15.798 * [backup-simplify]: Simplify -2.0 into -2.0 15.798 * [taylor]: Taking taylor expansion of PI in k 15.798 * [backup-simplify]: Simplify PI into PI 15.799 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 15.799 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 15.799 * [taylor]: Taking taylor expansion of (log n) in k 15.799 * [taylor]: Taking taylor expansion of n in k 15.799 * [backup-simplify]: Simplify n into n 15.799 * [backup-simplify]: Simplify (log n) into (log n) 15.800 * [backup-simplify]: Simplify (+ 1 0) into 1 15.800 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 15.800 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 15.801 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 15.802 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 15.803 * [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))))) 15.804 * [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))))) 15.805 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 15.806 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 15.807 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 15.808 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 15.808 * [backup-simplify]: Simplify (+ 0 0) into 0 15.808 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 15.810 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 15.811 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 15.813 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 15.813 * [taylor]: Taking taylor expansion of 0 in k 15.813 * [backup-simplify]: Simplify 0 into 0 15.813 * [backup-simplify]: Simplify 0 into 0 15.813 * [backup-simplify]: Simplify 0 into 0 15.814 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.815 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 15.818 * [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 15.818 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 15.819 * [backup-simplify]: Simplify (+ 0 0) into 0 15.819 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 15.821 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 15.823 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 15.825 * [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 15.825 * [taylor]: Taking taylor expansion of 0 in k 15.825 * [backup-simplify]: Simplify 0 into 0 15.825 * [backup-simplify]: Simplify 0 into 0 15.825 * [backup-simplify]: Simplify 0 into 0 15.825 * [backup-simplify]: Simplify 0 into 0 15.826 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.827 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 15.833 * [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 15.833 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 15.834 * [backup-simplify]: Simplify (+ 0 0) into 0 15.835 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 15.836 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 15.838 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 15.841 * [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 15.841 * [taylor]: Taking taylor expansion of 0 in k 15.841 * [backup-simplify]: Simplify 0 into 0 15.841 * [backup-simplify]: Simplify 0 into 0 15.842 * [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)))))) 15.842 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 15.842 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 15.842 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 15.842 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 15.842 * [taylor]: Taking taylor expansion of 1.0 in k 15.842 * [backup-simplify]: Simplify 1.0 into 1.0 15.843 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 15.843 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.843 * [taylor]: Taking taylor expansion of k in k 15.843 * [backup-simplify]: Simplify 0 into 0 15.843 * [backup-simplify]: Simplify 1 into 1 15.843 * [backup-simplify]: Simplify (/ 1 1) into 1 15.843 * [backup-simplify]: Simplify (sqrt 0) into 0 15.845 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 15.845 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 15.845 * [taylor]: Taking taylor expansion of 1.0 in k 15.845 * [backup-simplify]: Simplify 1.0 into 1.0 15.845 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 15.845 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.845 * [taylor]: Taking taylor expansion of k in k 15.845 * [backup-simplify]: Simplify 0 into 0 15.845 * [backup-simplify]: Simplify 1 into 1 15.845 * [backup-simplify]: Simplify (/ 1 1) into 1 15.846 * [backup-simplify]: Simplify (sqrt 0) into 0 15.847 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 15.847 * [backup-simplify]: Simplify (* 1.0 0) into 0 15.847 * [backup-simplify]: Simplify 0 into 0 15.849 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 15.849 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 15.850 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 15.852 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 15.855 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 15.855 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 15.856 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.859 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 15.861 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 15.862 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 15.863 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 15.863 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 15.863 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 15.863 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 15.863 * [taylor]: Taking taylor expansion of 1.0 in k 15.863 * [backup-simplify]: Simplify 1.0 into 1.0 15.863 * [taylor]: Taking taylor expansion of (sqrt k) in k 15.863 * [taylor]: Taking taylor expansion of k in k 15.863 * [backup-simplify]: Simplify 0 into 0 15.863 * [backup-simplify]: Simplify 1 into 1 15.864 * [backup-simplify]: Simplify (sqrt 0) into 0 15.865 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 15.865 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 15.865 * [taylor]: Taking taylor expansion of 1.0 in k 15.865 * [backup-simplify]: Simplify 1.0 into 1.0 15.865 * [taylor]: Taking taylor expansion of (sqrt k) in k 15.865 * [taylor]: Taking taylor expansion of k in k 15.865 * [backup-simplify]: Simplify 0 into 0 15.865 * [backup-simplify]: Simplify 1 into 1 15.866 * [backup-simplify]: Simplify (sqrt 0) into 0 15.867 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 15.867 * [backup-simplify]: Simplify (* 1.0 0) into 0 15.867 * [backup-simplify]: Simplify 0 into 0 15.869 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 15.869 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 15.880 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 15.882 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 15.883 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 15.886 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 15.888 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 15.888 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 15.889 * [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)))))))) 15.889 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 15.890 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 15.890 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 15.890 * [taylor]: Taking taylor expansion of 1.0 in k 15.890 * [backup-simplify]: Simplify 1.0 into 1.0 15.890 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 15.890 * [taylor]: Taking taylor expansion of (/ -1 k) in k 15.890 * [taylor]: Taking taylor expansion of -1 in k 15.890 * [backup-simplify]: Simplify -1 into -1 15.890 * [taylor]: Taking taylor expansion of k in k 15.890 * [backup-simplify]: Simplify 0 into 0 15.890 * [backup-simplify]: Simplify 1 into 1 15.890 * [backup-simplify]: Simplify (/ -1 1) into -1 15.890 * [backup-simplify]: Simplify (sqrt 0) into 0 15.891 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 15.891 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 15.891 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 15.891 * [taylor]: Taking taylor expansion of 1.0 in k 15.891 * [backup-simplify]: Simplify 1.0 into 1.0 15.891 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 15.891 * [taylor]: Taking taylor expansion of (/ -1 k) in k 15.891 * [taylor]: Taking taylor expansion of -1 in k 15.891 * [backup-simplify]: Simplify -1 into -1 15.892 * [taylor]: Taking taylor expansion of k in k 15.892 * [backup-simplify]: Simplify 0 into 0 15.892 * [backup-simplify]: Simplify 1 into 1 15.892 * [backup-simplify]: Simplify (/ -1 1) into -1 15.892 * [backup-simplify]: Simplify (sqrt 0) into 0 15.893 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 15.893 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 15.893 * [backup-simplify]: Simplify +nan.0 into +nan.0 15.894 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 15.896 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 15.897 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 15.897 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 15.898 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.900 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 15.903 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 15.904 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 15.905 * [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))))) 15.905 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 2 1) 15.905 * [backup-simplify]: Simplify (* n PI) into (* n PI) 15.905 * [approximate]: Taking taylor expansion of (* n PI) in (n) around 0 15.905 * [taylor]: Taking taylor expansion of (* n PI) in n 15.905 * [taylor]: Taking taylor expansion of n in n 15.905 * [backup-simplify]: Simplify 0 into 0 15.905 * [backup-simplify]: Simplify 1 into 1 15.905 * [taylor]: Taking taylor expansion of PI in n 15.905 * [backup-simplify]: Simplify PI into PI 15.905 * [taylor]: Taking taylor expansion of (* n PI) in n 15.905 * [taylor]: Taking taylor expansion of n in n 15.905 * [backup-simplify]: Simplify 0 into 0 15.905 * [backup-simplify]: Simplify 1 into 1 15.905 * [taylor]: Taking taylor expansion of PI in n 15.905 * [backup-simplify]: Simplify PI into PI 15.905 * [backup-simplify]: Simplify (* 0 PI) into 0 15.905 * [backup-simplify]: Simplify 0 into 0 15.907 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 15.907 * [backup-simplify]: Simplify PI into PI 15.907 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 15.907 * [backup-simplify]: Simplify 0 into 0 15.908 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 15.908 * [backup-simplify]: Simplify 0 into 0 15.909 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 15.909 * [backup-simplify]: Simplify 0 into 0 15.910 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 15.910 * [backup-simplify]: Simplify 0 into 0 15.911 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 15.911 * [backup-simplify]: Simplify 0 into 0 15.912 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 15.912 * [backup-simplify]: Simplify 0 into 0 15.912 * [backup-simplify]: Simplify (* PI n) into (* n PI) 15.913 * [backup-simplify]: Simplify (* (/ 1 n) PI) into (/ PI n) 15.913 * [approximate]: Taking taylor expansion of (/ PI n) in (n) around 0 15.913 * [taylor]: Taking taylor expansion of (/ PI n) in n 15.913 * [taylor]: Taking taylor expansion of PI in n 15.913 * [backup-simplify]: Simplify PI into PI 15.913 * [taylor]: Taking taylor expansion of n in n 15.913 * [backup-simplify]: Simplify 0 into 0 15.913 * [backup-simplify]: Simplify 1 into 1 15.913 * [backup-simplify]: Simplify (/ PI 1) into PI 15.913 * [taylor]: Taking taylor expansion of (/ PI n) in n 15.913 * [taylor]: Taking taylor expansion of PI in n 15.913 * [backup-simplify]: Simplify PI into PI 15.913 * [taylor]: Taking taylor expansion of n in n 15.913 * [backup-simplify]: Simplify 0 into 0 15.913 * [backup-simplify]: Simplify 1 into 1 15.914 * [backup-simplify]: Simplify (/ PI 1) into PI 15.914 * [backup-simplify]: Simplify PI into PI 15.914 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 15.914 * [backup-simplify]: Simplify 0 into 0 15.915 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.915 * [backup-simplify]: Simplify 0 into 0 15.916 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.916 * [backup-simplify]: Simplify 0 into 0 15.917 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.917 * [backup-simplify]: Simplify 0 into 0 15.918 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.918 * [backup-simplify]: Simplify 0 into 0 15.919 * [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 15.919 * [backup-simplify]: Simplify 0 into 0 15.920 * [backup-simplify]: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI) 15.920 * [backup-simplify]: Simplify (* (/ 1 (- n)) PI) into (* -1 (/ PI n)) 15.920 * [approximate]: Taking taylor expansion of (* -1 (/ PI n)) in (n) around 0 15.920 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 15.920 * [taylor]: Taking taylor expansion of -1 in n 15.920 * [backup-simplify]: Simplify -1 into -1 15.920 * [taylor]: Taking taylor expansion of (/ PI n) in n 15.920 * [taylor]: Taking taylor expansion of PI in n 15.920 * [backup-simplify]: Simplify PI into PI 15.920 * [taylor]: Taking taylor expansion of n in n 15.920 * [backup-simplify]: Simplify 0 into 0 15.920 * [backup-simplify]: Simplify 1 into 1 15.921 * [backup-simplify]: Simplify (/ PI 1) into PI 15.921 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 15.921 * [taylor]: Taking taylor expansion of -1 in n 15.921 * [backup-simplify]: Simplify -1 into -1 15.921 * [taylor]: Taking taylor expansion of (/ PI n) in n 15.921 * [taylor]: Taking taylor expansion of PI in n 15.921 * [backup-simplify]: Simplify PI into PI 15.921 * [taylor]: Taking taylor expansion of n in n 15.921 * [backup-simplify]: Simplify 0 into 0 15.921 * [backup-simplify]: Simplify 1 into 1 15.921 * [backup-simplify]: Simplify (/ PI 1) into PI 15.922 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 15.922 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 15.923 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 15.924 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0 15.924 * [backup-simplify]: Simplify 0 into 0 15.925 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.926 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 15.926 * [backup-simplify]: Simplify 0 into 0 15.927 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.929 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 15.929 * [backup-simplify]: Simplify 0 into 0 15.930 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.931 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 15.931 * [backup-simplify]: Simplify 0 into 0 15.932 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.934 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 15.934 * [backup-simplify]: Simplify 0 into 0 15.935 * [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 15.937 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 15.937 * [backup-simplify]: Simplify 0 into 0 15.937 * [backup-simplify]: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) 15.938 * * * [progress]: simplifying candidates 15.942 * [simplify]: Simplifying: (* (+ (log n) (log PI)) (/ (- 1.0 k) 2.0)) (* (log (* n PI)) (/ (- 1.0 k) 2.0)) (* (log (* n PI)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ 1.0 2.0)) (pow (* n PI) (/ k 2.0)) (pow (* n PI) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* n PI) (sqrt (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* n PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* n PI) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* n PI) (/ (sqrt (- 1.0 k)) 1)) (pow (* n PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ 1 (sqrt 2.0))) (pow (* n PI) (/ 1 1)) (pow (* n PI) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* n PI) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* n PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ 1 (sqrt 2.0))) (pow (* n PI) (/ 1 1)) (pow (* n PI) 1) (pow (* n PI) (- 1.0 k)) (pow n (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)) (log (pow (* n PI) (/ (- 1.0 k) 2.0))) (exp (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (* n PI) (+ (log n) (log PI)) (log (* n PI)) (exp (* n PI)) (* (* (* n n) n) (* (* PI PI) PI)) (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI)) (* (* (* n PI) (* n PI)) (* n PI)) (sqrt (* n PI)) (sqrt (* n PI)) (* (sqrt n) (sqrt PI)) (* (sqrt n) (sqrt PI)) (* n (* (cbrt PI) (cbrt PI))) (* n (sqrt PI)) (* n 1) (* (cbrt n) PI) (* (sqrt n) PI) (* n PI) (- (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log n) (log PI)))) (pow (log PI) 2)))) (+ (exp (* 0.5 (+ (log n) (log PI)))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log n) (log PI)))) (pow (log n) 2)))) (* 0.25 (* (pow k 2) (* (exp (* 0.5 (+ (log n) (log PI)))) (* (log n) (log PI)))))))) (+ (* 0.5 (* k (* (exp (* 0.5 (+ (log n) (log PI)))) (log PI)))) (* 0.5 (* k (* (exp (* 0.5 (+ (log n) (log PI)))) (log n)))))) (exp (* 0.5 (* (- 1.0 k) (- (log PI) (log (/ 1 n)))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -1 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* n PI) (* n PI) (* n PI) 15.953 * * [simplify]: Extracting # 0 : cost 0 15.954 * * [simplify]: Extracting # 1 : cost 0 15.955 * * [simplify]: Extracting # 2 : cost 0 15.956 * * [simplify]: Extracting # 3 : cost 0 15.957 * * [simplify]: Extracting # 4 : cost 0 15.958 * * [simplify]: Extracting # 5 : cost 0 15.960 * * [simplify]: Extracting # 6 : cost 0 15.961 * * [simplify]: Extracting # 7 : cost 0 15.962 * * [simplify]: Extracting # 8 : cost 0 15.964 * * [simplify]: Extracting # 9 : cost 0 15.965 * * [simplify]: Extracting # 10 : cost 0 15.966 * * [simplify]: Extracting # 11 : cost 0 15.968 * * [simplify]: Extracting # 12 : cost 0 15.969 * * [simplify]: Extracting # 13 : cost 0 15.970 * * [simplify]: iteration 0 : 393 enodes (cost 2527 ) 16.168 * * [simplify]: Extracting # 0 : cost 0 16.170 * * [simplify]: Extracting # 1 : cost 0 16.171 * * [simplify]: Extracting # 2 : cost 0 16.174 * * [simplify]: Extracting # 3 : cost 0 16.177 * * [simplify]: Extracting # 4 : cost 0 16.180 * * [simplify]: Extracting # 5 : cost 0 16.183 * * [simplify]: Extracting # 6 : cost 0 16.186 * * [simplify]: iteration 1 : 1003 enodes (cost 2328 ) 16.829 * * [simplify]: Extracting # 0 : cost 0 16.835 * * [simplify]: Extracting # 1 : cost 0 16.844 * * [simplify]: Extracting # 2 : cost 0 16.852 * * [simplify]: Extracting # 3 : cost 0 16.860 * * [simplify]: Extracting # 4 : cost 0 16.871 * * [simplify]: Extracting # 5 : cost 0 16.875 * * [simplify]: iteration 2 : 2778 enodes (cost 2235 ) 17.931 * * [simplify]: Extracting # 0 : cost 0 17.944 * * [simplify]: Extracting # 1 : cost 0 17.958 * * [simplify]: Extracting # 2 : cost 0 17.971 * * [simplify]: Extracting # 3 : cost 0 17.984 * * [simplify]: Extracting # 4 : cost 0 17.996 * * [simplify]: iteration done: 5000 enodes (cost 2233 ) 17.997 * [simplify]: Simplified to: (log (pow (* n PI) (/ (- 1.0 k) 2.0))) (log (pow (* n PI) (/ (- 1.0 k) 2.0))) (log (pow (* n PI) (/ (- 1.0 k) 2.0))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* n PI) (/ 1.0 2.0)) (pow (* n PI) (/ k 2.0)) (pow (* n PI) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* n PI) (sqrt (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* n PI) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* n PI) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* n PI) (sqrt (- 1.0 k))) (pow (* n PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ 1 (sqrt 2.0))) (* PI n) (pow (* n PI) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* PI n) (+ (sqrt 1.0) (sqrt k))) (pow (* n PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ 1 (sqrt 2.0))) (* PI n) (* PI n) (pow (* PI n) (- 1.0 k)) (pow n (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)) (log (pow (* n PI) (/ (- 1.0 k) 2.0))) (exp (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow (pow (* n PI) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* n PI) (/ (/ (- 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)) (* (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 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)) (* (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 (* n (* 2.0 PI)) (/ (* (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 (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2))) (pow (* n (* 2.0 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 (* n (* 2.0 PI)) (/ (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 (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (sqrt 2))) (pow (* n (* 2.0 PI)) (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 PI) n) (/ 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 (* n (* 2.0 PI)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* 2.0 n) PI) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (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 (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (/ (/ (+ (sqrt 1.0) (sqrt k)) (cbrt 2)) (cbrt 2))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2))) (pow (* n (* 2.0 PI)) (+ (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 PI) n) (/ 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 (* n (* 2.0 PI)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* 2.0 n) PI) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* 2.0 n) PI) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* 2.0 n) PI) (- 1.0 k)) (* (* 2.0 n) PI) (pow (* n (* 2.0 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 (* n (* 2.0 PI)) (/ (/ (- 1.0 k) 2.0) 4)) (pow (* n (* 2.0 PI)) (/ (/ (- 1.0 k) 2.0) 4)) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (/ (pow 1.0 3) (sqrt k)) k) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (* PI n) (log (* PI n)) (log (* PI n)) (exp (* n PI)) (pow (* PI n) 3) (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI)) (pow (* PI n) 3) (sqrt (* n PI)) (sqrt (* n PI)) (* (sqrt n) (sqrt PI)) (* (sqrt n) (sqrt PI)) (* n (* (cbrt PI) (cbrt PI))) (* n (sqrt PI)) n (* (cbrt n) PI) (* (sqrt n) PI) (* PI n) (+ (+ (pow (* PI n) 0.5) (* (* (* 0.125 (pow k 2)) (pow (log PI) 2)) (pow (* PI n) 0.5))) (- (+ (* (* (* (log n) (pow (* PI n) 0.5)) (* (log PI) (pow k 2))) 0.25) (* (pow k 2) (* (* (pow (* PI n) 0.5) (pow (log n) 2)) 0.125))) (* (* (* (pow (* PI n) 0.5) k) (log (* PI n))) 0.5))) (pow (pow (* PI n) (- 1.0 k)) 0.5) (exp (* (* (- (log (- PI)) (log (/ -1 n))) (- 1.0 k)) 0.5)) (+ (* (* 0.03125 (pow k 2)) (* (pow (* n (* 2.0 PI)) 0.25) (pow (log (* 2.0 PI)) 2))) (- (+ (+ (pow (* n (* 2.0 PI)) 0.25) (* (* 0.03125 (pow k 2)) (* (pow (* n (* 2.0 PI)) 0.25) (pow (log n) 2)))) (* (* (pow (* n (* 2.0 PI)) 0.25) (* (log (* 2.0 PI)) (log n))) (* 0.0625 (pow k 2)))) (* (* k (+ (* (pow (* n (* 2.0 PI)) 0.25) (log (* 2.0 PI))) (* (pow (* n (* 2.0 PI)) 0.25) (log n)))) 0.25))) (pow (pow (* n (* 2.0 PI)) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (- (* +nan.0 k) (- (* +nan.0 (pow k 2)) +nan.0))) (- (- (/ +nan.0 (pow k 2)) (- (/ +nan.0 k) (/ +nan.0 (pow k 3))))) (+ (- (/ +nan.0 k) +nan.0) (/ (- +nan.0) (pow k 2))) (* PI n) (* PI n) (* PI n) 17.999 * * * [progress]: adding candidates to table 19.214 * [progress]: [Phase 3 of 3] Extracting. 19.215 * * [regime]: Finding splitpoints for: (# # # # # # #) 19.222 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 19.222 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # #) 19.267 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # #) 19.290 * * * * [regimes]: Trying to branch on n from (# # # # # # #) 19.353 * * * * [regimes]: Trying to branch on k from (# # # # # # #) 19.397 * * * [regime]: Found split indices: #