48.689 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.157 * * * [progress]: [2/2] Setting up program. 0.162 * [progress]: [Phase 2 of 3] Improving. 0.162 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.162 * * [simplify]: Extracting # 0 : cost 0 0.162 * * [simplify]: Extracting # 1 : cost 0 0.163 * * [simplify]: Extracting # 2 : cost 0 0.163 * * [simplify]: Extracting # 3 : cost 0 0.163 * * [simplify]: Extracting # 4 : cost 0 0.163 * * [simplify]: Extracting # 5 : cost 0 0.163 * * [simplify]: Extracting # 6 : cost 0 0.163 * * [simplify]: Extracting # 7 : cost 0 0.163 * * [simplify]: iteration 0 : 13 enodes (cost 16 ) 0.169 * * [simplify]: Extracting # 0 : cost 0 0.169 * * [simplify]: Extracting # 1 : cost 0 0.169 * * [simplify]: Extracting # 2 : cost 0 0.169 * * [simplify]: Extracting # 3 : cost 0 0.169 * * [simplify]: Extracting # 4 : cost 0 0.169 * * [simplify]: Extracting # 5 : cost 0 0.169 * * [simplify]: iteration 1 : 29 enodes (cost 16 ) 0.181 * * [simplify]: Extracting # 0 : cost 0 0.181 * * [simplify]: Extracting # 1 : cost 0 0.182 * * [simplify]: Extracting # 2 : cost 0 0.182 * * [simplify]: Extracting # 3 : cost 0 0.182 * * [simplify]: Extracting # 4 : cost 0 0.182 * * [simplify]: iteration 2 : 59 enodes (cost 16 ) 0.205 * * [simplify]: Extracting # 0 : cost 0 0.205 * * [simplify]: Extracting # 1 : cost 0 0.205 * * [simplify]: Extracting # 2 : cost 0 0.206 * * [simplify]: Extracting # 3 : cost 0 0.206 * * [simplify]: Extracting # 4 : cost 0 0.206 * * [simplify]: iteration 3 : 120 enodes (cost 16 ) 0.298 * * [simplify]: Extracting # 0 : cost 0 0.299 * * [simplify]: Extracting # 1 : cost 0 0.299 * * [simplify]: Extracting # 2 : cost 0 0.299 * * [simplify]: Extracting # 3 : cost 0 0.300 * * [simplify]: Extracting # 4 : cost 0 0.300 * * [simplify]: iteration 4 : 330 enodes (cost 16 ) 0.532 * * [simplify]: Extracting # 0 : cost 0 0.535 * * [simplify]: Extracting # 1 : cost 0 0.538 * * [simplify]: Extracting # 2 : cost 0 0.542 * * [simplify]: Extracting # 3 : cost 0 0.545 * * [simplify]: Extracting # 4 : cost 0 0.548 * * [simplify]: Extracting # 5 : cost 0 0.551 * * [simplify]: iteration 5 : 1545 enodes (cost 16 ) 1.372 * * [simplify]: Extracting # 0 : cost 0 1.435 * * [simplify]: Extracting # 1 : cost 0 1.449 * * [simplify]: Extracting # 2 : cost 0 1.465 * * [simplify]: Extracting # 3 : cost 0 1.478 * * [simplify]: Extracting # 4 : cost 0 1.491 * * [simplify]: iteration done: 5000 enodes (cost 16 ) 1.491 * [simplify]: Simplified to: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1.492 * * [progress]: iteration 1 / 4 1.492 * * * [progress]: picking best candidate 1.496 * * * * [pick]: Picked # 1.496 * * * [progress]: localizing error 1.528 * * * [progress]: generating rewritten candidates 1.528 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 1.573 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 1.592 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 1.627 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 1.723 * * * [progress]: generating series expansions 1.723 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 1.724 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 1.724 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 1.725 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.725 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.725 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.725 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.725 * [taylor]: Taking taylor expansion of 0.5 in k 1.725 * [backup-simplify]: Simplify 0.5 into 0.5 1.725 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.725 * [taylor]: Taking taylor expansion of 1.0 in k 1.725 * [backup-simplify]: Simplify 1.0 into 1.0 1.725 * [taylor]: Taking taylor expansion of k in k 1.725 * [backup-simplify]: Simplify 0 into 0 1.725 * [backup-simplify]: Simplify 1 into 1 1.725 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.725 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.725 * [taylor]: Taking taylor expansion of 2.0 in k 1.725 * [backup-simplify]: Simplify 2.0 into 2.0 1.725 * [taylor]: Taking taylor expansion of (* n PI) in k 1.725 * [taylor]: Taking taylor expansion of n in k 1.725 * [backup-simplify]: Simplify n into n 1.725 * [taylor]: Taking taylor expansion of PI in k 1.725 * [backup-simplify]: Simplify PI into PI 1.725 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.725 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.725 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.726 * [backup-simplify]: Simplify (- 0) into 0 1.727 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.727 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 1.727 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 1.728 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 1.728 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.728 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.728 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.728 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.728 * [taylor]: Taking taylor expansion of 0.5 in n 1.728 * [backup-simplify]: Simplify 0.5 into 0.5 1.728 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.728 * [taylor]: Taking taylor expansion of 1.0 in n 1.728 * [backup-simplify]: Simplify 1.0 into 1.0 1.728 * [taylor]: Taking taylor expansion of k in n 1.728 * [backup-simplify]: Simplify k into k 1.728 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.728 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.728 * [taylor]: Taking taylor expansion of 2.0 in n 1.728 * [backup-simplify]: Simplify 2.0 into 2.0 1.728 * [taylor]: Taking taylor expansion of (* n PI) in n 1.728 * [taylor]: Taking taylor expansion of n in n 1.728 * [backup-simplify]: Simplify 0 into 0 1.728 * [backup-simplify]: Simplify 1 into 1 1.728 * [taylor]: Taking taylor expansion of PI in n 1.728 * [backup-simplify]: Simplify PI into PI 1.729 * [backup-simplify]: Simplify (* 0 PI) into 0 1.729 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.731 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.733 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.734 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.734 * [backup-simplify]: Simplify (- k) into (- k) 1.734 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.734 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.735 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.736 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.737 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.737 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.737 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.737 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.737 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.737 * [taylor]: Taking taylor expansion of 0.5 in n 1.737 * [backup-simplify]: Simplify 0.5 into 0.5 1.737 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.737 * [taylor]: Taking taylor expansion of 1.0 in n 1.737 * [backup-simplify]: Simplify 1.0 into 1.0 1.737 * [taylor]: Taking taylor expansion of k in n 1.737 * [backup-simplify]: Simplify k into k 1.737 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.737 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.737 * [taylor]: Taking taylor expansion of 2.0 in n 1.737 * [backup-simplify]: Simplify 2.0 into 2.0 1.737 * [taylor]: Taking taylor expansion of (* n PI) in n 1.737 * [taylor]: Taking taylor expansion of n in n 1.737 * [backup-simplify]: Simplify 0 into 0 1.737 * [backup-simplify]: Simplify 1 into 1 1.737 * [taylor]: Taking taylor expansion of PI in n 1.737 * [backup-simplify]: Simplify PI into PI 1.738 * [backup-simplify]: Simplify (* 0 PI) into 0 1.738 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.739 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.740 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.740 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.741 * [backup-simplify]: Simplify (- k) into (- k) 1.741 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.741 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.742 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.742 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.743 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.743 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.743 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.743 * [taylor]: Taking taylor expansion of 0.5 in k 1.743 * [backup-simplify]: Simplify 0.5 into 0.5 1.743 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.743 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.743 * [taylor]: Taking taylor expansion of 1.0 in k 1.743 * [backup-simplify]: Simplify 1.0 into 1.0 1.743 * [taylor]: Taking taylor expansion of k in k 1.743 * [backup-simplify]: Simplify 0 into 0 1.743 * [backup-simplify]: Simplify 1 into 1 1.743 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.744 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.744 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.744 * [taylor]: Taking taylor expansion of 2.0 in k 1.744 * [backup-simplify]: Simplify 2.0 into 2.0 1.744 * [taylor]: Taking taylor expansion of PI in k 1.744 * [backup-simplify]: Simplify PI into PI 1.744 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.745 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.745 * [taylor]: Taking taylor expansion of (log n) in k 1.745 * [taylor]: Taking taylor expansion of n in k 1.745 * [backup-simplify]: Simplify n into n 1.745 * [backup-simplify]: Simplify (log n) into (log n) 1.745 * [backup-simplify]: Simplify (- 0) into 0 1.745 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.746 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 1.747 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 1.747 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 1.748 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.749 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.749 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.750 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.751 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.751 * [backup-simplify]: Simplify (- 0) into 0 1.752 * [backup-simplify]: Simplify (+ 0 0) into 0 1.752 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 1.753 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.753 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 1.755 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.755 * [taylor]: Taking taylor expansion of 0 in k 1.755 * [backup-simplify]: Simplify 0 into 0 1.755 * [backup-simplify]: Simplify 0 into 0 1.755 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.757 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.758 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.758 * [backup-simplify]: Simplify (+ 0 0) into 0 1.758 * [backup-simplify]: Simplify (- 1) into -1 1.759 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.760 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 1.762 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1.766 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 1.769 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 1.770 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.771 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.775 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 1.775 * [backup-simplify]: Simplify (- 0) into 0 1.776 * [backup-simplify]: Simplify (+ 0 0) into 0 1.776 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 1.777 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.778 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.779 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.779 * [taylor]: Taking taylor expansion of 0 in k 1.779 * [backup-simplify]: Simplify 0 into 0 1.779 * [backup-simplify]: Simplify 0 into 0 1.779 * [backup-simplify]: Simplify 0 into 0 1.780 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.782 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 1.783 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.783 * [backup-simplify]: Simplify (+ 0 0) into 0 1.784 * [backup-simplify]: Simplify (- 0) into 0 1.784 * [backup-simplify]: Simplify (+ 0 0) into 0 1.785 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.787 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 1.789 * [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)))))) 1.792 * [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)))))) 1.799 * [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)))))) 1.799 * [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)))) 1.799 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 1.799 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.799 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.799 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.799 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.799 * [taylor]: Taking taylor expansion of 0.5 in k 1.800 * [backup-simplify]: Simplify 0.5 into 0.5 1.800 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.800 * [taylor]: Taking taylor expansion of 1.0 in k 1.800 * [backup-simplify]: Simplify 1.0 into 1.0 1.800 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.800 * [taylor]: Taking taylor expansion of k in k 1.800 * [backup-simplify]: Simplify 0 into 0 1.800 * [backup-simplify]: Simplify 1 into 1 1.800 * [backup-simplify]: Simplify (/ 1 1) into 1 1.800 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.800 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.800 * [taylor]: Taking taylor expansion of 2.0 in k 1.800 * [backup-simplify]: Simplify 2.0 into 2.0 1.800 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.800 * [taylor]: Taking taylor expansion of PI in k 1.800 * [backup-simplify]: Simplify PI into PI 1.800 * [taylor]: Taking taylor expansion of n in k 1.800 * [backup-simplify]: Simplify n into n 1.800 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.800 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.800 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.800 * [backup-simplify]: Simplify (- 1) into -1 1.801 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.801 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 1.801 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 1.802 * [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))))) 1.802 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.802 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.802 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.802 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.802 * [taylor]: Taking taylor expansion of 0.5 in n 1.802 * [backup-simplify]: Simplify 0.5 into 0.5 1.802 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.802 * [taylor]: Taking taylor expansion of 1.0 in n 1.802 * [backup-simplify]: Simplify 1.0 into 1.0 1.802 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.802 * [taylor]: Taking taylor expansion of k in n 1.802 * [backup-simplify]: Simplify k into k 1.802 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.802 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.802 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.802 * [taylor]: Taking taylor expansion of 2.0 in n 1.802 * [backup-simplify]: Simplify 2.0 into 2.0 1.802 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.802 * [taylor]: Taking taylor expansion of PI in n 1.802 * [backup-simplify]: Simplify PI into PI 1.802 * [taylor]: Taking taylor expansion of n in n 1.802 * [backup-simplify]: Simplify 0 into 0 1.802 * [backup-simplify]: Simplify 1 into 1 1.802 * [backup-simplify]: Simplify (/ PI 1) into PI 1.803 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.803 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.803 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.803 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.804 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.804 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.805 * [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)))) 1.806 * [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))))) 1.806 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.806 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.806 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.806 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.806 * [taylor]: Taking taylor expansion of 0.5 in n 1.806 * [backup-simplify]: Simplify 0.5 into 0.5 1.806 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.806 * [taylor]: Taking taylor expansion of 1.0 in n 1.806 * [backup-simplify]: Simplify 1.0 into 1.0 1.806 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.806 * [taylor]: Taking taylor expansion of k in n 1.806 * [backup-simplify]: Simplify k into k 1.806 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.806 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.806 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.806 * [taylor]: Taking taylor expansion of 2.0 in n 1.806 * [backup-simplify]: Simplify 2.0 into 2.0 1.806 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.806 * [taylor]: Taking taylor expansion of PI in n 1.806 * [backup-simplify]: Simplify PI into PI 1.806 * [taylor]: Taking taylor expansion of n in n 1.806 * [backup-simplify]: Simplify 0 into 0 1.806 * [backup-simplify]: Simplify 1 into 1 1.807 * [backup-simplify]: Simplify (/ PI 1) into PI 1.807 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.808 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.808 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.808 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.808 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.809 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.811 * [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)))) 1.812 * [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))))) 1.812 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.812 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.812 * [taylor]: Taking taylor expansion of 0.5 in k 1.812 * [backup-simplify]: Simplify 0.5 into 0.5 1.812 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.812 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.812 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.812 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.812 * [taylor]: Taking taylor expansion of 2.0 in k 1.812 * [backup-simplify]: Simplify 2.0 into 2.0 1.813 * [taylor]: Taking taylor expansion of PI in k 1.813 * [backup-simplify]: Simplify PI into PI 1.813 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.814 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.814 * [taylor]: Taking taylor expansion of (log n) in k 1.814 * [taylor]: Taking taylor expansion of n in k 1.814 * [backup-simplify]: Simplify n into n 1.814 * [backup-simplify]: Simplify (log n) into (log n) 1.814 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.814 * [taylor]: Taking taylor expansion of 1.0 in k 1.814 * [backup-simplify]: Simplify 1.0 into 1.0 1.814 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.814 * [taylor]: Taking taylor expansion of k in k 1.814 * [backup-simplify]: Simplify 0 into 0 1.814 * [backup-simplify]: Simplify 1 into 1 1.815 * [backup-simplify]: Simplify (/ 1 1) into 1 1.815 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.816 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 1.816 * [backup-simplify]: Simplify (- 1) into -1 1.817 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.818 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 1.819 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 1.820 * [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))))) 1.822 * [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))))) 1.823 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.824 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.825 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.826 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.826 * [backup-simplify]: Simplify (- 0) into 0 1.826 * [backup-simplify]: Simplify (+ 0 0) into 0 1.827 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 1.834 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.835 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 1.837 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.837 * [taylor]: Taking taylor expansion of 0 in k 1.837 * [backup-simplify]: Simplify 0 into 0 1.838 * [backup-simplify]: Simplify 0 into 0 1.838 * [backup-simplify]: Simplify 0 into 0 1.839 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.840 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.842 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 1.842 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.842 * [backup-simplify]: Simplify (- 0) into 0 1.842 * [backup-simplify]: Simplify (+ 0 0) into 0 1.843 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 1.844 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.845 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 1.846 * [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 1.846 * [taylor]: Taking taylor expansion of 0 in k 1.846 * [backup-simplify]: Simplify 0 into 0 1.846 * [backup-simplify]: Simplify 0 into 0 1.846 * [backup-simplify]: Simplify 0 into 0 1.846 * [backup-simplify]: Simplify 0 into 0 1.847 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.847 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.851 * [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 1.851 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.851 * [backup-simplify]: Simplify (- 0) into 0 1.851 * [backup-simplify]: Simplify (+ 0 0) into 0 1.852 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 1.853 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.854 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 1.856 * [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 1.856 * [taylor]: Taking taylor expansion of 0 in k 1.856 * [backup-simplify]: Simplify 0 into 0 1.856 * [backup-simplify]: Simplify 0 into 0 1.857 * [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)))) 1.857 * [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))) 1.857 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 1.857 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.857 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.857 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.857 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.857 * [taylor]: Taking taylor expansion of 0.5 in k 1.857 * [backup-simplify]: Simplify 0.5 into 0.5 1.857 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.857 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.857 * [taylor]: Taking taylor expansion of k in k 1.857 * [backup-simplify]: Simplify 0 into 0 1.857 * [backup-simplify]: Simplify 1 into 1 1.858 * [backup-simplify]: Simplify (/ 1 1) into 1 1.858 * [taylor]: Taking taylor expansion of 1.0 in k 1.858 * [backup-simplify]: Simplify 1.0 into 1.0 1.858 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.858 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.858 * [taylor]: Taking taylor expansion of -2.0 in k 1.858 * [backup-simplify]: Simplify -2.0 into -2.0 1.858 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.858 * [taylor]: Taking taylor expansion of PI in k 1.858 * [backup-simplify]: Simplify PI into PI 1.858 * [taylor]: Taking taylor expansion of n in k 1.858 * [backup-simplify]: Simplify n into n 1.858 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.858 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.858 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.858 * [backup-simplify]: Simplify (+ 1 0) into 1 1.858 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 1.858 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 1.859 * [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)))))) 1.859 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.859 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.859 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.859 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.859 * [taylor]: Taking taylor expansion of 0.5 in n 1.859 * [backup-simplify]: Simplify 0.5 into 0.5 1.859 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.859 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.859 * [taylor]: Taking taylor expansion of k in n 1.859 * [backup-simplify]: Simplify k into k 1.859 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.859 * [taylor]: Taking taylor expansion of 1.0 in n 1.859 * [backup-simplify]: Simplify 1.0 into 1.0 1.859 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.859 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.859 * [taylor]: Taking taylor expansion of -2.0 in n 1.859 * [backup-simplify]: Simplify -2.0 into -2.0 1.859 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.859 * [taylor]: Taking taylor expansion of PI in n 1.859 * [backup-simplify]: Simplify PI into PI 1.859 * [taylor]: Taking taylor expansion of n in n 1.859 * [backup-simplify]: Simplify 0 into 0 1.859 * [backup-simplify]: Simplify 1 into 1 1.859 * [backup-simplify]: Simplify (/ PI 1) into PI 1.860 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.860 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.860 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.860 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.861 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.862 * [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)))) 1.863 * [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))))) 1.863 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.863 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.863 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.863 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.863 * [taylor]: Taking taylor expansion of 0.5 in n 1.863 * [backup-simplify]: Simplify 0.5 into 0.5 1.863 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.863 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.863 * [taylor]: Taking taylor expansion of k in n 1.863 * [backup-simplify]: Simplify k into k 1.863 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.863 * [taylor]: Taking taylor expansion of 1.0 in n 1.863 * [backup-simplify]: Simplify 1.0 into 1.0 1.863 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.863 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.863 * [taylor]: Taking taylor expansion of -2.0 in n 1.863 * [backup-simplify]: Simplify -2.0 into -2.0 1.863 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.863 * [taylor]: Taking taylor expansion of PI in n 1.863 * [backup-simplify]: Simplify PI into PI 1.863 * [taylor]: Taking taylor expansion of n in n 1.863 * [backup-simplify]: Simplify 0 into 0 1.863 * [backup-simplify]: Simplify 1 into 1 1.864 * [backup-simplify]: Simplify (/ PI 1) into PI 1.864 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.864 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.865 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.865 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.865 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.866 * [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)))) 1.867 * [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))))) 1.867 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.867 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.867 * [taylor]: Taking taylor expansion of 0.5 in k 1.867 * [backup-simplify]: Simplify 0.5 into 0.5 1.867 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.867 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.867 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.867 * [taylor]: Taking taylor expansion of k in k 1.867 * [backup-simplify]: Simplify 0 into 0 1.867 * [backup-simplify]: Simplify 1 into 1 1.867 * [backup-simplify]: Simplify (/ 1 1) into 1 1.868 * [taylor]: Taking taylor expansion of 1.0 in k 1.868 * [backup-simplify]: Simplify 1.0 into 1.0 1.868 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.868 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.868 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.868 * [taylor]: Taking taylor expansion of -2.0 in k 1.868 * [backup-simplify]: Simplify -2.0 into -2.0 1.868 * [taylor]: Taking taylor expansion of PI in k 1.868 * [backup-simplify]: Simplify PI into PI 1.868 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.869 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.869 * [taylor]: Taking taylor expansion of (log n) in k 1.869 * [taylor]: Taking taylor expansion of n in k 1.869 * [backup-simplify]: Simplify n into n 1.869 * [backup-simplify]: Simplify (log n) into (log n) 1.870 * [backup-simplify]: Simplify (+ 1 0) into 1 1.870 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.871 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 1.872 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 1.874 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 1.875 * [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))))) 1.876 * [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))))) 1.877 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.878 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.880 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 1.880 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.880 * [backup-simplify]: Simplify (+ 0 0) into 0 1.881 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 1.882 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.883 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 1.885 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.885 * [taylor]: Taking taylor expansion of 0 in k 1.886 * [backup-simplify]: Simplify 0 into 0 1.886 * [backup-simplify]: Simplify 0 into 0 1.886 * [backup-simplify]: Simplify 0 into 0 1.887 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.888 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.892 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 1.892 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.892 * [backup-simplify]: Simplify (+ 0 0) into 0 1.893 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 1.895 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.896 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 1.899 * [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 1.899 * [taylor]: Taking taylor expansion of 0 in k 1.899 * [backup-simplify]: Simplify 0 into 0 1.899 * [backup-simplify]: Simplify 0 into 0 1.899 * [backup-simplify]: Simplify 0 into 0 1.899 * [backup-simplify]: Simplify 0 into 0 1.901 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.902 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.909 * [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 1.909 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.910 * [backup-simplify]: Simplify (+ 0 0) into 0 1.911 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 1.912 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.914 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 1.917 * [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 1.917 * [taylor]: Taking taylor expansion of 0 in k 1.917 * [backup-simplify]: Simplify 0 into 0 1.917 * [backup-simplify]: Simplify 0 into 0 1.918 * [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)))))) 1.918 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 1.918 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 1.918 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 1.919 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.919 * [taylor]: Taking taylor expansion of 1.0 in k 1.919 * [backup-simplify]: Simplify 1.0 into 1.0 1.919 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.919 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.919 * [taylor]: Taking taylor expansion of k in k 1.919 * [backup-simplify]: Simplify 0 into 0 1.919 * [backup-simplify]: Simplify 1 into 1 1.919 * [backup-simplify]: Simplify (/ 1 1) into 1 1.920 * [backup-simplify]: Simplify (sqrt 0) into 0 1.921 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.921 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.921 * [taylor]: Taking taylor expansion of 1.0 in k 1.921 * [backup-simplify]: Simplify 1.0 into 1.0 1.921 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.921 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.921 * [taylor]: Taking taylor expansion of k in k 1.921 * [backup-simplify]: Simplify 0 into 0 1.921 * [backup-simplify]: Simplify 1 into 1 1.921 * [backup-simplify]: Simplify (/ 1 1) into 1 1.922 * [backup-simplify]: Simplify (sqrt 0) into 0 1.923 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.923 * [backup-simplify]: Simplify (* 1.0 0) into 0 1.924 * [backup-simplify]: Simplify 0 into 0 1.925 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 1.925 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.926 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1.929 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.931 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 1.931 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.932 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.935 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.937 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 1.937 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.938 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 1.938 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 1.938 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 1.938 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.938 * [taylor]: Taking taylor expansion of 1.0 in k 1.938 * [backup-simplify]: Simplify 1.0 into 1.0 1.938 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.938 * [taylor]: Taking taylor expansion of k in k 1.938 * [backup-simplify]: Simplify 0 into 0 1.939 * [backup-simplify]: Simplify 1 into 1 1.939 * [backup-simplify]: Simplify (sqrt 0) into 0 1.940 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.940 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.940 * [taylor]: Taking taylor expansion of 1.0 in k 1.940 * [backup-simplify]: Simplify 1.0 into 1.0 1.940 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.940 * [taylor]: Taking taylor expansion of k in k 1.940 * [backup-simplify]: Simplify 0 into 0 1.940 * [backup-simplify]: Simplify 1 into 1 1.940 * [backup-simplify]: Simplify (sqrt 0) into 0 1.941 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.941 * [backup-simplify]: Simplify (* 1.0 0) into 0 1.941 * [backup-simplify]: Simplify 0 into 0 1.942 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 1.942 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.944 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.945 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 1.945 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.948 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.949 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 1.950 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.957 * [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)))))))) 1.957 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 1.957 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 1.957 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.957 * [taylor]: Taking taylor expansion of 1.0 in k 1.957 * [backup-simplify]: Simplify 1.0 into 1.0 1.957 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.957 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.957 * [taylor]: Taking taylor expansion of -1 in k 1.957 * [backup-simplify]: Simplify -1 into -1 1.957 * [taylor]: Taking taylor expansion of k in k 1.957 * [backup-simplify]: Simplify 0 into 0 1.957 * [backup-simplify]: Simplify 1 into 1 1.957 * [backup-simplify]: Simplify (/ -1 1) into -1 1.958 * [backup-simplify]: Simplify (sqrt 0) into 0 1.959 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1.959 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 1.959 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.959 * [taylor]: Taking taylor expansion of 1.0 in k 1.959 * [backup-simplify]: Simplify 1.0 into 1.0 1.959 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.959 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.959 * [taylor]: Taking taylor expansion of -1 in k 1.959 * [backup-simplify]: Simplify -1 into -1 1.959 * [taylor]: Taking taylor expansion of k in k 1.959 * [backup-simplify]: Simplify 0 into 0 1.959 * [backup-simplify]: Simplify 1 into 1 1.959 * [backup-simplify]: Simplify (/ -1 1) into -1 1.960 * [backup-simplify]: Simplify (sqrt 0) into 0 1.960 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1.961 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 1.961 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.961 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1.963 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.965 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 1.966 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.967 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.970 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.975 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 1.975 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.977 * [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))))) 1.977 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 1.977 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.977 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.977 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.977 * [taylor]: Taking taylor expansion of 2.0 in n 1.977 * [backup-simplify]: Simplify 2.0 into 2.0 1.977 * [taylor]: Taking taylor expansion of (* n PI) in n 1.977 * [taylor]: Taking taylor expansion of n in n 1.977 * [backup-simplify]: Simplify 0 into 0 1.977 * [backup-simplify]: Simplify 1 into 1 1.978 * [taylor]: Taking taylor expansion of PI in n 1.978 * [backup-simplify]: Simplify PI into PI 1.978 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.978 * [taylor]: Taking taylor expansion of 2.0 in n 1.978 * [backup-simplify]: Simplify 2.0 into 2.0 1.978 * [taylor]: Taking taylor expansion of (* n PI) in n 1.978 * [taylor]: Taking taylor expansion of n in n 1.978 * [backup-simplify]: Simplify 0 into 0 1.978 * [backup-simplify]: Simplify 1 into 1 1.978 * [taylor]: Taking taylor expansion of PI in n 1.978 * [backup-simplify]: Simplify PI into PI 1.978 * [backup-simplify]: Simplify (* 0 PI) into 0 1.979 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.979 * [backup-simplify]: Simplify 0 into 0 1.980 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.982 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.982 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.983 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.984 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.984 * [backup-simplify]: Simplify 0 into 0 1.985 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.987 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.987 * [backup-simplify]: Simplify 0 into 0 1.988 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.989 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1.989 * [backup-simplify]: Simplify 0 into 0 1.991 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.992 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1.992 * [backup-simplify]: Simplify 0 into 0 1.994 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.995 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1.995 * [backup-simplify]: Simplify 0 into 0 1.998 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.000 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.000 * [backup-simplify]: Simplify 0 into 0 2.000 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.001 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 2.001 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 2.001 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.001 * [taylor]: Taking taylor expansion of 2.0 in n 2.001 * [backup-simplify]: Simplify 2.0 into 2.0 2.001 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.001 * [taylor]: Taking taylor expansion of PI in n 2.001 * [backup-simplify]: Simplify PI into PI 2.001 * [taylor]: Taking taylor expansion of n in n 2.001 * [backup-simplify]: Simplify 0 into 0 2.001 * [backup-simplify]: Simplify 1 into 1 2.002 * [backup-simplify]: Simplify (/ PI 1) into PI 2.002 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.002 * [taylor]: Taking taylor expansion of 2.0 in n 2.002 * [backup-simplify]: Simplify 2.0 into 2.0 2.002 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.002 * [taylor]: Taking taylor expansion of PI in n 2.002 * [backup-simplify]: Simplify PI into PI 2.002 * [taylor]: Taking taylor expansion of n in n 2.002 * [backup-simplify]: Simplify 0 into 0 2.002 * [backup-simplify]: Simplify 1 into 1 2.003 * [backup-simplify]: Simplify (/ PI 1) into PI 2.003 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.004 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.005 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.005 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.005 * [backup-simplify]: Simplify 0 into 0 2.007 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.008 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.008 * [backup-simplify]: Simplify 0 into 0 2.009 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.010 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.010 * [backup-simplify]: Simplify 0 into 0 2.011 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.012 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.012 * [backup-simplify]: Simplify 0 into 0 2.013 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.015 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.015 * [backup-simplify]: Simplify 0 into 0 2.016 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.018 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.018 * [backup-simplify]: Simplify 0 into 0 2.018 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 2.019 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 2.019 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 2.019 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.019 * [taylor]: Taking taylor expansion of -2.0 in n 2.019 * [backup-simplify]: Simplify -2.0 into -2.0 2.019 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.019 * [taylor]: Taking taylor expansion of PI in n 2.019 * [backup-simplify]: Simplify PI into PI 2.019 * [taylor]: Taking taylor expansion of n in n 2.019 * [backup-simplify]: Simplify 0 into 0 2.019 * [backup-simplify]: Simplify 1 into 1 2.019 * [backup-simplify]: Simplify (/ PI 1) into PI 2.020 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.020 * [taylor]: Taking taylor expansion of -2.0 in n 2.020 * [backup-simplify]: Simplify -2.0 into -2.0 2.020 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.020 * [taylor]: Taking taylor expansion of PI in n 2.020 * [backup-simplify]: Simplify PI into PI 2.020 * [taylor]: Taking taylor expansion of n in n 2.020 * [backup-simplify]: Simplify 0 into 0 2.020 * [backup-simplify]: Simplify 1 into 1 2.020 * [backup-simplify]: Simplify (/ PI 1) into PI 2.021 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.021 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.022 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.023 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.023 * [backup-simplify]: Simplify 0 into 0 2.024 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.025 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.025 * [backup-simplify]: Simplify 0 into 0 2.026 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.027 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.027 * [backup-simplify]: Simplify 0 into 0 2.028 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.030 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.030 * [backup-simplify]: Simplify 0 into 0 2.031 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.032 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.032 * [backup-simplify]: Simplify 0 into 0 2.033 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.035 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.035 * [backup-simplify]: Simplify 0 into 0 2.036 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 2.036 * * * * [progress]: [ 4 / 4 ] generating series at (2) 2.036 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) 2.036 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in (k n) around 0 2.037 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 2.037 * [taylor]: Taking taylor expansion of 1.0 in n 2.037 * [backup-simplify]: Simplify 1.0 into 1.0 2.037 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 2.037 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.037 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.037 * [taylor]: Taking taylor expansion of k in n 2.037 * [backup-simplify]: Simplify k into k 2.037 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.037 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 2.037 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.037 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 2.037 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.037 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.037 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.037 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.037 * [taylor]: Taking taylor expansion of 0.5 in n 2.037 * [backup-simplify]: Simplify 0.5 into 0.5 2.037 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.037 * [taylor]: Taking taylor expansion of 1.0 in n 2.037 * [backup-simplify]: Simplify 1.0 into 1.0 2.037 * [taylor]: Taking taylor expansion of k in n 2.037 * [backup-simplify]: Simplify k into k 2.037 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.038 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.038 * [taylor]: Taking taylor expansion of 2.0 in n 2.038 * [backup-simplify]: Simplify 2.0 into 2.0 2.038 * [taylor]: Taking taylor expansion of (* n PI) in n 2.038 * [taylor]: Taking taylor expansion of n in n 2.038 * [backup-simplify]: Simplify 0 into 0 2.038 * [backup-simplify]: Simplify 1 into 1 2.038 * [taylor]: Taking taylor expansion of PI in n 2.038 * [backup-simplify]: Simplify PI into PI 2.038 * [backup-simplify]: Simplify (* 0 PI) into 0 2.039 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.040 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.042 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.043 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.043 * [backup-simplify]: Simplify (- k) into (- k) 2.043 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.043 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.044 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.045 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.046 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.047 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 2.047 * [taylor]: Taking taylor expansion of 1.0 in k 2.047 * [backup-simplify]: Simplify 1.0 into 1.0 2.047 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 2.047 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.047 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.047 * [taylor]: Taking taylor expansion of k in k 2.047 * [backup-simplify]: Simplify 0 into 0 2.047 * [backup-simplify]: Simplify 1 into 1 2.047 * [backup-simplify]: Simplify (/ 1 1) into 1 2.047 * [backup-simplify]: Simplify (sqrt 0) into 0 2.049 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.049 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.049 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.049 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.049 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.049 * [taylor]: Taking taylor expansion of 0.5 in k 2.049 * [backup-simplify]: Simplify 0.5 into 0.5 2.049 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.049 * [taylor]: Taking taylor expansion of 1.0 in k 2.049 * [backup-simplify]: Simplify 1.0 into 1.0 2.049 * [taylor]: Taking taylor expansion of k in k 2.049 * [backup-simplify]: Simplify 0 into 0 2.049 * [backup-simplify]: Simplify 1 into 1 2.049 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.049 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.049 * [taylor]: Taking taylor expansion of 2.0 in k 2.050 * [backup-simplify]: Simplify 2.0 into 2.0 2.050 * [taylor]: Taking taylor expansion of (* n PI) in k 2.050 * [taylor]: Taking taylor expansion of n in k 2.050 * [backup-simplify]: Simplify n into n 2.050 * [taylor]: Taking taylor expansion of PI in k 2.050 * [backup-simplify]: Simplify PI into PI 2.050 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.050 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.050 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.050 * [backup-simplify]: Simplify (- 0) into 0 2.051 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.051 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.051 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.051 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.051 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 2.051 * [taylor]: Taking taylor expansion of 1.0 in k 2.051 * [backup-simplify]: Simplify 1.0 into 1.0 2.051 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 2.052 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.052 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.052 * [taylor]: Taking taylor expansion of k in k 2.052 * [backup-simplify]: Simplify 0 into 0 2.052 * [backup-simplify]: Simplify 1 into 1 2.052 * [backup-simplify]: Simplify (/ 1 1) into 1 2.052 * [backup-simplify]: Simplify (sqrt 0) into 0 2.053 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.053 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.053 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.053 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.053 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.053 * [taylor]: Taking taylor expansion of 0.5 in k 2.053 * [backup-simplify]: Simplify 0.5 into 0.5 2.053 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.053 * [taylor]: Taking taylor expansion of 1.0 in k 2.053 * [backup-simplify]: Simplify 1.0 into 1.0 2.053 * [taylor]: Taking taylor expansion of k in k 2.053 * [backup-simplify]: Simplify 0 into 0 2.053 * [backup-simplify]: Simplify 1 into 1 2.053 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.053 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.053 * [taylor]: Taking taylor expansion of 2.0 in k 2.053 * [backup-simplify]: Simplify 2.0 into 2.0 2.053 * [taylor]: Taking taylor expansion of (* n PI) in k 2.053 * [taylor]: Taking taylor expansion of n in k 2.053 * [backup-simplify]: Simplify n into n 2.053 * [taylor]: Taking taylor expansion of PI in k 2.053 * [backup-simplify]: Simplify PI into PI 2.053 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.053 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.053 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.054 * [backup-simplify]: Simplify (- 0) into 0 2.054 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.054 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.054 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.054 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.055 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 2.055 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.055 * [taylor]: Taking taylor expansion of 0 in n 2.055 * [backup-simplify]: Simplify 0 into 0 2.055 * [backup-simplify]: Simplify 0 into 0 2.055 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 2.056 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 2.056 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 2.056 * [backup-simplify]: Simplify (- 1) into -1 2.057 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.057 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 2.058 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 2.058 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1)))) into (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 2.060 * [backup-simplify]: Simplify (+ (* 0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 2.061 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 2.061 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n 2.061 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 2.061 * [taylor]: Taking taylor expansion of +nan.0 in n 2.061 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.061 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 2.061 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.061 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.061 * [taylor]: Taking taylor expansion of 0.5 in n 2.061 * [backup-simplify]: Simplify 0.5 into 0.5 2.061 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.061 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.061 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.061 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.061 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.061 * [taylor]: Taking taylor expansion of 1.0 in n 2.061 * [backup-simplify]: Simplify 1.0 into 1.0 2.061 * [taylor]: Taking taylor expansion of (log PI) in n 2.061 * [taylor]: Taking taylor expansion of PI in n 2.061 * [backup-simplify]: Simplify PI into PI 2.061 * [backup-simplify]: Simplify (log PI) into (log PI) 2.062 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.063 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.063 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.063 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.063 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.063 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.063 * [taylor]: Taking taylor expansion of 1.0 in n 2.063 * [backup-simplify]: Simplify 1.0 into 1.0 2.063 * [taylor]: Taking taylor expansion of (log n) in n 2.063 * [taylor]: Taking taylor expansion of n in n 2.063 * [backup-simplify]: Simplify 0 into 0 2.063 * [backup-simplify]: Simplify 1 into 1 2.063 * [backup-simplify]: Simplify (log 1) into 0 2.064 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.064 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.064 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.064 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.064 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.064 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.064 * [taylor]: Taking taylor expansion of 1.0 in n 2.064 * [backup-simplify]: Simplify 1.0 into 1.0 2.064 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.064 * [taylor]: Taking taylor expansion of 2.0 in n 2.064 * [backup-simplify]: Simplify 2.0 into 2.0 2.064 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.065 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.066 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.066 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 2.067 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 2.068 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 2.069 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 2.069 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 2.070 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 2.071 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 2.072 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 2.072 * [backup-simplify]: Simplify 0 into 0 2.073 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 2.073 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 2.074 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 2) into 0 2.075 * [backup-simplify]: Simplify (- 0) into 0 2.075 * [backup-simplify]: Simplify (+ 0 0) into 0 2.075 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 2.076 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 2.077 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 2.077 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.079 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.084 * [backup-simplify]: Simplify (+ (* 0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5)))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) 2.087 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) 2.087 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) in n 2.087 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))) in n 2.087 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 2.087 * [taylor]: Taking taylor expansion of +nan.0 in n 2.087 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.087 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 2.088 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.088 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.088 * [taylor]: Taking taylor expansion of 0.5 in n 2.088 * [backup-simplify]: Simplify 0.5 into 0.5 2.088 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.088 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.088 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.088 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.088 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.088 * [taylor]: Taking taylor expansion of 1.0 in n 2.088 * [backup-simplify]: Simplify 1.0 into 1.0 2.088 * [taylor]: Taking taylor expansion of (log PI) in n 2.088 * [taylor]: Taking taylor expansion of PI in n 2.088 * [backup-simplify]: Simplify PI into PI 2.088 * [backup-simplify]: Simplify (log PI) into (log PI) 2.089 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.091 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.091 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.091 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.091 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.091 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.091 * [taylor]: Taking taylor expansion of 1.0 in n 2.091 * [backup-simplify]: Simplify 1.0 into 1.0 2.091 * [taylor]: Taking taylor expansion of (log n) in n 2.091 * [taylor]: Taking taylor expansion of n in n 2.091 * [backup-simplify]: Simplify 0 into 0 2.091 * [backup-simplify]: Simplify 1 into 1 2.092 * [backup-simplify]: Simplify (log 1) into 0 2.092 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.092 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.092 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.092 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.092 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.092 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.092 * [taylor]: Taking taylor expansion of 1.0 in n 2.092 * [backup-simplify]: Simplify 1.0 into 1.0 2.092 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.092 * [taylor]: Taking taylor expansion of 2.0 in n 2.092 * [backup-simplify]: Simplify 2.0 into 2.0 2.093 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.094 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.095 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.096 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 2.096 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 2.097 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 2.098 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 2.099 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 2.099 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))) in n 2.099 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 2.099 * [taylor]: Taking taylor expansion of +nan.0 in n 2.099 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.099 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 2.100 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 2.100 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 2.100 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 2.100 * [taylor]: Taking taylor expansion of 0.5 in n 2.100 * [backup-simplify]: Simplify 0.5 into 0.5 2.100 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 2.100 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 2.100 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.100 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.100 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.100 * [taylor]: Taking taylor expansion of 1.0 in n 2.100 * [backup-simplify]: Simplify 1.0 into 1.0 2.100 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.100 * [taylor]: Taking taylor expansion of 2.0 in n 2.100 * [backup-simplify]: Simplify 2.0 into 2.0 2.100 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.101 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.102 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.102 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 2.102 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.102 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.102 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.102 * [taylor]: Taking taylor expansion of 1.0 in n 2.102 * [backup-simplify]: Simplify 1.0 into 1.0 2.102 * [taylor]: Taking taylor expansion of (log PI) in n 2.102 * [taylor]: Taking taylor expansion of PI in n 2.102 * [backup-simplify]: Simplify PI into PI 2.102 * [backup-simplify]: Simplify (log PI) into (log PI) 2.103 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.104 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.104 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.104 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.104 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.104 * [taylor]: Taking taylor expansion of 1.0 in n 2.104 * [backup-simplify]: Simplify 1.0 into 1.0 2.104 * [taylor]: Taking taylor expansion of (log n) in n 2.104 * [taylor]: Taking taylor expansion of n in n 2.104 * [backup-simplify]: Simplify 0 into 0 2.104 * [backup-simplify]: Simplify 1 into 1 2.104 * [backup-simplify]: Simplify (log 1) into 0 2.105 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.105 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.105 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.105 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.106 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 2.107 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 2.108 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 2.108 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 2.109 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.109 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.109 * [taylor]: Taking taylor expansion of 2.0 in n 2.109 * [backup-simplify]: Simplify 2.0 into 2.0 2.109 * [taylor]: Taking taylor expansion of (* n PI) in n 2.109 * [taylor]: Taking taylor expansion of n in n 2.109 * [backup-simplify]: Simplify 0 into 0 2.109 * [backup-simplify]: Simplify 1 into 1 2.109 * [taylor]: Taking taylor expansion of PI in n 2.109 * [backup-simplify]: Simplify PI into PI 2.109 * [backup-simplify]: Simplify (* 0 PI) into 0 2.109 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.110 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.111 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.112 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.113 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 2.114 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.115 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 2.117 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 2.118 * [backup-simplify]: Simplify (- (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))) 2.122 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 2.126 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 2.132 * [backup-simplify]: Simplify (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 2.134 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 2.135 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 2.137 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 2.138 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.138 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.139 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 2.140 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.140 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 2.142 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 2.143 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 2.144 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 2.146 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 2.148 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1)))) 1) into 0 2.150 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)))) into 0 2.152 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.154 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5))) into 0 2.155 * [backup-simplify]: Simplify (- 0) into 0 2.155 * [backup-simplify]: Simplify 0 into 0 2.155 * [backup-simplify]: Simplify 0 into 0 2.156 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.156 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 2.158 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 6) into 0 2.158 * [backup-simplify]: Simplify (- 0) into 0 2.159 * [backup-simplify]: Simplify (+ 0 0) into 0 2.159 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 2.160 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 2.162 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 3) 6)) (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 2.162 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.164 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.168 * [backup-simplify]: Simplify (+ (* 0 (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 2.174 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))) (+ (* 0 (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 2.174 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) in n 2.174 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))) in n 2.174 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) in n 2.174 * [taylor]: Taking taylor expansion of +nan.0 in n 2.174 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.174 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 2.174 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 2.174 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 2.174 * [taylor]: Taking taylor expansion of 0.5 in n 2.174 * [backup-simplify]: Simplify 0.5 into 0.5 2.175 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 2.175 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 2.175 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.175 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.175 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.175 * [taylor]: Taking taylor expansion of 1.0 in n 2.175 * [backup-simplify]: Simplify 1.0 into 1.0 2.175 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.175 * [taylor]: Taking taylor expansion of 2.0 in n 2.175 * [backup-simplify]: Simplify 2.0 into 2.0 2.175 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.175 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.176 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.176 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 2.176 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.176 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.177 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.177 * [taylor]: Taking taylor expansion of 1.0 in n 2.177 * [backup-simplify]: Simplify 1.0 into 1.0 2.177 * [taylor]: Taking taylor expansion of (log n) in n 2.177 * [taylor]: Taking taylor expansion of n in n 2.177 * [backup-simplify]: Simplify 0 into 0 2.177 * [backup-simplify]: Simplify 1 into 1 2.177 * [backup-simplify]: Simplify (log 1) into 0 2.177 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.177 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.177 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.177 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.177 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.177 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.177 * [taylor]: Taking taylor expansion of 1.0 in n 2.177 * [backup-simplify]: Simplify 1.0 into 1.0 2.177 * [taylor]: Taking taylor expansion of (log PI) in n 2.177 * [taylor]: Taking taylor expansion of PI in n 2.177 * [backup-simplify]: Simplify PI into PI 2.178 * [backup-simplify]: Simplify (log PI) into (log PI) 2.178 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.179 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.180 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.180 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 2.181 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 2.182 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 2.183 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 2.183 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))) in n 2.183 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) in n 2.183 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 2.183 * [taylor]: Taking taylor expansion of +nan.0 in n 2.183 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.183 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 2.183 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 2.183 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 2.183 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 2.183 * [taylor]: Taking taylor expansion of 0.5 in n 2.183 * [backup-simplify]: Simplify 0.5 into 0.5 2.183 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 2.183 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 2.183 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.183 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.183 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.183 * [taylor]: Taking taylor expansion of 1.0 in n 2.183 * [backup-simplify]: Simplify 1.0 into 1.0 2.183 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.183 * [taylor]: Taking taylor expansion of 2.0 in n 2.183 * [backup-simplify]: Simplify 2.0 into 2.0 2.184 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.185 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.186 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.186 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 2.186 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.186 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.186 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.187 * [taylor]: Taking taylor expansion of 1.0 in n 2.187 * [backup-simplify]: Simplify 1.0 into 1.0 2.187 * [taylor]: Taking taylor expansion of (log PI) in n 2.187 * [taylor]: Taking taylor expansion of PI in n 2.187 * [backup-simplify]: Simplify PI into PI 2.187 * [backup-simplify]: Simplify (log PI) into (log PI) 2.188 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.190 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.190 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.190 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.190 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.190 * [taylor]: Taking taylor expansion of 1.0 in n 2.190 * [backup-simplify]: Simplify 1.0 into 1.0 2.190 * [taylor]: Taking taylor expansion of (log n) in n 2.190 * [taylor]: Taking taylor expansion of n in n 2.190 * [backup-simplify]: Simplify 0 into 0 2.190 * [backup-simplify]: Simplify 1 into 1 2.191 * [backup-simplify]: Simplify (log 1) into 0 2.191 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.191 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.192 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.192 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.199 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 2.201 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 2.202 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 2.204 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 2.204 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.204 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.204 * [taylor]: Taking taylor expansion of 2.0 in n 2.204 * [backup-simplify]: Simplify 2.0 into 2.0 2.204 * [taylor]: Taking taylor expansion of (* n PI) in n 2.204 * [taylor]: Taking taylor expansion of n in n 2.204 * [backup-simplify]: Simplify 0 into 0 2.204 * [backup-simplify]: Simplify 1 into 1 2.204 * [taylor]: Taking taylor expansion of PI in n 2.204 * [backup-simplify]: Simplify PI into PI 2.205 * [backup-simplify]: Simplify (* 0 PI) into 0 2.205 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.207 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.208 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.209 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.209 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) in n 2.210 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n 2.210 * [taylor]: Taking taylor expansion of +nan.0 in n 2.210 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.210 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n 2.210 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 2.210 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 2.210 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 2.210 * [taylor]: Taking taylor expansion of 0.5 in n 2.210 * [backup-simplify]: Simplify 0.5 into 0.5 2.210 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 2.210 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 2.210 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.210 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.210 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.210 * [taylor]: Taking taylor expansion of 1.0 in n 2.210 * [backup-simplify]: Simplify 1.0 into 1.0 2.210 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.210 * [taylor]: Taking taylor expansion of 2.0 in n 2.210 * [backup-simplify]: Simplify 2.0 into 2.0 2.211 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.212 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.213 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.213 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 2.213 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.213 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.213 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.213 * [taylor]: Taking taylor expansion of 1.0 in n 2.214 * [backup-simplify]: Simplify 1.0 into 1.0 2.214 * [taylor]: Taking taylor expansion of (log PI) in n 2.214 * [taylor]: Taking taylor expansion of PI in n 2.214 * [backup-simplify]: Simplify PI into PI 2.214 * [backup-simplify]: Simplify (log PI) into (log PI) 2.216 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.218 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.218 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.218 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.218 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.218 * [taylor]: Taking taylor expansion of 1.0 in n 2.218 * [backup-simplify]: Simplify 1.0 into 1.0 2.218 * [taylor]: Taking taylor expansion of (log n) in n 2.218 * [taylor]: Taking taylor expansion of n in n 2.218 * [backup-simplify]: Simplify 0 into 0 2.218 * [backup-simplify]: Simplify 1 into 1 2.218 * [backup-simplify]: Simplify (log 1) into 0 2.219 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.219 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.219 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.220 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.221 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 2.222 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 2.224 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 2.225 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 2.225 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 2.225 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.225 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.225 * [taylor]: Taking taylor expansion of 2.0 in n 2.225 * [backup-simplify]: Simplify 2.0 into 2.0 2.225 * [taylor]: Taking taylor expansion of (* n PI) in n 2.225 * [taylor]: Taking taylor expansion of n in n 2.225 * [backup-simplify]: Simplify 0 into 0 2.225 * [backup-simplify]: Simplify 1 into 1 2.225 * [taylor]: Taking taylor expansion of PI in n 2.225 * [backup-simplify]: Simplify PI into PI 2.225 * [backup-simplify]: Simplify (* 0 PI) into 0 2.225 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.226 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.227 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.228 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.229 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.230 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 2.231 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.232 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 2.234 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 2.235 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.236 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.237 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 2.239 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)) into (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 2.240 * [backup-simplify]: Simplify (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 2.242 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 2.253 * [backup-simplify]: Simplify (+ (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)))))))))))) 2.268 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))) 2.279 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 2.289 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 2.299 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 2.332 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) (pow (* 1 k) 2)) (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) (* 1 k)) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) into (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) 2.333 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 k))) (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) into (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) 2.333 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in (k n) around 0 2.333 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 2.333 * [taylor]: Taking taylor expansion of 1.0 in n 2.333 * [backup-simplify]: Simplify 1.0 into 1.0 2.333 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 2.333 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.333 * [taylor]: Taking taylor expansion of k in n 2.333 * [backup-simplify]: Simplify k into k 2.333 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.333 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.333 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.333 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.333 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.333 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.334 * [taylor]: Taking taylor expansion of 0.5 in n 2.334 * [backup-simplify]: Simplify 0.5 into 0.5 2.334 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.334 * [taylor]: Taking taylor expansion of 1.0 in n 2.334 * [backup-simplify]: Simplify 1.0 into 1.0 2.334 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.334 * [taylor]: Taking taylor expansion of k in n 2.334 * [backup-simplify]: Simplify k into k 2.334 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.334 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.334 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.334 * [taylor]: Taking taylor expansion of 2.0 in n 2.334 * [backup-simplify]: Simplify 2.0 into 2.0 2.334 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.334 * [taylor]: Taking taylor expansion of PI in n 2.334 * [backup-simplify]: Simplify PI into PI 2.334 * [taylor]: Taking taylor expansion of n in n 2.334 * [backup-simplify]: Simplify 0 into 0 2.334 * [backup-simplify]: Simplify 1 into 1 2.335 * [backup-simplify]: Simplify (/ PI 1) into PI 2.335 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.336 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.336 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.337 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.337 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.338 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.339 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.341 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.341 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 2.341 * [taylor]: Taking taylor expansion of 1.0 in k 2.341 * [backup-simplify]: Simplify 1.0 into 1.0 2.341 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 2.341 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.341 * [taylor]: Taking taylor expansion of k in k 2.341 * [backup-simplify]: Simplify 0 into 0 2.341 * [backup-simplify]: Simplify 1 into 1 2.341 * [backup-simplify]: Simplify (sqrt 0) into 0 2.343 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.343 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.343 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.343 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.343 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.343 * [taylor]: Taking taylor expansion of 0.5 in k 2.343 * [backup-simplify]: Simplify 0.5 into 0.5 2.343 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.343 * [taylor]: Taking taylor expansion of 1.0 in k 2.343 * [backup-simplify]: Simplify 1.0 into 1.0 2.343 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.343 * [taylor]: Taking taylor expansion of k in k 2.343 * [backup-simplify]: Simplify 0 into 0 2.343 * [backup-simplify]: Simplify 1 into 1 2.344 * [backup-simplify]: Simplify (/ 1 1) into 1 2.344 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.344 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.344 * [taylor]: Taking taylor expansion of 2.0 in k 2.344 * [backup-simplify]: Simplify 2.0 into 2.0 2.344 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.344 * [taylor]: Taking taylor expansion of PI in k 2.344 * [backup-simplify]: Simplify PI into PI 2.344 * [taylor]: Taking taylor expansion of n in k 2.344 * [backup-simplify]: Simplify n into n 2.344 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.344 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.344 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.345 * [backup-simplify]: Simplify (- 1) into -1 2.345 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.346 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.346 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.346 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 2.346 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 2.346 * [taylor]: Taking taylor expansion of 1.0 in k 2.346 * [backup-simplify]: Simplify 1.0 into 1.0 2.346 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 2.346 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.346 * [taylor]: Taking taylor expansion of k in k 2.346 * [backup-simplify]: Simplify 0 into 0 2.346 * [backup-simplify]: Simplify 1 into 1 2.347 * [backup-simplify]: Simplify (sqrt 0) into 0 2.348 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.348 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.348 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.348 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.348 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.348 * [taylor]: Taking taylor expansion of 0.5 in k 2.348 * [backup-simplify]: Simplify 0.5 into 0.5 2.348 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.348 * [taylor]: Taking taylor expansion of 1.0 in k 2.348 * [backup-simplify]: Simplify 1.0 into 1.0 2.348 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.348 * [taylor]: Taking taylor expansion of k in k 2.348 * [backup-simplify]: Simplify 0 into 0 2.348 * [backup-simplify]: Simplify 1 into 1 2.349 * [backup-simplify]: Simplify (/ 1 1) into 1 2.349 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.349 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.349 * [taylor]: Taking taylor expansion of 2.0 in k 2.349 * [backup-simplify]: Simplify 2.0 into 2.0 2.349 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.349 * [taylor]: Taking taylor expansion of PI in k 2.349 * [backup-simplify]: Simplify PI into PI 2.349 * [taylor]: Taking taylor expansion of n in k 2.349 * [backup-simplify]: Simplify n into n 2.349 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.349 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.349 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.350 * [backup-simplify]: Simplify (- 1) into -1 2.350 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.350 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.351 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.351 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 2.351 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 2.352 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.352 * [taylor]: Taking taylor expansion of 0 in n 2.352 * [backup-simplify]: Simplify 0 into 0 2.352 * [backup-simplify]: Simplify 0 into 0 2.352 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 2.353 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 2.353 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 2.353 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 2.353 * [taylor]: Taking taylor expansion of +nan.0 in n 2.353 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.353 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 2.353 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 2.353 * [taylor]: Taking taylor expansion of 0.5 in n 2.354 * [backup-simplify]: Simplify 0.5 into 0.5 2.354 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 2.354 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.354 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.354 * [taylor]: Taking taylor expansion of 2.0 in n 2.354 * [backup-simplify]: Simplify 2.0 into 2.0 2.354 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.354 * [taylor]: Taking taylor expansion of PI in n 2.354 * [backup-simplify]: Simplify PI into PI 2.354 * [taylor]: Taking taylor expansion of n in n 2.354 * [backup-simplify]: Simplify 0 into 0 2.354 * [backup-simplify]: Simplify 1 into 1 2.354 * [backup-simplify]: Simplify (/ PI 1) into PI 2.355 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.356 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.356 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.356 * [taylor]: Taking taylor expansion of 1.0 in n 2.356 * [backup-simplify]: Simplify 1.0 into 1.0 2.356 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.356 * [taylor]: Taking taylor expansion of k in n 2.356 * [backup-simplify]: Simplify k into k 2.356 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.358 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.358 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.358 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.359 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 2.360 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.362 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.363 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 2.364 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 2.365 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 2.366 * [backup-simplify]: Simplify 0 into 0 2.369 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.370 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 2.371 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 2.371 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 2.371 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 2.371 * [taylor]: Taking taylor expansion of +nan.0 in n 2.371 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.371 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 2.371 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 2.371 * [taylor]: Taking taylor expansion of 0.5 in n 2.371 * [backup-simplify]: Simplify 0.5 into 0.5 2.371 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 2.371 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.371 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.371 * [taylor]: Taking taylor expansion of 2.0 in n 2.371 * [backup-simplify]: Simplify 2.0 into 2.0 2.371 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.371 * [taylor]: Taking taylor expansion of PI in n 2.371 * [backup-simplify]: Simplify PI into PI 2.371 * [taylor]: Taking taylor expansion of n in n 2.372 * [backup-simplify]: Simplify 0 into 0 2.372 * [backup-simplify]: Simplify 1 into 1 2.372 * [backup-simplify]: Simplify (/ PI 1) into PI 2.373 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.374 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.374 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.374 * [taylor]: Taking taylor expansion of 1.0 in n 2.374 * [backup-simplify]: Simplify 1.0 into 1.0 2.374 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.374 * [taylor]: Taking taylor expansion of k in n 2.374 * [backup-simplify]: Simplify k into k 2.374 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.375 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.375 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.376 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.377 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 2.378 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.379 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.381 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 2.382 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 2.383 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 2.385 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.385 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.386 * [backup-simplify]: Simplify (- 0) into 0 2.386 * [backup-simplify]: Simplify (+ 0 0) into 0 2.387 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.388 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.390 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.391 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.393 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 2.395 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.396 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 2.397 * [backup-simplify]: Simplify (- 0) into 0 2.397 * [backup-simplify]: Simplify 0 into 0 2.397 * [backup-simplify]: Simplify 0 into 0 2.401 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.402 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 2.404 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 2.404 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 2.404 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 2.404 * [taylor]: Taking taylor expansion of +nan.0 in n 2.404 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.404 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 2.404 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 2.404 * [taylor]: Taking taylor expansion of 0.5 in n 2.404 * [backup-simplify]: Simplify 0.5 into 0.5 2.404 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 2.404 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.404 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.404 * [taylor]: Taking taylor expansion of 2.0 in n 2.404 * [backup-simplify]: Simplify 2.0 into 2.0 2.404 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.404 * [taylor]: Taking taylor expansion of PI in n 2.404 * [backup-simplify]: Simplify PI into PI 2.405 * [taylor]: Taking taylor expansion of n in n 2.405 * [backup-simplify]: Simplify 0 into 0 2.405 * [backup-simplify]: Simplify 1 into 1 2.405 * [backup-simplify]: Simplify (/ PI 1) into PI 2.406 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.407 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.407 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.407 * [taylor]: Taking taylor expansion of 1.0 in n 2.407 * [backup-simplify]: Simplify 1.0 into 1.0 2.407 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.407 * [taylor]: Taking taylor expansion of k in n 2.407 * [backup-simplify]: Simplify k into k 2.407 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.408 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.408 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.409 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.410 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 2.411 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.412 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.413 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 2.415 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 2.416 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 2.421 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) 2.422 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 2.422 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k n) around 0 2.422 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 2.422 * [taylor]: Taking taylor expansion of 1.0 in n 2.422 * [backup-simplify]: Simplify 1.0 into 1.0 2.422 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 2.422 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.422 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.422 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.422 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.422 * [taylor]: Taking taylor expansion of 0.5 in n 2.422 * [backup-simplify]: Simplify 0.5 into 0.5 2.422 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.422 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.422 * [taylor]: Taking taylor expansion of k in n 2.422 * [backup-simplify]: Simplify k into k 2.423 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.423 * [taylor]: Taking taylor expansion of 1.0 in n 2.423 * [backup-simplify]: Simplify 1.0 into 1.0 2.423 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.423 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.423 * [taylor]: Taking taylor expansion of -2.0 in n 2.423 * [backup-simplify]: Simplify -2.0 into -2.0 2.423 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.423 * [taylor]: Taking taylor expansion of PI in n 2.423 * [backup-simplify]: Simplify PI into PI 2.423 * [taylor]: Taking taylor expansion of n in n 2.423 * [backup-simplify]: Simplify 0 into 0 2.423 * [backup-simplify]: Simplify 1 into 1 2.423 * [backup-simplify]: Simplify (/ PI 1) into PI 2.424 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.425 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.425 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.425 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.427 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.428 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.429 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.429 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.429 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.429 * [taylor]: Taking taylor expansion of -1 in n 2.429 * [backup-simplify]: Simplify -1 into -1 2.429 * [taylor]: Taking taylor expansion of k in n 2.429 * [backup-simplify]: Simplify k into k 2.430 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.430 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.430 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.430 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.431 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) 2.431 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 2.431 * [taylor]: Taking taylor expansion of 1.0 in k 2.431 * [backup-simplify]: Simplify 1.0 into 1.0 2.431 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 2.431 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.431 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.431 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.432 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.432 * [taylor]: Taking taylor expansion of 0.5 in k 2.432 * [backup-simplify]: Simplify 0.5 into 0.5 2.432 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.432 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.432 * [taylor]: Taking taylor expansion of k in k 2.432 * [backup-simplify]: Simplify 0 into 0 2.432 * [backup-simplify]: Simplify 1 into 1 2.432 * [backup-simplify]: Simplify (/ 1 1) into 1 2.432 * [taylor]: Taking taylor expansion of 1.0 in k 2.432 * [backup-simplify]: Simplify 1.0 into 1.0 2.432 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.432 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.432 * [taylor]: Taking taylor expansion of -2.0 in k 2.432 * [backup-simplify]: Simplify -2.0 into -2.0 2.432 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.432 * [taylor]: Taking taylor expansion of PI in k 2.432 * [backup-simplify]: Simplify PI into PI 2.432 * [taylor]: Taking taylor expansion of n in k 2.432 * [backup-simplify]: Simplify n into n 2.433 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.433 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.433 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.433 * [backup-simplify]: Simplify (+ 1 0) into 1 2.434 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.434 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.434 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 2.434 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.434 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.434 * [taylor]: Taking taylor expansion of -1 in k 2.434 * [backup-simplify]: Simplify -1 into -1 2.434 * [taylor]: Taking taylor expansion of k in k 2.434 * [backup-simplify]: Simplify 0 into 0 2.434 * [backup-simplify]: Simplify 1 into 1 2.435 * [backup-simplify]: Simplify (/ -1 1) into -1 2.435 * [backup-simplify]: Simplify (sqrt 0) into 0 2.436 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.437 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 2.437 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 2.437 * [taylor]: Taking taylor expansion of 1.0 in k 2.437 * [backup-simplify]: Simplify 1.0 into 1.0 2.437 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 2.437 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.437 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.437 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.437 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.437 * [taylor]: Taking taylor expansion of 0.5 in k 2.437 * [backup-simplify]: Simplify 0.5 into 0.5 2.437 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.437 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.437 * [taylor]: Taking taylor expansion of k in k 2.437 * [backup-simplify]: Simplify 0 into 0 2.437 * [backup-simplify]: Simplify 1 into 1 2.438 * [backup-simplify]: Simplify (/ 1 1) into 1 2.438 * [taylor]: Taking taylor expansion of 1.0 in k 2.438 * [backup-simplify]: Simplify 1.0 into 1.0 2.438 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.438 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.438 * [taylor]: Taking taylor expansion of -2.0 in k 2.438 * [backup-simplify]: Simplify -2.0 into -2.0 2.438 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.438 * [taylor]: Taking taylor expansion of PI in k 2.438 * [backup-simplify]: Simplify PI into PI 2.438 * [taylor]: Taking taylor expansion of n in k 2.438 * [backup-simplify]: Simplify n into n 2.438 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.438 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.438 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.439 * [backup-simplify]: Simplify (+ 1 0) into 1 2.439 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.439 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.439 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 2.439 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.439 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.439 * [taylor]: Taking taylor expansion of -1 in k 2.440 * [backup-simplify]: Simplify -1 into -1 2.440 * [taylor]: Taking taylor expansion of k in k 2.440 * [backup-simplify]: Simplify 0 into 0 2.440 * [backup-simplify]: Simplify 1 into 1 2.440 * [backup-simplify]: Simplify (/ -1 1) into -1 2.440 * [backup-simplify]: Simplify (sqrt 0) into 0 2.441 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.441 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 2.442 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 2.442 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 2.442 * [taylor]: Taking taylor expansion of +nan.0 in n 2.442 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.442 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 2.442 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 2.442 * [taylor]: Taking taylor expansion of 0.5 in n 2.442 * [backup-simplify]: Simplify 0.5 into 0.5 2.442 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 2.442 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.442 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.442 * [taylor]: Taking taylor expansion of k in n 2.442 * [backup-simplify]: Simplify k into k 2.442 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.442 * [taylor]: Taking taylor expansion of 1.0 in n 2.442 * [backup-simplify]: Simplify 1.0 into 1.0 2.442 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.442 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.442 * [taylor]: Taking taylor expansion of -2.0 in n 2.442 * [backup-simplify]: Simplify -2.0 into -2.0 2.442 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.442 * [taylor]: Taking taylor expansion of PI in n 2.442 * [backup-simplify]: Simplify PI into PI 2.442 * [taylor]: Taking taylor expansion of n in n 2.442 * [backup-simplify]: Simplify 0 into 0 2.442 * [backup-simplify]: Simplify 1 into 1 2.442 * [backup-simplify]: Simplify (/ PI 1) into PI 2.443 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.443 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.443 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.444 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.445 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 2.446 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.447 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.448 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 2.449 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 2.449 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.451 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.452 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 2.452 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 2.452 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 2.452 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 2.452 * [taylor]: Taking taylor expansion of +nan.0 in n 2.452 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.452 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 2.452 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 2.452 * [taylor]: Taking taylor expansion of 0.5 in n 2.452 * [backup-simplify]: Simplify 0.5 into 0.5 2.452 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 2.452 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.452 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.452 * [taylor]: Taking taylor expansion of k in n 2.453 * [backup-simplify]: Simplify k into k 2.453 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.453 * [taylor]: Taking taylor expansion of 1.0 in n 2.453 * [backup-simplify]: Simplify 1.0 into 1.0 2.453 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.453 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.453 * [taylor]: Taking taylor expansion of -2.0 in n 2.453 * [backup-simplify]: Simplify -2.0 into -2.0 2.453 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.453 * [taylor]: Taking taylor expansion of PI in n 2.453 * [backup-simplify]: Simplify PI into PI 2.453 * [taylor]: Taking taylor expansion of n in n 2.453 * [backup-simplify]: Simplify 0 into 0 2.453 * [backup-simplify]: Simplify 1 into 1 2.453 * [backup-simplify]: Simplify (/ PI 1) into PI 2.453 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.454 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.454 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.455 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.456 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 2.457 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.457 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.458 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 2.459 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 2.460 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 2.460 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.461 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.462 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.462 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.462 * [backup-simplify]: Simplify (+ 0 0) into 0 2.467 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.468 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.469 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 2.471 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.472 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 2.472 * [backup-simplify]: Simplify 0 into 0 2.473 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.476 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.478 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 2.479 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 2.479 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 2.479 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 2.479 * [taylor]: Taking taylor expansion of +nan.0 in n 2.479 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.479 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 2.479 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 2.479 * [taylor]: Taking taylor expansion of 0.5 in n 2.479 * [backup-simplify]: Simplify 0.5 into 0.5 2.479 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 2.479 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.479 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.479 * [taylor]: Taking taylor expansion of k in n 2.479 * [backup-simplify]: Simplify k into k 2.479 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.479 * [taylor]: Taking taylor expansion of 1.0 in n 2.479 * [backup-simplify]: Simplify 1.0 into 1.0 2.479 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.479 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.479 * [taylor]: Taking taylor expansion of -2.0 in n 2.479 * [backup-simplify]: Simplify -2.0 into -2.0 2.479 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.479 * [taylor]: Taking taylor expansion of PI in n 2.479 * [backup-simplify]: Simplify PI into PI 2.479 * [taylor]: Taking taylor expansion of n in n 2.479 * [backup-simplify]: Simplify 0 into 0 2.479 * [backup-simplify]: Simplify 1 into 1 2.480 * [backup-simplify]: Simplify (/ PI 1) into PI 2.481 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.482 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.482 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.483 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.484 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 2.486 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.487 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.488 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 2.489 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 2.491 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 2.496 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 2.496 * * * [progress]: simplifying candidates 2.501 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (+ (- (log 1.0) (log (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (+ (log (/ 1.0 (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) 1) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 2.506 * * [simplify]: Extracting # 0 : cost 0 2.507 * * [simplify]: Extracting # 1 : cost 0 2.507 * * [simplify]: Extracting # 2 : cost 0 2.507 * * [simplify]: Extracting # 3 : cost 0 2.508 * * [simplify]: Extracting # 4 : cost 0 2.508 * * [simplify]: Extracting # 5 : cost 0 2.509 * * [simplify]: Extracting # 6 : cost 0 2.509 * * [simplify]: Extracting # 7 : cost 0 2.510 * * [simplify]: Extracting # 8 : cost 0 2.510 * * [simplify]: Extracting # 9 : cost 0 2.511 * * [simplify]: Extracting # 10 : cost 0 2.511 * * [simplify]: Extracting # 11 : cost 0 2.512 * * [simplify]: Extracting # 12 : cost 0 2.512 * * [simplify]: Extracting # 13 : cost 0 2.513 * * [simplify]: Extracting # 14 : cost 0 2.513 * * [simplify]: Extracting # 15 : cost 0 2.514 * * [simplify]: Extracting # 16 : cost 0 2.514 * * [simplify]: Extracting # 17 : cost 0 2.515 * * [simplify]: Extracting # 18 : cost 0 2.515 * * [simplify]: Extracting # 19 : cost 0 2.516 * * [simplify]: Extracting # 20 : cost 0 2.516 * * [simplify]: Extracting # 21 : cost 0 2.517 * * [simplify]: Extracting # 22 : cost 0 2.517 * * [simplify]: Extracting # 23 : cost 0 2.518 * * [simplify]: Extracting # 24 : cost 0 2.519 * * [simplify]: Extracting # 25 : cost 0 2.519 * * [simplify]: Extracting # 26 : cost 0 2.520 * * [simplify]: Extracting # 27 : cost 0 2.520 * * [simplify]: Extracting # 28 : cost 0 2.521 * * [simplify]: Extracting # 29 : cost 0 2.521 * * [simplify]: Extracting # 30 : cost 0 2.522 * * [simplify]: Extracting # 31 : cost 0 2.522 * * [simplify]: Extracting # 32 : cost 0 2.523 * * [simplify]: Extracting # 33 : cost 0 2.523 * * [simplify]: iteration 0 : 361 enodes (cost 2800 ) 2.635 * * [simplify]: Extracting # 0 : cost 0 2.636 * * [simplify]: Extracting # 1 : cost 0 2.642 * * [simplify]: Extracting # 2 : cost 0 2.643 * * [simplify]: Extracting # 3 : cost 0 2.645 * * [simplify]: Extracting # 4 : cost 0 2.646 * * [simplify]: Extracting # 5 : cost 0 2.647 * * [simplify]: Extracting # 6 : cost 0 2.649 * * [simplify]: iteration 1 : 1008 enodes (cost 2643 ) 3.370 * * [simplify]: Extracting # 0 : cost 0 3.380 * * [simplify]: Extracting # 1 : cost 0 3.392 * * [simplify]: Extracting # 2 : cost 0 3.398 * * [simplify]: Extracting # 3 : cost 0 3.404 * * [simplify]: Extracting # 4 : cost 0 3.410 * * [simplify]: Extracting # 5 : cost 0 3.418 * * [simplify]: iteration 2 : 4741 enodes (cost 2477 ) 4.990 * * [simplify]: Extracting # 0 : cost 0 5.003 * * [simplify]: Extracting # 1 : cost 0 5.015 * * [simplify]: Extracting # 2 : cost 0 5.027 * * [simplify]: Extracting # 3 : cost 0 5.042 * * [simplify]: iteration done: 5000 enodes (cost 2477 ) 5.044 * [simplify]: Simplified to: (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (pow 1.0 3) (* k (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (pow n 3) (pow PI 3)) (pow 2.0 3)) (* (pow n 3) (pow (* 2.0 PI) 3)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* n PI) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (pow 1.0 3) (* k (sqrt k))) (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3)) (pow (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (pow (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k)) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (+ (+ (* (* 0.125 (pow k 2)) (+ (* (pow (log (* 2.0 PI)) 2) (pow (* (* 2.0 PI) n) 0.5)) (* (pow (* (* 2.0 PI) n) 0.5) (pow (log n) 2)))) (* (* (pow k 2) (log (* 2.0 PI))) (* (* (pow (* (* 2.0 PI) n) 0.5) (log n)) 0.25))) (pow (* (* 2.0 PI) n) 0.5)) (* 0.5 (* k (+ (* (pow (* (* 2.0 PI) n) 0.5) (log (* 2.0 PI))) (* (pow (* (* 2.0 PI) n) 0.5) (log n)))))) (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (- (* +nan.0 k) (- (* +nan.0 (pow k 2)) +nan.0))) (+ (- (/ +nan.0 (pow k 2))) (- (/ +nan.0 k) (/ +nan.0 (pow k 3)))) (- (+ (- (/ +nan.0 (pow k 2)) (/ +nan.0 k)) +nan.0)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (- (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (- (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (+ (- (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5)))) (+ (- (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5)))) (+ (- (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (* +nan.0 (- (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))) (+ (* +nan.0 (- (/ (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) k) (/ (/ (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) k) k))) (* (- +nan.0) (/ (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (pow k 3)))) (+ (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k))) (* +nan.0 (- (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))) 5.045 * * * [progress]: adding candidates to table 5.696 * * [progress]: iteration 2 / 4 5.696 * * * [progress]: picking best candidate 5.732 * * * * [pick]: Picked # 5.732 * * * [progress]: localizing error 5.757 * * * [progress]: generating rewritten candidates 5.757 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 5.804 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 5.856 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 5.869 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2) 5.978 * * * [progress]: generating series expansions 5.978 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 5.979 * [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))) 5.979 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 5.979 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 5.979 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 5.979 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 5.979 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 5.979 * [taylor]: Taking taylor expansion of 0.25 in k 5.979 * [backup-simplify]: Simplify 0.25 into 0.25 5.979 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 5.979 * [taylor]: Taking taylor expansion of 1.0 in k 5.979 * [backup-simplify]: Simplify 1.0 into 1.0 5.979 * [taylor]: Taking taylor expansion of k in k 5.979 * [backup-simplify]: Simplify 0 into 0 5.979 * [backup-simplify]: Simplify 1 into 1 5.979 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 5.979 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 5.979 * [taylor]: Taking taylor expansion of 2.0 in k 5.980 * [backup-simplify]: Simplify 2.0 into 2.0 5.980 * [taylor]: Taking taylor expansion of (* n PI) in k 5.980 * [taylor]: Taking taylor expansion of n in k 5.980 * [backup-simplify]: Simplify n into n 5.980 * [taylor]: Taking taylor expansion of PI in k 5.980 * [backup-simplify]: Simplify PI into PI 5.980 * [backup-simplify]: Simplify (* n PI) into (* n PI) 5.980 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 5.980 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 5.980 * [backup-simplify]: Simplify (- 0) into 0 5.981 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 5.981 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 5.981 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 5.982 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 5.982 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 5.982 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 5.982 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 5.982 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 5.982 * [taylor]: Taking taylor expansion of 0.25 in n 5.982 * [backup-simplify]: Simplify 0.25 into 0.25 5.982 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 5.982 * [taylor]: Taking taylor expansion of 1.0 in n 5.982 * [backup-simplify]: Simplify 1.0 into 1.0 5.982 * [taylor]: Taking taylor expansion of k in n 5.982 * [backup-simplify]: Simplify k into k 5.982 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 5.982 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 5.982 * [taylor]: Taking taylor expansion of 2.0 in n 5.982 * [backup-simplify]: Simplify 2.0 into 2.0 5.982 * [taylor]: Taking taylor expansion of (* n PI) in n 5.982 * [taylor]: Taking taylor expansion of n in n 5.982 * [backup-simplify]: Simplify 0 into 0 5.982 * [backup-simplify]: Simplify 1 into 1 5.982 * [taylor]: Taking taylor expansion of PI in n 5.982 * [backup-simplify]: Simplify PI into PI 5.983 * [backup-simplify]: Simplify (* 0 PI) into 0 5.983 * [backup-simplify]: Simplify (* 2.0 0) into 0 5.985 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 5.986 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 5.988 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.988 * [backup-simplify]: Simplify (- k) into (- k) 5.988 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 5.988 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 5.989 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 5.990 * [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)))) 5.992 * [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))))) 5.992 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 5.992 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 5.992 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 5.992 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 5.992 * [taylor]: Taking taylor expansion of 0.25 in n 5.992 * [backup-simplify]: Simplify 0.25 into 0.25 5.992 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 5.992 * [taylor]: Taking taylor expansion of 1.0 in n 5.992 * [backup-simplify]: Simplify 1.0 into 1.0 5.992 * [taylor]: Taking taylor expansion of k in n 5.992 * [backup-simplify]: Simplify k into k 5.992 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 5.992 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 5.992 * [taylor]: Taking taylor expansion of 2.0 in n 5.992 * [backup-simplify]: Simplify 2.0 into 2.0 5.992 * [taylor]: Taking taylor expansion of (* n PI) in n 5.992 * [taylor]: Taking taylor expansion of n in n 5.992 * [backup-simplify]: Simplify 0 into 0 5.992 * [backup-simplify]: Simplify 1 into 1 5.992 * [taylor]: Taking taylor expansion of PI in n 5.992 * [backup-simplify]: Simplify PI into PI 5.993 * [backup-simplify]: Simplify (* 0 PI) into 0 5.993 * [backup-simplify]: Simplify (* 2.0 0) into 0 5.994 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 5.996 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 5.997 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.997 * [backup-simplify]: Simplify (- k) into (- k) 5.997 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 5.997 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 5.998 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 5.998 * [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)))) 5.999 * [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))))) 5.999 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 5.999 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 5.999 * [taylor]: Taking taylor expansion of 0.25 in k 5.999 * [backup-simplify]: Simplify 0.25 into 0.25 5.999 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 5.999 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 5.999 * [taylor]: Taking taylor expansion of 1.0 in k 5.999 * [backup-simplify]: Simplify 1.0 into 1.0 5.999 * [taylor]: Taking taylor expansion of k in k 5.999 * [backup-simplify]: Simplify 0 into 0 5.999 * [backup-simplify]: Simplify 1 into 1 5.999 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 5.999 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 5.999 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 5.999 * [taylor]: Taking taylor expansion of 2.0 in k 5.999 * [backup-simplify]: Simplify 2.0 into 2.0 5.999 * [taylor]: Taking taylor expansion of PI in k 5.999 * [backup-simplify]: Simplify PI into PI 6.000 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.000 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.000 * [taylor]: Taking taylor expansion of (log n) in k 6.001 * [taylor]: Taking taylor expansion of n in k 6.001 * [backup-simplify]: Simplify n into n 6.001 * [backup-simplify]: Simplify (log n) into (log n) 6.001 * [backup-simplify]: Simplify (- 0) into 0 6.001 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.002 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 6.002 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 6.003 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 6.004 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 6.005 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 6.005 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 6.006 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 6.007 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.007 * [backup-simplify]: Simplify (- 0) into 0 6.007 * [backup-simplify]: Simplify (+ 0 0) into 0 6.008 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 6.009 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.011 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 6.012 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.012 * [taylor]: Taking taylor expansion of 0 in k 6.012 * [backup-simplify]: Simplify 0 into 0 6.012 * [backup-simplify]: Simplify 0 into 0 6.012 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.013 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.014 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 6.014 * [backup-simplify]: Simplify (+ 0 0) into 0 6.015 * [backup-simplify]: Simplify (- 1) into -1 6.015 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.016 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 6.017 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 6.020 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 6.022 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 6.023 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 6.023 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 6.025 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 6.026 * [backup-simplify]: Simplify (- 0) into 0 6.026 * [backup-simplify]: Simplify (+ 0 0) into 0 6.027 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 6.027 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.028 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.030 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.030 * [taylor]: Taking taylor expansion of 0 in k 6.030 * [backup-simplify]: Simplify 0 into 0 6.030 * [backup-simplify]: Simplify 0 into 0 6.030 * [backup-simplify]: Simplify 0 into 0 6.031 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.033 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 6.034 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 6.034 * [backup-simplify]: Simplify (+ 0 0) into 0 6.035 * [backup-simplify]: Simplify (- 0) into 0 6.035 * [backup-simplify]: Simplify (+ 0 0) into 0 6.036 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.038 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 6.041 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 6.046 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 6.057 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 6.058 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 6.058 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 6.058 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 6.058 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 6.058 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 6.058 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 6.058 * [taylor]: Taking taylor expansion of 0.25 in k 6.058 * [backup-simplify]: Simplify 0.25 into 0.25 6.058 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.058 * [taylor]: Taking taylor expansion of 1.0 in k 6.058 * [backup-simplify]: Simplify 1.0 into 1.0 6.058 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.058 * [taylor]: Taking taylor expansion of k in k 6.058 * [backup-simplify]: Simplify 0 into 0 6.058 * [backup-simplify]: Simplify 1 into 1 6.059 * [backup-simplify]: Simplify (/ 1 1) into 1 6.059 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 6.059 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 6.059 * [taylor]: Taking taylor expansion of 2.0 in k 6.059 * [backup-simplify]: Simplify 2.0 into 2.0 6.059 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.059 * [taylor]: Taking taylor expansion of PI in k 6.059 * [backup-simplify]: Simplify PI into PI 6.059 * [taylor]: Taking taylor expansion of n in k 6.059 * [backup-simplify]: Simplify n into n 6.059 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.059 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 6.059 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 6.060 * [backup-simplify]: Simplify (- 1) into -1 6.060 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.061 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 6.061 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 6.061 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 6.061 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 6.061 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.061 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.061 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 6.061 * [taylor]: Taking taylor expansion of 0.25 in n 6.061 * [backup-simplify]: Simplify 0.25 into 0.25 6.061 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.061 * [taylor]: Taking taylor expansion of 1.0 in n 6.061 * [backup-simplify]: Simplify 1.0 into 1.0 6.062 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.062 * [taylor]: Taking taylor expansion of k in n 6.062 * [backup-simplify]: Simplify k into k 6.062 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.062 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.062 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.062 * [taylor]: Taking taylor expansion of 2.0 in n 6.062 * [backup-simplify]: Simplify 2.0 into 2.0 6.062 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.062 * [taylor]: Taking taylor expansion of PI in n 6.062 * [backup-simplify]: Simplify PI into PI 6.062 * [taylor]: Taking taylor expansion of n in n 6.062 * [backup-simplify]: Simplify 0 into 0 6.062 * [backup-simplify]: Simplify 1 into 1 6.062 * [backup-simplify]: Simplify (/ PI 1) into PI 6.063 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.064 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.064 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.064 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.064 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 6.066 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.067 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 6.069 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.069 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 6.069 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.069 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.069 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 6.069 * [taylor]: Taking taylor expansion of 0.25 in n 6.069 * [backup-simplify]: Simplify 0.25 into 0.25 6.069 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.069 * [taylor]: Taking taylor expansion of 1.0 in n 6.069 * [backup-simplify]: Simplify 1.0 into 1.0 6.069 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.069 * [taylor]: Taking taylor expansion of k in n 6.069 * [backup-simplify]: Simplify k into k 6.069 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.069 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.069 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.069 * [taylor]: Taking taylor expansion of 2.0 in n 6.069 * [backup-simplify]: Simplify 2.0 into 2.0 6.069 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.069 * [taylor]: Taking taylor expansion of PI in n 6.069 * [backup-simplify]: Simplify PI into PI 6.069 * [taylor]: Taking taylor expansion of n in n 6.069 * [backup-simplify]: Simplify 0 into 0 6.069 * [backup-simplify]: Simplify 1 into 1 6.070 * [backup-simplify]: Simplify (/ PI 1) into PI 6.070 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.072 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.072 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.072 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.073 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 6.074 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.075 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 6.077 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.077 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 6.077 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 6.077 * [taylor]: Taking taylor expansion of 0.25 in k 6.077 * [backup-simplify]: Simplify 0.25 into 0.25 6.077 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 6.077 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 6.077 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.077 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.077 * [taylor]: Taking taylor expansion of 2.0 in k 6.077 * [backup-simplify]: Simplify 2.0 into 2.0 6.077 * [taylor]: Taking taylor expansion of PI in k 6.077 * [backup-simplify]: Simplify PI into PI 6.078 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.079 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.079 * [taylor]: Taking taylor expansion of (log n) in k 6.079 * [taylor]: Taking taylor expansion of n in k 6.079 * [backup-simplify]: Simplify n into n 6.079 * [backup-simplify]: Simplify (log n) into (log n) 6.079 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.079 * [taylor]: Taking taylor expansion of 1.0 in k 6.079 * [backup-simplify]: Simplify 1.0 into 1.0 6.079 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.079 * [taylor]: Taking taylor expansion of k in k 6.079 * [backup-simplify]: Simplify 0 into 0 6.079 * [backup-simplify]: Simplify 1 into 1 6.079 * [backup-simplify]: Simplify (/ 1 1) into 1 6.080 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.081 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 6.081 * [backup-simplify]: Simplify (- 1) into -1 6.082 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.083 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 6.084 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 6.085 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.087 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.088 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.089 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.091 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.091 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.091 * [backup-simplify]: Simplify (- 0) into 0 6.092 * [backup-simplify]: Simplify (+ 0 0) into 0 6.092 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 6.094 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.095 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 6.097 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.097 * [taylor]: Taking taylor expansion of 0 in k 6.097 * [backup-simplify]: Simplify 0 into 0 6.097 * [backup-simplify]: Simplify 0 into 0 6.097 * [backup-simplify]: Simplify 0 into 0 6.098 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.099 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.103 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 6.103 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.104 * [backup-simplify]: Simplify (- 0) into 0 6.104 * [backup-simplify]: Simplify (+ 0 0) into 0 6.110 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 6.111 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.113 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 6.115 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.115 * [taylor]: Taking taylor expansion of 0 in k 6.116 * [backup-simplify]: Simplify 0 into 0 6.116 * [backup-simplify]: Simplify 0 into 0 6.116 * [backup-simplify]: Simplify 0 into 0 6.116 * [backup-simplify]: Simplify 0 into 0 6.117 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.118 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.124 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 6.124 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.125 * [backup-simplify]: Simplify (- 0) into 0 6.125 * [backup-simplify]: Simplify (+ 0 0) into 0 6.126 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 6.128 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.130 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 6.132 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 6.132 * [taylor]: Taking taylor expansion of 0 in k 6.132 * [backup-simplify]: Simplify 0 into 0 6.132 * [backup-simplify]: Simplify 0 into 0 6.133 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 6.134 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 6.134 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 6.134 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 6.134 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 6.134 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 6.134 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 6.134 * [taylor]: Taking taylor expansion of 0.25 in k 6.134 * [backup-simplify]: Simplify 0.25 into 0.25 6.134 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.134 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.134 * [taylor]: Taking taylor expansion of k in k 6.134 * [backup-simplify]: Simplify 0 into 0 6.134 * [backup-simplify]: Simplify 1 into 1 6.134 * [backup-simplify]: Simplify (/ 1 1) into 1 6.134 * [taylor]: Taking taylor expansion of 1.0 in k 6.134 * [backup-simplify]: Simplify 1.0 into 1.0 6.134 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 6.134 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 6.134 * [taylor]: Taking taylor expansion of -2.0 in k 6.134 * [backup-simplify]: Simplify -2.0 into -2.0 6.134 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.134 * [taylor]: Taking taylor expansion of PI in k 6.134 * [backup-simplify]: Simplify PI into PI 6.134 * [taylor]: Taking taylor expansion of n in k 6.135 * [backup-simplify]: Simplify n into n 6.135 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.135 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 6.135 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 6.135 * [backup-simplify]: Simplify (+ 1 0) into 1 6.135 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 6.135 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 6.135 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 6.135 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 6.135 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.136 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.136 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 6.136 * [taylor]: Taking taylor expansion of 0.25 in n 6.136 * [backup-simplify]: Simplify 0.25 into 0.25 6.136 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.136 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.136 * [taylor]: Taking taylor expansion of k in n 6.136 * [backup-simplify]: Simplify k into k 6.136 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.136 * [taylor]: Taking taylor expansion of 1.0 in n 6.136 * [backup-simplify]: Simplify 1.0 into 1.0 6.136 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.136 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.136 * [taylor]: Taking taylor expansion of -2.0 in n 6.136 * [backup-simplify]: Simplify -2.0 into -2.0 6.136 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.136 * [taylor]: Taking taylor expansion of PI in n 6.136 * [backup-simplify]: Simplify PI into PI 6.136 * [taylor]: Taking taylor expansion of n in n 6.136 * [backup-simplify]: Simplify 0 into 0 6.136 * [backup-simplify]: Simplify 1 into 1 6.136 * [backup-simplify]: Simplify (/ PI 1) into PI 6.136 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.137 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.137 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.137 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 6.138 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.139 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 6.140 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.140 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 6.140 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.140 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.140 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 6.140 * [taylor]: Taking taylor expansion of 0.25 in n 6.140 * [backup-simplify]: Simplify 0.25 into 0.25 6.140 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.140 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.140 * [taylor]: Taking taylor expansion of k in n 6.140 * [backup-simplify]: Simplify k into k 6.140 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.140 * [taylor]: Taking taylor expansion of 1.0 in n 6.140 * [backup-simplify]: Simplify 1.0 into 1.0 6.140 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.140 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.140 * [taylor]: Taking taylor expansion of -2.0 in n 6.140 * [backup-simplify]: Simplify -2.0 into -2.0 6.140 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.140 * [taylor]: Taking taylor expansion of PI in n 6.140 * [backup-simplify]: Simplify PI into PI 6.140 * [taylor]: Taking taylor expansion of n in n 6.140 * [backup-simplify]: Simplify 0 into 0 6.140 * [backup-simplify]: Simplify 1 into 1 6.140 * [backup-simplify]: Simplify (/ PI 1) into PI 6.141 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.141 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.141 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.141 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 6.142 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.143 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 6.144 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.144 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 6.144 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 6.144 * [taylor]: Taking taylor expansion of 0.25 in k 6.144 * [backup-simplify]: Simplify 0.25 into 0.25 6.144 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 6.144 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.144 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.144 * [taylor]: Taking taylor expansion of k in k 6.144 * [backup-simplify]: Simplify 0 into 0 6.144 * [backup-simplify]: Simplify 1 into 1 6.144 * [backup-simplify]: Simplify (/ 1 1) into 1 6.144 * [taylor]: Taking taylor expansion of 1.0 in k 6.144 * [backup-simplify]: Simplify 1.0 into 1.0 6.144 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 6.144 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 6.144 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 6.144 * [taylor]: Taking taylor expansion of -2.0 in k 6.144 * [backup-simplify]: Simplify -2.0 into -2.0 6.144 * [taylor]: Taking taylor expansion of PI in k 6.145 * [backup-simplify]: Simplify PI into PI 6.145 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.145 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.145 * [taylor]: Taking taylor expansion of (log n) in k 6.145 * [taylor]: Taking taylor expansion of n in k 6.145 * [backup-simplify]: Simplify n into n 6.146 * [backup-simplify]: Simplify (log n) into (log n) 6.146 * [backup-simplify]: Simplify (+ 1 0) into 1 6.146 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.147 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 6.147 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 6.148 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 6.149 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.149 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.150 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.150 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 6.151 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 6.152 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.152 * [backup-simplify]: Simplify (+ 0 0) into 0 6.152 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 6.153 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.154 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 6.155 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.155 * [taylor]: Taking taylor expansion of 0 in k 6.155 * [backup-simplify]: Simplify 0 into 0 6.155 * [backup-simplify]: Simplify 0 into 0 6.155 * [backup-simplify]: Simplify 0 into 0 6.156 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.156 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.158 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 6.158 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.159 * [backup-simplify]: Simplify (+ 0 0) into 0 6.159 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 6.160 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.161 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 6.163 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.163 * [taylor]: Taking taylor expansion of 0 in k 6.163 * [backup-simplify]: Simplify 0 into 0 6.163 * [backup-simplify]: Simplify 0 into 0 6.163 * [backup-simplify]: Simplify 0 into 0 6.163 * [backup-simplify]: Simplify 0 into 0 6.163 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.165 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.170 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 6.171 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.171 * [backup-simplify]: Simplify (+ 0 0) into 0 6.173 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 6.174 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.176 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 6.179 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 6.179 * [taylor]: Taking taylor expansion of 0 in k 6.179 * [backup-simplify]: Simplify 0 into 0 6.179 * [backup-simplify]: Simplify 0 into 0 6.180 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 6.181 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 6.181 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 6.181 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 6.181 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 6.181 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 6.182 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 6.182 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 6.182 * [taylor]: Taking taylor expansion of 0.25 in k 6.182 * [backup-simplify]: Simplify 0.25 into 0.25 6.182 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.182 * [taylor]: Taking taylor expansion of 1.0 in k 6.182 * [backup-simplify]: Simplify 1.0 into 1.0 6.182 * [taylor]: Taking taylor expansion of k in k 6.182 * [backup-simplify]: Simplify 0 into 0 6.182 * [backup-simplify]: Simplify 1 into 1 6.182 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 6.182 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 6.182 * [taylor]: Taking taylor expansion of 2.0 in k 6.182 * [backup-simplify]: Simplify 2.0 into 2.0 6.182 * [taylor]: Taking taylor expansion of (* n PI) in k 6.182 * [taylor]: Taking taylor expansion of n in k 6.182 * [backup-simplify]: Simplify n into n 6.182 * [taylor]: Taking taylor expansion of PI in k 6.182 * [backup-simplify]: Simplify PI into PI 6.182 * [backup-simplify]: Simplify (* n PI) into (* n PI) 6.183 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 6.183 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 6.183 * [backup-simplify]: Simplify (- 0) into 0 6.184 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.184 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 6.184 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 6.184 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 6.184 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 6.184 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.184 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.184 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 6.184 * [taylor]: Taking taylor expansion of 0.25 in n 6.184 * [backup-simplify]: Simplify 0.25 into 0.25 6.185 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.185 * [taylor]: Taking taylor expansion of 1.0 in n 6.185 * [backup-simplify]: Simplify 1.0 into 1.0 6.185 * [taylor]: Taking taylor expansion of k in n 6.185 * [backup-simplify]: Simplify k into k 6.185 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.185 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.185 * [taylor]: Taking taylor expansion of 2.0 in n 6.185 * [backup-simplify]: Simplify 2.0 into 2.0 6.185 * [taylor]: Taking taylor expansion of (* n PI) in n 6.185 * [taylor]: Taking taylor expansion of n in n 6.185 * [backup-simplify]: Simplify 0 into 0 6.185 * [backup-simplify]: Simplify 1 into 1 6.185 * [taylor]: Taking taylor expansion of PI in n 6.185 * [backup-simplify]: Simplify PI into PI 6.185 * [backup-simplify]: Simplify (* 0 PI) into 0 6.186 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.188 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.189 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.191 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.191 * [backup-simplify]: Simplify (- k) into (- k) 6.191 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.191 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 6.192 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.193 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 6.195 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 6.195 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 6.195 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.195 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.195 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 6.195 * [taylor]: Taking taylor expansion of 0.25 in n 6.195 * [backup-simplify]: Simplify 0.25 into 0.25 6.195 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.195 * [taylor]: Taking taylor expansion of 1.0 in n 6.195 * [backup-simplify]: Simplify 1.0 into 1.0 6.195 * [taylor]: Taking taylor expansion of k in n 6.195 * [backup-simplify]: Simplify k into k 6.195 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.195 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.195 * [taylor]: Taking taylor expansion of 2.0 in n 6.195 * [backup-simplify]: Simplify 2.0 into 2.0 6.195 * [taylor]: Taking taylor expansion of (* n PI) in n 6.195 * [taylor]: Taking taylor expansion of n in n 6.195 * [backup-simplify]: Simplify 0 into 0 6.195 * [backup-simplify]: Simplify 1 into 1 6.195 * [taylor]: Taking taylor expansion of PI in n 6.195 * [backup-simplify]: Simplify PI into PI 6.196 * [backup-simplify]: Simplify (* 0 PI) into 0 6.196 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.198 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.200 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.201 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.201 * [backup-simplify]: Simplify (- k) into (- k) 6.201 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.201 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 6.203 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.204 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 6.205 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 6.206 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 6.206 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 6.206 * [taylor]: Taking taylor expansion of 0.25 in k 6.206 * [backup-simplify]: Simplify 0.25 into 0.25 6.206 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 6.206 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.206 * [taylor]: Taking taylor expansion of 1.0 in k 6.206 * [backup-simplify]: Simplify 1.0 into 1.0 6.206 * [taylor]: Taking taylor expansion of k in k 6.206 * [backup-simplify]: Simplify 0 into 0 6.206 * [backup-simplify]: Simplify 1 into 1 6.206 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 6.206 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.206 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.206 * [taylor]: Taking taylor expansion of 2.0 in k 6.206 * [backup-simplify]: Simplify 2.0 into 2.0 6.206 * [taylor]: Taking taylor expansion of PI in k 6.206 * [backup-simplify]: Simplify PI into PI 6.207 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.208 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.208 * [taylor]: Taking taylor expansion of (log n) in k 6.208 * [taylor]: Taking taylor expansion of n in k 6.208 * [backup-simplify]: Simplify n into n 6.208 * [backup-simplify]: Simplify (log n) into (log n) 6.208 * [backup-simplify]: Simplify (- 0) into 0 6.209 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.210 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 6.211 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 6.212 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 6.213 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 6.213 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 6.214 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 6.215 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 6.216 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.216 * [backup-simplify]: Simplify (- 0) into 0 6.216 * [backup-simplify]: Simplify (+ 0 0) into 0 6.216 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 6.218 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.219 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 6.220 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.220 * [taylor]: Taking taylor expansion of 0 in k 6.220 * [backup-simplify]: Simplify 0 into 0 6.220 * [backup-simplify]: Simplify 0 into 0 6.220 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.221 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.222 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 6.222 * [backup-simplify]: Simplify (+ 0 0) into 0 6.222 * [backup-simplify]: Simplify (- 1) into -1 6.223 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.224 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 6.225 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 6.227 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 6.232 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 6.233 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 6.234 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 6.236 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 6.236 * [backup-simplify]: Simplify (- 0) into 0 6.236 * [backup-simplify]: Simplify (+ 0 0) into 0 6.237 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 6.238 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.239 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.242 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.242 * [taylor]: Taking taylor expansion of 0 in k 6.242 * [backup-simplify]: Simplify 0 into 0 6.242 * [backup-simplify]: Simplify 0 into 0 6.242 * [backup-simplify]: Simplify 0 into 0 6.243 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.247 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 6.249 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 6.250 * [backup-simplify]: Simplify (+ 0 0) into 0 6.250 * [backup-simplify]: Simplify (- 0) into 0 6.250 * [backup-simplify]: Simplify (+ 0 0) into 0 6.252 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.255 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 6.259 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 6.265 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 6.272 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 6.273 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 6.273 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 6.273 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 6.273 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 6.273 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 6.273 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 6.273 * [taylor]: Taking taylor expansion of 0.25 in k 6.273 * [backup-simplify]: Simplify 0.25 into 0.25 6.273 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.273 * [taylor]: Taking taylor expansion of 1.0 in k 6.273 * [backup-simplify]: Simplify 1.0 into 1.0 6.273 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.273 * [taylor]: Taking taylor expansion of k in k 6.273 * [backup-simplify]: Simplify 0 into 0 6.273 * [backup-simplify]: Simplify 1 into 1 6.273 * [backup-simplify]: Simplify (/ 1 1) into 1 6.273 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 6.273 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 6.273 * [taylor]: Taking taylor expansion of 2.0 in k 6.273 * [backup-simplify]: Simplify 2.0 into 2.0 6.273 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.273 * [taylor]: Taking taylor expansion of PI in k 6.273 * [backup-simplify]: Simplify PI into PI 6.273 * [taylor]: Taking taylor expansion of n in k 6.273 * [backup-simplify]: Simplify n into n 6.273 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.273 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 6.273 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 6.274 * [backup-simplify]: Simplify (- 1) into -1 6.274 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.274 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 6.274 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 6.275 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 6.275 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 6.275 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.275 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.275 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 6.275 * [taylor]: Taking taylor expansion of 0.25 in n 6.275 * [backup-simplify]: Simplify 0.25 into 0.25 6.275 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.275 * [taylor]: Taking taylor expansion of 1.0 in n 6.275 * [backup-simplify]: Simplify 1.0 into 1.0 6.275 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.275 * [taylor]: Taking taylor expansion of k in n 6.275 * [backup-simplify]: Simplify k into k 6.275 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.275 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.275 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.275 * [taylor]: Taking taylor expansion of 2.0 in n 6.275 * [backup-simplify]: Simplify 2.0 into 2.0 6.275 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.275 * [taylor]: Taking taylor expansion of PI in n 6.275 * [backup-simplify]: Simplify PI into PI 6.275 * [taylor]: Taking taylor expansion of n in n 6.275 * [backup-simplify]: Simplify 0 into 0 6.275 * [backup-simplify]: Simplify 1 into 1 6.275 * [backup-simplify]: Simplify (/ PI 1) into PI 6.276 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.276 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.276 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.276 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.276 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 6.277 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.278 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 6.279 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.279 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 6.279 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.279 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.279 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 6.279 * [taylor]: Taking taylor expansion of 0.25 in n 6.279 * [backup-simplify]: Simplify 0.25 into 0.25 6.279 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.279 * [taylor]: Taking taylor expansion of 1.0 in n 6.279 * [backup-simplify]: Simplify 1.0 into 1.0 6.279 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.279 * [taylor]: Taking taylor expansion of k in n 6.279 * [backup-simplify]: Simplify k into k 6.279 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.279 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.279 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.279 * [taylor]: Taking taylor expansion of 2.0 in n 6.279 * [backup-simplify]: Simplify 2.0 into 2.0 6.279 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.279 * [taylor]: Taking taylor expansion of PI in n 6.279 * [backup-simplify]: Simplify PI into PI 6.279 * [taylor]: Taking taylor expansion of n in n 6.279 * [backup-simplify]: Simplify 0 into 0 6.279 * [backup-simplify]: Simplify 1 into 1 6.280 * [backup-simplify]: Simplify (/ PI 1) into PI 6.280 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.281 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.281 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.281 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.281 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 6.282 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.283 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 6.283 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.284 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 6.284 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 6.284 * [taylor]: Taking taylor expansion of 0.25 in k 6.284 * [backup-simplify]: Simplify 0.25 into 0.25 6.284 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 6.284 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 6.284 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.284 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.284 * [taylor]: Taking taylor expansion of 2.0 in k 6.284 * [backup-simplify]: Simplify 2.0 into 2.0 6.284 * [taylor]: Taking taylor expansion of PI in k 6.284 * [backup-simplify]: Simplify PI into PI 6.284 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.285 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.285 * [taylor]: Taking taylor expansion of (log n) in k 6.285 * [taylor]: Taking taylor expansion of n in k 6.285 * [backup-simplify]: Simplify n into n 6.285 * [backup-simplify]: Simplify (log n) into (log n) 6.285 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.285 * [taylor]: Taking taylor expansion of 1.0 in k 6.285 * [backup-simplify]: Simplify 1.0 into 1.0 6.285 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.285 * [taylor]: Taking taylor expansion of k in k 6.285 * [backup-simplify]: Simplify 0 into 0 6.285 * [backup-simplify]: Simplify 1 into 1 6.285 * [backup-simplify]: Simplify (/ 1 1) into 1 6.285 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.286 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 6.286 * [backup-simplify]: Simplify (- 1) into -1 6.286 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.287 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 6.288 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 6.289 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.289 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.290 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.290 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.291 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.291 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.292 * [backup-simplify]: Simplify (- 0) into 0 6.292 * [backup-simplify]: Simplify (+ 0 0) into 0 6.292 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 6.293 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.294 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 6.295 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.295 * [taylor]: Taking taylor expansion of 0 in k 6.295 * [backup-simplify]: Simplify 0 into 0 6.295 * [backup-simplify]: Simplify 0 into 0 6.295 * [backup-simplify]: Simplify 0 into 0 6.296 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.296 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.298 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 6.298 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.299 * [backup-simplify]: Simplify (- 0) into 0 6.299 * [backup-simplify]: Simplify (+ 0 0) into 0 6.300 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 6.301 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.303 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 6.305 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.305 * [taylor]: Taking taylor expansion of 0 in k 6.305 * [backup-simplify]: Simplify 0 into 0 6.305 * [backup-simplify]: Simplify 0 into 0 6.305 * [backup-simplify]: Simplify 0 into 0 6.305 * [backup-simplify]: Simplify 0 into 0 6.306 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.308 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.312 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 6.313 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.313 * [backup-simplify]: Simplify (- 0) into 0 6.313 * [backup-simplify]: Simplify (+ 0 0) into 0 6.314 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 6.315 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.316 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 6.318 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 6.318 * [taylor]: Taking taylor expansion of 0 in k 6.318 * [backup-simplify]: Simplify 0 into 0 6.318 * [backup-simplify]: Simplify 0 into 0 6.319 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 6.319 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 6.319 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 6.319 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 6.319 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 6.319 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 6.319 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 6.319 * [taylor]: Taking taylor expansion of 0.25 in k 6.319 * [backup-simplify]: Simplify 0.25 into 0.25 6.319 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.319 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.319 * [taylor]: Taking taylor expansion of k in k 6.319 * [backup-simplify]: Simplify 0 into 0 6.319 * [backup-simplify]: Simplify 1 into 1 6.320 * [backup-simplify]: Simplify (/ 1 1) into 1 6.320 * [taylor]: Taking taylor expansion of 1.0 in k 6.320 * [backup-simplify]: Simplify 1.0 into 1.0 6.320 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 6.320 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 6.320 * [taylor]: Taking taylor expansion of -2.0 in k 6.320 * [backup-simplify]: Simplify -2.0 into -2.0 6.320 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.320 * [taylor]: Taking taylor expansion of PI in k 6.320 * [backup-simplify]: Simplify PI into PI 6.320 * [taylor]: Taking taylor expansion of n in k 6.320 * [backup-simplify]: Simplify n into n 6.320 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.320 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 6.320 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 6.320 * [backup-simplify]: Simplify (+ 1 0) into 1 6.321 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 6.321 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 6.321 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 6.321 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 6.321 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.321 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.321 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 6.321 * [taylor]: Taking taylor expansion of 0.25 in n 6.321 * [backup-simplify]: Simplify 0.25 into 0.25 6.321 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.321 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.321 * [taylor]: Taking taylor expansion of k in n 6.321 * [backup-simplify]: Simplify k into k 6.321 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.321 * [taylor]: Taking taylor expansion of 1.0 in n 6.321 * [backup-simplify]: Simplify 1.0 into 1.0 6.321 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.321 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.321 * [taylor]: Taking taylor expansion of -2.0 in n 6.321 * [backup-simplify]: Simplify -2.0 into -2.0 6.321 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.321 * [taylor]: Taking taylor expansion of PI in n 6.321 * [backup-simplify]: Simplify PI into PI 6.322 * [taylor]: Taking taylor expansion of n in n 6.322 * [backup-simplify]: Simplify 0 into 0 6.322 * [backup-simplify]: Simplify 1 into 1 6.322 * [backup-simplify]: Simplify (/ PI 1) into PI 6.322 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.323 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.323 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.323 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 6.324 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.325 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 6.325 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.325 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 6.325 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.326 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.326 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 6.326 * [taylor]: Taking taylor expansion of 0.25 in n 6.326 * [backup-simplify]: Simplify 0.25 into 0.25 6.326 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.326 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.326 * [taylor]: Taking taylor expansion of k in n 6.326 * [backup-simplify]: Simplify k into k 6.326 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.326 * [taylor]: Taking taylor expansion of 1.0 in n 6.326 * [backup-simplify]: Simplify 1.0 into 1.0 6.326 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.326 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.326 * [taylor]: Taking taylor expansion of -2.0 in n 6.326 * [backup-simplify]: Simplify -2.0 into -2.0 6.326 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.326 * [taylor]: Taking taylor expansion of PI in n 6.326 * [backup-simplify]: Simplify PI into PI 6.326 * [taylor]: Taking taylor expansion of n in n 6.326 * [backup-simplify]: Simplify 0 into 0 6.326 * [backup-simplify]: Simplify 1 into 1 6.326 * [backup-simplify]: Simplify (/ PI 1) into PI 6.327 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.327 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.327 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.327 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 6.328 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.329 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 6.330 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.330 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 6.330 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 6.330 * [taylor]: Taking taylor expansion of 0.25 in k 6.330 * [backup-simplify]: Simplify 0.25 into 0.25 6.330 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 6.330 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.330 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.330 * [taylor]: Taking taylor expansion of k in k 6.330 * [backup-simplify]: Simplify 0 into 0 6.330 * [backup-simplify]: Simplify 1 into 1 6.330 * [backup-simplify]: Simplify (/ 1 1) into 1 6.330 * [taylor]: Taking taylor expansion of 1.0 in k 6.330 * [backup-simplify]: Simplify 1.0 into 1.0 6.330 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 6.330 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 6.330 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 6.330 * [taylor]: Taking taylor expansion of -2.0 in k 6.330 * [backup-simplify]: Simplify -2.0 into -2.0 6.330 * [taylor]: Taking taylor expansion of PI in k 6.330 * [backup-simplify]: Simplify PI into PI 6.331 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.331 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.331 * [taylor]: Taking taylor expansion of (log n) in k 6.331 * [taylor]: Taking taylor expansion of n in k 6.332 * [backup-simplify]: Simplify n into n 6.332 * [backup-simplify]: Simplify (log n) into (log n) 6.332 * [backup-simplify]: Simplify (+ 1 0) into 1 6.332 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.333 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 6.333 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 6.334 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 6.335 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.336 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.336 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.337 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 6.338 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 6.338 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.338 * [backup-simplify]: Simplify (+ 0 0) into 0 6.338 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 6.343 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.344 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 6.345 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.345 * [taylor]: Taking taylor expansion of 0 in k 6.345 * [backup-simplify]: Simplify 0 into 0 6.345 * [backup-simplify]: Simplify 0 into 0 6.345 * [backup-simplify]: Simplify 0 into 0 6.346 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.346 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.348 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 6.349 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.349 * [backup-simplify]: Simplify (+ 0 0) into 0 6.350 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 6.350 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.351 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 6.353 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.353 * [taylor]: Taking taylor expansion of 0 in k 6.353 * [backup-simplify]: Simplify 0 into 0 6.353 * [backup-simplify]: Simplify 0 into 0 6.353 * [backup-simplify]: Simplify 0 into 0 6.353 * [backup-simplify]: Simplify 0 into 0 6.354 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.354 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.358 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 6.358 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.358 * [backup-simplify]: Simplify (+ 0 0) into 0 6.359 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 6.360 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.361 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 6.363 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 6.363 * [taylor]: Taking taylor expansion of 0 in k 6.363 * [backup-simplify]: Simplify 0 into 0 6.363 * [backup-simplify]: Simplify 0 into 0 6.364 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 6.364 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 6.364 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 6.364 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 6.364 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 6.364 * [taylor]: Taking taylor expansion of 1.0 in k 6.364 * [backup-simplify]: Simplify 1.0 into 1.0 6.364 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 6.364 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.364 * [taylor]: Taking taylor expansion of k in k 6.364 * [backup-simplify]: Simplify 0 into 0 6.364 * [backup-simplify]: Simplify 1 into 1 6.365 * [backup-simplify]: Simplify (/ 1 1) into 1 6.365 * [backup-simplify]: Simplify (sqrt 0) into 0 6.366 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.366 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 6.366 * [taylor]: Taking taylor expansion of 1.0 in k 6.366 * [backup-simplify]: Simplify 1.0 into 1.0 6.366 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 6.366 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.366 * [taylor]: Taking taylor expansion of k in k 6.366 * [backup-simplify]: Simplify 0 into 0 6.366 * [backup-simplify]: Simplify 1 into 1 6.366 * [backup-simplify]: Simplify (/ 1 1) into 1 6.366 * [backup-simplify]: Simplify (sqrt 0) into 0 6.367 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.367 * [backup-simplify]: Simplify (* 1.0 0) into 0 6.367 * [backup-simplify]: Simplify 0 into 0 6.368 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 6.369 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.369 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 6.371 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 6.372 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 6.372 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.373 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.375 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 6.377 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 6.377 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.378 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 6.379 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 6.379 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 6.379 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 6.379 * [taylor]: Taking taylor expansion of 1.0 in k 6.379 * [backup-simplify]: Simplify 1.0 into 1.0 6.379 * [taylor]: Taking taylor expansion of (sqrt k) in k 6.379 * [taylor]: Taking taylor expansion of k in k 6.379 * [backup-simplify]: Simplify 0 into 0 6.379 * [backup-simplify]: Simplify 1 into 1 6.379 * [backup-simplify]: Simplify (sqrt 0) into 0 6.381 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.381 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 6.381 * [taylor]: Taking taylor expansion of 1.0 in k 6.381 * [backup-simplify]: Simplify 1.0 into 1.0 6.381 * [taylor]: Taking taylor expansion of (sqrt k) in k 6.381 * [taylor]: Taking taylor expansion of k in k 6.381 * [backup-simplify]: Simplify 0 into 0 6.381 * [backup-simplify]: Simplify 1 into 1 6.381 * [backup-simplify]: Simplify (sqrt 0) into 0 6.382 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.383 * [backup-simplify]: Simplify (* 1.0 0) into 0 6.383 * [backup-simplify]: Simplify 0 into 0 6.385 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 6.385 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.388 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 6.391 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 6.391 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.395 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 6.397 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 6.398 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.399 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 6.399 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 6.400 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 6.400 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 6.400 * [taylor]: Taking taylor expansion of 1.0 in k 6.400 * [backup-simplify]: Simplify 1.0 into 1.0 6.400 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 6.400 * [taylor]: Taking taylor expansion of (/ -1 k) in k 6.400 * [taylor]: Taking taylor expansion of -1 in k 6.400 * [backup-simplify]: Simplify -1 into -1 6.400 * [taylor]: Taking taylor expansion of k in k 6.400 * [backup-simplify]: Simplify 0 into 0 6.400 * [backup-simplify]: Simplify 1 into 1 6.400 * [backup-simplify]: Simplify (/ -1 1) into -1 6.401 * [backup-simplify]: Simplify (sqrt 0) into 0 6.402 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 6.403 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 6.403 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 6.403 * [taylor]: Taking taylor expansion of 1.0 in k 6.403 * [backup-simplify]: Simplify 1.0 into 1.0 6.403 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 6.403 * [taylor]: Taking taylor expansion of (/ -1 k) in k 6.403 * [taylor]: Taking taylor expansion of -1 in k 6.403 * [backup-simplify]: Simplify -1 into -1 6.403 * [taylor]: Taking taylor expansion of k in k 6.403 * [backup-simplify]: Simplify 0 into 0 6.403 * [backup-simplify]: Simplify 1 into 1 6.403 * [backup-simplify]: Simplify (/ -1 1) into -1 6.404 * [backup-simplify]: Simplify (sqrt 0) into 0 6.404 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 6.405 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 6.405 * [backup-simplify]: Simplify +nan.0 into +nan.0 6.405 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 6.407 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 6.409 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 6.409 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.409 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.412 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 6.414 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 6.414 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.415 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 6.415 * * * * [progress]: [ 4 / 4 ] generating series at (2 2) 6.416 * [backup-simplify]: Simplify (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) into (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) 6.416 * [approximate]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) in (n k) around 0 6.416 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) in k 6.416 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 6.416 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 6.416 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 6.416 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 6.416 * [taylor]: Taking taylor expansion of 0.25 in k 6.416 * [backup-simplify]: Simplify 0.25 into 0.25 6.416 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.416 * [taylor]: Taking taylor expansion of 1.0 in k 6.416 * [backup-simplify]: Simplify 1.0 into 1.0 6.416 * [taylor]: Taking taylor expansion of k in k 6.416 * [backup-simplify]: Simplify 0 into 0 6.416 * [backup-simplify]: Simplify 1 into 1 6.416 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 6.416 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 6.416 * [taylor]: Taking taylor expansion of 2.0 in k 6.416 * [backup-simplify]: Simplify 2.0 into 2.0 6.416 * [taylor]: Taking taylor expansion of (* n PI) in k 6.416 * [taylor]: Taking taylor expansion of n in k 6.416 * [backup-simplify]: Simplify n into n 6.416 * [taylor]: Taking taylor expansion of PI in k 6.416 * [backup-simplify]: Simplify PI into PI 6.416 * [backup-simplify]: Simplify (* n PI) into (* n PI) 6.417 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 6.417 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 6.417 * [backup-simplify]: Simplify (- 0) into 0 6.417 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.417 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 6.417 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 6.418 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 6.418 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) in n 6.418 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 6.418 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.418 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.418 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 6.418 * [taylor]: Taking taylor expansion of 0.25 in n 6.418 * [backup-simplify]: Simplify 0.25 into 0.25 6.418 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.418 * [taylor]: Taking taylor expansion of 1.0 in n 6.418 * [backup-simplify]: Simplify 1.0 into 1.0 6.418 * [taylor]: Taking taylor expansion of k in n 6.418 * [backup-simplify]: Simplify k into k 6.418 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.418 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.418 * [taylor]: Taking taylor expansion of 2.0 in n 6.418 * [backup-simplify]: Simplify 2.0 into 2.0 6.418 * [taylor]: Taking taylor expansion of (* n PI) in n 6.418 * [taylor]: Taking taylor expansion of n in n 6.418 * [backup-simplify]: Simplify 0 into 0 6.418 * [backup-simplify]: Simplify 1 into 1 6.418 * [taylor]: Taking taylor expansion of PI in n 6.418 * [backup-simplify]: Simplify PI into PI 6.418 * [backup-simplify]: Simplify (* 0 PI) into 0 6.418 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.419 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.420 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.421 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.421 * [backup-simplify]: Simplify (- k) into (- k) 6.421 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.421 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 6.422 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.423 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 6.423 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 6.424 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) in n 6.424 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 6.424 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.424 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.424 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 6.424 * [taylor]: Taking taylor expansion of 0.25 in n 6.424 * [backup-simplify]: Simplify 0.25 into 0.25 6.424 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.424 * [taylor]: Taking taylor expansion of 1.0 in n 6.424 * [backup-simplify]: Simplify 1.0 into 1.0 6.424 * [taylor]: Taking taylor expansion of k in n 6.424 * [backup-simplify]: Simplify k into k 6.424 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.424 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.424 * [taylor]: Taking taylor expansion of 2.0 in n 6.424 * [backup-simplify]: Simplify 2.0 into 2.0 6.424 * [taylor]: Taking taylor expansion of (* n PI) in n 6.424 * [taylor]: Taking taylor expansion of n in n 6.424 * [backup-simplify]: Simplify 0 into 0 6.424 * [backup-simplify]: Simplify 1 into 1 6.424 * [taylor]: Taking taylor expansion of PI in n 6.424 * [backup-simplify]: Simplify PI into PI 6.424 * [backup-simplify]: Simplify (* 0 PI) into 0 6.425 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.425 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.426 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.427 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.427 * [backup-simplify]: Simplify (- k) into (- k) 6.427 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.427 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 6.428 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.429 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 6.430 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 6.431 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) into (pow (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2) 6.431 * [taylor]: Taking taylor expansion of (pow (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2) in k 6.431 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 6.431 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 6.431 * [taylor]: Taking taylor expansion of 0.25 in k 6.431 * [backup-simplify]: Simplify 0.25 into 0.25 6.431 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 6.431 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.431 * [taylor]: Taking taylor expansion of 1.0 in k 6.431 * [backup-simplify]: Simplify 1.0 into 1.0 6.431 * [taylor]: Taking taylor expansion of k in k 6.431 * [backup-simplify]: Simplify 0 into 0 6.431 * [backup-simplify]: Simplify 1 into 1 6.431 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 6.431 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.431 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.431 * [taylor]: Taking taylor expansion of 2.0 in k 6.431 * [backup-simplify]: Simplify 2.0 into 2.0 6.431 * [taylor]: Taking taylor expansion of PI in k 6.431 * [backup-simplify]: Simplify PI into PI 6.432 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.432 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.432 * [taylor]: Taking taylor expansion of (log n) in k 6.432 * [taylor]: Taking taylor expansion of n in k 6.432 * [backup-simplify]: Simplify n into n 6.433 * [backup-simplify]: Simplify (log n) into (log n) 6.433 * [backup-simplify]: Simplify (- 0) into 0 6.433 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.434 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 6.435 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 6.435 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 6.436 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 6.438 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) 6.440 * [backup-simplify]: Simplify (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) into (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) 6.441 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 6.442 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 6.444 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.444 * [backup-simplify]: Simplify (- 0) into 0 6.444 * [backup-simplify]: Simplify (+ 0 0) into 0 6.445 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 6.446 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.452 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 6.454 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.457 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))) into 0 6.457 * [taylor]: Taking taylor expansion of 0 in k 6.457 * [backup-simplify]: Simplify 0 into 0 6.457 * [backup-simplify]: Simplify 0 into 0 6.458 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.460 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.461 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 6.461 * [backup-simplify]: Simplify (+ 0 0) into 0 6.461 * [backup-simplify]: Simplify (- 1) into -1 6.462 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.463 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 6.465 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 6.467 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 6.472 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.5 (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n))) (* 0.5 (* (log (* 2.0 PI)) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))))) 6.475 * [backup-simplify]: Simplify (- (+ (* 0.5 (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n))) (* 0.5 (* (log (* 2.0 PI)) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))))) into (- (+ (* 0.5 (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n))) (* 0.5 (* (log (* 2.0 PI)) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))))) 6.476 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 6.476 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 6.478 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 6.479 * [backup-simplify]: Simplify (- 0) into 0 6.479 * [backup-simplify]: Simplify (+ 0 0) into 0 6.479 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 6.480 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.481 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.483 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.485 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))))) into 0 6.485 * [taylor]: Taking taylor expansion of 0 in k 6.485 * [backup-simplify]: Simplify 0 into 0 6.485 * [backup-simplify]: Simplify 0 into 0 6.485 * [backup-simplify]: Simplify 0 into 0 6.485 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.487 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 6.488 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 6.489 * [backup-simplify]: Simplify (+ 0 0) into 0 6.489 * [backup-simplify]: Simplify (- 0) into 0 6.489 * [backup-simplify]: Simplify (+ 0 0) into 0 6.490 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.492 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 6.494 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 6.514 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (* (+ (* 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)))))) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* (* (+ (* 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))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) into (+ (* 0.125 (* (pow (log (* 2.0 PI)) 2) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))) (+ (* 0.25 (* (log (* 2.0 PI)) (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n)))) (* 0.125 (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (pow (log n) 2))))) 6.522 * [backup-simplify]: Simplify (+ (* 0.125 (* (pow (log (* 2.0 PI)) 2) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))) (+ (* 0.25 (* (log (* 2.0 PI)) (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n)))) (* 0.125 (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (pow (log n) 2))))) into (+ (* 0.125 (* (pow (log (* 2.0 PI)) 2) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))) (+ (* 0.25 (* (log (* 2.0 PI)) (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n)))) (* 0.125 (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (pow (log n) 2))))) 6.531 * [backup-simplify]: Simplify (+ (* (+ (* 0.125 (* (pow (log (* 2.0 PI)) 2) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))) (+ (* 0.25 (* (log (* 2.0 PI)) (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n)))) (* 0.125 (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (pow (log n) 2))))) (pow (* k 1) 2)) (+ (* (- (+ (* 0.5 (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n))) (* 0.5 (* (log (* 2.0 PI)) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))))) (* k 1)) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))) into (- (+ (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n))))) (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2)))) (* 0.125 (* (pow k 2) (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (pow (log n) 2))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2)))) (* 0.5 (* k (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n)))))) 6.532 * [backup-simplify]: Simplify (* (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2))) into (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) 6.532 * [approximate]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) in (n k) around 0 6.532 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) in k 6.532 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 6.532 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 6.532 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 6.532 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 6.532 * [taylor]: Taking taylor expansion of 0.25 in k 6.532 * [backup-simplify]: Simplify 0.25 into 0.25 6.532 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.532 * [taylor]: Taking taylor expansion of 1.0 in k 6.533 * [backup-simplify]: Simplify 1.0 into 1.0 6.533 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.533 * [taylor]: Taking taylor expansion of k in k 6.533 * [backup-simplify]: Simplify 0 into 0 6.533 * [backup-simplify]: Simplify 1 into 1 6.533 * [backup-simplify]: Simplify (/ 1 1) into 1 6.533 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 6.533 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 6.533 * [taylor]: Taking taylor expansion of 2.0 in k 6.533 * [backup-simplify]: Simplify 2.0 into 2.0 6.533 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.533 * [taylor]: Taking taylor expansion of PI in k 6.533 * [backup-simplify]: Simplify PI into PI 6.533 * [taylor]: Taking taylor expansion of n in k 6.533 * [backup-simplify]: Simplify n into n 6.533 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.533 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 6.533 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 6.533 * [backup-simplify]: Simplify (- 1) into -1 6.534 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.534 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 6.534 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 6.534 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 6.534 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) in n 6.534 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 6.534 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.534 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.534 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 6.534 * [taylor]: Taking taylor expansion of 0.25 in n 6.535 * [backup-simplify]: Simplify 0.25 into 0.25 6.535 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.535 * [taylor]: Taking taylor expansion of 1.0 in n 6.535 * [backup-simplify]: Simplify 1.0 into 1.0 6.535 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.535 * [taylor]: Taking taylor expansion of k in n 6.535 * [backup-simplify]: Simplify k into k 6.535 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.535 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.535 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.535 * [taylor]: Taking taylor expansion of 2.0 in n 6.535 * [backup-simplify]: Simplify 2.0 into 2.0 6.535 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.535 * [taylor]: Taking taylor expansion of PI in n 6.535 * [backup-simplify]: Simplify PI into PI 6.535 * [taylor]: Taking taylor expansion of n in n 6.535 * [backup-simplify]: Simplify 0 into 0 6.535 * [backup-simplify]: Simplify 1 into 1 6.535 * [backup-simplify]: Simplify (/ PI 1) into PI 6.535 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.536 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.536 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.536 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.536 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 6.537 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.538 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 6.539 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.539 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) in n 6.539 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 6.539 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.539 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.539 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 6.539 * [taylor]: Taking taylor expansion of 0.25 in n 6.539 * [backup-simplify]: Simplify 0.25 into 0.25 6.539 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.539 * [taylor]: Taking taylor expansion of 1.0 in n 6.539 * [backup-simplify]: Simplify 1.0 into 1.0 6.539 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.539 * [taylor]: Taking taylor expansion of k in n 6.539 * [backup-simplify]: Simplify k into k 6.539 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.539 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.539 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.539 * [taylor]: Taking taylor expansion of 2.0 in n 6.539 * [backup-simplify]: Simplify 2.0 into 2.0 6.539 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.539 * [taylor]: Taking taylor expansion of PI in n 6.539 * [backup-simplify]: Simplify PI into PI 6.539 * [taylor]: Taking taylor expansion of n in n 6.539 * [backup-simplify]: Simplify 0 into 0 6.539 * [backup-simplify]: Simplify 1 into 1 6.540 * [backup-simplify]: Simplify (/ PI 1) into PI 6.540 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.540 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.541 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.541 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.541 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 6.542 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.542 * [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)))) 6.543 * [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))))) 6.545 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2) 6.545 * [taylor]: Taking taylor expansion of (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2) in k 6.545 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 6.545 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 6.545 * [taylor]: Taking taylor expansion of 0.25 in k 6.545 * [backup-simplify]: Simplify 0.25 into 0.25 6.545 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 6.545 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 6.545 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.545 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.545 * [taylor]: Taking taylor expansion of 2.0 in k 6.545 * [backup-simplify]: Simplify 2.0 into 2.0 6.545 * [taylor]: Taking taylor expansion of PI in k 6.545 * [backup-simplify]: Simplify PI into PI 6.545 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.546 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.546 * [taylor]: Taking taylor expansion of (log n) in k 6.546 * [taylor]: Taking taylor expansion of n in k 6.546 * [backup-simplify]: Simplify n into n 6.546 * [backup-simplify]: Simplify (log n) into (log n) 6.546 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.546 * [taylor]: Taking taylor expansion of 1.0 in k 6.546 * [backup-simplify]: Simplify 1.0 into 1.0 6.546 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.546 * [taylor]: Taking taylor expansion of k in k 6.546 * [backup-simplify]: Simplify 0 into 0 6.546 * [backup-simplify]: Simplify 1 into 1 6.546 * [backup-simplify]: Simplify (/ 1 1) into 1 6.546 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.547 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 6.547 * [backup-simplify]: Simplify (- 1) into -1 6.548 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.548 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 6.549 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 6.550 * [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))))) 6.551 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2) 6.552 * [backup-simplify]: Simplify (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2) into (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2) 6.553 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.553 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.554 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.554 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.555 * [backup-simplify]: Simplify (- 0) into 0 6.555 * [backup-simplify]: Simplify (+ 0 0) into 0 6.555 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 6.557 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.558 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 6.563 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.564 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0) (* 0 (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 6.564 * [taylor]: Taking taylor expansion of 0 in k 6.564 * [backup-simplify]: Simplify 0 into 0 6.564 * [backup-simplify]: Simplify 0 into 0 6.566 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0) (* 0 (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 6.566 * [backup-simplify]: Simplify 0 into 0 6.566 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.567 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.569 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 6.569 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.569 * [backup-simplify]: Simplify (- 0) into 0 6.570 * [backup-simplify]: Simplify (+ 0 0) into 0 6.570 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 6.571 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.572 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 6.573 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.575 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0 6.575 * [taylor]: Taking taylor expansion of 0 in k 6.575 * [backup-simplify]: Simplify 0 into 0 6.575 * [backup-simplify]: Simplify 0 into 0 6.575 * [backup-simplify]: Simplify 0 into 0 6.578 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0 6.578 * [backup-simplify]: Simplify 0 into 0 6.579 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.581 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.587 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 6.587 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.588 * [backup-simplify]: Simplify (- 0) into 0 6.588 * [backup-simplify]: Simplify (+ 0 0) into 0 6.589 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 6.591 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.592 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 6.594 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 6.596 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))) into 0 6.596 * [taylor]: Taking taylor expansion of 0 in k 6.596 * [backup-simplify]: Simplify 0 into 0 6.596 * [backup-simplify]: Simplify 0 into 0 6.597 * [backup-simplify]: Simplify (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) 2) into (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 2) 6.598 * [backup-simplify]: Simplify (* (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2))) into (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) 6.598 * [approximate]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) in (n k) around 0 6.598 * [taylor]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) in k 6.598 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 6.598 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 6.598 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 6.598 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 6.598 * [taylor]: Taking taylor expansion of 0.25 in k 6.598 * [backup-simplify]: Simplify 0.25 into 0.25 6.598 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.598 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.598 * [taylor]: Taking taylor expansion of k in k 6.598 * [backup-simplify]: Simplify 0 into 0 6.598 * [backup-simplify]: Simplify 1 into 1 6.598 * [backup-simplify]: Simplify (/ 1 1) into 1 6.598 * [taylor]: Taking taylor expansion of 1.0 in k 6.598 * [backup-simplify]: Simplify 1.0 into 1.0 6.598 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 6.598 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 6.599 * [taylor]: Taking taylor expansion of -2.0 in k 6.599 * [backup-simplify]: Simplify -2.0 into -2.0 6.599 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.599 * [taylor]: Taking taylor expansion of PI in k 6.599 * [backup-simplify]: Simplify PI into PI 6.599 * [taylor]: Taking taylor expansion of n in k 6.599 * [backup-simplify]: Simplify n into n 6.599 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.599 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 6.599 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 6.599 * [backup-simplify]: Simplify (+ 1 0) into 1 6.599 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 6.599 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 6.600 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 6.600 * [taylor]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) in n 6.600 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 6.600 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.600 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.600 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 6.600 * [taylor]: Taking taylor expansion of 0.25 in n 6.600 * [backup-simplify]: Simplify 0.25 into 0.25 6.600 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.600 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.600 * [taylor]: Taking taylor expansion of k in n 6.600 * [backup-simplify]: Simplify k into k 6.600 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.600 * [taylor]: Taking taylor expansion of 1.0 in n 6.600 * [backup-simplify]: Simplify 1.0 into 1.0 6.600 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.600 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.600 * [taylor]: Taking taylor expansion of -2.0 in n 6.600 * [backup-simplify]: Simplify -2.0 into -2.0 6.600 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.600 * [taylor]: Taking taylor expansion of PI in n 6.600 * [backup-simplify]: Simplify PI into PI 6.600 * [taylor]: Taking taylor expansion of n in n 6.600 * [backup-simplify]: Simplify 0 into 0 6.600 * [backup-simplify]: Simplify 1 into 1 6.600 * [backup-simplify]: Simplify (/ PI 1) into PI 6.601 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.601 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.601 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.601 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 6.602 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.603 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 6.604 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.604 * [taylor]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) in n 6.604 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 6.604 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.604 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.604 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 6.604 * [taylor]: Taking taylor expansion of 0.25 in n 6.604 * [backup-simplify]: Simplify 0.25 into 0.25 6.604 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.604 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.604 * [taylor]: Taking taylor expansion of k in n 6.604 * [backup-simplify]: Simplify k into k 6.604 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.604 * [taylor]: Taking taylor expansion of 1.0 in n 6.604 * [backup-simplify]: Simplify 1.0 into 1.0 6.604 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.604 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.604 * [taylor]: Taking taylor expansion of -2.0 in n 6.604 * [backup-simplify]: Simplify -2.0 into -2.0 6.604 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.604 * [taylor]: Taking taylor expansion of PI in n 6.604 * [backup-simplify]: Simplify PI into PI 6.604 * [taylor]: Taking taylor expansion of n in n 6.604 * [backup-simplify]: Simplify 0 into 0 6.604 * [backup-simplify]: Simplify 1 into 1 6.605 * [backup-simplify]: Simplify (/ PI 1) into PI 6.605 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.606 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.606 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.606 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 6.607 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.608 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 6.608 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.610 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (pow (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2) 6.610 * [taylor]: Taking taylor expansion of (pow (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2) in k 6.610 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 6.610 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 6.610 * [taylor]: Taking taylor expansion of 0.25 in k 6.610 * [backup-simplify]: Simplify 0.25 into 0.25 6.610 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 6.610 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.610 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.610 * [taylor]: Taking taylor expansion of k in k 6.610 * [backup-simplify]: Simplify 0 into 0 6.610 * [backup-simplify]: Simplify 1 into 1 6.611 * [backup-simplify]: Simplify (/ 1 1) into 1 6.611 * [taylor]: Taking taylor expansion of 1.0 in k 6.611 * [backup-simplify]: Simplify 1.0 into 1.0 6.611 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 6.611 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 6.611 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 6.611 * [taylor]: Taking taylor expansion of -2.0 in k 6.611 * [backup-simplify]: Simplify -2.0 into -2.0 6.611 * [taylor]: Taking taylor expansion of PI in k 6.611 * [backup-simplify]: Simplify PI into PI 6.611 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.612 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.612 * [taylor]: Taking taylor expansion of (log n) in k 6.612 * [taylor]: Taking taylor expansion of n in k 6.612 * [backup-simplify]: Simplify n into n 6.612 * [backup-simplify]: Simplify (log n) into (log n) 6.612 * [backup-simplify]: Simplify (+ 1 0) into 1 6.612 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.613 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 6.613 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 6.614 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 6.615 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.616 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (pow (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2) 6.617 * [backup-simplify]: Simplify (pow (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2) into (pow (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2) 6.619 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.619 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 6.621 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 6.621 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.621 * [backup-simplify]: Simplify (+ 0 0) into 0 6.622 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 6.623 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.624 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 6.626 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.628 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0) (* 0 (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 6.629 * [taylor]: Taking taylor expansion of 0 in k 6.629 * [backup-simplify]: Simplify 0 into 0 6.629 * [backup-simplify]: Simplify 0 into 0 6.631 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0) (* 0 (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 6.631 * [backup-simplify]: Simplify 0 into 0 6.632 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.633 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.636 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 6.636 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.636 * [backup-simplify]: Simplify (+ 0 0) into 0 6.637 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 6.639 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.640 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 6.642 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.644 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) into 0 6.644 * [taylor]: Taking taylor expansion of 0 in k 6.645 * [backup-simplify]: Simplify 0 into 0 6.645 * [backup-simplify]: Simplify 0 into 0 6.645 * [backup-simplify]: Simplify 0 into 0 6.646 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) into 0 6.647 * [backup-simplify]: Simplify 0 into 0 6.647 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.648 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.655 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 6.655 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.655 * [backup-simplify]: Simplify (+ 0 0) into 0 6.657 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 6.658 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.660 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 6.663 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 6.667 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))))) into 0 6.667 * [taylor]: Taking taylor expansion of 0 in k 6.667 * [backup-simplify]: Simplify 0 into 0 6.667 * [backup-simplify]: Simplify 0 into 0 6.668 * [backup-simplify]: Simplify (pow (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) 2) into (pow (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 2) 6.669 * * * [progress]: simplifying candidates 6.683 * [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) (/ (/ 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(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))))) (- (+ (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n))))) (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2)))) (* 0.125 (* (pow k 2) (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (pow (log n) 2))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2)))) (* 0.5 (* k (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n)))))) (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 2) (pow (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 2) 6.691 * * [simplify]: Extracting # 0 : cost 0 6.691 * * [simplify]: Extracting # 1 : cost 0 6.692 * * [simplify]: Extracting # 2 : cost 0 6.692 * * [simplify]: Extracting # 3 : cost 0 6.693 * * [simplify]: Extracting # 4 : cost 0 6.693 * * [simplify]: Extracting # 5 : cost 0 6.694 * * [simplify]: Extracting # 6 : cost 0 6.694 * * [simplify]: Extracting # 7 : cost 0 6.695 * * [simplify]: Extracting # 8 : cost 0 6.696 * * [simplify]: Extracting # 9 : cost 0 6.696 * * [simplify]: Extracting # 10 : cost 0 6.697 * * [simplify]: Extracting # 11 : cost 0 6.697 * * [simplify]: Extracting # 12 : cost 0 6.698 * * [simplify]: Extracting # 13 : cost 0 6.699 * * [simplify]: Extracting # 14 : cost 0 6.699 * * [simplify]: Extracting # 15 : cost 0 6.700 * * [simplify]: iteration 0 : 373 enodes (cost 5564 ) 6.811 * * [simplify]: Extracting # 0 : cost 0 6.813 * * [simplify]: Extracting # 1 : cost 0 6.816 * * [simplify]: Extracting # 2 : cost 0 6.820 * * [simplify]: Extracting # 3 : cost 0 6.823 * * [simplify]: Extracting # 4 : cost 0 6.827 * * [simplify]: Extracting # 5 : cost 0 6.831 * * [simplify]: iteration 1 : 1101 enodes (cost 4679 ) 7.678 * * [simplify]: Extracting # 0 : cost 0 7.691 * * [simplify]: Extracting # 1 : cost 0 7.698 * * [simplify]: Extracting # 2 : cost 0 7.704 * * [simplify]: Extracting # 3 : cost 0 7.715 * * [simplify]: Extracting # 4 : cost 0 7.721 * * [simplify]: Extracting # 5 : cost 0 7.727 * * [simplify]: iteration 2 : 4713 enodes (cost 4193 ) 9.356 * * [simplify]: Extracting # 0 : cost 0 9.363 * * [simplify]: Extracting # 1 : cost 0 9.373 * * [simplify]: Extracting # 2 : cost 0 9.380 * * [simplify]: Extracting # 3 : cost 0 9.386 * * [simplify]: iteration done: 5000 enodes (cost 4156 ) 9.388 * [simplify]: Simplified to: (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (/ (/ (- 1.0 k) 2.0) 2) (/ (/ (- 1.0 k) 2.0) 2) (/ (/ (- 1.0 k) 2.0) 2) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) 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(* (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 (* (* 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 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2) (cbrt 2)))) (pow (* 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(cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* PI (* 2.0 n)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 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 (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (+ (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 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 (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* PI (* 2.0 n)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* PI (* 2.0 n)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* 2.0 PI) n) (- 1.0 k)) (* PI (* 2.0 n)) (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 (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 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) 2) (* (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)) (* (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)) (* (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)) (* (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)) (* (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)) (* (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)) (* (log (* (* 2.0 PI) 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))) (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (* 2 (/ (/ 1.0 2.0) 2))) (pow (* (* 2.0 PI) n) (* 2 (/ (/ k 2.0) 2))) (pow (* 2.0 PI) (* 2 (/ (/ (- 1.0 k) 2.0) 2))) (pow n (* 2 (/ (/ (- 1.0 k) 2.0) 2))) (pow (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (+ 3 1)) (* (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)) 1 (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)) (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))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 4))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 4))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 4))) (* (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) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* 2 (/ (/ (- 1.0 k) 2.0) 2)) (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (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 (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) 3) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 4)) 3) (* (pow 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)) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (pow (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) 3) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 4)) 3) (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2))) (* (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (- (+ (* (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (* 2.0 PI) n) 0.25)) 0.03125) (+ (* (* (log n) (* (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.25))) (* 0.0625 (pow k 2))) (+ (* (* (* 0.03125 (pow k 2)) (pow (log n) 2)) (pow (* (* 2.0 PI) n) 0.25)) (pow (* (* 2.0 PI) n) 0.25)))) (* (* k (+ (* (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.25)) (* (log n) (pow (* (* 2.0 PI) n) 0.25)))) 0.25)) (pow (pow (* (* 2.0 PI) n) 0.25) (- 1.0 k)) (pow (exp 0.25) (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))) (- (+ (* (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (* 2.0 PI) n) 0.25)) 0.03125) (+ (* (* (log n) (* (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.25))) (* 0.0625 (pow k 2))) (+ (* (* (* 0.03125 (pow k 2)) (pow (log n) 2)) (pow (* (* 2.0 PI) n) 0.25)) (pow (* (* 2.0 PI) n) 0.25)))) (* (* k (+ (* (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.25)) (* (log n) (pow (* (* 2.0 PI) n) 0.25)))) 0.25)) (pow (pow (* (* 2.0 PI) n) 0.25) (- 1.0 k)) (pow (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 (pow k 2)) (- (/ +nan.0 k) +nan.0))) (+ (+ (* (* (* 0.25 (pow k 2)) (* (log n) (pow (pow (* (* 2.0 PI) n) 0.25) 2))) (log (* 2.0 PI))) (pow (pow (* (* 2.0 PI) n) 0.25) 2)) (- (* (* 0.125 (pow k 2)) (+ (* (pow (pow (* (* 2.0 PI) n) 0.25) 2) (pow (log (* 2.0 PI)) 2)) (* (pow (pow (* (* 2.0 PI) n) 0.25) 2) (pow (log n) 2)))) (* (* k (+ (* (log (* 2.0 PI)) (pow (pow (* (* 2.0 PI) n) 0.25) 2)) (* (log n) (pow (pow (* (* 2.0 PI) n) 0.25) 2)))) 0.5))) (pow (pow (pow (* (* 2.0 PI) n) 0.25) (- 1.0 k)) 2) (pow (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 2) 9.395 * * * [progress]: adding candidates to table 10.659 * * [progress]: iteration 3 / 4 10.659 * * * [progress]: picking best candidate 10.682 * * * * [pick]: Picked # 10.682 * * * [progress]: localizing error 10.716 * * * [progress]: generating rewritten candidates 10.716 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 2) 10.764 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 2) 10.786 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1) 10.793 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 1) 10.813 * * * [progress]: generating series expansions 10.813 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 2) 10.814 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 10.814 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 10.814 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 10.814 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 10.814 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 10.814 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 10.814 * [taylor]: Taking taylor expansion of 0.5 in k 10.814 * [backup-simplify]: Simplify 0.5 into 0.5 10.814 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 10.814 * [taylor]: Taking taylor expansion of 1.0 in k 10.814 * [backup-simplify]: Simplify 1.0 into 1.0 10.814 * [taylor]: Taking taylor expansion of k in k 10.814 * [backup-simplify]: Simplify 0 into 0 10.814 * [backup-simplify]: Simplify 1 into 1 10.814 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 10.814 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 10.814 * [taylor]: Taking taylor expansion of 2.0 in k 10.814 * [backup-simplify]: Simplify 2.0 into 2.0 10.814 * [taylor]: Taking taylor expansion of (* n PI) in k 10.814 * [taylor]: Taking taylor expansion of n in k 10.814 * [backup-simplify]: Simplify n into n 10.814 * [taylor]: Taking taylor expansion of PI in k 10.814 * [backup-simplify]: Simplify PI into PI 10.814 * [backup-simplify]: Simplify (* n PI) into (* n PI) 10.814 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 10.814 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 10.815 * [backup-simplify]: Simplify (- 0) into 0 10.815 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 10.816 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 10.816 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 10.816 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 10.816 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 10.816 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 10.816 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 10.816 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 10.816 * [taylor]: Taking taylor expansion of 0.5 in n 10.816 * [backup-simplify]: Simplify 0.5 into 0.5 10.816 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 10.816 * [taylor]: Taking taylor expansion of 1.0 in n 10.816 * [backup-simplify]: Simplify 1.0 into 1.0 10.816 * [taylor]: Taking taylor expansion of k in n 10.816 * [backup-simplify]: Simplify k into k 10.816 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 10.816 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 10.816 * [taylor]: Taking taylor expansion of 2.0 in n 10.816 * [backup-simplify]: Simplify 2.0 into 2.0 10.816 * [taylor]: Taking taylor expansion of (* n PI) in n 10.816 * [taylor]: Taking taylor expansion of n in n 10.816 * [backup-simplify]: Simplify 0 into 0 10.816 * [backup-simplify]: Simplify 1 into 1 10.816 * [taylor]: Taking taylor expansion of PI in n 10.816 * [backup-simplify]: Simplify PI into PI 10.817 * [backup-simplify]: Simplify (* 0 PI) into 0 10.817 * [backup-simplify]: Simplify (* 2.0 0) into 0 10.819 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.821 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 10.822 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.822 * [backup-simplify]: Simplify (- k) into (- k) 10.822 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 10.822 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 10.823 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.824 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 10.826 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 10.826 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 10.826 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 10.826 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 10.826 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 10.826 * [taylor]: Taking taylor expansion of 0.5 in n 10.826 * [backup-simplify]: Simplify 0.5 into 0.5 10.826 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 10.826 * [taylor]: Taking taylor expansion of 1.0 in n 10.826 * [backup-simplify]: Simplify 1.0 into 1.0 10.826 * [taylor]: Taking taylor expansion of k in n 10.826 * [backup-simplify]: Simplify k into k 10.826 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 10.826 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 10.826 * [taylor]: Taking taylor expansion of 2.0 in n 10.826 * [backup-simplify]: Simplify 2.0 into 2.0 10.826 * [taylor]: Taking taylor expansion of (* n PI) in n 10.826 * [taylor]: Taking taylor expansion of n in n 10.826 * [backup-simplify]: Simplify 0 into 0 10.826 * [backup-simplify]: Simplify 1 into 1 10.826 * [taylor]: Taking taylor expansion of PI in n 10.826 * [backup-simplify]: Simplify PI into PI 10.827 * [backup-simplify]: Simplify (* 0 PI) into 0 10.827 * [backup-simplify]: Simplify (* 2.0 0) into 0 10.828 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.830 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 10.831 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.831 * [backup-simplify]: Simplify (- k) into (- k) 10.831 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 10.831 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 10.832 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.833 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 10.834 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 10.834 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 10.834 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 10.834 * [taylor]: Taking taylor expansion of 0.5 in k 10.834 * [backup-simplify]: Simplify 0.5 into 0.5 10.834 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 10.835 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 10.835 * [taylor]: Taking taylor expansion of 1.0 in k 10.835 * [backup-simplify]: Simplify 1.0 into 1.0 10.835 * [taylor]: Taking taylor expansion of k in k 10.835 * [backup-simplify]: Simplify 0 into 0 10.835 * [backup-simplify]: Simplify 1 into 1 10.835 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 10.835 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 10.835 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 10.835 * [taylor]: Taking taylor expansion of 2.0 in k 10.835 * [backup-simplify]: Simplify 2.0 into 2.0 10.835 * [taylor]: Taking taylor expansion of PI in k 10.835 * [backup-simplify]: Simplify PI into PI 10.835 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.836 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.836 * [taylor]: Taking taylor expansion of (log n) in k 10.836 * [taylor]: Taking taylor expansion of n in k 10.836 * [backup-simplify]: Simplify n into n 10.836 * [backup-simplify]: Simplify (log n) into (log n) 10.837 * [backup-simplify]: Simplify (- 0) into 0 10.837 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 10.838 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 10.839 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 10.840 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 10.841 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 10.842 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 10.843 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 10.844 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 10.846 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 10.846 * [backup-simplify]: Simplify (- 0) into 0 10.847 * [backup-simplify]: Simplify (+ 0 0) into 0 10.847 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 10.848 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.849 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 10.851 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 10.851 * [taylor]: Taking taylor expansion of 0 in k 10.851 * [backup-simplify]: Simplify 0 into 0 10.851 * [backup-simplify]: Simplify 0 into 0 10.852 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 10.854 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 10.854 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 10.861 * [backup-simplify]: Simplify (+ 0 0) into 0 10.862 * [backup-simplify]: Simplify (- 1) into -1 10.862 * [backup-simplify]: Simplify (+ 0 -1) into -1 10.863 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 10.866 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 10.869 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 10.872 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 10.873 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 10.875 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 10.879 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 10.879 * [backup-simplify]: Simplify (- 0) into 0 10.880 * [backup-simplify]: Simplify (+ 0 0) into 0 10.881 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 10.882 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.884 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 10.887 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 10.887 * [taylor]: Taking taylor expansion of 0 in k 10.887 * [backup-simplify]: Simplify 0 into 0 10.887 * [backup-simplify]: Simplify 0 into 0 10.887 * [backup-simplify]: Simplify 0 into 0 10.889 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 10.893 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 10.895 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 10.896 * [backup-simplify]: Simplify (+ 0 0) into 0 10.896 * [backup-simplify]: Simplify (- 0) into 0 10.897 * [backup-simplify]: Simplify (+ 0 0) into 0 10.899 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 10.902 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 10.907 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 10.912 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 10.924 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 10.925 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 10.925 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 10.925 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 10.925 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 10.925 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 10.925 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 10.925 * [taylor]: Taking taylor expansion of 0.5 in k 10.925 * [backup-simplify]: Simplify 0.5 into 0.5 10.925 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 10.925 * [taylor]: Taking taylor expansion of 1.0 in k 10.925 * [backup-simplify]: Simplify 1.0 into 1.0 10.925 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.925 * [taylor]: Taking taylor expansion of k in k 10.925 * [backup-simplify]: Simplify 0 into 0 10.925 * [backup-simplify]: Simplify 1 into 1 10.926 * [backup-simplify]: Simplify (/ 1 1) into 1 10.926 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 10.926 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 10.926 * [taylor]: Taking taylor expansion of 2.0 in k 10.926 * [backup-simplify]: Simplify 2.0 into 2.0 10.926 * [taylor]: Taking taylor expansion of (/ PI n) in k 10.926 * [taylor]: Taking taylor expansion of PI in k 10.926 * [backup-simplify]: Simplify PI into PI 10.926 * [taylor]: Taking taylor expansion of n in k 10.926 * [backup-simplify]: Simplify n into n 10.926 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 10.926 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 10.926 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 10.927 * [backup-simplify]: Simplify (- 1) into -1 10.927 * [backup-simplify]: Simplify (+ 0 -1) into -1 10.928 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 10.928 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 10.928 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 10.928 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 10.928 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 10.928 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 10.928 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 10.928 * [taylor]: Taking taylor expansion of 0.5 in n 10.928 * [backup-simplify]: Simplify 0.5 into 0.5 10.928 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 10.928 * [taylor]: Taking taylor expansion of 1.0 in n 10.928 * [backup-simplify]: Simplify 1.0 into 1.0 10.928 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.929 * [taylor]: Taking taylor expansion of k in n 10.929 * [backup-simplify]: Simplify k into k 10.929 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.929 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 10.929 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 10.929 * [taylor]: Taking taylor expansion of 2.0 in n 10.929 * [backup-simplify]: Simplify 2.0 into 2.0 10.929 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.929 * [taylor]: Taking taylor expansion of PI in n 10.929 * [backup-simplify]: Simplify PI into PI 10.929 * [taylor]: Taking taylor expansion of n in n 10.929 * [backup-simplify]: Simplify 0 into 0 10.929 * [backup-simplify]: Simplify 1 into 1 10.929 * [backup-simplify]: Simplify (/ PI 1) into PI 10.930 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.931 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.931 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 10.931 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 10.931 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 10.933 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.934 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 10.935 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 10.936 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 10.936 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 10.936 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 10.936 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 10.936 * [taylor]: Taking taylor expansion of 0.5 in n 10.936 * [backup-simplify]: Simplify 0.5 into 0.5 10.936 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 10.936 * [taylor]: Taking taylor expansion of 1.0 in n 10.936 * [backup-simplify]: Simplify 1.0 into 1.0 10.936 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.936 * [taylor]: Taking taylor expansion of k in n 10.936 * [backup-simplify]: Simplify k into k 10.936 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.936 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 10.936 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 10.936 * [taylor]: Taking taylor expansion of 2.0 in n 10.936 * [backup-simplify]: Simplify 2.0 into 2.0 10.936 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.936 * [taylor]: Taking taylor expansion of PI in n 10.936 * [backup-simplify]: Simplify PI into PI 10.936 * [taylor]: Taking taylor expansion of n in n 10.936 * [backup-simplify]: Simplify 0 into 0 10.936 * [backup-simplify]: Simplify 1 into 1 10.937 * [backup-simplify]: Simplify (/ PI 1) into PI 10.937 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.938 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.938 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 10.939 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 10.939 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 10.940 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.942 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 10.943 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 10.943 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 10.944 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 10.944 * [taylor]: Taking taylor expansion of 0.5 in k 10.944 * [backup-simplify]: Simplify 0.5 into 0.5 10.944 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 10.944 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 10.944 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 10.944 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 10.944 * [taylor]: Taking taylor expansion of 2.0 in k 10.944 * [backup-simplify]: Simplify 2.0 into 2.0 10.944 * [taylor]: Taking taylor expansion of PI in k 10.944 * [backup-simplify]: Simplify PI into PI 10.944 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.945 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.946 * [taylor]: Taking taylor expansion of (log n) in k 10.946 * [taylor]: Taking taylor expansion of n in k 10.946 * [backup-simplify]: Simplify n into n 10.946 * [backup-simplify]: Simplify (log n) into (log n) 10.946 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 10.946 * [taylor]: Taking taylor expansion of 1.0 in k 10.946 * [backup-simplify]: Simplify 1.0 into 1.0 10.946 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.946 * [taylor]: Taking taylor expansion of k in k 10.946 * [backup-simplify]: Simplify 0 into 0 10.946 * [backup-simplify]: Simplify 1 into 1 10.946 * [backup-simplify]: Simplify (/ 1 1) into 1 10.946 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 10.948 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 10.948 * [backup-simplify]: Simplify (- 1) into -1 10.948 * [backup-simplify]: Simplify (+ 0 -1) into -1 10.950 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 10.951 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 10.952 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 10.954 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 10.955 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 10.956 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 10.958 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 10.958 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 10.958 * [backup-simplify]: Simplify (- 0) into 0 10.959 * [backup-simplify]: Simplify (+ 0 0) into 0 10.959 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 10.961 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.962 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 10.964 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 10.964 * [taylor]: Taking taylor expansion of 0 in k 10.964 * [backup-simplify]: Simplify 0 into 0 10.964 * [backup-simplify]: Simplify 0 into 0 10.964 * [backup-simplify]: Simplify 0 into 0 10.965 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.966 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 10.970 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 10.970 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.971 * [backup-simplify]: Simplify (- 0) into 0 10.971 * [backup-simplify]: Simplify (+ 0 0) into 0 10.972 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 10.974 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.975 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 10.978 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 10.978 * [taylor]: Taking taylor expansion of 0 in k 10.978 * [backup-simplify]: Simplify 0 into 0 10.978 * [backup-simplify]: Simplify 0 into 0 10.978 * [backup-simplify]: Simplify 0 into 0 10.978 * [backup-simplify]: Simplify 0 into 0 10.979 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.981 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 10.987 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 10.988 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.988 * [backup-simplify]: Simplify (- 0) into 0 10.988 * [backup-simplify]: Simplify (+ 0 0) into 0 10.989 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 10.990 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.991 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 10.995 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 10.995 * [taylor]: Taking taylor expansion of 0 in k 10.995 * [backup-simplify]: Simplify 0 into 0 10.995 * [backup-simplify]: Simplify 0 into 0 10.995 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 10.996 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 10.996 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 10.996 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 10.996 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 10.996 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 10.996 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 10.996 * [taylor]: Taking taylor expansion of 0.5 in k 10.996 * [backup-simplify]: Simplify 0.5 into 0.5 10.996 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 10.996 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.996 * [taylor]: Taking taylor expansion of k in k 10.996 * [backup-simplify]: Simplify 0 into 0 10.996 * [backup-simplify]: Simplify 1 into 1 10.996 * [backup-simplify]: Simplify (/ 1 1) into 1 10.997 * [taylor]: Taking taylor expansion of 1.0 in k 10.997 * [backup-simplify]: Simplify 1.0 into 1.0 10.997 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 10.997 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 10.997 * [taylor]: Taking taylor expansion of -2.0 in k 10.997 * [backup-simplify]: Simplify -2.0 into -2.0 10.997 * [taylor]: Taking taylor expansion of (/ PI n) in k 10.997 * [taylor]: Taking taylor expansion of PI in k 10.997 * [backup-simplify]: Simplify PI into PI 10.997 * [taylor]: Taking taylor expansion of n in k 10.997 * [backup-simplify]: Simplify n into n 10.997 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 10.997 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 10.997 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 10.997 * [backup-simplify]: Simplify (+ 1 0) into 1 10.997 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 10.997 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 10.998 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 10.998 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 10.998 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 10.998 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 10.998 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 10.998 * [taylor]: Taking taylor expansion of 0.5 in n 10.998 * [backup-simplify]: Simplify 0.5 into 0.5 10.998 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 10.998 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.998 * [taylor]: Taking taylor expansion of k in n 10.998 * [backup-simplify]: Simplify k into k 10.998 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.998 * [taylor]: Taking taylor expansion of 1.0 in n 10.998 * [backup-simplify]: Simplify 1.0 into 1.0 10.998 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 10.998 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 10.998 * [taylor]: Taking taylor expansion of -2.0 in n 10.998 * [backup-simplify]: Simplify -2.0 into -2.0 10.998 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.998 * [taylor]: Taking taylor expansion of PI in n 10.998 * [backup-simplify]: Simplify PI into PI 10.998 * [taylor]: Taking taylor expansion of n in n 10.998 * [backup-simplify]: Simplify 0 into 0 10.998 * [backup-simplify]: Simplify 1 into 1 10.998 * [backup-simplify]: Simplify (/ PI 1) into PI 10.999 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 10.999 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 10.999 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 11.000 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 11.000 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.001 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 11.002 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 11.002 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 11.002 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 11.002 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 11.002 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 11.002 * [taylor]: Taking taylor expansion of 0.5 in n 11.002 * [backup-simplify]: Simplify 0.5 into 0.5 11.002 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 11.002 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.002 * [taylor]: Taking taylor expansion of k in n 11.002 * [backup-simplify]: Simplify k into k 11.002 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.002 * [taylor]: Taking taylor expansion of 1.0 in n 11.002 * [backup-simplify]: Simplify 1.0 into 1.0 11.002 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 11.002 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 11.002 * [taylor]: Taking taylor expansion of -2.0 in n 11.002 * [backup-simplify]: Simplify -2.0 into -2.0 11.002 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.002 * [taylor]: Taking taylor expansion of PI in n 11.002 * [backup-simplify]: Simplify PI into PI 11.002 * [taylor]: Taking taylor expansion of n in n 11.002 * [backup-simplify]: Simplify 0 into 0 11.002 * [backup-simplify]: Simplify 1 into 1 11.003 * [backup-simplify]: Simplify (/ PI 1) into PI 11.003 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.004 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 11.004 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 11.004 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 11.005 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.005 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 11.006 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 11.006 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 11.006 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 11.006 * [taylor]: Taking taylor expansion of 0.5 in k 11.006 * [backup-simplify]: Simplify 0.5 into 0.5 11.006 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 11.006 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 11.007 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.007 * [taylor]: Taking taylor expansion of k in k 11.007 * [backup-simplify]: Simplify 0 into 0 11.007 * [backup-simplify]: Simplify 1 into 1 11.007 * [backup-simplify]: Simplify (/ 1 1) into 1 11.007 * [taylor]: Taking taylor expansion of 1.0 in k 11.007 * [backup-simplify]: Simplify 1.0 into 1.0 11.007 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 11.007 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 11.007 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 11.007 * [taylor]: Taking taylor expansion of -2.0 in k 11.007 * [backup-simplify]: Simplify -2.0 into -2.0 11.007 * [taylor]: Taking taylor expansion of PI in k 11.007 * [backup-simplify]: Simplify PI into PI 11.007 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.008 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 11.008 * [taylor]: Taking taylor expansion of (log n) in k 11.008 * [taylor]: Taking taylor expansion of n in k 11.008 * [backup-simplify]: Simplify n into n 11.008 * [backup-simplify]: Simplify (log n) into (log n) 11.008 * [backup-simplify]: Simplify (+ 1 0) into 1 11.008 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 11.012 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 11.013 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 11.014 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 11.015 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 11.015 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 11.016 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.017 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 11.018 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 11.018 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.018 * [backup-simplify]: Simplify (+ 0 0) into 0 11.018 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 11.019 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.020 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 11.023 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.023 * [taylor]: Taking taylor expansion of 0 in k 11.023 * [backup-simplify]: Simplify 0 into 0 11.023 * [backup-simplify]: Simplify 0 into 0 11.023 * [backup-simplify]: Simplify 0 into 0 11.024 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.025 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.029 * [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 11.029 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.029 * [backup-simplify]: Simplify (+ 0 0) into 0 11.030 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 11.032 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.033 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 11.036 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.036 * [taylor]: Taking taylor expansion of 0 in k 11.036 * [backup-simplify]: Simplify 0 into 0 11.036 * [backup-simplify]: Simplify 0 into 0 11.036 * [backup-simplify]: Simplify 0 into 0 11.036 * [backup-simplify]: Simplify 0 into 0 11.037 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.038 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.045 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 11.045 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.045 * [backup-simplify]: Simplify (+ 0 0) into 0 11.047 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 11.048 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.049 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 11.051 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 11.051 * [taylor]: Taking taylor expansion of 0 in k 11.051 * [backup-simplify]: Simplify 0 into 0 11.051 * [backup-simplify]: Simplify 0 into 0 11.052 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 11.052 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 2) 11.052 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 11.052 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 11.052 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 11.052 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 11.052 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 11.052 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 11.052 * [taylor]: Taking taylor expansion of 0.5 in k 11.052 * [backup-simplify]: Simplify 0.5 into 0.5 11.052 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 11.052 * [taylor]: Taking taylor expansion of 1.0 in k 11.052 * [backup-simplify]: Simplify 1.0 into 1.0 11.052 * [taylor]: Taking taylor expansion of k in k 11.052 * [backup-simplify]: Simplify 0 into 0 11.053 * [backup-simplify]: Simplify 1 into 1 11.053 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 11.053 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 11.053 * [taylor]: Taking taylor expansion of 2.0 in k 11.053 * [backup-simplify]: Simplify 2.0 into 2.0 11.053 * [taylor]: Taking taylor expansion of (* n PI) in k 11.053 * [taylor]: Taking taylor expansion of n in k 11.053 * [backup-simplify]: Simplify n into n 11.053 * [taylor]: Taking taylor expansion of PI in k 11.053 * [backup-simplify]: Simplify PI into PI 11.053 * [backup-simplify]: Simplify (* n PI) into (* n PI) 11.053 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 11.053 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 11.053 * [backup-simplify]: Simplify (- 0) into 0 11.053 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 11.054 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 11.054 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 11.054 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 11.054 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 11.054 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 11.054 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 11.054 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 11.054 * [taylor]: Taking taylor expansion of 0.5 in n 11.054 * [backup-simplify]: Simplify 0.5 into 0.5 11.054 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 11.054 * [taylor]: Taking taylor expansion of 1.0 in n 11.054 * [backup-simplify]: Simplify 1.0 into 1.0 11.054 * [taylor]: Taking taylor expansion of k in n 11.054 * [backup-simplify]: Simplify k into k 11.054 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 11.054 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 11.054 * [taylor]: Taking taylor expansion of 2.0 in n 11.054 * [backup-simplify]: Simplify 2.0 into 2.0 11.054 * [taylor]: Taking taylor expansion of (* n PI) in n 11.054 * [taylor]: Taking taylor expansion of n in n 11.054 * [backup-simplify]: Simplify 0 into 0 11.054 * [backup-simplify]: Simplify 1 into 1 11.054 * [taylor]: Taking taylor expansion of PI in n 11.054 * [backup-simplify]: Simplify PI into PI 11.054 * [backup-simplify]: Simplify (* 0 PI) into 0 11.055 * [backup-simplify]: Simplify (* 2.0 0) into 0 11.056 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.057 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 11.057 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.057 * [backup-simplify]: Simplify (- k) into (- k) 11.057 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 11.058 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 11.058 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.059 * [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)))) 11.060 * [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))))) 11.060 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 11.060 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 11.060 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 11.060 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 11.060 * [taylor]: Taking taylor expansion of 0.5 in n 11.060 * [backup-simplify]: Simplify 0.5 into 0.5 11.060 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 11.060 * [taylor]: Taking taylor expansion of 1.0 in n 11.060 * [backup-simplify]: Simplify 1.0 into 1.0 11.060 * [taylor]: Taking taylor expansion of k in n 11.060 * [backup-simplify]: Simplify k into k 11.060 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 11.060 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 11.060 * [taylor]: Taking taylor expansion of 2.0 in n 11.060 * [backup-simplify]: Simplify 2.0 into 2.0 11.060 * [taylor]: Taking taylor expansion of (* n PI) in n 11.060 * [taylor]: Taking taylor expansion of n in n 11.060 * [backup-simplify]: Simplify 0 into 0 11.060 * [backup-simplify]: Simplify 1 into 1 11.060 * [taylor]: Taking taylor expansion of PI in n 11.060 * [backup-simplify]: Simplify PI into PI 11.061 * [backup-simplify]: Simplify (* 0 PI) into 0 11.061 * [backup-simplify]: Simplify (* 2.0 0) into 0 11.062 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.063 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 11.063 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.063 * [backup-simplify]: Simplify (- k) into (- k) 11.064 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 11.064 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 11.065 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.065 * [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)))) 11.066 * [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))))) 11.066 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 11.066 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 11.066 * [taylor]: Taking taylor expansion of 0.5 in k 11.066 * [backup-simplify]: Simplify 0.5 into 0.5 11.066 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 11.066 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 11.066 * [taylor]: Taking taylor expansion of 1.0 in k 11.066 * [backup-simplify]: Simplify 1.0 into 1.0 11.066 * [taylor]: Taking taylor expansion of k in k 11.066 * [backup-simplify]: Simplify 0 into 0 11.066 * [backup-simplify]: Simplify 1 into 1 11.066 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 11.066 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 11.066 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 11.066 * [taylor]: Taking taylor expansion of 2.0 in k 11.066 * [backup-simplify]: Simplify 2.0 into 2.0 11.066 * [taylor]: Taking taylor expansion of PI in k 11.066 * [backup-simplify]: Simplify PI into PI 11.067 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.067 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.067 * [taylor]: Taking taylor expansion of (log n) in k 11.067 * [taylor]: Taking taylor expansion of n in k 11.067 * [backup-simplify]: Simplify n into n 11.067 * [backup-simplify]: Simplify (log n) into (log n) 11.068 * [backup-simplify]: Simplify (- 0) into 0 11.068 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 11.069 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 11.069 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 11.070 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 11.071 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 11.071 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 11.072 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.073 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 11.074 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 11.074 * [backup-simplify]: Simplify (- 0) into 0 11.074 * [backup-simplify]: Simplify (+ 0 0) into 0 11.075 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 11.075 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.076 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 11.077 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.077 * [taylor]: Taking taylor expansion of 0 in k 11.078 * [backup-simplify]: Simplify 0 into 0 11.078 * [backup-simplify]: Simplify 0 into 0 11.078 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 11.079 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 11.080 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 11.080 * [backup-simplify]: Simplify (+ 0 0) into 0 11.081 * [backup-simplify]: Simplify (- 1) into -1 11.081 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.083 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 11.085 * [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)))) 11.089 * [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)))))) 11.092 * [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)))))) 11.093 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 11.094 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 11.098 * [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 11.099 * [backup-simplify]: Simplify (- 0) into 0 11.099 * [backup-simplify]: Simplify (+ 0 0) into 0 11.100 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 11.102 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.103 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 11.106 * [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 11.106 * [taylor]: Taking taylor expansion of 0 in k 11.106 * [backup-simplify]: Simplify 0 into 0 11.106 * [backup-simplify]: Simplify 0 into 0 11.106 * [backup-simplify]: Simplify 0 into 0 11.107 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.111 * [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 11.113 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 11.114 * [backup-simplify]: Simplify (+ 0 0) into 0 11.114 * [backup-simplify]: Simplify (- 0) into 0 11.114 * [backup-simplify]: Simplify (+ 0 0) into 0 11.116 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 11.119 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 11.124 * [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)))))) 11.129 * [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)))))) 11.145 * [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)))))) 11.146 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 11.146 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 11.147 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 11.147 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 11.147 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 11.147 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 11.147 * [taylor]: Taking taylor expansion of 0.5 in k 11.147 * [backup-simplify]: Simplify 0.5 into 0.5 11.147 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 11.147 * [taylor]: Taking taylor expansion of 1.0 in k 11.147 * [backup-simplify]: Simplify 1.0 into 1.0 11.147 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.147 * [taylor]: Taking taylor expansion of k in k 11.147 * [backup-simplify]: Simplify 0 into 0 11.147 * [backup-simplify]: Simplify 1 into 1 11.147 * [backup-simplify]: Simplify (/ 1 1) into 1 11.147 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 11.147 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 11.147 * [taylor]: Taking taylor expansion of 2.0 in k 11.148 * [backup-simplify]: Simplify 2.0 into 2.0 11.148 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.148 * [taylor]: Taking taylor expansion of PI in k 11.148 * [backup-simplify]: Simplify PI into PI 11.148 * [taylor]: Taking taylor expansion of n in k 11.148 * [backup-simplify]: Simplify n into n 11.148 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.148 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 11.148 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 11.148 * [backup-simplify]: Simplify (- 1) into -1 11.149 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.149 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 11.149 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 11.150 * [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))))) 11.150 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 11.150 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 11.150 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 11.150 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 11.150 * [taylor]: Taking taylor expansion of 0.5 in n 11.150 * [backup-simplify]: Simplify 0.5 into 0.5 11.150 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 11.150 * [taylor]: Taking taylor expansion of 1.0 in n 11.150 * [backup-simplify]: Simplify 1.0 into 1.0 11.150 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.150 * [taylor]: Taking taylor expansion of k in n 11.150 * [backup-simplify]: Simplify k into k 11.150 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.150 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 11.150 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 11.150 * [taylor]: Taking taylor expansion of 2.0 in n 11.150 * [backup-simplify]: Simplify 2.0 into 2.0 11.150 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.150 * [taylor]: Taking taylor expansion of PI in n 11.150 * [backup-simplify]: Simplify PI into PI 11.150 * [taylor]: Taking taylor expansion of n in n 11.151 * [backup-simplify]: Simplify 0 into 0 11.151 * [backup-simplify]: Simplify 1 into 1 11.151 * [backup-simplify]: Simplify (/ PI 1) into PI 11.152 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.153 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.153 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.153 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 11.153 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 11.155 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.156 * [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)))) 11.157 * [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))))) 11.157 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 11.157 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 11.157 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 11.157 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 11.157 * [taylor]: Taking taylor expansion of 0.5 in n 11.157 * [backup-simplify]: Simplify 0.5 into 0.5 11.157 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 11.157 * [taylor]: Taking taylor expansion of 1.0 in n 11.158 * [backup-simplify]: Simplify 1.0 into 1.0 11.158 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.158 * [taylor]: Taking taylor expansion of k in n 11.158 * [backup-simplify]: Simplify k into k 11.158 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.158 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 11.158 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 11.158 * [taylor]: Taking taylor expansion of 2.0 in n 11.158 * [backup-simplify]: Simplify 2.0 into 2.0 11.158 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.158 * [taylor]: Taking taylor expansion of PI in n 11.158 * [backup-simplify]: Simplify PI into PI 11.158 * [taylor]: Taking taylor expansion of n in n 11.158 * [backup-simplify]: Simplify 0 into 0 11.158 * [backup-simplify]: Simplify 1 into 1 11.159 * [backup-simplify]: Simplify (/ PI 1) into PI 11.159 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.160 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.160 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.160 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 11.161 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 11.162 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.163 * [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)))) 11.165 * [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))))) 11.165 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 11.165 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 11.165 * [taylor]: Taking taylor expansion of 0.5 in k 11.165 * [backup-simplify]: Simplify 0.5 into 0.5 11.165 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 11.165 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 11.165 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 11.165 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 11.165 * [taylor]: Taking taylor expansion of 2.0 in k 11.165 * [backup-simplify]: Simplify 2.0 into 2.0 11.165 * [taylor]: Taking taylor expansion of PI in k 11.165 * [backup-simplify]: Simplify PI into PI 11.166 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.167 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.167 * [taylor]: Taking taylor expansion of (log n) in k 11.167 * [taylor]: Taking taylor expansion of n in k 11.167 * [backup-simplify]: Simplify n into n 11.167 * [backup-simplify]: Simplify (log n) into (log n) 11.167 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 11.167 * [taylor]: Taking taylor expansion of 1.0 in k 11.167 * [backup-simplify]: Simplify 1.0 into 1.0 11.167 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.167 * [taylor]: Taking taylor expansion of k in k 11.167 * [backup-simplify]: Simplify 0 into 0 11.167 * [backup-simplify]: Simplify 1 into 1 11.168 * [backup-simplify]: Simplify (/ 1 1) into 1 11.168 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 11.169 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 11.170 * [backup-simplify]: Simplify (- 1) into -1 11.170 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.171 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 11.172 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 11.174 * [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))))) 11.175 * [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))))) 11.176 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.177 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 11.179 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 11.180 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.180 * [backup-simplify]: Simplify (- 0) into 0 11.180 * [backup-simplify]: Simplify (+ 0 0) into 0 11.181 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 11.183 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.184 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 11.186 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.186 * [taylor]: Taking taylor expansion of 0 in k 11.186 * [backup-simplify]: Simplify 0 into 0 11.186 * [backup-simplify]: Simplify 0 into 0 11.186 * [backup-simplify]: Simplify 0 into 0 11.188 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.189 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.193 * [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 11.193 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.193 * [backup-simplify]: Simplify (- 0) into 0 11.194 * [backup-simplify]: Simplify (+ 0 0) into 0 11.195 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 11.196 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.198 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 11.201 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.201 * [taylor]: Taking taylor expansion of 0 in k 11.201 * [backup-simplify]: Simplify 0 into 0 11.201 * [backup-simplify]: Simplify 0 into 0 11.201 * [backup-simplify]: Simplify 0 into 0 11.201 * [backup-simplify]: Simplify 0 into 0 11.203 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.204 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.212 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 11.212 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.213 * [backup-simplify]: Simplify (- 0) into 0 11.213 * [backup-simplify]: Simplify (+ 0 0) into 0 11.215 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 11.217 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.219 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 11.222 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 11.222 * [taylor]: Taking taylor expansion of 0 in k 11.222 * [backup-simplify]: Simplify 0 into 0 11.222 * [backup-simplify]: Simplify 0 into 0 11.224 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 11.224 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 11.224 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 11.225 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 11.225 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 11.225 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 11.225 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 11.225 * [taylor]: Taking taylor expansion of 0.5 in k 11.225 * [backup-simplify]: Simplify 0.5 into 0.5 11.225 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 11.225 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.225 * [taylor]: Taking taylor expansion of k in k 11.225 * [backup-simplify]: Simplify 0 into 0 11.225 * [backup-simplify]: Simplify 1 into 1 11.225 * [backup-simplify]: Simplify (/ 1 1) into 1 11.225 * [taylor]: Taking taylor expansion of 1.0 in k 11.225 * [backup-simplify]: Simplify 1.0 into 1.0 11.225 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 11.225 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 11.225 * [taylor]: Taking taylor expansion of -2.0 in k 11.225 * [backup-simplify]: Simplify -2.0 into -2.0 11.226 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.226 * [taylor]: Taking taylor expansion of PI in k 11.226 * [backup-simplify]: Simplify PI into PI 11.226 * [taylor]: Taking taylor expansion of n in k 11.226 * [backup-simplify]: Simplify n into n 11.226 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.226 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 11.226 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 11.226 * [backup-simplify]: Simplify (+ 1 0) into 1 11.227 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 11.227 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 11.227 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 11.227 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 11.227 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 11.227 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 11.227 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 11.227 * [taylor]: Taking taylor expansion of 0.5 in n 11.228 * [backup-simplify]: Simplify 0.5 into 0.5 11.228 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 11.228 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.228 * [taylor]: Taking taylor expansion of k in n 11.228 * [backup-simplify]: Simplify k into k 11.228 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.228 * [taylor]: Taking taylor expansion of 1.0 in n 11.228 * [backup-simplify]: Simplify 1.0 into 1.0 11.228 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 11.228 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 11.228 * [taylor]: Taking taylor expansion of -2.0 in n 11.228 * [backup-simplify]: Simplify -2.0 into -2.0 11.228 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.228 * [taylor]: Taking taylor expansion of PI in n 11.228 * [backup-simplify]: Simplify PI into PI 11.228 * [taylor]: Taking taylor expansion of n in n 11.228 * [backup-simplify]: Simplify 0 into 0 11.228 * [backup-simplify]: Simplify 1 into 1 11.229 * [backup-simplify]: Simplify (/ PI 1) into PI 11.229 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.230 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 11.231 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 11.231 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 11.232 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.233 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 11.235 * [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))))) 11.235 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 11.235 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 11.235 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 11.235 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 11.235 * [taylor]: Taking taylor expansion of 0.5 in n 11.235 * [backup-simplify]: Simplify 0.5 into 0.5 11.235 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 11.235 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.235 * [taylor]: Taking taylor expansion of k in n 11.235 * [backup-simplify]: Simplify k into k 11.235 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.235 * [taylor]: Taking taylor expansion of 1.0 in n 11.235 * [backup-simplify]: Simplify 1.0 into 1.0 11.235 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 11.235 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 11.235 * [taylor]: Taking taylor expansion of -2.0 in n 11.236 * [backup-simplify]: Simplify -2.0 into -2.0 11.236 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.236 * [taylor]: Taking taylor expansion of PI in n 11.236 * [backup-simplify]: Simplify PI into PI 11.236 * [taylor]: Taking taylor expansion of n in n 11.236 * [backup-simplify]: Simplify 0 into 0 11.236 * [backup-simplify]: Simplify 1 into 1 11.236 * [backup-simplify]: Simplify (/ PI 1) into PI 11.237 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.238 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 11.238 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 11.238 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 11.240 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.241 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 11.242 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 11.242 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 11.242 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 11.242 * [taylor]: Taking taylor expansion of 0.5 in k 11.242 * [backup-simplify]: Simplify 0.5 into 0.5 11.242 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 11.243 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 11.243 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.243 * [taylor]: Taking taylor expansion of k in k 11.243 * [backup-simplify]: Simplify 0 into 0 11.243 * [backup-simplify]: Simplify 1 into 1 11.243 * [backup-simplify]: Simplify (/ 1 1) into 1 11.243 * [taylor]: Taking taylor expansion of 1.0 in k 11.243 * [backup-simplify]: Simplify 1.0 into 1.0 11.243 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 11.243 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 11.243 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 11.243 * [taylor]: Taking taylor expansion of -2.0 in k 11.243 * [backup-simplify]: Simplify -2.0 into -2.0 11.243 * [taylor]: Taking taylor expansion of PI in k 11.243 * [backup-simplify]: Simplify PI into PI 11.244 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.245 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 11.245 * [taylor]: Taking taylor expansion of (log n) in k 11.245 * [taylor]: Taking taylor expansion of n in k 11.245 * [backup-simplify]: Simplify n into n 11.245 * [backup-simplify]: Simplify (log n) into (log n) 11.246 * [backup-simplify]: Simplify (+ 1 0) into 1 11.246 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 11.247 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 11.248 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 11.249 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 11.250 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 11.252 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 11.253 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.254 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 11.256 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 11.256 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.256 * [backup-simplify]: Simplify (+ 0 0) into 0 11.257 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 11.259 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.260 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 11.262 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.262 * [taylor]: Taking taylor expansion of 0 in k 11.262 * [backup-simplify]: Simplify 0 into 0 11.262 * [backup-simplify]: Simplify 0 into 0 11.263 * [backup-simplify]: Simplify 0 into 0 11.264 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.265 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.269 * [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 11.269 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.270 * [backup-simplify]: Simplify (+ 0 0) into 0 11.270 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 11.272 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.274 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 11.276 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.277 * [taylor]: Taking taylor expansion of 0 in k 11.277 * [backup-simplify]: Simplify 0 into 0 11.277 * [backup-simplify]: Simplify 0 into 0 11.277 * [backup-simplify]: Simplify 0 into 0 11.277 * [backup-simplify]: Simplify 0 into 0 11.278 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.279 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.285 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 11.286 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.286 * [backup-simplify]: Simplify (+ 0 0) into 0 11.288 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 11.289 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.291 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 11.294 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 11.294 * [taylor]: Taking taylor expansion of 0 in k 11.295 * [backup-simplify]: Simplify 0 into 0 11.295 * [backup-simplify]: Simplify 0 into 0 11.296 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 11.296 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1) 11.296 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 11.296 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 11.296 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 11.296 * [taylor]: Taking taylor expansion of 1.0 in k 11.296 * [backup-simplify]: Simplify 1.0 into 1.0 11.296 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.296 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.296 * [taylor]: Taking taylor expansion of k in k 11.296 * [backup-simplify]: Simplify 0 into 0 11.297 * [backup-simplify]: Simplify 1 into 1 11.297 * [backup-simplify]: Simplify (/ 1 1) into 1 11.297 * [backup-simplify]: Simplify (sqrt 0) into 0 11.299 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.299 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 11.299 * [taylor]: Taking taylor expansion of 1.0 in k 11.299 * [backup-simplify]: Simplify 1.0 into 1.0 11.299 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.299 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.299 * [taylor]: Taking taylor expansion of k in k 11.299 * [backup-simplify]: Simplify 0 into 0 11.299 * [backup-simplify]: Simplify 1 into 1 11.300 * [backup-simplify]: Simplify (/ 1 1) into 1 11.300 * [backup-simplify]: Simplify (sqrt 0) into 0 11.301 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.302 * [backup-simplify]: Simplify (* 1.0 0) into 0 11.302 * [backup-simplify]: Simplify 0 into 0 11.304 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 11.304 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.305 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 11.313 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.315 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 11.316 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.317 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.321 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.323 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 11.323 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.325 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 11.325 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 11.325 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 11.325 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 11.325 * [taylor]: Taking taylor expansion of 1.0 in k 11.325 * [backup-simplify]: Simplify 1.0 into 1.0 11.325 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.325 * [taylor]: Taking taylor expansion of k in k 11.325 * [backup-simplify]: Simplify 0 into 0 11.325 * [backup-simplify]: Simplify 1 into 1 11.326 * [backup-simplify]: Simplify (sqrt 0) into 0 11.327 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.327 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 11.327 * [taylor]: Taking taylor expansion of 1.0 in k 11.327 * [backup-simplify]: Simplify 1.0 into 1.0 11.327 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.327 * [taylor]: Taking taylor expansion of k in k 11.327 * [backup-simplify]: Simplify 0 into 0 11.327 * [backup-simplify]: Simplify 1 into 1 11.328 * [backup-simplify]: Simplify (sqrt 0) into 0 11.329 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.330 * [backup-simplify]: Simplify (* 1.0 0) into 0 11.330 * [backup-simplify]: Simplify 0 into 0 11.331 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 11.332 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.335 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.337 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 11.337 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.341 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.344 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 11.344 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.346 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 11.346 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 11.346 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 11.346 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 11.346 * [taylor]: Taking taylor expansion of 1.0 in k 11.346 * [backup-simplify]: Simplify 1.0 into 1.0 11.346 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.346 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.346 * [taylor]: Taking taylor expansion of -1 in k 11.346 * [backup-simplify]: Simplify -1 into -1 11.346 * [taylor]: Taking taylor expansion of k in k 11.347 * [backup-simplify]: Simplify 0 into 0 11.347 * [backup-simplify]: Simplify 1 into 1 11.347 * [backup-simplify]: Simplify (/ -1 1) into -1 11.347 * [backup-simplify]: Simplify (sqrt 0) into 0 11.349 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.350 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 11.350 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 11.350 * [taylor]: Taking taylor expansion of 1.0 in k 11.350 * [backup-simplify]: Simplify 1.0 into 1.0 11.350 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.350 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.350 * [taylor]: Taking taylor expansion of -1 in k 11.350 * [backup-simplify]: Simplify -1 into -1 11.350 * [taylor]: Taking taylor expansion of k in k 11.350 * [backup-simplify]: Simplify 0 into 0 11.350 * [backup-simplify]: Simplify 1 into 1 11.350 * [backup-simplify]: Simplify (/ -1 1) into -1 11.351 * [backup-simplify]: Simplify (sqrt 0) into 0 11.352 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.353 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 11.353 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.354 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 11.357 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.360 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 11.360 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.361 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.365 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.370 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 11.370 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.371 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 11.371 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 1) 11.372 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 11.372 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 11.372 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 11.372 * [taylor]: Taking taylor expansion of 1.0 in k 11.372 * [backup-simplify]: Simplify 1.0 into 1.0 11.372 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.372 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.372 * [taylor]: Taking taylor expansion of k in k 11.372 * [backup-simplify]: Simplify 0 into 0 11.372 * [backup-simplify]: Simplify 1 into 1 11.372 * [backup-simplify]: Simplify (/ 1 1) into 1 11.373 * [backup-simplify]: Simplify (sqrt 0) into 0 11.374 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.374 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 11.374 * [taylor]: Taking taylor expansion of 1.0 in k 11.374 * [backup-simplify]: Simplify 1.0 into 1.0 11.374 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.374 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.374 * [taylor]: Taking taylor expansion of k in k 11.374 * [backup-simplify]: Simplify 0 into 0 11.374 * [backup-simplify]: Simplify 1 into 1 11.375 * [backup-simplify]: Simplify (/ 1 1) into 1 11.375 * [backup-simplify]: Simplify (sqrt 0) into 0 11.376 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.377 * [backup-simplify]: Simplify (* 1.0 0) into 0 11.377 * [backup-simplify]: Simplify 0 into 0 11.378 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 11.379 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.380 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 11.383 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.385 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 11.385 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.386 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.390 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.392 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 11.393 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.394 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 11.394 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 11.394 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 11.394 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 11.394 * [taylor]: Taking taylor expansion of 1.0 in k 11.394 * [backup-simplify]: Simplify 1.0 into 1.0 11.394 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.394 * [taylor]: Taking taylor expansion of k in k 11.394 * [backup-simplify]: Simplify 0 into 0 11.394 * [backup-simplify]: Simplify 1 into 1 11.395 * [backup-simplify]: Simplify (sqrt 0) into 0 11.396 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.396 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 11.396 * [taylor]: Taking taylor expansion of 1.0 in k 11.396 * [backup-simplify]: Simplify 1.0 into 1.0 11.396 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.396 * [taylor]: Taking taylor expansion of k in k 11.396 * [backup-simplify]: Simplify 0 into 0 11.396 * [backup-simplify]: Simplify 1 into 1 11.397 * [backup-simplify]: Simplify (sqrt 0) into 0 11.398 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.399 * [backup-simplify]: Simplify (* 1.0 0) into 0 11.399 * [backup-simplify]: Simplify 0 into 0 11.400 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 11.400 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.404 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.406 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 11.406 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.410 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.413 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 11.413 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.415 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 11.415 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 11.415 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 11.415 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 11.415 * [taylor]: Taking taylor expansion of 1.0 in k 11.415 * [backup-simplify]: Simplify 1.0 into 1.0 11.415 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.415 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.415 * [taylor]: Taking taylor expansion of -1 in k 11.415 * [backup-simplify]: Simplify -1 into -1 11.415 * [taylor]: Taking taylor expansion of k in k 11.415 * [backup-simplify]: Simplify 0 into 0 11.415 * [backup-simplify]: Simplify 1 into 1 11.416 * [backup-simplify]: Simplify (/ -1 1) into -1 11.416 * [backup-simplify]: Simplify (sqrt 0) into 0 11.417 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.418 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 11.418 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 11.418 * [taylor]: Taking taylor expansion of 1.0 in k 11.418 * [backup-simplify]: Simplify 1.0 into 1.0 11.418 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.418 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.418 * [taylor]: Taking taylor expansion of -1 in k 11.418 * [backup-simplify]: Simplify -1 into -1 11.418 * [taylor]: Taking taylor expansion of k in k 11.418 * [backup-simplify]: Simplify 0 into 0 11.418 * [backup-simplify]: Simplify 1 into 1 11.418 * [backup-simplify]: Simplify (/ -1 1) into -1 11.419 * [backup-simplify]: Simplify (sqrt 0) into 0 11.420 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.420 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 11.420 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.421 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 11.425 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.427 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 11.428 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.429 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.433 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.437 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 11.437 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.439 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 11.439 * * * [progress]: simplifying candidates 11.444 * [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 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 11.451 * * [simplify]: Extracting # 0 : cost 0 11.451 * * [simplify]: Extracting # 1 : cost 0 11.451 * * [simplify]: Extracting # 2 : cost 0 11.452 * * [simplify]: Extracting # 3 : cost 0 11.452 * * [simplify]: Extracting # 4 : cost 0 11.453 * * [simplify]: Extracting # 5 : cost 0 11.453 * * [simplify]: Extracting # 6 : cost 0 11.454 * * [simplify]: Extracting # 7 : cost 0 11.454 * * [simplify]: Extracting # 8 : cost 0 11.455 * * [simplify]: Extracting # 9 : cost 0 11.455 * * [simplify]: Extracting # 10 : cost 0 11.456 * * [simplify]: Extracting # 11 : cost 0 11.456 * * [simplify]: Extracting # 12 : cost 0 11.457 * * [simplify]: iteration 0 : 208 enodes (cost 2140 ) 11.522 * * [simplify]: Extracting # 0 : cost 0 11.522 * * [simplify]: Extracting # 1 : cost 0 11.523 * * [simplify]: Extracting # 2 : cost 0 11.524 * * [simplify]: Extracting # 3 : cost 0 11.525 * * [simplify]: Extracting # 4 : cost 0 11.526 * * [simplify]: iteration 1 : 518 enodes (cost 1966 ) 11.747 * * [simplify]: Extracting # 0 : cost 0 11.749 * * [simplify]: Extracting # 1 : cost 0 11.751 * * [simplify]: Extracting # 2 : cost 0 11.753 * * [simplify]: Extracting # 3 : cost 0 11.755 * * [simplify]: Extracting # 4 : cost 0 11.758 * * [simplify]: iteration 2 : 1841 enodes (cost 1854 ) 12.358 * * [simplify]: Extracting # 0 : cost 0 12.369 * * [simplify]: Extracting # 1 : cost 0 12.382 * * [simplify]: Extracting # 2 : cost 0 12.396 * * [simplify]: Extracting # 3 : cost 0 12.413 * * [simplify]: Extracting # 4 : cost 0 12.419 * * [simplify]: iteration done: 5001 enodes (cost 1854 ) 12.420 * [simplify]: Simplified to: (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (/ (pow 1.0 3) k) (sqrt k)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (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) (- (+ (+ (* (* 0.25 (pow k 2)) (* (pow (* (* 2.0 PI) n) 0.5) (* (log (* 2.0 PI)) (log n)))) (pow (* (* 2.0 PI) n) 0.5)) (* (* 0.125 (pow k 2)) (+ (* (pow (log (* 2.0 PI)) 2) (pow (* (* 2.0 PI) n) 0.5)) (* (pow (log n) 2) (pow (* (* 2.0 PI) n) 0.5))))) (* (* k (+ (* (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.5)) (* (log n) (pow (* (* 2.0 PI) n) 0.5)))) 0.5)) (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (+ (* (* 0.25 (pow k 2)) (* (pow (* (* 2.0 PI) n) 0.5) (* (log (* 2.0 PI)) (log n)))) (pow (* (* 2.0 PI) n) 0.5)) (* (* 0.125 (pow k 2)) (+ (* (pow (log (* 2.0 PI)) 2) (pow (* (* 2.0 PI) n) 0.5)) (* (pow (log n) 2) (pow (* (* 2.0 PI) n) 0.5))))) (* (* k (+ (* (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.5)) (* (log n) (pow (* (* 2.0 PI) n) 0.5)))) 0.5)) (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (- (* +nan.0 k) (- (* +nan.0 (pow k 2)) +nan.0))) (+ (- (/ +nan.0 k) (/ +nan.0 (pow k 3))) (- (/ +nan.0 (pow k 2)))) (+ (- (/ +nan.0 (pow k 2))) (- (/ +nan.0 k) +nan.0)) (- (- (* +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)) 12.421 * * * [progress]: adding candidates to table 13.318 * * [progress]: iteration 4 / 4 13.318 * * * [progress]: picking best candidate 13.351 * * * * [pick]: Picked # 13.351 * * * [progress]: localizing error 13.424 * * * [progress]: generating rewritten candidates 13.424 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 2) 13.469 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 2) 13.513 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1 2 2 1) 13.515 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1 1 2 1) 13.529 * * * [progress]: generating series expansions 13.529 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 2) 13.530 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 13.530 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 13.530 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 13.530 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 13.530 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 13.530 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 13.530 * [taylor]: Taking taylor expansion of 0.5 in k 13.530 * [backup-simplify]: Simplify 0.5 into 0.5 13.530 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 13.530 * [taylor]: Taking taylor expansion of 1.0 in k 13.530 * [backup-simplify]: Simplify 1.0 into 1.0 13.530 * [taylor]: Taking taylor expansion of k in k 13.530 * [backup-simplify]: Simplify 0 into 0 13.530 * [backup-simplify]: Simplify 1 into 1 13.530 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 13.530 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 13.530 * [taylor]: Taking taylor expansion of 2.0 in k 13.530 * [backup-simplify]: Simplify 2.0 into 2.0 13.531 * [taylor]: Taking taylor expansion of (* n PI) in k 13.531 * [taylor]: Taking taylor expansion of n in k 13.531 * [backup-simplify]: Simplify n into n 13.531 * [taylor]: Taking taylor expansion of PI in k 13.531 * [backup-simplify]: Simplify PI into PI 13.531 * [backup-simplify]: Simplify (* n PI) into (* n PI) 13.531 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 13.531 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 13.531 * [backup-simplify]: Simplify (- 0) into 0 13.532 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 13.532 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 13.533 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 13.533 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 13.533 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 13.533 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 13.533 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 13.533 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 13.533 * [taylor]: Taking taylor expansion of 0.5 in n 13.533 * [backup-simplify]: Simplify 0.5 into 0.5 13.533 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 13.533 * [taylor]: Taking taylor expansion of 1.0 in n 13.533 * [backup-simplify]: Simplify 1.0 into 1.0 13.533 * [taylor]: Taking taylor expansion of k in n 13.533 * [backup-simplify]: Simplify k into k 13.533 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 13.533 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 13.533 * [taylor]: Taking taylor expansion of 2.0 in n 13.533 * [backup-simplify]: Simplify 2.0 into 2.0 13.533 * [taylor]: Taking taylor expansion of (* n PI) in n 13.533 * [taylor]: Taking taylor expansion of n in n 13.533 * [backup-simplify]: Simplify 0 into 0 13.533 * [backup-simplify]: Simplify 1 into 1 13.533 * [taylor]: Taking taylor expansion of PI in n 13.533 * [backup-simplify]: Simplify PI into PI 13.534 * [backup-simplify]: Simplify (* 0 PI) into 0 13.534 * [backup-simplify]: Simplify (* 2.0 0) into 0 13.536 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.538 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 13.539 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.539 * [backup-simplify]: Simplify (- k) into (- k) 13.539 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 13.539 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 13.540 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.542 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 13.543 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 13.543 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 13.543 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 13.543 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 13.543 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 13.543 * [taylor]: Taking taylor expansion of 0.5 in n 13.543 * [backup-simplify]: Simplify 0.5 into 0.5 13.543 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 13.543 * [taylor]: Taking taylor expansion of 1.0 in n 13.543 * [backup-simplify]: Simplify 1.0 into 1.0 13.543 * [taylor]: Taking taylor expansion of k in n 13.543 * [backup-simplify]: Simplify k into k 13.543 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 13.543 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 13.543 * [taylor]: Taking taylor expansion of 2.0 in n 13.543 * [backup-simplify]: Simplify 2.0 into 2.0 13.543 * [taylor]: Taking taylor expansion of (* n PI) in n 13.544 * [taylor]: Taking taylor expansion of n in n 13.544 * [backup-simplify]: Simplify 0 into 0 13.544 * [backup-simplify]: Simplify 1 into 1 13.544 * [taylor]: Taking taylor expansion of PI in n 13.544 * [backup-simplify]: Simplify PI into PI 13.544 * [backup-simplify]: Simplify (* 0 PI) into 0 13.545 * [backup-simplify]: Simplify (* 2.0 0) into 0 13.546 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.548 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 13.548 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.548 * [backup-simplify]: Simplify (- k) into (- k) 13.548 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 13.548 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 13.549 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.550 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 13.551 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 13.551 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 13.551 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 13.551 * [taylor]: Taking taylor expansion of 0.5 in k 13.551 * [backup-simplify]: Simplify 0.5 into 0.5 13.551 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 13.551 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 13.551 * [taylor]: Taking taylor expansion of 1.0 in k 13.551 * [backup-simplify]: Simplify 1.0 into 1.0 13.551 * [taylor]: Taking taylor expansion of k in k 13.551 * [backup-simplify]: Simplify 0 into 0 13.551 * [backup-simplify]: Simplify 1 into 1 13.551 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 13.551 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 13.551 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 13.551 * [taylor]: Taking taylor expansion of 2.0 in k 13.551 * [backup-simplify]: Simplify 2.0 into 2.0 13.551 * [taylor]: Taking taylor expansion of PI in k 13.551 * [backup-simplify]: Simplify PI into PI 13.551 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.552 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.552 * [taylor]: Taking taylor expansion of (log n) in k 13.552 * [taylor]: Taking taylor expansion of n in k 13.552 * [backup-simplify]: Simplify n into n 13.552 * [backup-simplify]: Simplify (log n) into (log n) 13.552 * [backup-simplify]: Simplify (- 0) into 0 13.553 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 13.553 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 13.554 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 13.555 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 13.555 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 13.556 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 13.557 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.557 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 13.558 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 13.559 * [backup-simplify]: Simplify (- 0) into 0 13.559 * [backup-simplify]: Simplify (+ 0 0) into 0 13.559 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 13.560 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.561 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 13.562 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.562 * [taylor]: Taking taylor expansion of 0 in k 13.562 * [backup-simplify]: Simplify 0 into 0 13.562 * [backup-simplify]: Simplify 0 into 0 13.563 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 13.564 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 13.564 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 13.565 * [backup-simplify]: Simplify (+ 0 0) into 0 13.565 * [backup-simplify]: Simplify (- 1) into -1 13.566 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.567 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 13.568 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 13.570 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 13.572 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 13.573 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 13.573 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 13.575 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 13.576 * [backup-simplify]: Simplify (- 0) into 0 13.576 * [backup-simplify]: Simplify (+ 0 0) into 0 13.577 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 13.578 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.580 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 13.582 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.583 * [taylor]: Taking taylor expansion of 0 in k 13.583 * [backup-simplify]: Simplify 0 into 0 13.583 * [backup-simplify]: Simplify 0 into 0 13.583 * [backup-simplify]: Simplify 0 into 0 13.584 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.588 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 13.590 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 13.590 * [backup-simplify]: Simplify (+ 0 0) into 0 13.591 * [backup-simplify]: Simplify (- 0) into 0 13.591 * [backup-simplify]: Simplify (+ 0 0) into 0 13.593 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 13.596 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 13.600 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 13.605 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 13.611 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 13.612 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 13.612 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 13.612 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 13.612 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 13.612 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 13.612 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 13.612 * [taylor]: Taking taylor expansion of 0.5 in k 13.612 * [backup-simplify]: Simplify 0.5 into 0.5 13.612 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.612 * [taylor]: Taking taylor expansion of 1.0 in k 13.612 * [backup-simplify]: Simplify 1.0 into 1.0 13.612 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.612 * [taylor]: Taking taylor expansion of k in k 13.612 * [backup-simplify]: Simplify 0 into 0 13.612 * [backup-simplify]: Simplify 1 into 1 13.612 * [backup-simplify]: Simplify (/ 1 1) into 1 13.612 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 13.612 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 13.613 * [taylor]: Taking taylor expansion of 2.0 in k 13.613 * [backup-simplify]: Simplify 2.0 into 2.0 13.613 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.613 * [taylor]: Taking taylor expansion of PI in k 13.613 * [backup-simplify]: Simplify PI into PI 13.613 * [taylor]: Taking taylor expansion of n in k 13.613 * [backup-simplify]: Simplify n into n 13.613 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.613 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 13.613 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 13.613 * [backup-simplify]: Simplify (- 1) into -1 13.613 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.614 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 13.614 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 13.614 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 13.614 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 13.614 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 13.614 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 13.614 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 13.614 * [taylor]: Taking taylor expansion of 0.5 in n 13.614 * [backup-simplify]: Simplify 0.5 into 0.5 13.614 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 13.614 * [taylor]: Taking taylor expansion of 1.0 in n 13.614 * [backup-simplify]: Simplify 1.0 into 1.0 13.614 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.614 * [taylor]: Taking taylor expansion of k in n 13.614 * [backup-simplify]: Simplify k into k 13.614 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.614 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 13.614 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.614 * [taylor]: Taking taylor expansion of 2.0 in n 13.614 * [backup-simplify]: Simplify 2.0 into 2.0 13.614 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.614 * [taylor]: Taking taylor expansion of PI in n 13.614 * [backup-simplify]: Simplify PI into PI 13.614 * [taylor]: Taking taylor expansion of n in n 13.614 * [backup-simplify]: Simplify 0 into 0 13.614 * [backup-simplify]: Simplify 1 into 1 13.615 * [backup-simplify]: Simplify (/ PI 1) into PI 13.615 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.616 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.616 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 13.616 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 13.616 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 13.617 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.618 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 13.618 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 13.618 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 13.618 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 13.618 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 13.618 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 13.618 * [taylor]: Taking taylor expansion of 0.5 in n 13.618 * [backup-simplify]: Simplify 0.5 into 0.5 13.618 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 13.618 * [taylor]: Taking taylor expansion of 1.0 in n 13.619 * [backup-simplify]: Simplify 1.0 into 1.0 13.619 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.619 * [taylor]: Taking taylor expansion of k in n 13.619 * [backup-simplify]: Simplify k into k 13.619 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.619 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 13.619 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.619 * [taylor]: Taking taylor expansion of 2.0 in n 13.619 * [backup-simplify]: Simplify 2.0 into 2.0 13.619 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.619 * [taylor]: Taking taylor expansion of PI in n 13.619 * [backup-simplify]: Simplify PI into PI 13.619 * [taylor]: Taking taylor expansion of n in n 13.619 * [backup-simplify]: Simplify 0 into 0 13.619 * [backup-simplify]: Simplify 1 into 1 13.619 * [backup-simplify]: Simplify (/ PI 1) into PI 13.619 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.620 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.620 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 13.620 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 13.620 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 13.621 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.622 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 13.623 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 13.623 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 13.623 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 13.623 * [taylor]: Taking taylor expansion of 0.5 in k 13.623 * [backup-simplify]: Simplify 0.5 into 0.5 13.623 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 13.623 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 13.623 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 13.623 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 13.623 * [taylor]: Taking taylor expansion of 2.0 in k 13.623 * [backup-simplify]: Simplify 2.0 into 2.0 13.623 * [taylor]: Taking taylor expansion of PI in k 13.623 * [backup-simplify]: Simplify PI into PI 13.623 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.624 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.624 * [taylor]: Taking taylor expansion of (log n) in k 13.624 * [taylor]: Taking taylor expansion of n in k 13.624 * [backup-simplify]: Simplify n into n 13.624 * [backup-simplify]: Simplify (log n) into (log n) 13.624 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.624 * [taylor]: Taking taylor expansion of 1.0 in k 13.624 * [backup-simplify]: Simplify 1.0 into 1.0 13.624 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.624 * [taylor]: Taking taylor expansion of k in k 13.624 * [backup-simplify]: Simplify 0 into 0 13.624 * [backup-simplify]: Simplify 1 into 1 13.624 * [backup-simplify]: Simplify (/ 1 1) into 1 13.625 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.625 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 13.626 * [backup-simplify]: Simplify (- 1) into -1 13.626 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.627 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 13.628 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 13.628 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 13.629 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 13.630 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.630 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 13.631 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 13.631 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.632 * [backup-simplify]: Simplify (- 0) into 0 13.632 * [backup-simplify]: Simplify (+ 0 0) into 0 13.633 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 13.634 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.635 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 13.637 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.638 * [taylor]: Taking taylor expansion of 0 in k 13.638 * [backup-simplify]: Simplify 0 into 0 13.638 * [backup-simplify]: Simplify 0 into 0 13.638 * [backup-simplify]: Simplify 0 into 0 13.639 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.640 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.648 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 13.649 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.649 * [backup-simplify]: Simplify (- 0) into 0 13.650 * [backup-simplify]: Simplify (+ 0 0) into 0 13.651 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 13.652 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.654 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 13.657 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.657 * [taylor]: Taking taylor expansion of 0 in k 13.657 * [backup-simplify]: Simplify 0 into 0 13.657 * [backup-simplify]: Simplify 0 into 0 13.657 * [backup-simplify]: Simplify 0 into 0 13.657 * [backup-simplify]: Simplify 0 into 0 13.658 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.659 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.663 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 13.663 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.664 * [backup-simplify]: Simplify (- 0) into 0 13.664 * [backup-simplify]: Simplify (+ 0 0) into 0 13.665 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 13.666 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.667 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 13.669 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.669 * [taylor]: Taking taylor expansion of 0 in k 13.669 * [backup-simplify]: Simplify 0 into 0 13.669 * [backup-simplify]: Simplify 0 into 0 13.670 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 13.671 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 13.671 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 13.671 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 13.671 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 13.671 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 13.671 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 13.671 * [taylor]: Taking taylor expansion of 0.5 in k 13.671 * [backup-simplify]: Simplify 0.5 into 0.5 13.671 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.671 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.671 * [taylor]: Taking taylor expansion of k in k 13.671 * [backup-simplify]: Simplify 0 into 0 13.671 * [backup-simplify]: Simplify 1 into 1 13.671 * [backup-simplify]: Simplify (/ 1 1) into 1 13.671 * [taylor]: Taking taylor expansion of 1.0 in k 13.671 * [backup-simplify]: Simplify 1.0 into 1.0 13.671 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 13.671 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 13.671 * [taylor]: Taking taylor expansion of -2.0 in k 13.671 * [backup-simplify]: Simplify -2.0 into -2.0 13.671 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.671 * [taylor]: Taking taylor expansion of PI in k 13.671 * [backup-simplify]: Simplify PI into PI 13.671 * [taylor]: Taking taylor expansion of n in k 13.671 * [backup-simplify]: Simplify n into n 13.671 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.671 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 13.671 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 13.672 * [backup-simplify]: Simplify (+ 1 0) into 1 13.672 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 13.672 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 13.672 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 13.672 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 13.672 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 13.672 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 13.672 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 13.672 * [taylor]: Taking taylor expansion of 0.5 in n 13.672 * [backup-simplify]: Simplify 0.5 into 0.5 13.672 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 13.672 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.672 * [taylor]: Taking taylor expansion of k in n 13.672 * [backup-simplify]: Simplify k into k 13.672 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.672 * [taylor]: Taking taylor expansion of 1.0 in n 13.673 * [backup-simplify]: Simplify 1.0 into 1.0 13.673 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 13.673 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.673 * [taylor]: Taking taylor expansion of -2.0 in n 13.673 * [backup-simplify]: Simplify -2.0 into -2.0 13.673 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.673 * [taylor]: Taking taylor expansion of PI in n 13.673 * [backup-simplify]: Simplify PI into PI 13.673 * [taylor]: Taking taylor expansion of n in n 13.673 * [backup-simplify]: Simplify 0 into 0 13.673 * [backup-simplify]: Simplify 1 into 1 13.673 * [backup-simplify]: Simplify (/ PI 1) into PI 13.673 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.674 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.674 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 13.674 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 13.675 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.676 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 13.677 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 13.677 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 13.677 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 13.677 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 13.677 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 13.677 * [taylor]: Taking taylor expansion of 0.5 in n 13.677 * [backup-simplify]: Simplify 0.5 into 0.5 13.677 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 13.677 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.677 * [taylor]: Taking taylor expansion of k in n 13.677 * [backup-simplify]: Simplify k into k 13.677 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.677 * [taylor]: Taking taylor expansion of 1.0 in n 13.677 * [backup-simplify]: Simplify 1.0 into 1.0 13.677 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 13.677 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.677 * [taylor]: Taking taylor expansion of -2.0 in n 13.677 * [backup-simplify]: Simplify -2.0 into -2.0 13.677 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.677 * [taylor]: Taking taylor expansion of PI in n 13.677 * [backup-simplify]: Simplify PI into PI 13.677 * [taylor]: Taking taylor expansion of n in n 13.677 * [backup-simplify]: Simplify 0 into 0 13.677 * [backup-simplify]: Simplify 1 into 1 13.677 * [backup-simplify]: Simplify (/ PI 1) into PI 13.678 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.678 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.678 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 13.678 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 13.679 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.680 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 13.681 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 13.681 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 13.681 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 13.681 * [taylor]: Taking taylor expansion of 0.5 in k 13.681 * [backup-simplify]: Simplify 0.5 into 0.5 13.681 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 13.681 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.681 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.681 * [taylor]: Taking taylor expansion of k in k 13.681 * [backup-simplify]: Simplify 0 into 0 13.681 * [backup-simplify]: Simplify 1 into 1 13.682 * [backup-simplify]: Simplify (/ 1 1) into 1 13.682 * [taylor]: Taking taylor expansion of 1.0 in k 13.682 * [backup-simplify]: Simplify 1.0 into 1.0 13.682 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 13.682 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 13.682 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 13.682 * [taylor]: Taking taylor expansion of -2.0 in k 13.682 * [backup-simplify]: Simplify -2.0 into -2.0 13.682 * [taylor]: Taking taylor expansion of PI in k 13.682 * [backup-simplify]: Simplify PI into PI 13.682 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.683 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.683 * [taylor]: Taking taylor expansion of (log n) in k 13.683 * [taylor]: Taking taylor expansion of n in k 13.683 * [backup-simplify]: Simplify n into n 13.683 * [backup-simplify]: Simplify (log n) into (log n) 13.683 * [backup-simplify]: Simplify (+ 1 0) into 1 13.683 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.684 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 13.684 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 13.685 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 13.686 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 13.687 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 13.688 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.688 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 13.689 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 13.690 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.690 * [backup-simplify]: Simplify (+ 0 0) into 0 13.690 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 13.691 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.692 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 13.694 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.694 * [taylor]: Taking taylor expansion of 0 in k 13.694 * [backup-simplify]: Simplify 0 into 0 13.694 * [backup-simplify]: Simplify 0 into 0 13.694 * [backup-simplify]: Simplify 0 into 0 13.694 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.695 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.697 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 13.697 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.697 * [backup-simplify]: Simplify (+ 0 0) into 0 13.698 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 13.699 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.700 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 13.702 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.702 * [taylor]: Taking taylor expansion of 0 in k 13.702 * [backup-simplify]: Simplify 0 into 0 13.702 * [backup-simplify]: Simplify 0 into 0 13.702 * [backup-simplify]: Simplify 0 into 0 13.702 * [backup-simplify]: Simplify 0 into 0 13.703 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.703 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.707 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 13.707 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.707 * [backup-simplify]: Simplify (+ 0 0) into 0 13.708 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 13.709 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.710 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 13.712 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.712 * [taylor]: Taking taylor expansion of 0 in k 13.712 * [backup-simplify]: Simplify 0 into 0 13.712 * [backup-simplify]: Simplify 0 into 0 13.713 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 13.713 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 2) 13.713 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 13.713 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 13.713 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 13.713 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 13.713 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 13.714 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 13.714 * [taylor]: Taking taylor expansion of 0.5 in k 13.714 * [backup-simplify]: Simplify 0.5 into 0.5 13.714 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 13.714 * [taylor]: Taking taylor expansion of 1.0 in k 13.714 * [backup-simplify]: Simplify 1.0 into 1.0 13.714 * [taylor]: Taking taylor expansion of k in k 13.714 * [backup-simplify]: Simplify 0 into 0 13.714 * [backup-simplify]: Simplify 1 into 1 13.714 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 13.714 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 13.714 * [taylor]: Taking taylor expansion of 2.0 in k 13.714 * [backup-simplify]: Simplify 2.0 into 2.0 13.714 * [taylor]: Taking taylor expansion of (* n PI) in k 13.714 * [taylor]: Taking taylor expansion of n in k 13.714 * [backup-simplify]: Simplify n into n 13.714 * [taylor]: Taking taylor expansion of PI in k 13.714 * [backup-simplify]: Simplify PI into PI 13.714 * [backup-simplify]: Simplify (* n PI) into (* n PI) 13.714 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 13.714 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 13.714 * [backup-simplify]: Simplify (- 0) into 0 13.714 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 13.715 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 13.715 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 13.715 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 13.715 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 13.715 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 13.715 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 13.715 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 13.715 * [taylor]: Taking taylor expansion of 0.5 in n 13.715 * [backup-simplify]: Simplify 0.5 into 0.5 13.715 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 13.715 * [taylor]: Taking taylor expansion of 1.0 in n 13.715 * [backup-simplify]: Simplify 1.0 into 1.0 13.715 * [taylor]: Taking taylor expansion of k in n 13.715 * [backup-simplify]: Simplify k into k 13.715 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 13.715 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 13.715 * [taylor]: Taking taylor expansion of 2.0 in n 13.715 * [backup-simplify]: Simplify 2.0 into 2.0 13.715 * [taylor]: Taking taylor expansion of (* n PI) in n 13.715 * [taylor]: Taking taylor expansion of n in n 13.715 * [backup-simplify]: Simplify 0 into 0 13.715 * [backup-simplify]: Simplify 1 into 1 13.715 * [taylor]: Taking taylor expansion of PI in n 13.715 * [backup-simplify]: Simplify PI into PI 13.716 * [backup-simplify]: Simplify (* 0 PI) into 0 13.716 * [backup-simplify]: Simplify (* 2.0 0) into 0 13.717 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.718 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 13.718 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.718 * [backup-simplify]: Simplify (- k) into (- k) 13.719 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 13.719 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 13.719 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.720 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 13.721 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 13.721 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 13.721 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 13.721 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 13.721 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 13.721 * [taylor]: Taking taylor expansion of 0.5 in n 13.721 * [backup-simplify]: Simplify 0.5 into 0.5 13.721 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 13.721 * [taylor]: Taking taylor expansion of 1.0 in n 13.721 * [backup-simplify]: Simplify 1.0 into 1.0 13.721 * [taylor]: Taking taylor expansion of k in n 13.721 * [backup-simplify]: Simplify k into k 13.721 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 13.721 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 13.721 * [taylor]: Taking taylor expansion of 2.0 in n 13.721 * [backup-simplify]: Simplify 2.0 into 2.0 13.721 * [taylor]: Taking taylor expansion of (* n PI) in n 13.721 * [taylor]: Taking taylor expansion of n in n 13.721 * [backup-simplify]: Simplify 0 into 0 13.721 * [backup-simplify]: Simplify 1 into 1 13.721 * [taylor]: Taking taylor expansion of PI in n 13.721 * [backup-simplify]: Simplify PI into PI 13.722 * [backup-simplify]: Simplify (* 0 PI) into 0 13.722 * [backup-simplify]: Simplify (* 2.0 0) into 0 13.723 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.724 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 13.725 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.725 * [backup-simplify]: Simplify (- k) into (- k) 13.725 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 13.725 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 13.726 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.726 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 13.727 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 13.727 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 13.727 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 13.727 * [taylor]: Taking taylor expansion of 0.5 in k 13.727 * [backup-simplify]: Simplify 0.5 into 0.5 13.727 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 13.727 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 13.727 * [taylor]: Taking taylor expansion of 1.0 in k 13.727 * [backup-simplify]: Simplify 1.0 into 1.0 13.727 * [taylor]: Taking taylor expansion of k in k 13.727 * [backup-simplify]: Simplify 0 into 0 13.727 * [backup-simplify]: Simplify 1 into 1 13.727 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 13.727 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 13.727 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 13.727 * [taylor]: Taking taylor expansion of 2.0 in k 13.727 * [backup-simplify]: Simplify 2.0 into 2.0 13.728 * [taylor]: Taking taylor expansion of PI in k 13.728 * [backup-simplify]: Simplify PI into PI 13.728 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.729 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.729 * [taylor]: Taking taylor expansion of (log n) in k 13.729 * [taylor]: Taking taylor expansion of n in k 13.729 * [backup-simplify]: Simplify n into n 13.729 * [backup-simplify]: Simplify (log n) into (log n) 13.729 * [backup-simplify]: Simplify (- 0) into 0 13.729 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 13.730 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 13.731 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 13.731 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 13.732 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 13.733 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 13.733 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.734 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 13.735 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 13.735 * [backup-simplify]: Simplify (- 0) into 0 13.736 * [backup-simplify]: Simplify (+ 0 0) into 0 13.736 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 13.737 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.737 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 13.739 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.739 * [taylor]: Taking taylor expansion of 0 in k 13.739 * [backup-simplify]: Simplify 0 into 0 13.739 * [backup-simplify]: Simplify 0 into 0 13.739 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 13.740 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 13.741 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 13.741 * [backup-simplify]: Simplify (+ 0 0) into 0 13.741 * [backup-simplify]: Simplify (- 1) into -1 13.742 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.743 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 13.744 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 13.746 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 13.752 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 13.753 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 13.753 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 13.755 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 13.756 * [backup-simplify]: Simplify (- 0) into 0 13.756 * [backup-simplify]: Simplify (+ 0 0) into 0 13.756 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 13.757 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.758 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 13.760 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.760 * [taylor]: Taking taylor expansion of 0 in k 13.760 * [backup-simplify]: Simplify 0 into 0 13.760 * [backup-simplify]: Simplify 0 into 0 13.760 * [backup-simplify]: Simplify 0 into 0 13.761 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.763 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 13.764 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 13.764 * [backup-simplify]: Simplify (+ 0 0) into 0 13.764 * [backup-simplify]: Simplify (- 0) into 0 13.764 * [backup-simplify]: Simplify (+ 0 0) into 0 13.766 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 13.767 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 13.770 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 13.773 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 13.779 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 13.780 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 13.780 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 13.780 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 13.780 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 13.780 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 13.780 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 13.780 * [taylor]: Taking taylor expansion of 0.5 in k 13.780 * [backup-simplify]: Simplify 0.5 into 0.5 13.780 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.780 * [taylor]: Taking taylor expansion of 1.0 in k 13.780 * [backup-simplify]: Simplify 1.0 into 1.0 13.780 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.780 * [taylor]: Taking taylor expansion of k in k 13.780 * [backup-simplify]: Simplify 0 into 0 13.780 * [backup-simplify]: Simplify 1 into 1 13.780 * [backup-simplify]: Simplify (/ 1 1) into 1 13.780 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 13.780 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 13.780 * [taylor]: Taking taylor expansion of 2.0 in k 13.780 * [backup-simplify]: Simplify 2.0 into 2.0 13.780 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.780 * [taylor]: Taking taylor expansion of PI in k 13.780 * [backup-simplify]: Simplify PI into PI 13.780 * [taylor]: Taking taylor expansion of n in k 13.781 * [backup-simplify]: Simplify n into n 13.781 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.781 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 13.781 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 13.781 * [backup-simplify]: Simplify (- 1) into -1 13.781 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.781 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 13.782 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 13.782 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 13.782 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 13.782 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 13.782 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 13.782 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 13.782 * [taylor]: Taking taylor expansion of 0.5 in n 13.782 * [backup-simplify]: Simplify 0.5 into 0.5 13.782 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 13.782 * [taylor]: Taking taylor expansion of 1.0 in n 13.782 * [backup-simplify]: Simplify 1.0 into 1.0 13.782 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.782 * [taylor]: Taking taylor expansion of k in n 13.782 * [backup-simplify]: Simplify k into k 13.782 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.782 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 13.782 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.782 * [taylor]: Taking taylor expansion of 2.0 in n 13.782 * [backup-simplify]: Simplify 2.0 into 2.0 13.782 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.782 * [taylor]: Taking taylor expansion of PI in n 13.782 * [backup-simplify]: Simplify PI into PI 13.782 * [taylor]: Taking taylor expansion of n in n 13.782 * [backup-simplify]: Simplify 0 into 0 13.782 * [backup-simplify]: Simplify 1 into 1 13.782 * [backup-simplify]: Simplify (/ PI 1) into PI 13.783 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.783 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.783 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 13.784 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 13.784 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 13.785 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.785 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 13.786 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 13.786 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 13.786 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 13.786 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 13.786 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 13.786 * [taylor]: Taking taylor expansion of 0.5 in n 13.786 * [backup-simplify]: Simplify 0.5 into 0.5 13.786 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 13.786 * [taylor]: Taking taylor expansion of 1.0 in n 13.786 * [backup-simplify]: Simplify 1.0 into 1.0 13.786 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.786 * [taylor]: Taking taylor expansion of k in n 13.786 * [backup-simplify]: Simplify k into k 13.786 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.786 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 13.786 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.786 * [taylor]: Taking taylor expansion of 2.0 in n 13.786 * [backup-simplify]: Simplify 2.0 into 2.0 13.786 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.786 * [taylor]: Taking taylor expansion of PI in n 13.786 * [backup-simplify]: Simplify PI into PI 13.786 * [taylor]: Taking taylor expansion of n in n 13.786 * [backup-simplify]: Simplify 0 into 0 13.786 * [backup-simplify]: Simplify 1 into 1 13.787 * [backup-simplify]: Simplify (/ PI 1) into PI 13.787 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.788 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.788 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 13.788 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 13.788 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 13.789 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.790 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 13.790 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 13.790 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 13.791 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 13.791 * [taylor]: Taking taylor expansion of 0.5 in k 13.791 * [backup-simplify]: Simplify 0.5 into 0.5 13.791 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 13.791 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 13.791 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 13.791 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 13.791 * [taylor]: Taking taylor expansion of 2.0 in k 13.791 * [backup-simplify]: Simplify 2.0 into 2.0 13.791 * [taylor]: Taking taylor expansion of PI in k 13.791 * [backup-simplify]: Simplify PI into PI 13.791 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.792 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.792 * [taylor]: Taking taylor expansion of (log n) in k 13.792 * [taylor]: Taking taylor expansion of n in k 13.792 * [backup-simplify]: Simplify n into n 13.792 * [backup-simplify]: Simplify (log n) into (log n) 13.792 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.792 * [taylor]: Taking taylor expansion of 1.0 in k 13.792 * [backup-simplify]: Simplify 1.0 into 1.0 13.792 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.792 * [taylor]: Taking taylor expansion of k in k 13.792 * [backup-simplify]: Simplify 0 into 0 13.792 * [backup-simplify]: Simplify 1 into 1 13.792 * [backup-simplify]: Simplify (/ 1 1) into 1 13.792 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.793 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 13.793 * [backup-simplify]: Simplify (- 1) into -1 13.793 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.794 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 13.795 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 13.796 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 13.796 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 13.797 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.797 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 13.798 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 13.799 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.799 * [backup-simplify]: Simplify (- 0) into 0 13.799 * [backup-simplify]: Simplify (+ 0 0) into 0 13.799 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 13.800 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.801 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 13.802 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.802 * [taylor]: Taking taylor expansion of 0 in k 13.802 * [backup-simplify]: Simplify 0 into 0 13.802 * [backup-simplify]: Simplify 0 into 0 13.802 * [backup-simplify]: Simplify 0 into 0 13.803 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.804 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.806 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 13.806 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.806 * [backup-simplify]: Simplify (- 0) into 0 13.807 * [backup-simplify]: Simplify (+ 0 0) into 0 13.808 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 13.809 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.810 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 13.812 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.812 * [taylor]: Taking taylor expansion of 0 in k 13.812 * [backup-simplify]: Simplify 0 into 0 13.812 * [backup-simplify]: Simplify 0 into 0 13.812 * [backup-simplify]: Simplify 0 into 0 13.812 * [backup-simplify]: Simplify 0 into 0 13.813 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.815 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.821 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 13.821 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.822 * [backup-simplify]: Simplify (- 0) into 0 13.822 * [backup-simplify]: Simplify (+ 0 0) into 0 13.824 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 13.826 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.828 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 13.831 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.831 * [taylor]: Taking taylor expansion of 0 in k 13.831 * [backup-simplify]: Simplify 0 into 0 13.831 * [backup-simplify]: Simplify 0 into 0 13.833 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 13.834 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 13.834 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 13.834 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 13.834 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 13.834 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 13.834 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 13.835 * [taylor]: Taking taylor expansion of 0.5 in k 13.835 * [backup-simplify]: Simplify 0.5 into 0.5 13.835 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.835 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.835 * [taylor]: Taking taylor expansion of k in k 13.835 * [backup-simplify]: Simplify 0 into 0 13.835 * [backup-simplify]: Simplify 1 into 1 13.835 * [backup-simplify]: Simplify (/ 1 1) into 1 13.835 * [taylor]: Taking taylor expansion of 1.0 in k 13.835 * [backup-simplify]: Simplify 1.0 into 1.0 13.835 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 13.835 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 13.835 * [taylor]: Taking taylor expansion of -2.0 in k 13.835 * [backup-simplify]: Simplify -2.0 into -2.0 13.835 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.835 * [taylor]: Taking taylor expansion of PI in k 13.835 * [backup-simplify]: Simplify PI into PI 13.836 * [taylor]: Taking taylor expansion of n in k 13.836 * [backup-simplify]: Simplify n into n 13.836 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.836 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 13.836 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 13.836 * [backup-simplify]: Simplify (+ 1 0) into 1 13.837 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 13.837 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 13.837 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 13.837 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 13.837 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 13.837 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 13.837 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 13.838 * [taylor]: Taking taylor expansion of 0.5 in n 13.838 * [backup-simplify]: Simplify 0.5 into 0.5 13.838 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 13.838 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.838 * [taylor]: Taking taylor expansion of k in n 13.838 * [backup-simplify]: Simplify k into k 13.838 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.838 * [taylor]: Taking taylor expansion of 1.0 in n 13.838 * [backup-simplify]: Simplify 1.0 into 1.0 13.838 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 13.838 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.838 * [taylor]: Taking taylor expansion of -2.0 in n 13.838 * [backup-simplify]: Simplify -2.0 into -2.0 13.838 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.838 * [taylor]: Taking taylor expansion of PI in n 13.838 * [backup-simplify]: Simplify PI into PI 13.838 * [taylor]: Taking taylor expansion of n in n 13.838 * [backup-simplify]: Simplify 0 into 0 13.838 * [backup-simplify]: Simplify 1 into 1 13.839 * [backup-simplify]: Simplify (/ PI 1) into PI 13.839 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.840 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.841 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 13.841 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 13.842 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.844 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 13.845 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 13.845 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 13.845 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 13.845 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 13.845 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 13.845 * [taylor]: Taking taylor expansion of 0.5 in n 13.845 * [backup-simplify]: Simplify 0.5 into 0.5 13.845 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 13.845 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.845 * [taylor]: Taking taylor expansion of k in n 13.845 * [backup-simplify]: Simplify k into k 13.845 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.845 * [taylor]: Taking taylor expansion of 1.0 in n 13.846 * [backup-simplify]: Simplify 1.0 into 1.0 13.846 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 13.846 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.846 * [taylor]: Taking taylor expansion of -2.0 in n 13.846 * [backup-simplify]: Simplify -2.0 into -2.0 13.846 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.846 * [taylor]: Taking taylor expansion of PI in n 13.846 * [backup-simplify]: Simplify PI into PI 13.846 * [taylor]: Taking taylor expansion of n in n 13.846 * [backup-simplify]: Simplify 0 into 0 13.846 * [backup-simplify]: Simplify 1 into 1 13.846 * [backup-simplify]: Simplify (/ PI 1) into PI 13.847 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.848 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.848 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 13.848 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 13.850 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.851 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 13.853 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 13.853 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 13.853 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 13.853 * [taylor]: Taking taylor expansion of 0.5 in k 13.853 * [backup-simplify]: Simplify 0.5 into 0.5 13.853 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 13.853 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.853 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.853 * [taylor]: Taking taylor expansion of k in k 13.853 * [backup-simplify]: Simplify 0 into 0 13.853 * [backup-simplify]: Simplify 1 into 1 13.854 * [backup-simplify]: Simplify (/ 1 1) into 1 13.854 * [taylor]: Taking taylor expansion of 1.0 in k 13.854 * [backup-simplify]: Simplify 1.0 into 1.0 13.854 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 13.854 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 13.854 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 13.854 * [taylor]: Taking taylor expansion of -2.0 in k 13.854 * [backup-simplify]: Simplify -2.0 into -2.0 13.854 * [taylor]: Taking taylor expansion of PI in k 13.854 * [backup-simplify]: Simplify PI into PI 13.855 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.856 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.856 * [taylor]: Taking taylor expansion of (log n) in k 13.856 * [taylor]: Taking taylor expansion of n in k 13.856 * [backup-simplify]: Simplify n into n 13.856 * [backup-simplify]: Simplify (log n) into (log n) 13.856 * [backup-simplify]: Simplify (+ 1 0) into 1 13.856 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.858 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 13.859 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 13.860 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 13.861 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 13.862 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 13.863 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.864 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 13.865 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 13.865 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.869 * [backup-simplify]: Simplify (+ 0 0) into 0 13.869 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 13.870 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.871 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 13.872 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.872 * [taylor]: Taking taylor expansion of 0 in k 13.872 * [backup-simplify]: Simplify 0 into 0 13.872 * [backup-simplify]: Simplify 0 into 0 13.873 * [backup-simplify]: Simplify 0 into 0 13.873 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.874 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.876 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 13.876 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.876 * [backup-simplify]: Simplify (+ 0 0) into 0 13.877 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 13.878 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.879 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 13.880 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.880 * [taylor]: Taking taylor expansion of 0 in k 13.880 * [backup-simplify]: Simplify 0 into 0 13.880 * [backup-simplify]: Simplify 0 into 0 13.880 * [backup-simplify]: Simplify 0 into 0 13.880 * [backup-simplify]: Simplify 0 into 0 13.881 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.881 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.885 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 13.885 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.885 * [backup-simplify]: Simplify (+ 0 0) into 0 13.886 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 13.887 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.888 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 13.890 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.890 * [taylor]: Taking taylor expansion of 0 in k 13.890 * [backup-simplify]: Simplify 0 into 0 13.890 * [backup-simplify]: Simplify 0 into 0 13.891 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 13.891 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1 2 2 1) 13.891 * [backup-simplify]: Simplify (cbrt k) into (pow k 1/3) 13.891 * [approximate]: Taking taylor expansion of (pow k 1/3) in (k) around 0 13.891 * [taylor]: Taking taylor expansion of (pow k 1/3) in k 13.891 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log k))) in k 13.891 * [taylor]: Taking taylor expansion of (* 1/3 (log k)) in k 13.891 * [taylor]: Taking taylor expansion of 1/3 in k 13.891 * [backup-simplify]: Simplify 1/3 into 1/3 13.891 * [taylor]: Taking taylor expansion of (log k) in k 13.891 * [taylor]: Taking taylor expansion of k in k 13.891 * [backup-simplify]: Simplify 0 into 0 13.891 * [backup-simplify]: Simplify 1 into 1 13.891 * [backup-simplify]: Simplify (log 1) into 0 13.892 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 13.892 * [backup-simplify]: Simplify (* 1/3 (log k)) into (* 1/3 (log k)) 13.892 * [backup-simplify]: Simplify (exp (* 1/3 (log k))) into (pow k 1/3) 13.892 * [taylor]: Taking taylor expansion of (pow k 1/3) in k 13.892 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log k))) in k 13.892 * [taylor]: Taking taylor expansion of (* 1/3 (log k)) in k 13.892 * [taylor]: Taking taylor expansion of 1/3 in k 13.892 * [backup-simplify]: Simplify 1/3 into 1/3 13.892 * [taylor]: Taking taylor expansion of (log k) in k 13.892 * [taylor]: Taking taylor expansion of k in k 13.892 * [backup-simplify]: Simplify 0 into 0 13.892 * [backup-simplify]: Simplify 1 into 1 13.892 * [backup-simplify]: Simplify (log 1) into 0 13.892 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 13.892 * [backup-simplify]: Simplify (* 1/3 (log k)) into (* 1/3 (log k)) 13.892 * [backup-simplify]: Simplify (exp (* 1/3 (log k))) into (pow k 1/3) 13.893 * [backup-simplify]: Simplify (pow k 1/3) into (pow k 1/3) 13.893 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 13.894 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 13.894 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (log k))) into 0 13.895 * [backup-simplify]: Simplify (* (exp (* 1/3 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 13.895 * [backup-simplify]: Simplify 0 into 0 13.896 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 13.896 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 13.897 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (log k)))) into 0 13.898 * [backup-simplify]: Simplify (* (exp (* 1/3 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.898 * [backup-simplify]: Simplify 0 into 0 13.902 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 13.902 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 13.903 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0 13.905 * [backup-simplify]: Simplify (* (exp (* 1/3 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.905 * [backup-simplify]: Simplify 0 into 0 13.917 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 13.918 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 13.919 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0 13.922 * [backup-simplify]: Simplify (* (exp (* 1/3 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.922 * [backup-simplify]: Simplify 0 into 0 13.941 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 13.941 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 13.943 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0 13.947 * [backup-simplify]: Simplify (* (exp (* 1/3 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.947 * [backup-simplify]: Simplify 0 into 0 13.982 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 13.983 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 13.985 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0 13.992 * [backup-simplify]: Simplify (* (exp (* 1/3 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.992 * [backup-simplify]: Simplify 0 into 0 13.992 * [backup-simplify]: Simplify (pow k 1/3) into (pow k 1/3) 13.992 * [backup-simplify]: Simplify (cbrt (/ 1 k)) into (pow (/ 1 k) 1/3) 13.992 * [approximate]: Taking taylor expansion of (pow (/ 1 k) 1/3) in (k) around 0 13.992 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 13.992 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 13.992 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 13.992 * [taylor]: Taking taylor expansion of 1/3 in k 13.992 * [backup-simplify]: Simplify 1/3 into 1/3 13.992 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 13.992 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.992 * [taylor]: Taking taylor expansion of k in k 13.992 * [backup-simplify]: Simplify 0 into 0 13.992 * [backup-simplify]: Simplify 1 into 1 13.993 * [backup-simplify]: Simplify (/ 1 1) into 1 13.994 * [backup-simplify]: Simplify (log 1) into 0 13.994 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 13.994 * [backup-simplify]: Simplify (* 1/3 (- (log k))) into (* -1/3 (log k)) 13.994 * [backup-simplify]: Simplify (exp (* -1/3 (log k))) into (pow k -1/3) 13.994 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 13.995 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 13.995 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 13.995 * [taylor]: Taking taylor expansion of 1/3 in k 13.995 * [backup-simplify]: Simplify 1/3 into 1/3 13.995 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 13.995 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.995 * [taylor]: Taking taylor expansion of k in k 13.995 * [backup-simplify]: Simplify 0 into 0 13.995 * [backup-simplify]: Simplify 1 into 1 13.995 * [backup-simplify]: Simplify (/ 1 1) into 1 13.996 * [backup-simplify]: Simplify (log 1) into 0 13.996 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 13.996 * [backup-simplify]: Simplify (* 1/3 (- (log k))) into (* -1/3 (log k)) 13.996 * [backup-simplify]: Simplify (exp (* -1/3 (log k))) into (pow k -1/3) 13.996 * [backup-simplify]: Simplify (pow k -1/3) into (pow k -1/3) 13.997 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 13.999 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 13.999 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.000 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log k)))) into 0 14.001 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 14.001 * [backup-simplify]: Simplify 0 into 0 14.002 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.009 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 14.010 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.011 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 14.013 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.013 * [backup-simplify]: Simplify 0 into 0 14.014 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.017 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 14.018 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.019 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0 14.020 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 14.020 * [backup-simplify]: Simplify 0 into 0 14.020 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.026 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 14.027 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.028 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0 14.029 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.029 * [backup-simplify]: Simplify 0 into 0 14.030 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.040 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 14.040 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.041 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0 14.043 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 14.043 * [backup-simplify]: Simplify 0 into 0 14.044 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.061 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 14.062 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.063 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0 14.069 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.069 * [backup-simplify]: Simplify 0 into 0 14.070 * [backup-simplify]: Simplify (pow (/ 1 k) -1/3) into (pow (/ 1 k) -1/3) 14.070 * [backup-simplify]: Simplify (cbrt (/ 1 (- k))) into (* (pow (/ 1 k) 1/3) (cbrt -1)) 14.070 * [approximate]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in (k) around 0 14.070 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in k 14.070 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 14.070 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 14.070 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 14.070 * [taylor]: Taking taylor expansion of 1/3 in k 14.070 * [backup-simplify]: Simplify 1/3 into 1/3 14.070 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 14.070 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.070 * [taylor]: Taking taylor expansion of k in k 14.070 * [backup-simplify]: Simplify 0 into 0 14.070 * [backup-simplify]: Simplify 1 into 1 14.071 * [backup-simplify]: Simplify (/ 1 1) into 1 14.071 * [backup-simplify]: Simplify (log 1) into 0 14.072 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.072 * [backup-simplify]: Simplify (* 1/3 (- (log k))) into (* -1/3 (log k)) 14.072 * [backup-simplify]: Simplify (exp (* -1/3 (log k))) into (pow k -1/3) 14.072 * [taylor]: Taking taylor expansion of (cbrt -1) in k 14.072 * [taylor]: Taking taylor expansion of -1 in k 14.072 * [backup-simplify]: Simplify -1 into -1 14.072 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 14.073 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 14.073 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in k 14.073 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 14.073 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 14.073 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 14.073 * [taylor]: Taking taylor expansion of 1/3 in k 14.073 * [backup-simplify]: Simplify 1/3 into 1/3 14.073 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 14.073 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.074 * [taylor]: Taking taylor expansion of k in k 14.074 * [backup-simplify]: Simplify 0 into 0 14.074 * [backup-simplify]: Simplify 1 into 1 14.074 * [backup-simplify]: Simplify (/ 1 1) into 1 14.074 * [backup-simplify]: Simplify (log 1) into 0 14.075 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.075 * [backup-simplify]: Simplify (* 1/3 (- (log k))) into (* -1/3 (log k)) 14.075 * [backup-simplify]: Simplify (exp (* -1/3 (log k))) into (pow k -1/3) 14.075 * [taylor]: Taking taylor expansion of (cbrt -1) in k 14.075 * [taylor]: Taking taylor expansion of -1 in k 14.075 * [backup-simplify]: Simplify -1 into -1 14.076 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 14.076 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 14.077 * [backup-simplify]: Simplify (* (pow k -1/3) (cbrt -1)) into (* (pow (/ 1 k) 1/3) (cbrt -1)) 14.078 * [backup-simplify]: Simplify (* (pow (/ 1 k) 1/3) (cbrt -1)) into (* (pow (/ 1 k) 1/3) (cbrt -1)) 14.079 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 14.080 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 14.081 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.081 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log k)))) into 0 14.082 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 14.083 * [backup-simplify]: Simplify (+ (* (pow k -1/3) 0) (* 0 (cbrt -1))) into 0 14.083 * [backup-simplify]: Simplify 0 into 0 14.085 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 14.086 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.089 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 14.089 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.090 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 14.092 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.093 * [backup-simplify]: Simplify (+ (* (pow k -1/3) 0) (+ (* 0 0) (* 0 (cbrt -1)))) into 0 14.093 * [backup-simplify]: Simplify 0 into 0 14.094 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 14.095 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.101 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 14.101 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.102 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0 14.104 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 14.105 * [backup-simplify]: Simplify (+ (* (pow k -1/3) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (cbrt -1))))) into 0 14.105 * [backup-simplify]: Simplify 0 into 0 14.106 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 14.106 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.112 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 14.113 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.114 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0 14.118 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.119 * [backup-simplify]: Simplify (+ (* (pow k -1/3) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (cbrt -1)))))) into 0 14.119 * [backup-simplify]: Simplify 0 into 0 14.120 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 14.121 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.131 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 14.131 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.133 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0 14.136 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 14.137 * [backup-simplify]: Simplify (+ (* (pow k -1/3) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (cbrt -1))))))) into 0 14.137 * [backup-simplify]: Simplify 0 into 0 14.138 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 14.139 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.169 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 14.170 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.172 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0 14.179 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.181 * [backup-simplify]: Simplify (+ (* (pow k -1/3) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (cbrt -1)))))))) into 0 14.181 * [backup-simplify]: Simplify 0 into 0 14.182 * [backup-simplify]: Simplify (* (pow (/ 1 (/ 1 (- k))) 1/3) (cbrt -1)) into (* (pow (* -1 k) 1/3) (cbrt -1)) 14.182 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1 1 2 1) 14.182 * [backup-simplify]: Simplify (cbrt k) into (pow k 1/3) 14.182 * [approximate]: Taking taylor expansion of (pow k 1/3) in (k) around 0 14.182 * [taylor]: Taking taylor expansion of (pow k 1/3) in k 14.182 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log k))) in k 14.182 * [taylor]: Taking taylor expansion of (* 1/3 (log k)) in k 14.182 * [taylor]: Taking taylor expansion of 1/3 in k 14.182 * [backup-simplify]: Simplify 1/3 into 1/3 14.183 * [taylor]: Taking taylor expansion of (log k) in k 14.183 * [taylor]: Taking taylor expansion of k in k 14.183 * [backup-simplify]: Simplify 0 into 0 14.183 * [backup-simplify]: Simplify 1 into 1 14.183 * [backup-simplify]: Simplify (log 1) into 0 14.184 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 14.184 * [backup-simplify]: Simplify (* 1/3 (log k)) into (* 1/3 (log k)) 14.184 * [backup-simplify]: Simplify (exp (* 1/3 (log k))) into (pow k 1/3) 14.184 * [taylor]: Taking taylor expansion of (pow k 1/3) in k 14.184 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log k))) in k 14.184 * [taylor]: Taking taylor expansion of (* 1/3 (log k)) in k 14.184 * [taylor]: Taking taylor expansion of 1/3 in k 14.184 * [backup-simplify]: Simplify 1/3 into 1/3 14.184 * [taylor]: Taking taylor expansion of (log k) in k 14.184 * [taylor]: Taking taylor expansion of k in k 14.184 * [backup-simplify]: Simplify 0 into 0 14.184 * [backup-simplify]: Simplify 1 into 1 14.184 * [backup-simplify]: Simplify (log 1) into 0 14.185 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 14.185 * [backup-simplify]: Simplify (* 1/3 (log k)) into (* 1/3 (log k)) 14.185 * [backup-simplify]: Simplify (exp (* 1/3 (log k))) into (pow k 1/3) 14.185 * [backup-simplify]: Simplify (pow k 1/3) into (pow k 1/3) 14.187 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 14.187 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 14.188 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (log k))) into 0 14.189 * [backup-simplify]: Simplify (* (exp (* 1/3 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 14.189 * [backup-simplify]: Simplify 0 into 0 14.192 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 14.192 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 14.193 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (log k)))) into 0 14.195 * [backup-simplify]: Simplify (* (exp (* 1/3 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.195 * [backup-simplify]: Simplify 0 into 0 14.200 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 14.201 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 14.202 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0 14.204 * [backup-simplify]: Simplify (* (exp (* 1/3 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 14.204 * [backup-simplify]: Simplify 0 into 0 14.215 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 14.216 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 14.218 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0 14.220 * [backup-simplify]: Simplify (* (exp (* 1/3 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.220 * [backup-simplify]: Simplify 0 into 0 14.231 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 14.232 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 14.233 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0 14.235 * [backup-simplify]: Simplify (* (exp (* 1/3 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 14.235 * [backup-simplify]: Simplify 0 into 0 14.255 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 14.256 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 14.257 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0 14.261 * [backup-simplify]: Simplify (* (exp (* 1/3 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.261 * [backup-simplify]: Simplify 0 into 0 14.261 * [backup-simplify]: Simplify (pow k 1/3) into (pow k 1/3) 14.262 * [backup-simplify]: Simplify (cbrt (/ 1 k)) into (pow (/ 1 k) 1/3) 14.262 * [approximate]: Taking taylor expansion of (pow (/ 1 k) 1/3) in (k) around 0 14.262 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 14.262 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 14.262 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 14.262 * [taylor]: Taking taylor expansion of 1/3 in k 14.262 * [backup-simplify]: Simplify 1/3 into 1/3 14.262 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 14.262 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.262 * [taylor]: Taking taylor expansion of k in k 14.262 * [backup-simplify]: Simplify 0 into 0 14.262 * [backup-simplify]: Simplify 1 into 1 14.262 * [backup-simplify]: Simplify (/ 1 1) into 1 14.263 * [backup-simplify]: Simplify (log 1) into 0 14.263 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.263 * [backup-simplify]: Simplify (* 1/3 (- (log k))) into (* -1/3 (log k)) 14.264 * [backup-simplify]: Simplify (exp (* -1/3 (log k))) into (pow k -1/3) 14.264 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 14.264 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 14.264 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 14.264 * [taylor]: Taking taylor expansion of 1/3 in k 14.264 * [backup-simplify]: Simplify 1/3 into 1/3 14.264 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 14.264 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.264 * [taylor]: Taking taylor expansion of k in k 14.264 * [backup-simplify]: Simplify 0 into 0 14.264 * [backup-simplify]: Simplify 1 into 1 14.264 * [backup-simplify]: Simplify (/ 1 1) into 1 14.265 * [backup-simplify]: Simplify (log 1) into 0 14.265 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.265 * [backup-simplify]: Simplify (* 1/3 (- (log k))) into (* -1/3 (log k)) 14.265 * [backup-simplify]: Simplify (exp (* -1/3 (log k))) into (pow k -1/3) 14.266 * [backup-simplify]: Simplify (pow k -1/3) into (pow k -1/3) 14.266 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 14.268 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 14.269 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.269 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log k)))) into 0 14.270 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 14.270 * [backup-simplify]: Simplify 0 into 0 14.271 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.274 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 14.274 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.275 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 14.277 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.277 * [backup-simplify]: Simplify 0 into 0 14.278 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.284 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 14.284 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.286 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0 14.287 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 14.288 * [backup-simplify]: Simplify 0 into 0 14.289 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.300 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 14.301 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.302 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0 14.305 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.305 * [backup-simplify]: Simplify 0 into 0 14.306 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.316 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 14.316 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.317 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0 14.320 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 14.320 * [backup-simplify]: Simplify 0 into 0 14.320 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.338 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 14.339 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.342 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0 14.347 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.347 * [backup-simplify]: Simplify 0 into 0 14.348 * [backup-simplify]: Simplify (pow (/ 1 k) -1/3) into (pow (/ 1 k) -1/3) 14.348 * [backup-simplify]: Simplify (cbrt (/ 1 (- k))) into (* (pow (/ 1 k) 1/3) (cbrt -1)) 14.348 * [approximate]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in (k) around 0 14.348 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in k 14.348 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 14.348 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 14.348 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 14.348 * [taylor]: Taking taylor expansion of 1/3 in k 14.348 * [backup-simplify]: Simplify 1/3 into 1/3 14.348 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 14.348 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.348 * [taylor]: Taking taylor expansion of k in k 14.348 * [backup-simplify]: Simplify 0 into 0 14.348 * [backup-simplify]: Simplify 1 into 1 14.349 * [backup-simplify]: Simplify (/ 1 1) into 1 14.349 * [backup-simplify]: Simplify (log 1) into 0 14.349 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.350 * [backup-simplify]: Simplify (* 1/3 (- (log k))) into (* -1/3 (log k)) 14.350 * [backup-simplify]: Simplify (exp (* -1/3 (log k))) into (pow k -1/3) 14.350 * [taylor]: Taking taylor expansion of (cbrt -1) in k 14.350 * [taylor]: Taking taylor expansion of -1 in k 14.350 * [backup-simplify]: Simplify -1 into -1 14.350 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 14.351 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 14.351 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/3) (cbrt -1)) in k 14.351 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 14.351 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 14.351 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 14.351 * [taylor]: Taking taylor expansion of 1/3 in k 14.351 * [backup-simplify]: Simplify 1/3 into 1/3 14.351 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 14.351 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.351 * [taylor]: Taking taylor expansion of k in k 14.351 * [backup-simplify]: Simplify 0 into 0 14.351 * [backup-simplify]: Simplify 1 into 1 14.352 * [backup-simplify]: Simplify (/ 1 1) into 1 14.352 * [backup-simplify]: Simplify (log 1) into 0 14.352 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.352 * [backup-simplify]: Simplify (* 1/3 (- (log k))) into (* -1/3 (log k)) 14.352 * [backup-simplify]: Simplify (exp (* -1/3 (log k))) into (pow k -1/3) 14.352 * [taylor]: Taking taylor expansion of (cbrt -1) in k 14.352 * [taylor]: Taking taylor expansion of -1 in k 14.352 * [backup-simplify]: Simplify -1 into -1 14.353 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 14.353 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 14.353 * [backup-simplify]: Simplify (* (pow k -1/3) (cbrt -1)) into (* (pow (/ 1 k) 1/3) (cbrt -1)) 14.354 * [backup-simplify]: Simplify (* (pow (/ 1 k) 1/3) (cbrt -1)) into (* (pow (/ 1 k) 1/3) (cbrt -1)) 14.354 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 14.355 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 14.355 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.356 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log k)))) into 0 14.356 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 14.357 * [backup-simplify]: Simplify (+ (* (pow k -1/3) 0) (* 0 (cbrt -1))) into 0 14.357 * [backup-simplify]: Simplify 0 into 0 14.358 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 14.358 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.360 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 14.360 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.361 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 14.368 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.370 * [backup-simplify]: Simplify (+ (* (pow k -1/3) 0) (+ (* 0 0) (* 0 (cbrt -1)))) into 0 14.370 * [backup-simplify]: Simplify 0 into 0 14.371 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 14.372 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.374 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 14.375 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.375 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0 14.376 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 14.377 * [backup-simplify]: Simplify (+ (* (pow k -1/3) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (cbrt -1))))) into 0 14.377 * [backup-simplify]: Simplify 0 into 0 14.378 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 14.379 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.385 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 14.386 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.388 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0 14.391 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.392 * [backup-simplify]: Simplify (+ (* (pow k -1/3) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (cbrt -1)))))) into 0 14.392 * [backup-simplify]: Simplify 0 into 0 14.394 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 14.395 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.406 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 14.406 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.407 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0 14.409 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 14.410 * [backup-simplify]: Simplify (+ (* (pow k -1/3) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (cbrt -1))))))) into 0 14.410 * [backup-simplify]: Simplify 0 into 0 14.411 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 14.412 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.429 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 14.430 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.431 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0 14.436 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.438 * [backup-simplify]: Simplify (+ (* (pow k -1/3) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (cbrt -1)))))))) into 0 14.438 * [backup-simplify]: Simplify 0 into 0 14.439 * [backup-simplify]: Simplify (* (pow (/ 1 (/ 1 (- k))) 1/3) (cbrt -1)) into (* (pow (* -1 k) 1/3) (cbrt -1)) 14.439 * * * [progress]: simplifying candidates 14.442 * [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 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 (cbrt k)) (exp (cbrt k)) (cbrt (* (cbrt k) (cbrt k))) (cbrt (cbrt k)) (cbrt (sqrt k)) (cbrt (sqrt k)) (cbrt 1) (cbrt k) (* (cbrt (cbrt k)) (cbrt (cbrt k))) (cbrt (cbrt k)) (* (* (cbrt k) (cbrt k)) (cbrt k)) (sqrt (cbrt k)) (sqrt (cbrt k)) (log (cbrt k)) (exp (cbrt k)) (cbrt (* (cbrt k) (cbrt k))) (cbrt (cbrt k)) (cbrt (sqrt k)) (cbrt (sqrt k)) (cbrt 1) (cbrt k) (* (cbrt (cbrt k)) (cbrt (cbrt k))) (cbrt (cbrt k)) (* (* (cbrt k) (cbrt k)) (cbrt k)) (sqrt (cbrt k)) (sqrt (cbrt k)) (- (+ (* 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)))))) (- (+ (* 0.125 (* (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)))))) (pow k 1/3) (pow (/ 1 k) -1/3) (* (pow (* -1 k) 1/3) (cbrt -1)) (pow k 1/3) (pow (/ 1 k) -1/3) (* (pow (* -1 k) 1/3) (cbrt -1)) 14.447 * * [simplify]: Extracting # 0 : cost 0 14.447 * * [simplify]: Extracting # 1 : cost 0 14.447 * * [simplify]: Extracting # 2 : cost 0 14.447 * * [simplify]: Extracting # 3 : cost 0 14.448 * * [simplify]: Extracting # 4 : cost 0 14.448 * * [simplify]: Extracting # 5 : cost 0 14.449 * * [simplify]: Extracting # 6 : cost 0 14.449 * * [simplify]: Extracting # 7 : cost 0 14.449 * * [simplify]: Extracting # 8 : cost 0 14.450 * * [simplify]: Extracting # 9 : cost 0 14.450 * * [simplify]: Extracting # 10 : cost 0 14.450 * * [simplify]: Extracting # 11 : cost 0 14.451 * * [simplify]: iteration 0 : 143 enodes (cost 1440 ) 14.502 * * [simplify]: Extracting # 0 : cost 0 14.502 * * [simplify]: Extracting # 1 : cost 0 14.502 * * [simplify]: Extracting # 2 : cost 0 14.503 * * [simplify]: Extracting # 3 : cost 0 14.503 * * [simplify]: Extracting # 4 : cost 0 14.504 * * [simplify]: Extracting # 5 : cost 0 14.505 * * [simplify]: Extracting # 6 : cost 0 14.506 * * [simplify]: Extracting # 7 : cost 0 14.507 * * [simplify]: iteration 1 : 382 enodes (cost 1344 ) 14.690 * * [simplify]: Extracting # 0 : cost 0 14.693 * * [simplify]: Extracting # 1 : cost 0 14.697 * * [simplify]: Extracting # 2 : cost 0 14.700 * * [simplify]: Extracting # 3 : cost 0 14.703 * * [simplify]: Extracting # 4 : cost 0 14.706 * * [simplify]: iteration 2 : 1411 enodes (cost 1260 ) 15.191 * * [simplify]: Extracting # 0 : cost 0 15.203 * * [simplify]: Extracting # 1 : cost 0 15.215 * * [simplify]: Extracting # 2 : cost 0 15.223 * * [simplify]: Extracting # 3 : cost 0 15.236 * * [simplify]: Extracting # 4 : cost 0 15.246 * * [simplify]: iteration done: 5000 enodes (cost 1254 ) 15.247 * [simplify]: Simplified to: (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (log (cbrt k)) (exp (cbrt k)) (cbrt (pow k 2/3)) (cbrt (cbrt k)) (cbrt (sqrt k)) (cbrt (sqrt k)) 1 (cbrt k) (* (cbrt (cbrt k)) (cbrt (cbrt k))) (cbrt (cbrt k)) k (sqrt (cbrt k)) (sqrt (cbrt k)) (log (cbrt k)) (exp (cbrt k)) (cbrt (pow k 2/3)) (cbrt (cbrt k)) (cbrt (sqrt k)) (cbrt (sqrt k)) 1 (cbrt k) (* (cbrt (cbrt k)) (cbrt (cbrt k))) (cbrt (cbrt k)) k (sqrt (cbrt k)) (sqrt (cbrt k)) (- (+ (+ (* (* 0.125 (pow k 2)) (+ (* (pow (* (* 2.0 PI) n) 0.5) (pow (log (* 2.0 PI)) 2)) (* (pow (* (* 2.0 PI) n) 0.5) (pow (log n) 2)))) (pow (* (* 2.0 PI) n) 0.5)) (* (* (* (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.5)) (log n)) (* 0.25 (pow k 2)))) (* (* 0.5 k) (+ (* (log n) (pow (* (* 2.0 PI) n) 0.5)) (* (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.5))))) (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (+ (* (* 0.125 (pow k 2)) (+ (* (pow (* (* 2.0 PI) n) 0.5) (pow (log (* 2.0 PI)) 2)) (* (pow (* (* 2.0 PI) n) 0.5) (pow (log n) 2)))) (pow (* (* 2.0 PI) n) 0.5)) (* (* (* (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.5)) (log n)) (* 0.25 (pow k 2)))) (* (* 0.5 k) (+ (* (log n) (pow (* (* 2.0 PI) n) 0.5)) (* (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.5))))) (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (cbrt k) (pow (/ 1 k) -1/3) (* (cbrt -1) (cbrt (- k))) (cbrt k) (pow (/ 1 k) -1/3) (* (cbrt -1) (cbrt (- k))) 15.248 * * * [progress]: adding candidates to table 16.092 * [progress]: [Phase 3 of 3] Extracting. 16.092 * * [regime]: Finding splitpoints for: (# # # # # # # # #) 16.098 * * * [regime-changes]: Trying 4 branch expressions: ((* (* 2.0 PI) n) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) n k) 16.098 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # # # #) 16.146 * * * * [regimes]: Trying to branch on (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) from (# # # # # # # # #) 16.221 * * * * [regimes]: Trying to branch on n from (# # # # # # # # #) 16.314 * * * * [regimes]: Trying to branch on k from (# # # # # # # # #) 16.369 * * * [regime]: Found split indices: #