48.865 * [progress]: [Phase 1 of 3] Setting up. 0.002 * * * [progress]: [1/2] Preparing points 0.181 * * * [progress]: [2/2] Setting up program. 0.184 * [progress]: [Phase 2 of 3] Improving. 0.184 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.184 * * [simplify]: Extracting # 0 : cost 0 0.184 * * [simplify]: Extracting # 1 : cost 0 0.184 * * [simplify]: Extracting # 2 : cost 0 0.184 * * [simplify]: Extracting # 3 : cost 0 0.184 * * [simplify]: Extracting # 4 : cost 0 0.185 * * [simplify]: Extracting # 5 : cost 0 0.185 * * [simplify]: Extracting # 6 : cost 0 0.185 * * [simplify]: Extracting # 7 : cost 0 0.185 * * [simplify]: iteration 0 : 13 enodes (cost 16 ) 0.188 * * [simplify]: Extracting # 0 : cost 0 0.188 * * [simplify]: Extracting # 1 : cost 0 0.188 * * [simplify]: Extracting # 2 : cost 0 0.188 * * [simplify]: Extracting # 3 : cost 0 0.188 * * [simplify]: Extracting # 4 : cost 0 0.188 * * [simplify]: Extracting # 5 : cost 0 0.188 * * [simplify]: iteration 1 : 29 enodes (cost 16 ) 0.194 * * [simplify]: Extracting # 0 : cost 0 0.194 * * [simplify]: Extracting # 1 : cost 0 0.194 * * [simplify]: Extracting # 2 : cost 0 0.194 * * [simplify]: Extracting # 3 : cost 0 0.194 * * [simplify]: Extracting # 4 : cost 0 0.195 * * [simplify]: iteration 2 : 59 enodes (cost 16 ) 0.207 * * [simplify]: Extracting # 0 : cost 0 0.207 * * [simplify]: Extracting # 1 : cost 0 0.207 * * [simplify]: Extracting # 2 : cost 0 0.207 * * [simplify]: Extracting # 3 : cost 0 0.207 * * [simplify]: Extracting # 4 : cost 0 0.208 * * [simplify]: iteration 3 : 120 enodes (cost 16 ) 0.258 * * [simplify]: Extracting # 0 : cost 0 0.259 * * [simplify]: Extracting # 1 : cost 0 0.259 * * [simplify]: Extracting # 2 : cost 0 0.259 * * [simplify]: Extracting # 3 : cost 0 0.259 * * [simplify]: Extracting # 4 : cost 0 0.260 * * [simplify]: iteration 4 : 330 enodes (cost 16 ) 0.495 * * [simplify]: Extracting # 0 : cost 0 0.498 * * [simplify]: Extracting # 1 : cost 0 0.501 * * [simplify]: Extracting # 2 : cost 0 0.504 * * [simplify]: Extracting # 3 : cost 0 0.506 * * [simplify]: Extracting # 4 : cost 0 0.508 * * [simplify]: Extracting # 5 : cost 0 0.509 * * [simplify]: iteration 5 : 1555 enodes (cost 16 ) 1.419 * * [simplify]: Extracting # 0 : cost 0 1.451 * * [simplify]: Extracting # 1 : cost 0 1.458 * * [simplify]: Extracting # 2 : cost 0 1.470 * * [simplify]: Extracting # 3 : cost 0 1.484 * * [simplify]: Extracting # 4 : cost 0 1.496 * * [simplify]: iteration done: 5001 enodes (cost 16 ) 1.496 * [simplify]: Simplified to: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1.497 * * [progress]: iteration 1 / 4 1.497 * * * [progress]: picking best candidate 1.501 * * * * [pick]: Picked # 1.501 * * * [progress]: localizing error 1.533 * * * [progress]: generating rewritten candidates 1.533 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 1.562 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 1.569 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 1.609 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 1.706 * * * [progress]: generating series expansions 1.706 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 1.707 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 1.707 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 1.708 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.708 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.708 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.708 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.708 * [taylor]: Taking taylor expansion of 0.5 in k 1.708 * [backup-simplify]: Simplify 0.5 into 0.5 1.708 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.708 * [taylor]: Taking taylor expansion of 1.0 in k 1.708 * [backup-simplify]: Simplify 1.0 into 1.0 1.708 * [taylor]: Taking taylor expansion of k in k 1.708 * [backup-simplify]: Simplify 0 into 0 1.708 * [backup-simplify]: Simplify 1 into 1 1.708 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.708 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.708 * [taylor]: Taking taylor expansion of 2.0 in k 1.708 * [backup-simplify]: Simplify 2.0 into 2.0 1.708 * [taylor]: Taking taylor expansion of (* n PI) in k 1.708 * [taylor]: Taking taylor expansion of n in k 1.708 * [backup-simplify]: Simplify n into n 1.708 * [taylor]: Taking taylor expansion of PI in k 1.708 * [backup-simplify]: Simplify PI into PI 1.708 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.708 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.708 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.709 * [backup-simplify]: Simplify (- 0) into 0 1.709 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.714 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 1.714 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 1.715 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 1.715 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.715 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.715 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.715 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.715 * [taylor]: Taking taylor expansion of 0.5 in n 1.715 * [backup-simplify]: Simplify 0.5 into 0.5 1.715 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.715 * [taylor]: Taking taylor expansion of 1.0 in n 1.715 * [backup-simplify]: Simplify 1.0 into 1.0 1.715 * [taylor]: Taking taylor expansion of k in n 1.715 * [backup-simplify]: Simplify k into k 1.715 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.715 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.715 * [taylor]: Taking taylor expansion of 2.0 in n 1.715 * [backup-simplify]: Simplify 2.0 into 2.0 1.715 * [taylor]: Taking taylor expansion of (* n PI) in n 1.715 * [taylor]: Taking taylor expansion of n in n 1.715 * [backup-simplify]: Simplify 0 into 0 1.715 * [backup-simplify]: Simplify 1 into 1 1.715 * [taylor]: Taking taylor expansion of PI in n 1.715 * [backup-simplify]: Simplify PI into PI 1.716 * [backup-simplify]: Simplify (* 0 PI) into 0 1.716 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.718 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.720 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.721 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.721 * [backup-simplify]: Simplify (- k) into (- k) 1.721 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.721 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.722 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.723 * [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)))) 1.725 * [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))))) 1.725 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.725 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.725 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.725 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.725 * [taylor]: Taking taylor expansion of 0.5 in n 1.725 * [backup-simplify]: Simplify 0.5 into 0.5 1.725 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.725 * [taylor]: Taking taylor expansion of 1.0 in n 1.725 * [backup-simplify]: Simplify 1.0 into 1.0 1.725 * [taylor]: Taking taylor expansion of k in n 1.725 * [backup-simplify]: Simplify k into k 1.725 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.725 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.725 * [taylor]: Taking taylor expansion of 2.0 in n 1.725 * [backup-simplify]: Simplify 2.0 into 2.0 1.725 * [taylor]: Taking taylor expansion of (* n PI) in n 1.725 * [taylor]: Taking taylor expansion of n in n 1.725 * [backup-simplify]: Simplify 0 into 0 1.725 * [backup-simplify]: Simplify 1 into 1 1.725 * [taylor]: Taking taylor expansion of PI in n 1.725 * [backup-simplify]: Simplify PI into PI 1.726 * [backup-simplify]: Simplify (* 0 PI) into 0 1.726 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.727 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.728 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.729 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.729 * [backup-simplify]: Simplify (- k) into (- k) 1.729 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.729 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.730 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.731 * [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)))) 1.731 * [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))))) 1.731 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.731 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.732 * [taylor]: Taking taylor expansion of 0.5 in k 1.732 * [backup-simplify]: Simplify 0.5 into 0.5 1.732 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.732 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.732 * [taylor]: Taking taylor expansion of 1.0 in k 1.732 * [backup-simplify]: Simplify 1.0 into 1.0 1.732 * [taylor]: Taking taylor expansion of k in k 1.732 * [backup-simplify]: Simplify 0 into 0 1.732 * [backup-simplify]: Simplify 1 into 1 1.732 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.732 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.732 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.732 * [taylor]: Taking taylor expansion of 2.0 in k 1.732 * [backup-simplify]: Simplify 2.0 into 2.0 1.732 * [taylor]: Taking taylor expansion of PI in k 1.732 * [backup-simplify]: Simplify PI into PI 1.732 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.733 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.733 * [taylor]: Taking taylor expansion of (log n) in k 1.733 * [taylor]: Taking taylor expansion of n in k 1.733 * [backup-simplify]: Simplify n into n 1.733 * [backup-simplify]: Simplify (log n) into (log n) 1.733 * [backup-simplify]: Simplify (- 0) into 0 1.733 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.734 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 1.735 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 1.735 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 1.736 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.737 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.737 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.738 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.739 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.739 * [backup-simplify]: Simplify (- 0) into 0 1.740 * [backup-simplify]: Simplify (+ 0 0) into 0 1.740 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 1.741 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.741 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 1.743 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.743 * [taylor]: Taking taylor expansion of 0 in k 1.743 * [backup-simplify]: Simplify 0 into 0 1.743 * [backup-simplify]: Simplify 0 into 0 1.743 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.744 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.745 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.745 * [backup-simplify]: Simplify (+ 0 0) into 0 1.745 * [backup-simplify]: Simplify (- 1) into -1 1.746 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.746 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 1.748 * [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)))) 1.750 * [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)))))) 1.752 * [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)))))) 1.752 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.753 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.755 * [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 1.756 * [backup-simplify]: Simplify (- 0) into 0 1.756 * [backup-simplify]: Simplify (+ 0 0) into 0 1.756 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 1.757 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.758 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.760 * [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 1.760 * [taylor]: Taking taylor expansion of 0 in k 1.760 * [backup-simplify]: Simplify 0 into 0 1.760 * [backup-simplify]: Simplify 0 into 0 1.760 * [backup-simplify]: Simplify 0 into 0 1.760 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.762 * [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 1.764 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.764 * [backup-simplify]: Simplify (+ 0 0) into 0 1.764 * [backup-simplify]: Simplify (- 0) into 0 1.764 * [backup-simplify]: Simplify (+ 0 0) into 0 1.765 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.767 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 1.770 * [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)))))) 1.776 * [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)))))) 1.787 * [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)))))) 1.788 * [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)))) 1.788 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 1.788 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.788 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.788 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.788 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.788 * [taylor]: Taking taylor expansion of 0.5 in k 1.789 * [backup-simplify]: Simplify 0.5 into 0.5 1.789 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.789 * [taylor]: Taking taylor expansion of 1.0 in k 1.789 * [backup-simplify]: Simplify 1.0 into 1.0 1.789 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.789 * [taylor]: Taking taylor expansion of k in k 1.789 * [backup-simplify]: Simplify 0 into 0 1.789 * [backup-simplify]: Simplify 1 into 1 1.789 * [backup-simplify]: Simplify (/ 1 1) into 1 1.789 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.789 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.789 * [taylor]: Taking taylor expansion of 2.0 in k 1.789 * [backup-simplify]: Simplify 2.0 into 2.0 1.789 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.789 * [taylor]: Taking taylor expansion of PI in k 1.789 * [backup-simplify]: Simplify PI into PI 1.789 * [taylor]: Taking taylor expansion of n in k 1.789 * [backup-simplify]: Simplify n into n 1.789 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.790 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.790 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.790 * [backup-simplify]: Simplify (- 1) into -1 1.791 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.791 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 1.791 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 1.791 * [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))))) 1.792 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.792 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.792 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.792 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.792 * [taylor]: Taking taylor expansion of 0.5 in n 1.792 * [backup-simplify]: Simplify 0.5 into 0.5 1.792 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.792 * [taylor]: Taking taylor expansion of 1.0 in n 1.792 * [backup-simplify]: Simplify 1.0 into 1.0 1.792 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.792 * [taylor]: Taking taylor expansion of k in n 1.792 * [backup-simplify]: Simplify k into k 1.792 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.792 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.792 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.792 * [taylor]: Taking taylor expansion of 2.0 in n 1.792 * [backup-simplify]: Simplify 2.0 into 2.0 1.792 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.792 * [taylor]: Taking taylor expansion of PI in n 1.792 * [backup-simplify]: Simplify PI into PI 1.792 * [taylor]: Taking taylor expansion of n in n 1.792 * [backup-simplify]: Simplify 0 into 0 1.792 * [backup-simplify]: Simplify 1 into 1 1.793 * [backup-simplify]: Simplify (/ PI 1) into PI 1.793 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.794 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.795 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.795 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.795 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.796 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.798 * [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)))) 1.799 * [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))))) 1.799 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.799 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.799 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.799 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.799 * [taylor]: Taking taylor expansion of 0.5 in n 1.799 * [backup-simplify]: Simplify 0.5 into 0.5 1.799 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.799 * [taylor]: Taking taylor expansion of 1.0 in n 1.799 * [backup-simplify]: Simplify 1.0 into 1.0 1.799 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.799 * [taylor]: Taking taylor expansion of k in n 1.799 * [backup-simplify]: Simplify k into k 1.799 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.799 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.799 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.799 * [taylor]: Taking taylor expansion of 2.0 in n 1.799 * [backup-simplify]: Simplify 2.0 into 2.0 1.800 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.800 * [taylor]: Taking taylor expansion of PI in n 1.800 * [backup-simplify]: Simplify PI into PI 1.800 * [taylor]: Taking taylor expansion of n in n 1.800 * [backup-simplify]: Simplify 0 into 0 1.800 * [backup-simplify]: Simplify 1 into 1 1.800 * [backup-simplify]: Simplify (/ PI 1) into PI 1.801 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.802 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.802 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.802 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.802 * [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 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.806 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.807 * [taylor]: Taking taylor expansion of 0.5 in k 1.807 * [backup-simplify]: Simplify 0.5 into 0.5 1.807 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.807 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.807 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.807 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.807 * [taylor]: Taking taylor expansion of 2.0 in k 1.807 * [backup-simplify]: Simplify 2.0 into 2.0 1.807 * [taylor]: Taking taylor expansion of PI in k 1.807 * [backup-simplify]: Simplify PI 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 * [taylor]: Taking taylor expansion of (log n) in k 1.808 * [taylor]: Taking taylor expansion of n in k 1.808 * [backup-simplify]: Simplify n into n 1.809 * [backup-simplify]: Simplify (log n) into (log n) 1.809 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.809 * [taylor]: Taking taylor expansion of 1.0 in k 1.809 * [backup-simplify]: Simplify 1.0 into 1.0 1.809 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.809 * [taylor]: Taking taylor expansion of k in k 1.809 * [backup-simplify]: Simplify 0 into 0 1.809 * [backup-simplify]: Simplify 1 into 1 1.809 * [backup-simplify]: Simplify (/ 1 1) into 1 1.809 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.811 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 1.811 * [backup-simplify]: Simplify (- 1) into -1 1.811 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.813 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 1.814 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 1.815 * [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))))) 1.817 * [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))))) 1.818 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.818 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.819 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.819 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.820 * [backup-simplify]: Simplify (- 0) into 0 1.820 * [backup-simplify]: Simplify (+ 0 0) into 0 1.820 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 1.821 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.822 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 1.823 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.823 * [taylor]: Taking taylor expansion of 0 in k 1.823 * [backup-simplify]: Simplify 0 into 0 1.823 * [backup-simplify]: Simplify 0 into 0 1.823 * [backup-simplify]: Simplify 0 into 0 1.824 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.824 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.826 * [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 1.826 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.827 * [backup-simplify]: Simplify (- 0) into 0 1.827 * [backup-simplify]: Simplify (+ 0 0) into 0 1.827 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 1.828 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.833 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 1.834 * [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 1.834 * [taylor]: Taking taylor expansion of 0 in k 1.834 * [backup-simplify]: Simplify 0 into 0 1.834 * [backup-simplify]: Simplify 0 into 0 1.834 * [backup-simplify]: Simplify 0 into 0 1.834 * [backup-simplify]: Simplify 0 into 0 1.835 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.836 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.839 * [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 1.839 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.839 * [backup-simplify]: Simplify (- 0) into 0 1.840 * [backup-simplify]: Simplify (+ 0 0) into 0 1.840 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 1.841 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.842 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 1.844 * [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 1.844 * [taylor]: Taking taylor expansion of 0 in k 1.844 * [backup-simplify]: Simplify 0 into 0 1.844 * [backup-simplify]: Simplify 0 into 0 1.845 * [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)))) 1.845 * [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))) 1.845 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 1.846 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.846 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.846 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.846 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.846 * [taylor]: Taking taylor expansion of 0.5 in k 1.846 * [backup-simplify]: Simplify 0.5 into 0.5 1.846 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.846 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.846 * [taylor]: Taking taylor expansion of k in k 1.846 * [backup-simplify]: Simplify 0 into 0 1.846 * [backup-simplify]: Simplify 1 into 1 1.846 * [backup-simplify]: Simplify (/ 1 1) into 1 1.846 * [taylor]: Taking taylor expansion of 1.0 in k 1.846 * [backup-simplify]: Simplify 1.0 into 1.0 1.846 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.846 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.846 * [taylor]: Taking taylor expansion of -2.0 in k 1.846 * [backup-simplify]: Simplify -2.0 into -2.0 1.846 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.846 * [taylor]: Taking taylor expansion of PI in k 1.846 * [backup-simplify]: Simplify PI into PI 1.846 * [taylor]: Taking taylor expansion of n in k 1.846 * [backup-simplify]: Simplify n into n 1.846 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.846 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.846 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.847 * [backup-simplify]: Simplify (+ 1 0) into 1 1.847 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 1.847 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 1.847 * [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)))))) 1.847 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.847 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.847 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.847 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.847 * [taylor]: Taking taylor expansion of 0.5 in n 1.847 * [backup-simplify]: Simplify 0.5 into 0.5 1.847 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.847 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.847 * [taylor]: Taking taylor expansion of k in n 1.847 * [backup-simplify]: Simplify k into k 1.847 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.847 * [taylor]: Taking taylor expansion of 1.0 in n 1.847 * [backup-simplify]: Simplify 1.0 into 1.0 1.847 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.847 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.847 * [taylor]: Taking taylor expansion of -2.0 in n 1.847 * [backup-simplify]: Simplify -2.0 into -2.0 1.848 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.848 * [taylor]: Taking taylor expansion of PI in n 1.848 * [backup-simplify]: Simplify PI into PI 1.848 * [taylor]: Taking taylor expansion of n in n 1.848 * [backup-simplify]: Simplify 0 into 0 1.848 * [backup-simplify]: Simplify 1 into 1 1.848 * [backup-simplify]: Simplify (/ PI 1) into PI 1.848 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.849 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.849 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.849 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.850 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.851 * [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)))) 1.852 * [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))))) 1.852 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.852 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.852 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.852 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.853 * [taylor]: Taking taylor expansion of 0.5 in n 1.853 * [backup-simplify]: Simplify 0.5 into 0.5 1.853 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.853 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.853 * [taylor]: Taking taylor expansion of k in n 1.853 * [backup-simplify]: Simplify k into k 1.853 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.853 * [taylor]: Taking taylor expansion of 1.0 in n 1.853 * [backup-simplify]: Simplify 1.0 into 1.0 1.853 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.853 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.853 * [taylor]: Taking taylor expansion of -2.0 in n 1.853 * [backup-simplify]: Simplify -2.0 into -2.0 1.853 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.853 * [taylor]: Taking taylor expansion of PI in n 1.853 * [backup-simplify]: Simplify PI into PI 1.853 * [taylor]: Taking taylor expansion of n in n 1.853 * [backup-simplify]: Simplify 0 into 0 1.853 * [backup-simplify]: Simplify 1 into 1 1.853 * [backup-simplify]: Simplify (/ PI 1) into PI 1.854 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.855 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.855 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.855 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.857 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.858 * [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)))) 1.859 * [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))))) 1.859 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.859 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.859 * [taylor]: Taking taylor expansion of 0.5 in k 1.859 * [backup-simplify]: Simplify 0.5 into 0.5 1.859 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.859 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.859 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.859 * [taylor]: Taking taylor expansion of k in k 1.859 * [backup-simplify]: Simplify 0 into 0 1.859 * [backup-simplify]: Simplify 1 into 1 1.860 * [backup-simplify]: Simplify (/ 1 1) into 1 1.860 * [taylor]: Taking taylor expansion of 1.0 in k 1.860 * [backup-simplify]: Simplify 1.0 into 1.0 1.860 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.860 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.860 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.860 * [taylor]: Taking taylor expansion of -2.0 in k 1.860 * [backup-simplify]: Simplify -2.0 into -2.0 1.860 * [taylor]: Taking taylor expansion of PI in k 1.860 * [backup-simplify]: Simplify PI into PI 1.861 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.862 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.862 * [taylor]: Taking taylor expansion of (log n) in k 1.862 * [taylor]: Taking taylor expansion of n in k 1.862 * [backup-simplify]: Simplify n into n 1.862 * [backup-simplify]: Simplify (log n) into (log n) 1.862 * [backup-simplify]: Simplify (+ 1 0) into 1 1.863 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.864 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 1.865 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 1.866 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 1.868 * [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))))) 1.869 * [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))))) 1.870 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.871 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.872 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 1.873 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.873 * [backup-simplify]: Simplify (+ 0 0) into 0 1.874 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 1.875 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.876 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 1.878 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.879 * [taylor]: Taking taylor expansion of 0 in k 1.879 * [backup-simplify]: Simplify 0 into 0 1.879 * [backup-simplify]: Simplify 0 into 0 1.879 * [backup-simplify]: Simplify 0 into 0 1.880 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.881 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.883 * [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 1.883 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.884 * [backup-simplify]: Simplify (+ 0 0) into 0 1.884 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 1.885 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.886 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 1.887 * [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 1.887 * [taylor]: Taking taylor expansion of 0 in k 1.888 * [backup-simplify]: Simplify 0 into 0 1.888 * [backup-simplify]: Simplify 0 into 0 1.888 * [backup-simplify]: Simplify 0 into 0 1.888 * [backup-simplify]: Simplify 0 into 0 1.888 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.889 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.892 * [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 1.892 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.893 * [backup-simplify]: Simplify (+ 0 0) into 0 1.894 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 1.894 * [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 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 1.897 * [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 1.897 * [taylor]: Taking taylor expansion of 0 in k 1.897 * [backup-simplify]: Simplify 0 into 0 1.897 * [backup-simplify]: Simplify 0 into 0 1.898 * [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)))))) 1.898 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 1.898 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 1.898 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 1.898 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.898 * [taylor]: Taking taylor expansion of 1.0 in k 1.898 * [backup-simplify]: Simplify 1.0 into 1.0 1.899 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.899 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.899 * [taylor]: Taking taylor expansion of k in k 1.899 * [backup-simplify]: Simplify 0 into 0 1.899 * [backup-simplify]: Simplify 1 into 1 1.899 * [backup-simplify]: Simplify (/ 1 1) into 1 1.899 * [backup-simplify]: Simplify (sqrt 0) into 0 1.900 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.900 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.900 * [taylor]: Taking taylor expansion of 1.0 in k 1.900 * [backup-simplify]: Simplify 1.0 into 1.0 1.900 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.900 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.900 * [taylor]: Taking taylor expansion of k in k 1.900 * [backup-simplify]: Simplify 0 into 0 1.900 * [backup-simplify]: Simplify 1 into 1 1.901 * [backup-simplify]: Simplify (/ 1 1) into 1 1.901 * [backup-simplify]: Simplify (sqrt 0) into 0 1.902 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.902 * [backup-simplify]: Simplify (* 1.0 0) into 0 1.902 * [backup-simplify]: Simplify 0 into 0 1.903 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 1.903 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.904 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1.906 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.907 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 1.907 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.907 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.910 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.911 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 1.911 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.912 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 1.912 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 1.912 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 1.912 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.912 * [taylor]: Taking taylor expansion of 1.0 in k 1.912 * [backup-simplify]: Simplify 1.0 into 1.0 1.912 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.912 * [taylor]: Taking taylor expansion of k in k 1.912 * [backup-simplify]: Simplify 0 into 0 1.912 * [backup-simplify]: Simplify 1 into 1 1.913 * [backup-simplify]: Simplify (sqrt 0) into 0 1.913 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.913 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.914 * [taylor]: Taking taylor expansion of 1.0 in k 1.914 * [backup-simplify]: Simplify 1.0 into 1.0 1.914 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.914 * [taylor]: Taking taylor expansion of k in k 1.914 * [backup-simplify]: Simplify 0 into 0 1.914 * [backup-simplify]: Simplify 1 into 1 1.914 * [backup-simplify]: Simplify (sqrt 0) into 0 1.915 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.915 * [backup-simplify]: Simplify (* 1.0 0) into 0 1.915 * [backup-simplify]: Simplify 0 into 0 1.916 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 1.916 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.918 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.919 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 1.920 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.922 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.923 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 1.924 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.925 * [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)))))))) 1.925 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 1.925 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 1.925 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.925 * [taylor]: Taking taylor expansion of 1.0 in k 1.925 * [backup-simplify]: Simplify 1.0 into 1.0 1.925 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.925 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.925 * [taylor]: Taking taylor expansion of -1 in k 1.925 * [backup-simplify]: Simplify -1 into -1 1.925 * [taylor]: Taking taylor expansion of k in k 1.925 * [backup-simplify]: Simplify 0 into 0 1.925 * [backup-simplify]: Simplify 1 into 1 1.925 * [backup-simplify]: Simplify (/ -1 1) into -1 1.925 * [backup-simplify]: Simplify (sqrt 0) into 0 1.926 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1.927 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 1.927 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.927 * [taylor]: Taking taylor expansion of 1.0 in k 1.927 * [backup-simplify]: Simplify 1.0 into 1.0 1.927 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.927 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.927 * [taylor]: Taking taylor expansion of -1 in k 1.927 * [backup-simplify]: Simplify -1 into -1 1.927 * [taylor]: Taking taylor expansion of k in k 1.927 * [backup-simplify]: Simplify 0 into 0 1.927 * [backup-simplify]: Simplify 1 into 1 1.927 * [backup-simplify]: Simplify (/ -1 1) into -1 1.927 * [backup-simplify]: Simplify (sqrt 0) into 0 1.928 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1.928 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 1.928 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.929 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1.931 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.932 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 1.935 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.936 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.939 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.941 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 1.941 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.942 * [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))))) 1.942 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 1.942 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.942 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.942 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.942 * [taylor]: Taking taylor expansion of 2.0 in n 1.943 * [backup-simplify]: Simplify 2.0 into 2.0 1.943 * [taylor]: Taking taylor expansion of (* n PI) in n 1.943 * [taylor]: Taking taylor expansion of n in n 1.943 * [backup-simplify]: Simplify 0 into 0 1.943 * [backup-simplify]: Simplify 1 into 1 1.943 * [taylor]: Taking taylor expansion of PI in n 1.943 * [backup-simplify]: Simplify PI into PI 1.943 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.943 * [taylor]: Taking taylor expansion of 2.0 in n 1.943 * [backup-simplify]: Simplify 2.0 into 2.0 1.943 * [taylor]: Taking taylor expansion of (* n PI) in n 1.943 * [taylor]: Taking taylor expansion of n in n 1.943 * [backup-simplify]: Simplify 0 into 0 1.943 * [backup-simplify]: Simplify 1 into 1 1.943 * [taylor]: Taking taylor expansion of PI in n 1.943 * [backup-simplify]: Simplify PI into PI 1.943 * [backup-simplify]: Simplify (* 0 PI) into 0 1.943 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.943 * [backup-simplify]: Simplify 0 into 0 1.944 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.945 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.945 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.946 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.947 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.947 * [backup-simplify]: Simplify 0 into 0 1.947 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.948 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.948 * [backup-simplify]: Simplify 0 into 0 1.949 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.949 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1.950 * [backup-simplify]: Simplify 0 into 0 1.950 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.951 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1.951 * [backup-simplify]: Simplify 0 into 0 1.952 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.953 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1.953 * [backup-simplify]: Simplify 0 into 0 1.954 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1.955 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1.955 * [backup-simplify]: Simplify 0 into 0 1.956 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.956 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 1.956 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.956 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.956 * [taylor]: Taking taylor expansion of 2.0 in n 1.956 * [backup-simplify]: Simplify 2.0 into 2.0 1.956 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.956 * [taylor]: Taking taylor expansion of PI in n 1.956 * [backup-simplify]: Simplify PI into PI 1.956 * [taylor]: Taking taylor expansion of n in n 1.956 * [backup-simplify]: Simplify 0 into 0 1.956 * [backup-simplify]: Simplify 1 into 1 1.956 * [backup-simplify]: Simplify (/ PI 1) into PI 1.956 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.957 * [taylor]: Taking taylor expansion of 2.0 in n 1.957 * [backup-simplify]: Simplify 2.0 into 2.0 1.957 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.957 * [taylor]: Taking taylor expansion of PI in n 1.957 * [backup-simplify]: Simplify PI into PI 1.957 * [taylor]: Taking taylor expansion of n in n 1.957 * [backup-simplify]: Simplify 0 into 0 1.957 * [backup-simplify]: Simplify 1 into 1 1.957 * [backup-simplify]: Simplify (/ PI 1) into PI 1.957 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.958 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.958 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.959 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.959 * [backup-simplify]: Simplify 0 into 0 1.959 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.960 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.960 * [backup-simplify]: Simplify 0 into 0 1.960 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.961 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.961 * [backup-simplify]: Simplify 0 into 0 1.962 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.962 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.962 * [backup-simplify]: Simplify 0 into 0 1.963 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.964 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.964 * [backup-simplify]: Simplify 0 into 0 1.965 * [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 1.965 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.965 * [backup-simplify]: Simplify 0 into 0 1.966 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 1.966 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 1.966 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.966 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.966 * [taylor]: Taking taylor expansion of -2.0 in n 1.966 * [backup-simplify]: Simplify -2.0 into -2.0 1.966 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.966 * [taylor]: Taking taylor expansion of PI in n 1.966 * [backup-simplify]: Simplify PI into PI 1.966 * [taylor]: Taking taylor expansion of n in n 1.966 * [backup-simplify]: Simplify 0 into 0 1.966 * [backup-simplify]: Simplify 1 into 1 1.967 * [backup-simplify]: Simplify (/ PI 1) into PI 1.967 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.967 * [taylor]: Taking taylor expansion of -2.0 in n 1.967 * [backup-simplify]: Simplify -2.0 into -2.0 1.967 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.967 * [taylor]: Taking taylor expansion of PI in n 1.967 * [backup-simplify]: Simplify PI into PI 1.967 * [taylor]: Taking taylor expansion of n in n 1.967 * [backup-simplify]: Simplify 0 into 0 1.967 * [backup-simplify]: Simplify 1 into 1 1.967 * [backup-simplify]: Simplify (/ PI 1) into PI 1.968 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.968 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.969 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.969 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.969 * [backup-simplify]: Simplify 0 into 0 1.970 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.971 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.971 * [backup-simplify]: Simplify 0 into 0 1.971 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.972 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.972 * [backup-simplify]: Simplify 0 into 0 1.973 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.973 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.973 * [backup-simplify]: Simplify 0 into 0 1.974 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.975 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.975 * [backup-simplify]: Simplify 0 into 0 1.975 * [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 1.976 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.976 * [backup-simplify]: Simplify 0 into 0 1.977 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 1.977 * * * * [progress]: [ 4 / 4 ] generating series at (2) 1.977 * [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))))) 1.977 * [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 1.977 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 1.977 * [taylor]: Taking taylor expansion of 1.0 in n 1.977 * [backup-simplify]: Simplify 1.0 into 1.0 1.977 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 1.977 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 1.978 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.978 * [taylor]: Taking taylor expansion of k in n 1.978 * [backup-simplify]: Simplify k into k 1.978 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.978 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1.978 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.978 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1.978 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.978 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.978 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.978 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.978 * [taylor]: Taking taylor expansion of 0.5 in n 1.978 * [backup-simplify]: Simplify 0.5 into 0.5 1.978 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.978 * [taylor]: Taking taylor expansion of 1.0 in n 1.978 * [backup-simplify]: Simplify 1.0 into 1.0 1.978 * [taylor]: Taking taylor expansion of k in n 1.978 * [backup-simplify]: Simplify k into k 1.978 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 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 1.980 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.981 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.981 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.981 * [backup-simplify]: Simplify (- k) into (- k) 1.981 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.981 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.982 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.983 * [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)))) 1.984 * [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))))) 1.984 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 1.984 * [taylor]: Taking taylor expansion of 1.0 in k 1.984 * [backup-simplify]: Simplify 1.0 into 1.0 1.984 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 1.984 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.984 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.984 * [taylor]: Taking taylor expansion of k in k 1.984 * [backup-simplify]: Simplify 0 into 0 1.984 * [backup-simplify]: Simplify 1 into 1 1.984 * [backup-simplify]: Simplify (/ 1 1) into 1 1.984 * [backup-simplify]: Simplify (sqrt 0) into 0 1.985 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.985 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.985 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.985 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.985 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.985 * [taylor]: Taking taylor expansion of 0.5 in k 1.985 * [backup-simplify]: Simplify 0.5 into 0.5 1.985 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.985 * [taylor]: Taking taylor expansion of 1.0 in k 1.985 * [backup-simplify]: Simplify 1.0 into 1.0 1.985 * [taylor]: Taking taylor expansion of k in k 1.985 * [backup-simplify]: Simplify 0 into 0 1.985 * [backup-simplify]: Simplify 1 into 1 1.985 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.986 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.986 * [taylor]: Taking taylor expansion of 2.0 in k 1.986 * [backup-simplify]: Simplify 2.0 into 2.0 1.986 * [taylor]: Taking taylor expansion of (* n PI) in k 1.986 * [taylor]: Taking taylor expansion of n in k 1.986 * [backup-simplify]: Simplify n into n 1.986 * [taylor]: Taking taylor expansion of PI in k 1.986 * [backup-simplify]: Simplify PI into PI 1.986 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.986 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.986 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.986 * [backup-simplify]: Simplify (- 0) into 0 1.987 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.987 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 1.987 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 1.987 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 1.987 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 1.987 * [taylor]: Taking taylor expansion of 1.0 in k 1.987 * [backup-simplify]: Simplify 1.0 into 1.0 1.987 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 1.987 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.988 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.988 * [taylor]: Taking taylor expansion of k in k 1.988 * [backup-simplify]: Simplify 0 into 0 1.988 * [backup-simplify]: Simplify 1 into 1 1.988 * [backup-simplify]: Simplify (/ 1 1) into 1 1.988 * [backup-simplify]: Simplify (sqrt 0) into 0 1.989 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.989 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.989 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.990 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.990 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.990 * [taylor]: Taking taylor expansion of 0.5 in k 1.990 * [backup-simplify]: Simplify 0.5 into 0.5 1.990 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.990 * [taylor]: Taking taylor expansion of 1.0 in k 1.990 * [backup-simplify]: Simplify 1.0 into 1.0 1.990 * [taylor]: Taking taylor expansion of k in k 1.990 * [backup-simplify]: Simplify 0 into 0 1.990 * [backup-simplify]: Simplify 1 into 1 1.990 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.990 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.990 * [taylor]: Taking taylor expansion of 2.0 in k 1.990 * [backup-simplify]: Simplify 2.0 into 2.0 1.990 * [taylor]: Taking taylor expansion of (* n PI) in k 1.990 * [taylor]: Taking taylor expansion of n in k 1.990 * [backup-simplify]: Simplify n into n 1.990 * [taylor]: Taking taylor expansion of PI in k 1.990 * [backup-simplify]: Simplify PI into PI 1.990 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.990 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.990 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.991 * [backup-simplify]: Simplify (- 0) into 0 1.991 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.991 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 1.991 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 1.992 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 1.992 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 1.992 * [backup-simplify]: Simplify (* 1.0 0) into 0 1.992 * [taylor]: Taking taylor expansion of 0 in n 1.992 * [backup-simplify]: Simplify 0 into 0 1.992 * [backup-simplify]: Simplify 0 into 0 1.993 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 1.993 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 1.994 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 1.995 * [backup-simplify]: Simplify (- 1) into -1 1.995 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.997 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 1.998 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 1.998 * [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))) 2.000 * [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))) 2.002 * [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))) 2.002 * [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 2.002 * [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 2.002 * [taylor]: Taking taylor expansion of +nan.0 in n 2.002 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.002 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 2.002 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.002 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.002 * [taylor]: Taking taylor expansion of 0.5 in n 2.002 * [backup-simplify]: Simplify 0.5 into 0.5 2.002 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.002 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.002 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.002 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.003 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.003 * [taylor]: Taking taylor expansion of 1.0 in n 2.003 * [backup-simplify]: Simplify 1.0 into 1.0 2.003 * [taylor]: Taking taylor expansion of (log PI) in n 2.003 * [taylor]: Taking taylor expansion of PI in n 2.003 * [backup-simplify]: Simplify PI into PI 2.003 * [backup-simplify]: Simplify (log PI) into (log PI) 2.004 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.006 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.006 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.006 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.006 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.006 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.006 * [taylor]: Taking taylor expansion of 1.0 in n 2.006 * [backup-simplify]: Simplify 1.0 into 1.0 2.006 * [taylor]: Taking taylor expansion of (log n) in n 2.006 * [taylor]: Taking taylor expansion of n in n 2.006 * [backup-simplify]: Simplify 0 into 0 2.006 * [backup-simplify]: Simplify 1 into 1 2.006 * [backup-simplify]: Simplify (log 1) into 0 2.007 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.007 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.007 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.007 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.007 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.007 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.007 * [taylor]: Taking taylor expansion of 1.0 in n 2.007 * [backup-simplify]: Simplify 1.0 into 1.0 2.007 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.007 * [taylor]: Taking taylor expansion of 2.0 in n 2.007 * [backup-simplify]: Simplify 2.0 into 2.0 2.008 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.009 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.010 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.011 * [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) 2.012 * [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) 2.013 * [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)) 2.015 * [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))) 2.016 * [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) 2.018 * [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)) 2.019 * [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))) 2.021 * [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))) 2.021 * [backup-simplify]: Simplify 0 into 0 2.022 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 2.023 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 2.025 * [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 2.025 * [backup-simplify]: Simplify (- 0) into 0 2.025 * [backup-simplify]: Simplify (+ 0 0) into 0 2.026 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 2.028 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 2.029 * [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))) 2.030 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.033 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.036 * [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)))))))) 2.042 * [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)))))))) 2.042 * [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 2.042 * [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 2.042 * [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 2.042 * [taylor]: Taking taylor expansion of +nan.0 in n 2.042 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.042 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 2.042 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.042 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.042 * [taylor]: Taking taylor expansion of 0.5 in n 2.042 * [backup-simplify]: Simplify 0.5 into 0.5 2.043 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.043 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.043 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.043 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.043 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.043 * [taylor]: Taking taylor expansion of 1.0 in n 2.043 * [backup-simplify]: Simplify 1.0 into 1.0 2.043 * [taylor]: Taking taylor expansion of (log PI) in n 2.043 * [taylor]: Taking taylor expansion of PI in n 2.043 * [backup-simplify]: Simplify PI into PI 2.043 * [backup-simplify]: Simplify (log PI) into (log PI) 2.044 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.046 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.046 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.046 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.046 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.046 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.046 * [taylor]: Taking taylor expansion of 1.0 in n 2.046 * [backup-simplify]: Simplify 1.0 into 1.0 2.046 * [taylor]: Taking taylor expansion of (log n) in n 2.046 * [taylor]: Taking taylor expansion of n in n 2.046 * [backup-simplify]: Simplify 0 into 0 2.046 * [backup-simplify]: Simplify 1 into 1 2.047 * [backup-simplify]: Simplify (log 1) into 0 2.047 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.047 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.047 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.047 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.047 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.047 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.047 * [taylor]: Taking taylor expansion of 1.0 in n 2.047 * [backup-simplify]: Simplify 1.0 into 1.0 2.047 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.048 * [taylor]: Taking taylor expansion of 2.0 in n 2.048 * [backup-simplify]: Simplify 2.0 into 2.0 2.048 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.053 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.055 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.056 * [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) 2.057 * [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) 2.058 * [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)) 2.060 * [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))) 2.061 * [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) 2.061 * [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 2.061 * [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 2.061 * [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 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 2.061 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 2.061 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 2.062 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 2.062 * [taylor]: Taking taylor expansion of 0.5 in n 2.062 * [backup-simplify]: Simplify 0.5 into 0.5 2.062 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 2.062 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 2.062 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.062 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.062 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.062 * [taylor]: Taking taylor expansion of 1.0 in n 2.062 * [backup-simplify]: Simplify 1.0 into 1.0 2.062 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.062 * [taylor]: Taking taylor expansion of 2.0 in n 2.062 * [backup-simplify]: Simplify 2.0 into 2.0 2.062 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.063 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.065 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.065 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 2.065 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.065 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.065 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.065 * [taylor]: Taking taylor expansion of 1.0 in n 2.065 * [backup-simplify]: Simplify 1.0 into 1.0 2.065 * [taylor]: Taking taylor expansion of (log PI) in n 2.065 * [taylor]: Taking taylor expansion of PI in n 2.065 * [backup-simplify]: Simplify PI into PI 2.066 * [backup-simplify]: Simplify (log PI) into (log PI) 2.067 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.068 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.068 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.068 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.068 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.068 * [taylor]: Taking taylor expansion of 1.0 in n 2.068 * [backup-simplify]: Simplify 1.0 into 1.0 2.068 * [taylor]: Taking taylor expansion of (log n) in n 2.069 * [taylor]: Taking taylor expansion of n in n 2.069 * [backup-simplify]: Simplify 0 into 0 2.069 * [backup-simplify]: Simplify 1 into 1 2.070 * [backup-simplify]: Simplify (log 1) into 0 2.070 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.070 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.070 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.071 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.072 * [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) 2.074 * [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)) 2.075 * [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))) 2.077 * [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) 2.077 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.077 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.077 * [taylor]: Taking taylor expansion of 2.0 in n 2.077 * [backup-simplify]: Simplify 2.0 into 2.0 2.077 * [taylor]: Taking taylor expansion of (* n PI) in n 2.077 * [taylor]: Taking taylor expansion of n in n 2.077 * [backup-simplify]: Simplify 0 into 0 2.077 * [backup-simplify]: Simplify 1 into 1 2.077 * [taylor]: Taking taylor expansion of PI in n 2.077 * [backup-simplify]: Simplify PI into PI 2.077 * [backup-simplify]: Simplify (* 0 PI) into 0 2.078 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.079 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.081 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.082 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.083 * [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)) 2.084 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.085 * [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)) 2.087 * [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))) 2.089 * [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)))))) 2.092 * [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)))))))) 2.096 * [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)))))))) 2.100 * [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)))))))) 2.101 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 2.101 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 2.102 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 2.103 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.103 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.103 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 2.104 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.104 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 2.105 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 2.106 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 2.107 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 2.108 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 2.109 * [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 2.110 * [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 2.111 * [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 2.113 * [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 2.113 * [backup-simplify]: Simplify (- 0) into 0 2.113 * [backup-simplify]: Simplify 0 into 0 2.113 * [backup-simplify]: Simplify 0 into 0 2.113 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.114 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 2.117 * [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 2.118 * [backup-simplify]: Simplify (- 0) into 0 2.118 * [backup-simplify]: Simplify (+ 0 0) into 0 2.120 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 2.121 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 2.123 * [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))) 2.124 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.128 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.134 * [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)))))))) 2.145 * [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)))))))) 2.146 * [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 2.146 * [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 2.146 * [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 2.146 * [taylor]: Taking taylor expansion of +nan.0 in n 2.146 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.146 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 2.146 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 2.146 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 2.146 * [taylor]: Taking taylor expansion of 0.5 in n 2.146 * [backup-simplify]: Simplify 0.5 into 0.5 2.146 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 2.146 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 2.146 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.146 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.146 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.146 * [taylor]: Taking taylor expansion of 1.0 in n 2.146 * [backup-simplify]: Simplify 1.0 into 1.0 2.146 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.146 * [taylor]: Taking taylor expansion of 2.0 in n 2.146 * [backup-simplify]: Simplify 2.0 into 2.0 2.146 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.147 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.148 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.148 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 2.148 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.148 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.148 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.148 * [taylor]: Taking taylor expansion of 1.0 in n 2.148 * [backup-simplify]: Simplify 1.0 into 1.0 2.148 * [taylor]: Taking taylor expansion of (log n) in n 2.148 * [taylor]: Taking taylor expansion of n in n 2.148 * [backup-simplify]: Simplify 0 into 0 2.148 * [backup-simplify]: Simplify 1 into 1 2.148 * [backup-simplify]: Simplify (log 1) into 0 2.149 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.149 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.149 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.149 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.149 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.149 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.149 * [taylor]: Taking taylor expansion of 1.0 in n 2.149 * [backup-simplify]: Simplify 1.0 into 1.0 2.149 * [taylor]: Taking taylor expansion of (log PI) in n 2.149 * [taylor]: Taking taylor expansion of PI in n 2.149 * [backup-simplify]: Simplify PI into PI 2.149 * [backup-simplify]: Simplify (log PI) into (log PI) 2.150 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.151 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.151 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.152 * [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) 2.153 * [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)) 2.154 * [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))) 2.154 * [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) 2.154 * [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 2.155 * [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 2.155 * [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 2.155 * [taylor]: Taking taylor expansion of +nan.0 in n 2.155 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.155 * [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 2.155 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 2.155 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 2.155 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 2.155 * [taylor]: Taking taylor expansion of 0.5 in n 2.155 * [backup-simplify]: Simplify 0.5 into 0.5 2.155 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 2.155 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 2.155 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.155 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.155 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.155 * [taylor]: Taking taylor expansion of 1.0 in n 2.155 * [backup-simplify]: Simplify 1.0 into 1.0 2.155 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.155 * [taylor]: Taking taylor expansion of 2.0 in n 2.155 * [backup-simplify]: Simplify 2.0 into 2.0 2.155 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.156 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.157 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.157 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 2.157 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.157 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.157 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.157 * [taylor]: Taking taylor expansion of 1.0 in n 2.157 * [backup-simplify]: Simplify 1.0 into 1.0 2.157 * [taylor]: Taking taylor expansion of (log PI) in n 2.157 * [taylor]: Taking taylor expansion of PI in n 2.157 * [backup-simplify]: Simplify PI into PI 2.157 * [backup-simplify]: Simplify (log PI) into (log PI) 2.158 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.159 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.159 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.159 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.159 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.159 * [taylor]: Taking taylor expansion of 1.0 in n 2.159 * [backup-simplify]: Simplify 1.0 into 1.0 2.159 * [taylor]: Taking taylor expansion of (log n) in n 2.159 * [taylor]: Taking taylor expansion of n in n 2.159 * [backup-simplify]: Simplify 0 into 0 2.159 * [backup-simplify]: Simplify 1 into 1 2.159 * [backup-simplify]: Simplify (log 1) into 0 2.159 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.159 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.159 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.160 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.161 * [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) 2.161 * [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)) 2.162 * [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))) 2.163 * [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) 2.163 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.163 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.163 * [taylor]: Taking taylor expansion of 2.0 in n 2.163 * [backup-simplify]: Simplify 2.0 into 2.0 2.163 * [taylor]: Taking taylor expansion of (* n PI) in n 2.163 * [taylor]: Taking taylor expansion of n in n 2.163 * [backup-simplify]: Simplify 0 into 0 2.163 * [backup-simplify]: Simplify 1 into 1 2.163 * [taylor]: Taking taylor expansion of PI in n 2.163 * [backup-simplify]: Simplify PI into PI 2.164 * [backup-simplify]: Simplify (* 0 PI) into 0 2.164 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.165 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.166 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.166 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.166 * [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 2.166 * [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 2.166 * [taylor]: Taking taylor expansion of +nan.0 in n 2.166 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.167 * [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 2.167 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 2.167 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 2.167 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 2.167 * [taylor]: Taking taylor expansion of 0.5 in n 2.167 * [backup-simplify]: Simplify 0.5 into 0.5 2.167 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 2.167 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 2.167 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.167 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.167 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.167 * [taylor]: Taking taylor expansion of 1.0 in n 2.167 * [backup-simplify]: Simplify 1.0 into 1.0 2.167 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.167 * [taylor]: Taking taylor expansion of 2.0 in n 2.167 * [backup-simplify]: Simplify 2.0 into 2.0 2.167 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.168 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.168 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.169 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 2.169 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.169 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.169 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.169 * [taylor]: Taking taylor expansion of 1.0 in n 2.169 * [backup-simplify]: Simplify 1.0 into 1.0 2.169 * [taylor]: Taking taylor expansion of (log PI) in n 2.169 * [taylor]: Taking taylor expansion of PI in n 2.169 * [backup-simplify]: Simplify PI into PI 2.173 * [backup-simplify]: Simplify (log PI) into (log PI) 2.174 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.176 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 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 2.176 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.176 * [taylor]: Taking taylor expansion of 1.0 in n 2.176 * [backup-simplify]: Simplify 1.0 into 1.0 2.176 * [taylor]: Taking taylor expansion of (log n) in n 2.176 * [taylor]: Taking taylor expansion of n in n 2.176 * [backup-simplify]: Simplify 0 into 0 2.176 * [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) 2.178 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 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)) 2.183 * [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))) 2.185 * [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) 2.185 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 2.185 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.185 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.185 * [taylor]: Taking taylor expansion of 2.0 in n 2.185 * [backup-simplify]: Simplify 2.0 into 2.0 2.185 * [taylor]: Taking taylor expansion of (* n PI) in n 2.185 * [taylor]: Taking taylor expansion of n in n 2.185 * [backup-simplify]: Simplify 0 into 0 2.185 * [backup-simplify]: Simplify 1 into 1 2.185 * [taylor]: Taking taylor expansion of PI in n 2.185 * [backup-simplify]: Simplify PI into PI 2.185 * [backup-simplify]: Simplify (* 0 PI) into 0 2.186 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.188 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.189 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.190 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.191 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.193 * [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)) 2.193 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.195 * [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)) 2.197 * [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))) 2.197 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.198 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.200 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 2.201 * [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)) 2.203 * [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))) 2.205 * [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)))))))) 2.212 * [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)))))))))))) 2.221 * [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)))))))))))) 2.231 * [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)))))))))))))) 2.249 * [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)))))))))))))) 2.260 * [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)))))))))))))) 2.277 * [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)))))))))))))))))))))) 2.277 * [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)))))) 2.277 * [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 2.277 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 2.278 * [taylor]: Taking taylor expansion of 1.0 in n 2.278 * [backup-simplify]: Simplify 1.0 into 1.0 2.278 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 2.278 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.278 * [taylor]: Taking taylor expansion of k in n 2.278 * [backup-simplify]: Simplify k into k 2.278 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.278 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.278 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.278 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.278 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.278 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.278 * [taylor]: Taking taylor expansion of 0.5 in n 2.278 * [backup-simplify]: Simplify 0.5 into 0.5 2.278 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.278 * [taylor]: Taking taylor expansion of 1.0 in n 2.278 * [backup-simplify]: Simplify 1.0 into 1.0 2.278 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.278 * [taylor]: Taking taylor expansion of k in n 2.278 * [backup-simplify]: Simplify k into k 2.278 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.278 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.278 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.278 * [taylor]: Taking taylor expansion of 2.0 in n 2.278 * [backup-simplify]: Simplify 2.0 into 2.0 2.278 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.278 * [taylor]: Taking taylor expansion of PI in n 2.278 * [backup-simplify]: Simplify PI into PI 2.278 * [taylor]: Taking taylor expansion of n in n 2.278 * [backup-simplify]: Simplify 0 into 0 2.278 * [backup-simplify]: Simplify 1 into 1 2.278 * [backup-simplify]: Simplify (/ PI 1) into PI 2.279 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.283 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.283 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.283 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.283 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.284 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.285 * [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)))) 2.285 * [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))))) 2.285 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 2.286 * [taylor]: Taking taylor expansion of 1.0 in k 2.286 * [backup-simplify]: Simplify 1.0 into 1.0 2.286 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 2.286 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.286 * [taylor]: Taking taylor expansion of k in k 2.286 * [backup-simplify]: Simplify 0 into 0 2.286 * [backup-simplify]: Simplify 1 into 1 2.286 * [backup-simplify]: Simplify (sqrt 0) into 0 2.287 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.287 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.287 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.287 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.287 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.287 * [taylor]: Taking taylor expansion of 0.5 in k 2.287 * [backup-simplify]: Simplify 0.5 into 0.5 2.287 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.287 * [taylor]: Taking taylor expansion of 1.0 in k 2.287 * [backup-simplify]: Simplify 1.0 into 1.0 2.287 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.287 * [taylor]: Taking taylor expansion of k in k 2.287 * [backup-simplify]: Simplify 0 into 0 2.287 * [backup-simplify]: Simplify 1 into 1 2.287 * [backup-simplify]: Simplify (/ 1 1) into 1 2.287 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.287 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.287 * [taylor]: Taking taylor expansion of 2.0 in k 2.287 * [backup-simplify]: Simplify 2.0 into 2.0 2.287 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.287 * [taylor]: Taking taylor expansion of PI in k 2.287 * [backup-simplify]: Simplify PI into PI 2.287 * [taylor]: Taking taylor expansion of n in k 2.287 * [backup-simplify]: Simplify n into n 2.287 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.288 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.288 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.288 * [backup-simplify]: Simplify (- 1) into -1 2.288 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.288 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.288 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.289 * [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))))) 2.289 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 2.289 * [taylor]: Taking taylor expansion of 1.0 in k 2.289 * [backup-simplify]: Simplify 1.0 into 1.0 2.289 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 2.289 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.289 * [taylor]: Taking taylor expansion of k in k 2.289 * [backup-simplify]: Simplify 0 into 0 2.289 * [backup-simplify]: Simplify 1 into 1 2.289 * [backup-simplify]: Simplify (sqrt 0) into 0 2.290 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.290 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.290 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.290 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.290 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.290 * [taylor]: Taking taylor expansion of 0.5 in k 2.290 * [backup-simplify]: Simplify 0.5 into 0.5 2.290 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.290 * [taylor]: Taking taylor expansion of 1.0 in k 2.290 * [backup-simplify]: Simplify 1.0 into 1.0 2.290 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.290 * [taylor]: Taking taylor expansion of k in k 2.290 * [backup-simplify]: Simplify 0 into 0 2.290 * [backup-simplify]: Simplify 1 into 1 2.291 * [backup-simplify]: Simplify (/ 1 1) into 1 2.291 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.291 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.291 * [taylor]: Taking taylor expansion of 2.0 in k 2.291 * [backup-simplify]: Simplify 2.0 into 2.0 2.291 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.291 * [taylor]: Taking taylor expansion of PI in k 2.291 * [backup-simplify]: Simplify PI into PI 2.291 * [taylor]: Taking taylor expansion of n in k 2.291 * [backup-simplify]: Simplify n into n 2.291 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.291 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.291 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.292 * [backup-simplify]: Simplify (- 1) into -1 2.292 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.292 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.293 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.293 * [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))))) 2.293 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 2.294 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.294 * [taylor]: Taking taylor expansion of 0 in n 2.294 * [backup-simplify]: Simplify 0 into 0 2.294 * [backup-simplify]: Simplify 0 into 0 2.295 * [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))))))) 2.295 * [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))))))) 2.295 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 2.296 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 2.296 * [taylor]: Taking taylor expansion of +nan.0 in n 2.296 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.296 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 2.296 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 2.296 * [taylor]: Taking taylor expansion of 0.5 in n 2.296 * [backup-simplify]: Simplify 0.5 into 0.5 2.296 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 2.296 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.296 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.296 * [taylor]: Taking taylor expansion of 2.0 in n 2.296 * [backup-simplify]: Simplify 2.0 into 2.0 2.296 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.296 * [taylor]: Taking taylor expansion of PI in n 2.296 * [backup-simplify]: Simplify PI into PI 2.296 * [taylor]: Taking taylor expansion of n in n 2.296 * [backup-simplify]: Simplify 0 into 0 2.296 * [backup-simplify]: Simplify 1 into 1 2.297 * [backup-simplify]: Simplify (/ PI 1) into PI 2.297 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.298 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.298 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.299 * [taylor]: Taking taylor expansion of 1.0 in n 2.299 * [backup-simplify]: Simplify 1.0 into 1.0 2.299 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.299 * [taylor]: Taking taylor expansion of k in n 2.299 * [backup-simplify]: Simplify k into k 2.299 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.301 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.301 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.301 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.302 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 2.304 * [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)))) 2.305 * [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))))) 2.306 * [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)))))) 2.308 * [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))))))) 2.309 * [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))))))) 2.309 * [backup-simplify]: Simplify 0 into 0 2.312 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.313 * [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))))))) 2.314 * [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))))))) 2.315 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 2.315 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 2.315 * [taylor]: Taking taylor expansion of +nan.0 in n 2.315 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.315 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 2.315 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 2.315 * [taylor]: Taking taylor expansion of 0.5 in n 2.315 * [backup-simplify]: Simplify 0.5 into 0.5 2.315 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 2.315 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.315 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.315 * [taylor]: Taking taylor expansion of 2.0 in n 2.315 * [backup-simplify]: Simplify 2.0 into 2.0 2.315 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.315 * [taylor]: Taking taylor expansion of PI in n 2.315 * [backup-simplify]: Simplify PI into PI 2.315 * [taylor]: Taking taylor expansion of n in n 2.315 * [backup-simplify]: Simplify 0 into 0 2.315 * [backup-simplify]: Simplify 1 into 1 2.316 * [backup-simplify]: Simplify (/ PI 1) into PI 2.316 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.317 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.317 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.317 * [taylor]: Taking taylor expansion of 1.0 in n 2.317 * [backup-simplify]: Simplify 1.0 into 1.0 2.317 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.317 * [taylor]: Taking taylor expansion of k in n 2.317 * [backup-simplify]: Simplify k into k 2.318 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.319 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.319 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.319 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.319 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 2.320 * [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)))) 2.321 * [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))))) 2.322 * [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)))))) 2.322 * [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))))))) 2.323 * [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))))))) 2.324 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.324 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.325 * [backup-simplify]: Simplify (- 0) into 0 2.325 * [backup-simplify]: Simplify (+ 0 0) into 0 2.325 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.326 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.327 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.328 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.328 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 2.330 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.331 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 2.331 * [backup-simplify]: Simplify (- 0) into 0 2.331 * [backup-simplify]: Simplify 0 into 0 2.331 * [backup-simplify]: Simplify 0 into 0 2.333 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.334 * [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))))))) 2.335 * [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))))))) 2.335 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 2.335 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 2.335 * [taylor]: Taking taylor expansion of +nan.0 in n 2.335 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.335 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 2.335 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 2.335 * [taylor]: Taking taylor expansion of 0.5 in n 2.335 * [backup-simplify]: Simplify 0.5 into 0.5 2.335 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 2.335 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.335 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.335 * [taylor]: Taking taylor expansion of 2.0 in n 2.335 * [backup-simplify]: Simplify 2.0 into 2.0 2.335 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.335 * [taylor]: Taking taylor expansion of PI in n 2.335 * [backup-simplify]: Simplify PI into PI 2.335 * [taylor]: Taking taylor expansion of n in n 2.335 * [backup-simplify]: Simplify 0 into 0 2.335 * [backup-simplify]: Simplify 1 into 1 2.336 * [backup-simplify]: Simplify (/ PI 1) into PI 2.336 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.337 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.337 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.337 * [taylor]: Taking taylor expansion of 1.0 in n 2.337 * [backup-simplify]: Simplify 1.0 into 1.0 2.337 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.337 * [taylor]: Taking taylor expansion of k in n 2.337 * [backup-simplify]: Simplify k into k 2.337 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.338 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.338 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.338 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.339 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 2.339 * [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)))) 2.340 * [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 * [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)))))) 2.342 * [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))))))) 2.342 * [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))))))) 2.345 * [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)))))))) 2.346 * [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)))) 2.346 * [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 2.346 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 2.346 * [taylor]: Taking taylor expansion of 1.0 in n 2.346 * [backup-simplify]: Simplify 1.0 into 1.0 2.346 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 2.346 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.346 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.346 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.346 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.346 * [taylor]: Taking taylor expansion of 0.5 in n 2.346 * [backup-simplify]: Simplify 0.5 into 0.5 2.346 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.346 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.346 * [taylor]: Taking taylor expansion of k in n 2.346 * [backup-simplify]: Simplify k into k 2.346 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.346 * [taylor]: Taking taylor expansion of 1.0 in n 2.346 * [backup-simplify]: Simplify 1.0 into 1.0 2.346 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.346 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.346 * [taylor]: Taking taylor expansion of -2.0 in n 2.346 * [backup-simplify]: Simplify -2.0 into -2.0 2.347 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.347 * [taylor]: Taking taylor expansion of PI in n 2.347 * [backup-simplify]: Simplify PI into PI 2.347 * [taylor]: Taking taylor expansion of n in n 2.347 * [backup-simplify]: Simplify 0 into 0 2.347 * [backup-simplify]: Simplify 1 into 1 2.347 * [backup-simplify]: Simplify (/ PI 1) into PI 2.347 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.348 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.348 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.348 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.349 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.350 * [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)))) 2.350 * [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))))) 2.350 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.350 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.350 * [taylor]: Taking taylor expansion of -1 in n 2.350 * [backup-simplify]: Simplify -1 into -1 2.350 * [taylor]: Taking taylor expansion of k in n 2.350 * [backup-simplify]: Simplify k into k 2.351 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.351 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.351 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.351 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.352 * [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))) 2.352 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 2.352 * [taylor]: Taking taylor expansion of 1.0 in k 2.352 * [backup-simplify]: Simplify 1.0 into 1.0 2.352 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 2.352 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.352 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.352 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.352 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.352 * [taylor]: Taking taylor expansion of 0.5 in k 2.352 * [backup-simplify]: Simplify 0.5 into 0.5 2.352 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.352 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.352 * [taylor]: Taking taylor expansion of k in k 2.352 * [backup-simplify]: Simplify 0 into 0 2.352 * [backup-simplify]: Simplify 1 into 1 2.352 * [backup-simplify]: Simplify (/ 1 1) into 1 2.352 * [taylor]: Taking taylor expansion of 1.0 in k 2.352 * [backup-simplify]: Simplify 1.0 into 1.0 2.352 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.352 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.352 * [taylor]: Taking taylor expansion of -2.0 in k 2.352 * [backup-simplify]: Simplify -2.0 into -2.0 2.352 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.352 * [taylor]: Taking taylor expansion of PI in k 2.352 * [backup-simplify]: Simplify PI into PI 2.352 * [taylor]: Taking taylor expansion of n in k 2.352 * [backup-simplify]: Simplify n into n 2.352 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.352 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.352 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.353 * [backup-simplify]: Simplify (+ 1 0) into 1 2.353 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.353 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.353 * [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)))))) 2.353 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.353 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.353 * [taylor]: Taking taylor expansion of -1 in k 2.353 * [backup-simplify]: Simplify -1 into -1 2.353 * [taylor]: Taking taylor expansion of k in k 2.353 * [backup-simplify]: Simplify 0 into 0 2.353 * [backup-simplify]: Simplify 1 into 1 2.354 * [backup-simplify]: Simplify (/ -1 1) into -1 2.354 * [backup-simplify]: Simplify (sqrt 0) into 0 2.355 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.355 * [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))))))) 2.355 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 2.355 * [taylor]: Taking taylor expansion of 1.0 in k 2.355 * [backup-simplify]: Simplify 1.0 into 1.0 2.355 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 2.355 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.355 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.355 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.355 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.355 * [taylor]: Taking taylor expansion of 0.5 in k 2.355 * [backup-simplify]: Simplify 0.5 into 0.5 2.355 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.355 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.355 * [taylor]: Taking taylor expansion of k in k 2.355 * [backup-simplify]: Simplify 0 into 0 2.355 * [backup-simplify]: Simplify 1 into 1 2.355 * [backup-simplify]: Simplify (/ 1 1) into 1 2.355 * [taylor]: Taking taylor expansion of 1.0 in k 2.355 * [backup-simplify]: Simplify 1.0 into 1.0 2.355 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.355 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.355 * [taylor]: Taking taylor expansion of -2.0 in k 2.355 * [backup-simplify]: Simplify -2.0 into -2.0 2.356 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.356 * [taylor]: Taking taylor expansion of PI in k 2.356 * [backup-simplify]: Simplify PI into PI 2.356 * [taylor]: Taking taylor expansion of n in k 2.356 * [backup-simplify]: Simplify n into n 2.356 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.356 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.356 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.356 * [backup-simplify]: Simplify (+ 1 0) into 1 2.356 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.356 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.357 * [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)))))) 2.357 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.357 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.357 * [taylor]: Taking taylor expansion of -1 in k 2.357 * [backup-simplify]: Simplify -1 into -1 2.357 * [taylor]: Taking taylor expansion of k in k 2.357 * [backup-simplify]: Simplify 0 into 0 2.357 * [backup-simplify]: Simplify 1 into 1 2.357 * [backup-simplify]: Simplify (/ -1 1) into -1 2.357 * [backup-simplify]: Simplify (sqrt 0) into 0 2.358 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.358 * [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))))))) 2.358 * [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))))))) 2.358 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 2.358 * [taylor]: Taking taylor expansion of +nan.0 in n 2.358 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.358 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 2.358 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 2.358 * [taylor]: Taking taylor expansion of 0.5 in n 2.358 * [backup-simplify]: Simplify 0.5 into 0.5 2.359 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 2.359 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.359 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.359 * [taylor]: Taking taylor expansion of k in n 2.359 * [backup-simplify]: Simplify k into k 2.359 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.359 * [taylor]: Taking taylor expansion of 1.0 in n 2.359 * [backup-simplify]: Simplify 1.0 into 1.0 2.359 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.359 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.359 * [taylor]: Taking taylor expansion of -2.0 in n 2.359 * [backup-simplify]: Simplify -2.0 into -2.0 2.359 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.359 * [taylor]: Taking taylor expansion of PI in n 2.359 * [backup-simplify]: Simplify PI into PI 2.359 * [taylor]: Taking taylor expansion of n in n 2.359 * [backup-simplify]: Simplify 0 into 0 2.359 * [backup-simplify]: Simplify 1 into 1 2.359 * [backup-simplify]: Simplify (/ PI 1) into PI 2.359 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.360 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.360 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.361 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.362 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 2.363 * [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)))) 2.364 * [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))))) 2.364 * [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)))))) 2.365 * [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)))))) 2.366 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.368 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.368 * [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)))))))) 2.369 * [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)))))))) 2.369 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 2.369 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 2.369 * [taylor]: Taking taylor expansion of +nan.0 in n 2.369 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.369 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 2.369 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 2.369 * [taylor]: Taking taylor expansion of 0.5 in n 2.369 * [backup-simplify]: Simplify 0.5 into 0.5 2.369 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 2.369 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.369 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.369 * [taylor]: Taking taylor expansion of k in n 2.369 * [backup-simplify]: Simplify k into k 2.369 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.369 * [taylor]: Taking taylor expansion of 1.0 in n 2.369 * [backup-simplify]: Simplify 1.0 into 1.0 2.369 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.369 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.369 * [taylor]: Taking taylor expansion of -2.0 in n 2.369 * [backup-simplify]: Simplify -2.0 into -2.0 2.369 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.369 * [taylor]: Taking taylor expansion of PI in n 2.369 * [backup-simplify]: Simplify PI into PI 2.369 * [taylor]: Taking taylor expansion of n in n 2.369 * [backup-simplify]: Simplify 0 into 0 2.369 * [backup-simplify]: Simplify 1 into 1 2.370 * [backup-simplify]: Simplify (/ PI 1) into PI 2.370 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.370 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.371 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.371 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.372 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 2.373 * [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)))) 2.374 * [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))))) 2.374 * [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)))))) 2.375 * [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))))))) 2.376 * [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))))))) 2.377 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.377 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.378 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.378 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.379 * [backup-simplify]: Simplify (+ 0 0) into 0 2.379 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.380 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.381 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 2.383 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.385 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 2.385 * [backup-simplify]: Simplify 0 into 0 2.386 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.395 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.397 * [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)))))))) 2.398 * [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)))))))) 2.398 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 2.398 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 2.398 * [taylor]: Taking taylor expansion of +nan.0 in n 2.398 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.398 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 2.398 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 2.398 * [taylor]: Taking taylor expansion of 0.5 in n 2.399 * [backup-simplify]: Simplify 0.5 into 0.5 2.399 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 2.399 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.399 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.399 * [taylor]: Taking taylor expansion of k in n 2.399 * [backup-simplify]: Simplify k into k 2.399 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.399 * [taylor]: Taking taylor expansion of 1.0 in n 2.399 * [backup-simplify]: Simplify 1.0 into 1.0 2.399 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.399 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.399 * [taylor]: Taking taylor expansion of -2.0 in n 2.399 * [backup-simplify]: Simplify -2.0 into -2.0 2.399 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.399 * [taylor]: Taking taylor expansion of PI in n 2.399 * [backup-simplify]: Simplify PI into PI 2.399 * [taylor]: Taking taylor expansion of n in n 2.399 * [backup-simplify]: Simplify 0 into 0 2.399 * [backup-simplify]: Simplify 1 into 1 2.400 * [backup-simplify]: Simplify (/ PI 1) into PI 2.400 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.401 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.401 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.403 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.404 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 2.406 * [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)))) 2.407 * [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))))) 2.408 * [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)))))) 2.410 * [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))))))) 2.412 * [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))))))) 2.417 * [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)))))))))))) 2.417 * * * [progress]: simplifying candidates 2.422 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (expm1 (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log1p (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (+ (- (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)))))))))))) 2.432 * * [simplify]: Extracting # 0 : cost 0 2.432 * * [simplify]: Extracting # 1 : cost 0 2.433 * * [simplify]: Extracting # 2 : cost 0 2.434 * * [simplify]: Extracting # 3 : cost 0 2.434 * * [simplify]: Extracting # 4 : cost 0 2.435 * * [simplify]: Extracting # 5 : cost 0 2.436 * * [simplify]: Extracting # 6 : cost 0 2.437 * * [simplify]: Extracting # 7 : cost 0 2.438 * * [simplify]: Extracting # 8 : cost 0 2.439 * * [simplify]: Extracting # 9 : cost 0 2.440 * * [simplify]: Extracting # 10 : cost 0 2.441 * * [simplify]: Extracting # 11 : cost 0 2.443 * * [simplify]: Extracting # 12 : cost 0 2.444 * * [simplify]: Extracting # 13 : cost 0 2.445 * * [simplify]: Extracting # 14 : cost 0 2.446 * * [simplify]: Extracting # 15 : cost 0 2.447 * * [simplify]: Extracting # 16 : cost 0 2.448 * * [simplify]: Extracting # 17 : cost 0 2.449 * * [simplify]: Extracting # 18 : cost 0 2.451 * * [simplify]: Extracting # 19 : cost 0 2.452 * * [simplify]: Extracting # 20 : cost 0 2.453 * * [simplify]: Extracting # 21 : cost 0 2.454 * * [simplify]: Extracting # 22 : cost 0 2.455 * * [simplify]: Extracting # 23 : cost 0 2.456 * * [simplify]: Extracting # 24 : cost 0 2.457 * * [simplify]: Extracting # 25 : cost 0 2.458 * * [simplify]: Extracting # 26 : cost 0 2.459 * * [simplify]: Extracting # 27 : cost 0 2.460 * * [simplify]: Extracting # 28 : cost 0 2.461 * * [simplify]: Extracting # 29 : cost 0 2.462 * * [simplify]: Extracting # 30 : cost 0 2.463 * * [simplify]: Extracting # 31 : cost 0 2.464 * * [simplify]: Extracting # 32 : cost 0 2.466 * * [simplify]: iteration 0 : 369 enodes (cost 2880 ) 2.610 * * [simplify]: Extracting # 0 : cost 0 2.617 * * [simplify]: Extracting # 1 : cost 0 2.620 * * [simplify]: Extracting # 2 : cost 0 2.623 * * [simplify]: Extracting # 3 : cost 0 2.626 * * [simplify]: Extracting # 4 : cost 0 2.629 * * [simplify]: Extracting # 5 : cost 0 2.632 * * [simplify]: Extracting # 6 : cost 0 2.635 * * [simplify]: iteration 1 : 1037 enodes (cost 2720 ) 3.369 * * [simplify]: Extracting # 0 : cost 0 3.380 * * [simplify]: Extracting # 1 : cost 0 3.393 * * [simplify]: Extracting # 2 : cost 0 3.405 * * [simplify]: Extracting # 3 : cost 0 3.419 * * [simplify]: Extracting # 4 : cost 0 3.432 * * [simplify]: iteration 2 : 4934 enodes (cost 2550 ) 5.175 * * [simplify]: Extracting # 0 : cost 0 5.187 * * [simplify]: Extracting # 1 : cost 0 5.199 * * [simplify]: Extracting # 2 : cost 0 5.212 * * [simplify]: Extracting # 3 : cost 0 5.224 * * [simplify]: Extracting # 4 : cost 0 5.238 * * [simplify]: iteration done: 5000 enodes (cost 2548 ) 5.240 * [simplify]: Simplified to: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (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))) (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)) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (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) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* PI n) (expm1 (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log1p (* (/ 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)))) (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 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (pow 1.0 3)) (* k (sqrt k))) (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))) (- (+ (fma (* 0.25 (pow k 2)) (* (* (pow (* (* 2.0 PI) n) 0.5) (log n)) (log (* 2.0 PI))) (pow (* (* 2.0 PI) n) 0.5)) (* (* 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))))) (* (* k (+ (* (pow (* (* 2.0 PI) n) 0.5) (log (* 2.0 PI))) (* (pow (* (* 2.0 PI) n) 0.5) (log 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)))))) (- (fma +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)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (- (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (fma +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)) (fma (- (* +nan.0 (* (pow k 2) (log n)))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (fma (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) +nan.0 (+ (- (* +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)))) (fma (* +nan.0 (* k (log n))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (fma +nan.0 (- (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (* +nan.0 (- (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))) (- (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))) (+ (- (/ (* (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) +nan.0) (pow k 3))) (* +nan.0 (- (/ (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) k) (/ (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (pow k 2))))) (+ (* +nan.0 (- (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)))) 5.242 * * * [progress]: adding candidates to table 5.882 * * [progress]: iteration 2 / 4 5.882 * * * [progress]: picking best candidate 5.909 * * * * [pick]: Picked # 5.909 * * * [progress]: localizing error 5.952 * * * [progress]: generating rewritten candidates 5.952 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 5.994 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 6.026 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 6.036 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2) 6.134 * * * [progress]: generating series expansions 6.134 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 6.135 * [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))) 6.135 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 6.135 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 6.135 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 6.135 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 6.135 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 6.135 * [taylor]: Taking taylor expansion of 0.25 in k 6.135 * [backup-simplify]: Simplify 0.25 into 0.25 6.136 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.136 * [taylor]: Taking taylor expansion of 1.0 in k 6.136 * [backup-simplify]: Simplify 1.0 into 1.0 6.136 * [taylor]: Taking taylor expansion of k in k 6.136 * [backup-simplify]: Simplify 0 into 0 6.136 * [backup-simplify]: Simplify 1 into 1 6.136 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 6.136 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 6.136 * [taylor]: Taking taylor expansion of 2.0 in k 6.136 * [backup-simplify]: Simplify 2.0 into 2.0 6.136 * [taylor]: Taking taylor expansion of (* n PI) in k 6.136 * [taylor]: Taking taylor expansion of n in k 6.136 * [backup-simplify]: Simplify n into n 6.136 * [taylor]: Taking taylor expansion of PI in k 6.136 * [backup-simplify]: Simplify PI into PI 6.136 * [backup-simplify]: Simplify (* n PI) into (* n PI) 6.136 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 6.136 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 6.136 * [backup-simplify]: Simplify (- 0) into 0 6.137 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.137 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 6.137 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 6.137 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 6.137 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 6.137 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.137 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.137 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 6.137 * [taylor]: Taking taylor expansion of 0.25 in n 6.137 * [backup-simplify]: Simplify 0.25 into 0.25 6.137 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.137 * [taylor]: Taking taylor expansion of 1.0 in n 6.137 * [backup-simplify]: Simplify 1.0 into 1.0 6.137 * [taylor]: Taking taylor expansion of k in n 6.137 * [backup-simplify]: Simplify k into k 6.137 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.137 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.137 * [taylor]: Taking taylor expansion of 2.0 in n 6.137 * [backup-simplify]: Simplify 2.0 into 2.0 6.137 * [taylor]: Taking taylor expansion of (* n PI) in n 6.137 * [taylor]: Taking taylor expansion of n in n 6.137 * [backup-simplify]: Simplify 0 into 0 6.137 * [backup-simplify]: Simplify 1 into 1 6.137 * [taylor]: Taking taylor expansion of PI in n 6.137 * [backup-simplify]: Simplify PI into PI 6.138 * [backup-simplify]: Simplify (* 0 PI) into 0 6.138 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.139 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.140 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.141 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.141 * [backup-simplify]: Simplify (- k) into (- k) 6.141 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.141 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 6.142 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.142 * [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)))) 6.143 * [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))))) 6.143 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 6.143 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.143 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.143 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 6.143 * [taylor]: Taking taylor expansion of 0.25 in n 6.143 * [backup-simplify]: Simplify 0.25 into 0.25 6.143 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.143 * [taylor]: Taking taylor expansion of 1.0 in n 6.143 * [backup-simplify]: Simplify 1.0 into 1.0 6.143 * [taylor]: Taking taylor expansion of k in n 6.143 * [backup-simplify]: Simplify k into k 6.143 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.143 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.143 * [taylor]: Taking taylor expansion of 2.0 in n 6.143 * [backup-simplify]: Simplify 2.0 into 2.0 6.143 * [taylor]: Taking taylor expansion of (* n PI) in n 6.143 * [taylor]: Taking taylor expansion of n in n 6.143 * [backup-simplify]: Simplify 0 into 0 6.143 * [backup-simplify]: Simplify 1 into 1 6.143 * [taylor]: Taking taylor expansion of PI in n 6.143 * [backup-simplify]: Simplify PI into PI 6.144 * [backup-simplify]: Simplify (* 0 PI) into 0 6.144 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.145 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.146 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.147 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.147 * [backup-simplify]: Simplify (- k) into (- k) 6.147 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.147 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 6.148 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.148 * [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)))) 6.149 * [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))))) 6.149 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 6.149 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 6.149 * [taylor]: Taking taylor expansion of 0.25 in k 6.149 * [backup-simplify]: Simplify 0.25 into 0.25 6.149 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 6.149 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.149 * [taylor]: Taking taylor expansion of 1.0 in k 6.149 * [backup-simplify]: Simplify 1.0 into 1.0 6.149 * [taylor]: Taking taylor expansion of k in k 6.149 * [backup-simplify]: Simplify 0 into 0 6.150 * [backup-simplify]: Simplify 1 into 1 6.150 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 6.150 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.150 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.150 * [taylor]: Taking taylor expansion of 2.0 in k 6.150 * [backup-simplify]: Simplify 2.0 into 2.0 6.150 * [taylor]: Taking taylor expansion of PI in k 6.150 * [backup-simplify]: Simplify PI into PI 6.150 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.151 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.151 * [taylor]: Taking taylor expansion of (log n) in k 6.151 * [taylor]: Taking taylor expansion of n in k 6.151 * [backup-simplify]: Simplify n into n 6.151 * [backup-simplify]: Simplify (log n) into (log n) 6.151 * [backup-simplify]: Simplify (- 0) into 0 6.151 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.152 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 6.152 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 6.153 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 6.154 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 6.155 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 6.155 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 6.156 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 6.157 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.157 * [backup-simplify]: Simplify (- 0) into 0 6.157 * [backup-simplify]: Simplify (+ 0 0) into 0 6.158 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 6.158 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.159 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 6.160 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.160 * [taylor]: Taking taylor expansion of 0 in k 6.160 * [backup-simplify]: Simplify 0 into 0 6.161 * [backup-simplify]: Simplify 0 into 0 6.161 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.162 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.163 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 6.163 * [backup-simplify]: Simplify (+ 0 0) into 0 6.163 * [backup-simplify]: Simplify (- 1) into -1 6.163 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.164 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 6.166 * [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)))) 6.169 * [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)))))) 6.172 * [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)))))) 6.174 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 6.175 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 6.179 * [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 6.179 * [backup-simplify]: Simplify (- 0) into 0 6.180 * [backup-simplify]: Simplify (+ 0 0) into 0 6.181 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 6.182 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.184 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.187 * [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 6.187 * [taylor]: Taking taylor expansion of 0 in k 6.187 * [backup-simplify]: Simplify 0 into 0 6.187 * [backup-simplify]: Simplify 0 into 0 6.187 * [backup-simplify]: Simplify 0 into 0 6.188 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.191 * [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 6.193 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 6.194 * [backup-simplify]: Simplify (+ 0 0) into 0 6.194 * [backup-simplify]: Simplify (- 0) into 0 6.195 * [backup-simplify]: Simplify (+ 0 0) into 0 6.197 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.200 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 6.204 * [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))))) 6.210 * [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))))) 6.222 * [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)))))) 6.222 * [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)))) 6.222 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 6.222 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 6.222 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 6.223 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 6.223 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 6.223 * [taylor]: Taking taylor expansion of 0.25 in k 6.223 * [backup-simplify]: Simplify 0.25 into 0.25 6.223 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.223 * [taylor]: Taking taylor expansion of 1.0 in k 6.223 * [backup-simplify]: Simplify 1.0 into 1.0 6.223 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.223 * [taylor]: Taking taylor expansion of k in k 6.223 * [backup-simplify]: Simplify 0 into 0 6.223 * [backup-simplify]: Simplify 1 into 1 6.223 * [backup-simplify]: Simplify (/ 1 1) into 1 6.223 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 6.223 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 6.223 * [taylor]: Taking taylor expansion of 2.0 in k 6.223 * [backup-simplify]: Simplify 2.0 into 2.0 6.223 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.223 * [taylor]: Taking taylor expansion of PI in k 6.223 * [backup-simplify]: Simplify PI into PI 6.223 * [taylor]: Taking taylor expansion of n in k 6.223 * [backup-simplify]: Simplify n into n 6.223 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.223 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 6.223 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 6.224 * [backup-simplify]: Simplify (- 1) into -1 6.224 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.224 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 6.224 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 6.224 * [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))))) 6.224 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 6.224 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.224 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.224 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 6.224 * [taylor]: Taking taylor expansion of 0.25 in n 6.224 * [backup-simplify]: Simplify 0.25 into 0.25 6.224 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.224 * [taylor]: Taking taylor expansion of 1.0 in n 6.224 * [backup-simplify]: Simplify 1.0 into 1.0 6.224 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.225 * [taylor]: Taking taylor expansion of k in n 6.225 * [backup-simplify]: Simplify k into k 6.225 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.225 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.225 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.225 * [taylor]: Taking taylor expansion of 2.0 in n 6.225 * [backup-simplify]: Simplify 2.0 into 2.0 6.225 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.225 * [taylor]: Taking taylor expansion of PI in n 6.225 * [backup-simplify]: Simplify PI into PI 6.225 * [taylor]: Taking taylor expansion of n in n 6.225 * [backup-simplify]: Simplify 0 into 0 6.225 * [backup-simplify]: Simplify 1 into 1 6.225 * [backup-simplify]: Simplify (/ PI 1) into PI 6.225 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.226 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.226 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.226 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.226 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 6.227 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.228 * [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)))) 6.229 * [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))))) 6.229 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 6.229 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.229 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.229 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 6.229 * [taylor]: Taking taylor expansion of 0.25 in n 6.229 * [backup-simplify]: Simplify 0.25 into 0.25 6.229 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.229 * [taylor]: Taking taylor expansion of 1.0 in n 6.229 * [backup-simplify]: Simplify 1.0 into 1.0 6.229 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.229 * [taylor]: Taking taylor expansion of k in n 6.229 * [backup-simplify]: Simplify k into k 6.229 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.229 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.229 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.229 * [taylor]: Taking taylor expansion of 2.0 in n 6.229 * [backup-simplify]: Simplify 2.0 into 2.0 6.229 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.229 * [taylor]: Taking taylor expansion of PI in n 6.229 * [backup-simplify]: Simplify PI into PI 6.229 * [taylor]: Taking taylor expansion of n in n 6.229 * [backup-simplify]: Simplify 0 into 0 6.229 * [backup-simplify]: Simplify 1 into 1 6.229 * [backup-simplify]: Simplify (/ PI 1) into PI 6.230 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.230 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.230 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.230 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.231 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 6.231 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.232 * [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)))) 6.233 * [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))))) 6.233 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 6.233 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 6.233 * [taylor]: Taking taylor expansion of 0.25 in k 6.233 * [backup-simplify]: Simplify 0.25 into 0.25 6.233 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 6.233 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 6.233 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.233 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.233 * [taylor]: Taking taylor expansion of 2.0 in k 6.233 * [backup-simplify]: Simplify 2.0 into 2.0 6.233 * [taylor]: Taking taylor expansion of PI in k 6.233 * [backup-simplify]: Simplify PI into PI 6.233 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.234 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.234 * [taylor]: Taking taylor expansion of (log n) in k 6.234 * [taylor]: Taking taylor expansion of n in k 6.234 * [backup-simplify]: Simplify n into n 6.234 * [backup-simplify]: Simplify (log n) into (log n) 6.234 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.234 * [taylor]: Taking taylor expansion of 1.0 in k 6.234 * [backup-simplify]: Simplify 1.0 into 1.0 6.234 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.234 * [taylor]: Taking taylor expansion of k in k 6.234 * [backup-simplify]: Simplify 0 into 0 6.234 * [backup-simplify]: Simplify 1 into 1 6.235 * [backup-simplify]: Simplify (/ 1 1) into 1 6.235 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.235 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 6.236 * [backup-simplify]: Simplify (- 1) into -1 6.236 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.236 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 6.237 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 6.238 * [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))))) 6.239 * [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))))) 6.240 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.240 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.241 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.241 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.242 * [backup-simplify]: Simplify (- 0) into 0 6.242 * [backup-simplify]: Simplify (+ 0 0) into 0 6.242 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 6.243 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.249 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 6.250 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.251 * [taylor]: Taking taylor expansion of 0 in k 6.251 * [backup-simplify]: Simplify 0 into 0 6.251 * [backup-simplify]: Simplify 0 into 0 6.251 * [backup-simplify]: Simplify 0 into 0 6.251 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.252 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.254 * [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 6.254 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.254 * [backup-simplify]: Simplify (- 0) into 0 6.254 * [backup-simplify]: Simplify (+ 0 0) into 0 6.255 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 6.256 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.258 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 6.260 * [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 6.260 * [taylor]: Taking taylor expansion of 0 in k 6.261 * [backup-simplify]: Simplify 0 into 0 6.261 * [backup-simplify]: Simplify 0 into 0 6.261 * [backup-simplify]: Simplify 0 into 0 6.261 * [backup-simplify]: Simplify 0 into 0 6.262 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.263 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.269 * [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 6.270 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.270 * [backup-simplify]: Simplify (- 0) into 0 6.270 * [backup-simplify]: Simplify (+ 0 0) into 0 6.272 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 6.273 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.275 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 6.278 * [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 6.278 * [taylor]: Taking taylor expansion of 0 in k 6.279 * [backup-simplify]: Simplify 0 into 0 6.279 * [backup-simplify]: Simplify 0 into 0 6.280 * [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)))) 6.281 * [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))) 6.281 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 6.281 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 6.281 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 6.281 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 6.281 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 6.281 * [taylor]: Taking taylor expansion of 0.25 in k 6.281 * [backup-simplify]: Simplify 0.25 into 0.25 6.281 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.281 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.281 * [taylor]: Taking taylor expansion of k in k 6.281 * [backup-simplify]: Simplify 0 into 0 6.281 * [backup-simplify]: Simplify 1 into 1 6.282 * [backup-simplify]: Simplify (/ 1 1) into 1 6.282 * [taylor]: Taking taylor expansion of 1.0 in k 6.282 * [backup-simplify]: Simplify 1.0 into 1.0 6.282 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 6.282 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 6.282 * [taylor]: Taking taylor expansion of -2.0 in k 6.282 * [backup-simplify]: Simplify -2.0 into -2.0 6.282 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.282 * [taylor]: Taking taylor expansion of PI in k 6.282 * [backup-simplify]: Simplify PI into PI 6.282 * [taylor]: Taking taylor expansion of n in k 6.282 * [backup-simplify]: Simplify n into n 6.282 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.282 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 6.282 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 6.283 * [backup-simplify]: Simplify (+ 1 0) into 1 6.283 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 6.283 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 6.284 * [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)))))) 6.284 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 6.284 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.284 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.284 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 6.284 * [taylor]: Taking taylor expansion of 0.25 in n 6.284 * [backup-simplify]: Simplify 0.25 into 0.25 6.284 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.284 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.284 * [taylor]: Taking taylor expansion of k in n 6.284 * [backup-simplify]: Simplify k into k 6.284 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.284 * [taylor]: Taking taylor expansion of 1.0 in n 6.284 * [backup-simplify]: Simplify 1.0 into 1.0 6.284 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.284 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.284 * [taylor]: Taking taylor expansion of -2.0 in n 6.284 * [backup-simplify]: Simplify -2.0 into -2.0 6.284 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.284 * [taylor]: Taking taylor expansion of PI in n 6.284 * [backup-simplify]: Simplify PI into PI 6.284 * [taylor]: Taking taylor expansion of n in n 6.284 * [backup-simplify]: Simplify 0 into 0 6.284 * [backup-simplify]: Simplify 1 into 1 6.285 * [backup-simplify]: Simplify (/ PI 1) into PI 6.285 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.286 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.287 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.287 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 6.288 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.290 * [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)))) 6.291 * [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))))) 6.291 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 6.291 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.291 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.291 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 6.291 * [taylor]: Taking taylor expansion of 0.25 in n 6.291 * [backup-simplify]: Simplify 0.25 into 0.25 6.291 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.291 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.291 * [taylor]: Taking taylor expansion of k in n 6.291 * [backup-simplify]: Simplify k into k 6.291 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.291 * [taylor]: Taking taylor expansion of 1.0 in n 6.291 * [backup-simplify]: Simplify 1.0 into 1.0 6.291 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.291 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.291 * [taylor]: Taking taylor expansion of -2.0 in n 6.291 * [backup-simplify]: Simplify -2.0 into -2.0 6.292 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.292 * [taylor]: Taking taylor expansion of PI in n 6.292 * [backup-simplify]: Simplify PI into PI 6.292 * [taylor]: Taking taylor expansion of n in n 6.292 * [backup-simplify]: Simplify 0 into 0 6.292 * [backup-simplify]: Simplify 1 into 1 6.292 * [backup-simplify]: Simplify (/ PI 1) into PI 6.293 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.294 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.294 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.294 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 6.295 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.297 * [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)))) 6.298 * [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))))) 6.298 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 6.298 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 6.298 * [taylor]: Taking taylor expansion of 0.25 in k 6.298 * [backup-simplify]: Simplify 0.25 into 0.25 6.298 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 6.298 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.298 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.298 * [taylor]: Taking taylor expansion of k in k 6.298 * [backup-simplify]: Simplify 0 into 0 6.298 * [backup-simplify]: Simplify 1 into 1 6.299 * [backup-simplify]: Simplify (/ 1 1) into 1 6.299 * [taylor]: Taking taylor expansion of 1.0 in k 6.299 * [backup-simplify]: Simplify 1.0 into 1.0 6.299 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 6.299 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 6.299 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 6.299 * [taylor]: Taking taylor expansion of -2.0 in k 6.299 * [backup-simplify]: Simplify -2.0 into -2.0 6.299 * [taylor]: Taking taylor expansion of PI in k 6.299 * [backup-simplify]: Simplify PI into PI 6.300 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.301 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.301 * [taylor]: Taking taylor expansion of (log n) in k 6.301 * [taylor]: Taking taylor expansion of n in k 6.301 * [backup-simplify]: Simplify n into n 6.301 * [backup-simplify]: Simplify (log n) into (log n) 6.301 * [backup-simplify]: Simplify (+ 1 0) into 1 6.301 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.302 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 6.304 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 6.305 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 6.306 * [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))))) 6.308 * [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))))) 6.309 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.309 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 6.311 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 6.311 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.312 * [backup-simplify]: Simplify (+ 0 0) into 0 6.312 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 6.314 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.315 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 6.317 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.317 * [taylor]: Taking taylor expansion of 0 in k 6.318 * [backup-simplify]: Simplify 0 into 0 6.318 * [backup-simplify]: Simplify 0 into 0 6.318 * [backup-simplify]: Simplify 0 into 0 6.319 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.320 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.323 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 6.324 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.324 * [backup-simplify]: Simplify (+ 0 0) into 0 6.325 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 6.327 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.328 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 6.331 * [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 6.331 * [taylor]: Taking taylor expansion of 0 in k 6.331 * [backup-simplify]: Simplify 0 into 0 6.331 * [backup-simplify]: Simplify 0 into 0 6.331 * [backup-simplify]: Simplify 0 into 0 6.331 * [backup-simplify]: Simplify 0 into 0 6.332 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.334 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.339 * [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 6.340 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.340 * [backup-simplify]: Simplify (+ 0 0) into 0 6.341 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 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)) 6.345 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 6.348 * [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 6.348 * [taylor]: Taking taylor expansion of 0 in k 6.348 * [backup-simplify]: Simplify 0 into 0 6.348 * [backup-simplify]: Simplify 0 into 0 6.349 * [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)))))) 6.349 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 6.350 * [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))) 6.350 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 6.350 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 6.350 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 6.350 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 6.350 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 6.350 * [taylor]: Taking taylor expansion of 0.25 in k 6.350 * [backup-simplify]: Simplify 0.25 into 0.25 6.350 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.350 * [taylor]: Taking taylor expansion of 1.0 in k 6.350 * [backup-simplify]: Simplify 1.0 into 1.0 6.350 * [taylor]: Taking taylor expansion of k in k 6.350 * [backup-simplify]: Simplify 0 into 0 6.350 * [backup-simplify]: Simplify 1 into 1 6.350 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 6.350 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 6.350 * [taylor]: Taking taylor expansion of 2.0 in k 6.350 * [backup-simplify]: Simplify 2.0 into 2.0 6.351 * [taylor]: Taking taylor expansion of (* n PI) in k 6.351 * [taylor]: Taking taylor expansion of n in k 6.351 * [backup-simplify]: Simplify n into n 6.351 * [taylor]: Taking taylor expansion of PI in k 6.351 * [backup-simplify]: Simplify PI into PI 6.351 * [backup-simplify]: Simplify (* n PI) into (* n PI) 6.351 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 6.351 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 6.351 * [backup-simplify]: Simplify (- 0) into 0 6.352 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.352 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 6.352 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 6.352 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 6.352 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 6.352 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.353 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.353 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 6.353 * [taylor]: Taking taylor expansion of 0.25 in n 6.353 * [backup-simplify]: Simplify 0.25 into 0.25 6.353 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.353 * [taylor]: Taking taylor expansion of 1.0 in n 6.353 * [backup-simplify]: Simplify 1.0 into 1.0 6.353 * [taylor]: Taking taylor expansion of k in n 6.353 * [backup-simplify]: Simplify k into k 6.353 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.353 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.353 * [taylor]: Taking taylor expansion of 2.0 in n 6.353 * [backup-simplify]: Simplify 2.0 into 2.0 6.353 * [taylor]: Taking taylor expansion of (* n PI) in n 6.353 * [taylor]: Taking taylor expansion of n in n 6.353 * [backup-simplify]: Simplify 0 into 0 6.353 * [backup-simplify]: Simplify 1 into 1 6.353 * [taylor]: Taking taylor expansion of PI in n 6.353 * [backup-simplify]: Simplify PI into PI 6.353 * [backup-simplify]: Simplify (* 0 PI) into 0 6.354 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.355 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.357 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.358 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.358 * [backup-simplify]: Simplify (- k) into (- k) 6.358 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.359 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 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 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 6.363 * [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))))) 6.363 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 6.363 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.363 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.363 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 6.363 * [taylor]: Taking taylor expansion of 0.25 in n 6.363 * [backup-simplify]: Simplify 0.25 into 0.25 6.363 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.363 * [taylor]: Taking taylor expansion of 1.0 in n 6.363 * [backup-simplify]: Simplify 1.0 into 1.0 6.363 * [taylor]: Taking taylor expansion of k in n 6.363 * [backup-simplify]: Simplify k into k 6.363 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.363 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.363 * [taylor]: Taking taylor expansion of 2.0 in n 6.363 * [backup-simplify]: Simplify 2.0 into 2.0 6.363 * [taylor]: Taking taylor expansion of (* n PI) in n 6.363 * [taylor]: Taking taylor expansion of n in n 6.363 * [backup-simplify]: Simplify 0 into 0 6.363 * [backup-simplify]: Simplify 1 into 1 6.363 * [taylor]: Taking taylor expansion of PI in n 6.363 * [backup-simplify]: Simplify PI into PI 6.364 * [backup-simplify]: Simplify (* 0 PI) into 0 6.364 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.366 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.367 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.368 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.368 * [backup-simplify]: Simplify (- k) into (- k) 6.368 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.368 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 6.370 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.371 * [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)))) 6.372 * [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))))) 6.372 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 6.373 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 6.373 * [taylor]: Taking taylor expansion of 0.25 in k 6.373 * [backup-simplify]: Simplify 0.25 into 0.25 6.373 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 6.373 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.373 * [taylor]: Taking taylor expansion of 1.0 in k 6.373 * [backup-simplify]: Simplify 1.0 into 1.0 6.373 * [taylor]: Taking taylor expansion of k in k 6.373 * [backup-simplify]: Simplify 0 into 0 6.373 * [backup-simplify]: Simplify 1 into 1 6.373 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 6.373 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.373 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.373 * [taylor]: Taking taylor expansion of 2.0 in k 6.373 * [backup-simplify]: Simplify 2.0 into 2.0 6.373 * [taylor]: Taking taylor expansion of PI in k 6.373 * [backup-simplify]: Simplify PI into PI 6.374 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.375 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.375 * [taylor]: Taking taylor expansion of (log n) in k 6.375 * [taylor]: Taking taylor expansion of n in k 6.375 * [backup-simplify]: Simplify n into n 6.375 * [backup-simplify]: Simplify (log n) into (log n) 6.375 * [backup-simplify]: Simplify (- 0) into 0 6.376 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.377 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 6.378 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 6.379 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 6.380 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 6.381 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 6.382 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 6.383 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 6.386 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.386 * [backup-simplify]: Simplify (- 0) into 0 6.386 * [backup-simplify]: Simplify (+ 0 0) into 0 6.387 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 6.389 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.390 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 6.392 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.392 * [taylor]: Taking taylor expansion of 0 in k 6.392 * [backup-simplify]: Simplify 0 into 0 6.392 * [backup-simplify]: Simplify 0 into 0 6.393 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.395 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.396 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 6.396 * [backup-simplify]: Simplify (+ 0 0) into 0 6.406 * [backup-simplify]: Simplify (- 1) into -1 6.407 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.409 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 6.412 * [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)))) 6.416 * [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)))))) 6.419 * [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)))))) 6.421 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 6.422 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 6.425 * [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 6.426 * [backup-simplify]: Simplify (- 0) into 0 6.426 * [backup-simplify]: Simplify (+ 0 0) into 0 6.427 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 6.429 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.430 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.433 * [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 6.433 * [taylor]: Taking taylor expansion of 0 in k 6.433 * [backup-simplify]: Simplify 0 into 0 6.433 * [backup-simplify]: Simplify 0 into 0 6.433 * [backup-simplify]: Simplify 0 into 0 6.434 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.438 * [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 6.440 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 6.440 * [backup-simplify]: Simplify (+ 0 0) into 0 6.440 * [backup-simplify]: Simplify (- 0) into 0 6.441 * [backup-simplify]: Simplify (+ 0 0) into 0 6.443 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.445 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 6.450 * [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))))) 6.455 * [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))))) 6.463 * [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)))))) 6.464 * [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)))) 6.464 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 6.464 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 6.464 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 6.464 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 6.464 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 6.464 * [taylor]: Taking taylor expansion of 0.25 in k 6.464 * [backup-simplify]: Simplify 0.25 into 0.25 6.464 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.464 * [taylor]: Taking taylor expansion of 1.0 in k 6.464 * [backup-simplify]: Simplify 1.0 into 1.0 6.464 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.464 * [taylor]: Taking taylor expansion of k in k 6.464 * [backup-simplify]: Simplify 0 into 0 6.464 * [backup-simplify]: Simplify 1 into 1 6.464 * [backup-simplify]: Simplify (/ 1 1) into 1 6.464 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 6.464 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 6.464 * [taylor]: Taking taylor expansion of 2.0 in k 6.464 * [backup-simplify]: Simplify 2.0 into 2.0 6.464 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.464 * [taylor]: Taking taylor expansion of PI in k 6.464 * [backup-simplify]: Simplify PI into PI 6.464 * [taylor]: Taking taylor expansion of n in k 6.464 * [backup-simplify]: Simplify n into n 6.464 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.465 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 6.465 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 6.465 * [backup-simplify]: Simplify (- 1) into -1 6.465 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.465 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 6.466 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 6.466 * [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))))) 6.466 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 6.466 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.466 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.466 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 6.466 * [taylor]: Taking taylor expansion of 0.25 in n 6.466 * [backup-simplify]: Simplify 0.25 into 0.25 6.466 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.466 * [taylor]: Taking taylor expansion of 1.0 in n 6.466 * [backup-simplify]: Simplify 1.0 into 1.0 6.466 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.466 * [taylor]: Taking taylor expansion of k in n 6.466 * [backup-simplify]: Simplify k into k 6.466 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.466 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.466 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.466 * [taylor]: Taking taylor expansion of 2.0 in n 6.466 * [backup-simplify]: Simplify 2.0 into 2.0 6.466 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.466 * [taylor]: Taking taylor expansion of PI in n 6.466 * [backup-simplify]: Simplify PI into PI 6.466 * [taylor]: Taking taylor expansion of n in n 6.466 * [backup-simplify]: Simplify 0 into 0 6.466 * [backup-simplify]: Simplify 1 into 1 6.467 * [backup-simplify]: Simplify (/ PI 1) into PI 6.467 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.468 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.468 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.468 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.468 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 6.469 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.470 * [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)))) 6.470 * [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))))) 6.471 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 6.471 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.471 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.471 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 6.471 * [taylor]: Taking taylor expansion of 0.25 in n 6.471 * [backup-simplify]: Simplify 0.25 into 0.25 6.471 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.471 * [taylor]: Taking taylor expansion of 1.0 in n 6.471 * [backup-simplify]: Simplify 1.0 into 1.0 6.471 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.471 * [taylor]: Taking taylor expansion of k in n 6.471 * [backup-simplify]: Simplify k into k 6.471 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.471 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.471 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.471 * [taylor]: Taking taylor expansion of 2.0 in n 6.471 * [backup-simplify]: Simplify 2.0 into 2.0 6.471 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.471 * [taylor]: Taking taylor expansion of PI in n 6.471 * [backup-simplify]: Simplify PI into PI 6.471 * [taylor]: Taking taylor expansion of n in n 6.471 * [backup-simplify]: Simplify 0 into 0 6.471 * [backup-simplify]: Simplify 1 into 1 6.471 * [backup-simplify]: Simplify (/ PI 1) into PI 6.472 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.473 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.473 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.473 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.473 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 6.475 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.476 * [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)))) 6.477 * [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))))) 6.477 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 6.477 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 6.477 * [taylor]: Taking taylor expansion of 0.25 in k 6.477 * [backup-simplify]: Simplify 0.25 into 0.25 6.477 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 6.477 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 6.477 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.477 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.477 * [taylor]: Taking taylor expansion of 2.0 in k 6.477 * [backup-simplify]: Simplify 2.0 into 2.0 6.477 * [taylor]: Taking taylor expansion of PI in k 6.477 * [backup-simplify]: Simplify PI into PI 6.478 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.479 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.479 * [taylor]: Taking taylor expansion of (log n) in k 6.479 * [taylor]: Taking taylor expansion of n in k 6.479 * [backup-simplify]: Simplify n into n 6.479 * [backup-simplify]: Simplify (log n) into (log n) 6.479 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.479 * [taylor]: Taking taylor expansion of 1.0 in k 6.479 * [backup-simplify]: Simplify 1.0 into 1.0 6.479 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.479 * [taylor]: Taking taylor expansion of k in k 6.479 * [backup-simplify]: Simplify 0 into 0 6.479 * [backup-simplify]: Simplify 1 into 1 6.479 * [backup-simplify]: Simplify (/ 1 1) into 1 6.480 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.481 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 6.481 * [backup-simplify]: Simplify (- 1) into -1 6.481 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.483 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 6.484 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 6.485 * [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))))) 6.486 * [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))))) 6.487 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.488 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.490 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.490 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.491 * [backup-simplify]: Simplify (- 0) into 0 6.491 * [backup-simplify]: Simplify (+ 0 0) into 0 6.492 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 6.493 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.494 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 6.496 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.496 * [taylor]: Taking taylor expansion of 0 in k 6.496 * [backup-simplify]: Simplify 0 into 0 6.496 * [backup-simplify]: Simplify 0 into 0 6.497 * [backup-simplify]: Simplify 0 into 0 6.498 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.499 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.502 * [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 6.502 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.503 * [backup-simplify]: Simplify (- 0) into 0 6.503 * [backup-simplify]: Simplify (+ 0 0) into 0 6.504 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 6.505 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.506 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 6.507 * [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 6.507 * [taylor]: Taking taylor expansion of 0 in k 6.507 * [backup-simplify]: Simplify 0 into 0 6.508 * [backup-simplify]: Simplify 0 into 0 6.508 * [backup-simplify]: Simplify 0 into 0 6.508 * [backup-simplify]: Simplify 0 into 0 6.508 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.509 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.512 * [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 6.512 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.513 * [backup-simplify]: Simplify (- 0) into 0 6.513 * [backup-simplify]: Simplify (+ 0 0) into 0 6.514 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 6.515 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.516 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 6.518 * [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 6.518 * [taylor]: Taking taylor expansion of 0 in k 6.518 * [backup-simplify]: Simplify 0 into 0 6.518 * [backup-simplify]: Simplify 0 into 0 6.519 * [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)))) 6.519 * [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))) 6.519 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 6.519 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 6.519 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 6.519 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 6.519 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 6.519 * [taylor]: Taking taylor expansion of 0.25 in k 6.519 * [backup-simplify]: Simplify 0.25 into 0.25 6.519 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.519 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.520 * [taylor]: Taking taylor expansion of k in k 6.520 * [backup-simplify]: Simplify 0 into 0 6.520 * [backup-simplify]: Simplify 1 into 1 6.520 * [backup-simplify]: Simplify (/ 1 1) into 1 6.520 * [taylor]: Taking taylor expansion of 1.0 in k 6.520 * [backup-simplify]: Simplify 1.0 into 1.0 6.520 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 6.520 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 6.520 * [taylor]: Taking taylor expansion of -2.0 in k 6.520 * [backup-simplify]: Simplify -2.0 into -2.0 6.520 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.520 * [taylor]: Taking taylor expansion of PI in k 6.520 * [backup-simplify]: Simplify PI into PI 6.520 * [taylor]: Taking taylor expansion of n in k 6.520 * [backup-simplify]: Simplify n into n 6.520 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.520 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 6.520 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 6.521 * [backup-simplify]: Simplify (+ 1 0) into 1 6.521 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 6.521 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 6.521 * [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)))))) 6.521 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 6.521 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.521 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.521 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 6.521 * [taylor]: Taking taylor expansion of 0.25 in n 6.521 * [backup-simplify]: Simplify 0.25 into 0.25 6.521 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.521 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.521 * [taylor]: Taking taylor expansion of k in n 6.521 * [backup-simplify]: Simplify k into k 6.521 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.521 * [taylor]: Taking taylor expansion of 1.0 in n 6.521 * [backup-simplify]: Simplify 1.0 into 1.0 6.521 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.521 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.521 * [taylor]: Taking taylor expansion of -2.0 in n 6.521 * [backup-simplify]: Simplify -2.0 into -2.0 6.521 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.521 * [taylor]: Taking taylor expansion of PI in n 6.522 * [backup-simplify]: Simplify PI into PI 6.522 * [taylor]: Taking taylor expansion of n in n 6.522 * [backup-simplify]: Simplify 0 into 0 6.522 * [backup-simplify]: Simplify 1 into 1 6.522 * [backup-simplify]: Simplify (/ PI 1) into PI 6.522 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.523 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.523 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.523 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 6.524 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.525 * [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)))) 6.525 * [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))))) 6.525 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 6.525 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.525 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.526 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 6.526 * [taylor]: Taking taylor expansion of 0.25 in n 6.526 * [backup-simplify]: Simplify 0.25 into 0.25 6.526 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.526 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.526 * [taylor]: Taking taylor expansion of k in n 6.526 * [backup-simplify]: Simplify k into k 6.526 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.526 * [taylor]: Taking taylor expansion of 1.0 in n 6.526 * [backup-simplify]: Simplify 1.0 into 1.0 6.526 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.526 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.526 * [taylor]: Taking taylor expansion of -2.0 in n 6.526 * [backup-simplify]: Simplify -2.0 into -2.0 6.526 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.526 * [taylor]: Taking taylor expansion of PI in n 6.526 * [backup-simplify]: Simplify PI into PI 6.526 * [taylor]: Taking taylor expansion of n in n 6.526 * [backup-simplify]: Simplify 0 into 0 6.526 * [backup-simplify]: Simplify 1 into 1 6.526 * [backup-simplify]: Simplify (/ PI 1) into PI 6.526 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.527 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.527 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.527 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 6.528 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.529 * [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)))) 6.530 * [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))))) 6.530 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 6.530 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 6.530 * [taylor]: Taking taylor expansion of 0.25 in k 6.530 * [backup-simplify]: Simplify 0.25 into 0.25 6.530 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 6.530 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.530 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.530 * [taylor]: Taking taylor expansion of k in k 6.530 * [backup-simplify]: Simplify 0 into 0 6.530 * [backup-simplify]: Simplify 1 into 1 6.530 * [backup-simplify]: Simplify (/ 1 1) into 1 6.531 * [taylor]: Taking taylor expansion of 1.0 in k 6.531 * [backup-simplify]: Simplify 1.0 into 1.0 6.531 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 6.531 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 6.531 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 6.531 * [taylor]: Taking taylor expansion of -2.0 in k 6.531 * [backup-simplify]: Simplify -2.0 into -2.0 6.531 * [taylor]: Taking taylor expansion of PI in k 6.531 * [backup-simplify]: Simplify PI into PI 6.531 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.532 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.532 * [taylor]: Taking taylor expansion of (log n) in k 6.532 * [taylor]: Taking taylor expansion of n in k 6.532 * [backup-simplify]: Simplify n into n 6.532 * [backup-simplify]: Simplify (log n) into (log n) 6.533 * [backup-simplify]: Simplify (+ 1 0) into 1 6.533 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.534 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 6.543 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 6.544 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 6.545 * [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))))) 6.546 * [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))))) 6.547 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.548 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 6.550 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 6.550 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.551 * [backup-simplify]: Simplify (+ 0 0) into 0 6.551 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 6.553 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.554 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 6.556 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.556 * [taylor]: Taking taylor expansion of 0 in k 6.556 * [backup-simplify]: Simplify 0 into 0 6.556 * [backup-simplify]: Simplify 0 into 0 6.556 * [backup-simplify]: Simplify 0 into 0 6.557 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.558 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.561 * [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 6.562 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.562 * [backup-simplify]: Simplify (+ 0 0) into 0 6.563 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 6.564 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.566 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 6.570 * [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 6.570 * [taylor]: Taking taylor expansion of 0 in k 6.570 * [backup-simplify]: Simplify 0 into 0 6.570 * [backup-simplify]: Simplify 0 into 0 6.570 * [backup-simplify]: Simplify 0 into 0 6.570 * [backup-simplify]: Simplify 0 into 0 6.571 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.572 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.578 * [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 6.579 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.579 * [backup-simplify]: Simplify (+ 0 0) into 0 6.580 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 6.582 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.584 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 6.587 * [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 6.587 * [taylor]: Taking taylor expansion of 0 in k 6.587 * [backup-simplify]: Simplify 0 into 0 6.587 * [backup-simplify]: Simplify 0 into 0 6.588 * [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)))))) 6.588 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 6.588 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 6.588 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 6.588 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 6.588 * [taylor]: Taking taylor expansion of 1.0 in k 6.588 * [backup-simplify]: Simplify 1.0 into 1.0 6.589 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 6.589 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.589 * [taylor]: Taking taylor expansion of k in k 6.589 * [backup-simplify]: Simplify 0 into 0 6.589 * [backup-simplify]: Simplify 1 into 1 6.589 * [backup-simplify]: Simplify (/ 1 1) into 1 6.589 * [backup-simplify]: Simplify (sqrt 0) into 0 6.591 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.591 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 6.591 * [taylor]: Taking taylor expansion of 1.0 in k 6.591 * [backup-simplify]: Simplify 1.0 into 1.0 6.591 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 6.591 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.591 * [taylor]: Taking taylor expansion of k in k 6.591 * [backup-simplify]: Simplify 0 into 0 6.591 * [backup-simplify]: Simplify 1 into 1 6.591 * [backup-simplify]: Simplify (/ 1 1) into 1 6.592 * [backup-simplify]: Simplify (sqrt 0) into 0 6.593 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.594 * [backup-simplify]: Simplify (* 1.0 0) into 0 6.594 * [backup-simplify]: Simplify 0 into 0 6.595 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 6.595 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.596 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 6.599 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 6.601 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 6.601 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.602 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.606 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 6.608 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 6.609 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.610 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 6.610 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 6.610 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 6.610 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 6.610 * [taylor]: Taking taylor expansion of 1.0 in k 6.610 * [backup-simplify]: Simplify 1.0 into 1.0 6.610 * [taylor]: Taking taylor expansion of (sqrt 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 (sqrt 0) into 0 6.612 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.612 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 6.612 * [taylor]: Taking taylor expansion of 1.0 in k 6.612 * [backup-simplify]: Simplify 1.0 into 1.0 6.612 * [taylor]: Taking taylor expansion of (sqrt k) in k 6.612 * [taylor]: Taking taylor expansion of k in k 6.612 * [backup-simplify]: Simplify 0 into 0 6.612 * [backup-simplify]: Simplify 1 into 1 6.613 * [backup-simplify]: Simplify (sqrt 0) into 0 6.614 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.614 * [backup-simplify]: Simplify (* 1.0 0) into 0 6.614 * [backup-simplify]: Simplify 0 into 0 6.616 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 6.616 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.620 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 6.622 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 6.622 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.626 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 6.628 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 6.629 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.631 * [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)))))))) 6.631 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 6.631 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 6.631 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 6.631 * [taylor]: Taking taylor expansion of 1.0 in k 6.631 * [backup-simplify]: Simplify 1.0 into 1.0 6.631 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 6.631 * [taylor]: Taking taylor expansion of (/ -1 k) in k 6.631 * [taylor]: Taking taylor expansion of -1 in k 6.631 * [backup-simplify]: Simplify -1 into -1 6.631 * [taylor]: Taking taylor expansion of k in k 6.631 * [backup-simplify]: Simplify 0 into 0 6.631 * [backup-simplify]: Simplify 1 into 1 6.631 * [backup-simplify]: Simplify (/ -1 1) into -1 6.632 * [backup-simplify]: Simplify (sqrt 0) into 0 6.633 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 6.634 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 6.634 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 6.634 * [taylor]: Taking taylor expansion of 1.0 in k 6.634 * [backup-simplify]: Simplify 1.0 into 1.0 6.634 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 6.634 * [taylor]: Taking taylor expansion of (/ -1 k) in k 6.634 * [taylor]: Taking taylor expansion of -1 in k 6.634 * [backup-simplify]: Simplify -1 into -1 6.634 * [taylor]: Taking taylor expansion of k in k 6.634 * [backup-simplify]: Simplify 0 into 0 6.634 * [backup-simplify]: Simplify 1 into 1 6.635 * [backup-simplify]: Simplify (/ -1 1) into -1 6.635 * [backup-simplify]: Simplify (sqrt 0) into 0 6.636 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 6.637 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 6.637 * [backup-simplify]: Simplify +nan.0 into +nan.0 6.638 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 6.641 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 6.643 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 6.644 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.645 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.648 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 6.653 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 6.653 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.654 * [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))))) 6.654 * * * * [progress]: [ 4 / 4 ] generating series at (2 2) 6.656 * [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) 6.656 * [approximate]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) in (n k) around 0 6.656 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) in k 6.656 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 6.656 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 6.656 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 6.656 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 6.656 * [taylor]: Taking taylor expansion of 0.25 in k 6.656 * [backup-simplify]: Simplify 0.25 into 0.25 6.656 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.656 * [taylor]: Taking taylor expansion of 1.0 in k 6.656 * [backup-simplify]: Simplify 1.0 into 1.0 6.656 * [taylor]: Taking taylor expansion of k in k 6.656 * [backup-simplify]: Simplify 0 into 0 6.656 * [backup-simplify]: Simplify 1 into 1 6.656 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 6.656 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 6.656 * [taylor]: Taking taylor expansion of 2.0 in k 6.656 * [backup-simplify]: Simplify 2.0 into 2.0 6.656 * [taylor]: Taking taylor expansion of (* n PI) in k 6.656 * [taylor]: Taking taylor expansion of n in k 6.656 * [backup-simplify]: Simplify n into n 6.656 * [taylor]: Taking taylor expansion of PI in k 6.657 * [backup-simplify]: Simplify PI into PI 6.657 * [backup-simplify]: Simplify (* n PI) into (* n PI) 6.657 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 6.657 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 6.657 * [backup-simplify]: Simplify (- 0) into 0 6.658 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.658 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 6.658 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 6.658 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 6.658 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) in n 6.658 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 6.658 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.659 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.659 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 6.659 * [taylor]: Taking taylor expansion of 0.25 in n 6.659 * [backup-simplify]: Simplify 0.25 into 0.25 6.659 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.659 * [taylor]: Taking taylor expansion of 1.0 in n 6.659 * [backup-simplify]: Simplify 1.0 into 1.0 6.659 * [taylor]: Taking taylor expansion of k in n 6.659 * [backup-simplify]: Simplify k into k 6.659 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.659 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.659 * [taylor]: Taking taylor expansion of 2.0 in n 6.659 * [backup-simplify]: Simplify 2.0 into 2.0 6.659 * [taylor]: Taking taylor expansion of (* n PI) in n 6.659 * [taylor]: Taking taylor expansion of n in n 6.659 * [backup-simplify]: Simplify 0 into 0 6.659 * [backup-simplify]: Simplify 1 into 1 6.659 * [taylor]: Taking taylor expansion of PI in n 6.659 * [backup-simplify]: Simplify PI into PI 6.660 * [backup-simplify]: Simplify (* 0 PI) into 0 6.660 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.662 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.663 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.664 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.664 * [backup-simplify]: Simplify (- k) into (- k) 6.664 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.664 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 6.666 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.667 * [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)))) 6.668 * [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))))) 6.668 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) in n 6.668 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 6.668 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.669 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.669 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 6.669 * [taylor]: Taking taylor expansion of 0.25 in n 6.669 * [backup-simplify]: Simplify 0.25 into 0.25 6.669 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.669 * [taylor]: Taking taylor expansion of 1.0 in n 6.669 * [backup-simplify]: Simplify 1.0 into 1.0 6.669 * [taylor]: Taking taylor expansion of k in n 6.669 * [backup-simplify]: Simplify k into k 6.669 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.669 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.669 * [taylor]: Taking taylor expansion of 2.0 in n 6.669 * [backup-simplify]: Simplify 2.0 into 2.0 6.669 * [taylor]: Taking taylor expansion of (* n PI) in n 6.669 * [taylor]: Taking taylor expansion of n in n 6.669 * [backup-simplify]: Simplify 0 into 0 6.669 * [backup-simplify]: Simplify 1 into 1 6.669 * [taylor]: Taking taylor expansion of PI in n 6.669 * [backup-simplify]: Simplify PI into PI 6.669 * [backup-simplify]: Simplify (* 0 PI) into 0 6.670 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.671 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.673 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.674 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.674 * [backup-simplify]: Simplify (- k) into (- k) 6.674 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.674 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 6.676 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.677 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 6.678 * [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))))) 6.681 * [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) 6.681 * [taylor]: Taking taylor expansion of (pow (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2) in k 6.681 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 6.681 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 6.681 * [taylor]: Taking taylor expansion of 0.25 in k 6.681 * [backup-simplify]: Simplify 0.25 into 0.25 6.681 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 6.681 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.681 * [taylor]: Taking taylor expansion of 1.0 in k 6.681 * [backup-simplify]: Simplify 1.0 into 1.0 6.681 * [taylor]: Taking taylor expansion of k in k 6.681 * [backup-simplify]: Simplify 0 into 0 6.682 * [backup-simplify]: Simplify 1 into 1 6.682 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 6.682 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.682 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.682 * [taylor]: Taking taylor expansion of 2.0 in k 6.682 * [backup-simplify]: Simplify 2.0 into 2.0 6.682 * [taylor]: Taking taylor expansion of PI in k 6.682 * [backup-simplify]: Simplify PI into PI 6.682 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.683 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.683 * [taylor]: Taking taylor expansion of (log n) in k 6.683 * [taylor]: Taking taylor expansion of n in k 6.683 * [backup-simplify]: Simplify n into n 6.683 * [backup-simplify]: Simplify (log n) into (log n) 6.684 * [backup-simplify]: Simplify (- 0) into 0 6.684 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.685 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 6.686 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 6.688 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 6.696 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 6.699 * [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) 6.700 * [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) 6.701 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 6.702 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 6.704 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.705 * [backup-simplify]: Simplify (- 0) into 0 6.705 * [backup-simplify]: Simplify (+ 0 0) into 0 6.705 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 6.707 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.708 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 6.710 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.712 * [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 6.712 * [taylor]: Taking taylor expansion of 0 in k 6.712 * [backup-simplify]: Simplify 0 into 0 6.712 * [backup-simplify]: Simplify 0 into 0 6.713 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.715 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.716 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 6.716 * [backup-simplify]: Simplify (+ 0 0) into 0 6.716 * [backup-simplify]: Simplify (- 1) into -1 6.717 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.718 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 6.720 * [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)))) 6.724 * [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)))))) 6.732 * [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))))) 6.736 * [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))))) 6.737 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 6.739 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 6.743 * [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 6.743 * [backup-simplify]: Simplify (- 0) into 0 6.743 * [backup-simplify]: Simplify (+ 0 0) into 0 6.744 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 6.746 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.747 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.750 * [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 6.753 * [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 6.753 * [taylor]: Taking taylor expansion of 0 in k 6.753 * [backup-simplify]: Simplify 0 into 0 6.753 * [backup-simplify]: Simplify 0 into 0 6.753 * [backup-simplify]: Simplify 0 into 0 6.754 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.758 * [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 6.760 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 6.761 * [backup-simplify]: Simplify (+ 0 0) into 0 6.761 * [backup-simplify]: Simplify (- 0) into 0 6.761 * [backup-simplify]: Simplify (+ 0 0) into 0 6.763 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.766 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 6.770 * [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))))) 6.790 * [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))))) 6.795 * [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))))) 6.803 * [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)))))) 6.805 * [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) 6.805 * [approximate]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) in (n k) around 0 6.805 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) in k 6.805 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 6.805 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 6.805 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 6.805 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 6.805 * [taylor]: Taking taylor expansion of 0.25 in k 6.805 * [backup-simplify]: Simplify 0.25 into 0.25 6.805 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.805 * [taylor]: Taking taylor expansion of 1.0 in k 6.805 * [backup-simplify]: Simplify 1.0 into 1.0 6.805 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.805 * [taylor]: Taking taylor expansion of k in k 6.805 * [backup-simplify]: Simplify 0 into 0 6.805 * [backup-simplify]: Simplify 1 into 1 6.805 * [backup-simplify]: Simplify (/ 1 1) into 1 6.805 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 6.805 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 6.805 * [taylor]: Taking taylor expansion of 2.0 in k 6.805 * [backup-simplify]: Simplify 2.0 into 2.0 6.805 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.805 * [taylor]: Taking taylor expansion of PI in k 6.805 * [backup-simplify]: Simplify PI into PI 6.805 * [taylor]: Taking taylor expansion of n in k 6.805 * [backup-simplify]: Simplify n into n 6.805 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.805 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 6.805 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 6.806 * [backup-simplify]: Simplify (- 1) into -1 6.806 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.806 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 6.806 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 6.806 * [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))))) 6.806 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) in n 6.807 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 6.807 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.807 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.807 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 6.807 * [taylor]: Taking taylor expansion of 0.25 in n 6.807 * [backup-simplify]: Simplify 0.25 into 0.25 6.807 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.807 * [taylor]: Taking taylor expansion of 1.0 in n 6.807 * [backup-simplify]: Simplify 1.0 into 1.0 6.807 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.807 * [taylor]: Taking taylor expansion of k in n 6.807 * [backup-simplify]: Simplify k into k 6.807 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.807 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.807 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.807 * [taylor]: Taking taylor expansion of 2.0 in n 6.807 * [backup-simplify]: Simplify 2.0 into 2.0 6.807 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.807 * [taylor]: Taking taylor expansion of PI in n 6.807 * [backup-simplify]: Simplify PI into PI 6.807 * [taylor]: Taking taylor expansion of n in n 6.807 * [backup-simplify]: Simplify 0 into 0 6.807 * [backup-simplify]: Simplify 1 into 1 6.807 * [backup-simplify]: Simplify (/ PI 1) into PI 6.808 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.808 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.808 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.808 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.808 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 6.809 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.810 * [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)))) 6.811 * [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))))) 6.811 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) in n 6.811 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 6.811 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.811 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.811 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 6.811 * [taylor]: Taking taylor expansion of 0.25 in n 6.811 * [backup-simplify]: Simplify 0.25 into 0.25 6.811 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.811 * [taylor]: Taking taylor expansion of 1.0 in n 6.811 * [backup-simplify]: Simplify 1.0 into 1.0 6.811 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.811 * [taylor]: Taking taylor expansion of k in n 6.811 * [backup-simplify]: Simplify k into k 6.811 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.811 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.811 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.811 * [taylor]: Taking taylor expansion of 2.0 in n 6.811 * [backup-simplify]: Simplify 2.0 into 2.0 6.811 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.811 * [taylor]: Taking taylor expansion of PI in n 6.811 * [backup-simplify]: Simplify PI into PI 6.811 * [taylor]: Taking taylor expansion of n in n 6.811 * [backup-simplify]: Simplify 0 into 0 6.811 * [backup-simplify]: Simplify 1 into 1 6.812 * [backup-simplify]: Simplify (/ PI 1) into PI 6.812 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.813 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.813 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.813 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.813 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 6.814 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.814 * [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)))) 6.815 * [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))))) 6.817 * [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) 6.817 * [taylor]: Taking taylor expansion of (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2) in k 6.817 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 6.817 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 6.817 * [taylor]: Taking taylor expansion of 0.25 in k 6.817 * [backup-simplify]: Simplify 0.25 into 0.25 6.817 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 6.817 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 6.817 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.817 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.817 * [taylor]: Taking taylor expansion of 2.0 in k 6.817 * [backup-simplify]: Simplify 2.0 into 2.0 6.817 * [taylor]: Taking taylor expansion of PI in k 6.817 * [backup-simplify]: Simplify PI into PI 6.817 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.818 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.818 * [taylor]: Taking taylor expansion of (log n) in k 6.818 * [taylor]: Taking taylor expansion of n in k 6.818 * [backup-simplify]: Simplify n into n 6.818 * [backup-simplify]: Simplify (log n) into (log n) 6.818 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.818 * [taylor]: Taking taylor expansion of 1.0 in k 6.818 * [backup-simplify]: Simplify 1.0 into 1.0 6.818 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.818 * [taylor]: Taking taylor expansion of k in k 6.818 * [backup-simplify]: Simplify 0 into 0 6.818 * [backup-simplify]: Simplify 1 into 1 6.818 * [backup-simplify]: Simplify (/ 1 1) into 1 6.818 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.819 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 6.819 * [backup-simplify]: Simplify (- 1) into -1 6.820 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.820 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 6.821 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 6.822 * [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))))) 6.829 * [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) 6.830 * [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) 6.831 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.831 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.832 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.833 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.833 * [backup-simplify]: Simplify (- 0) into 0 6.833 * [backup-simplify]: Simplify (+ 0 0) into 0 6.833 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 6.834 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.835 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 6.836 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.838 * [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 6.838 * [taylor]: Taking taylor expansion of 0 in k 6.838 * [backup-simplify]: Simplify 0 into 0 6.838 * [backup-simplify]: Simplify 0 into 0 6.840 * [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 6.840 * [backup-simplify]: Simplify 0 into 0 6.841 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.842 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.846 * [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 6.846 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.846 * [backup-simplify]: Simplify (- 0) into 0 6.847 * [backup-simplify]: Simplify (+ 0 0) into 0 6.848 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 6.849 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.851 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 6.854 * [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 6.857 * [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 6.857 * [taylor]: Taking taylor expansion of 0 in k 6.857 * [backup-simplify]: Simplify 0 into 0 6.857 * [backup-simplify]: Simplify 0 into 0 6.857 * [backup-simplify]: Simplify 0 into 0 6.860 * [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 6.860 * [backup-simplify]: Simplify 0 into 0 6.861 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.862 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.869 * [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 6.869 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.870 * [backup-simplify]: Simplify (- 0) into 0 6.870 * [backup-simplify]: Simplify (+ 0 0) into 0 6.871 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 6.873 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.875 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 6.877 * [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 6.881 * [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 6.881 * [taylor]: Taking taylor expansion of 0 in k 6.881 * [backup-simplify]: Simplify 0 into 0 6.881 * [backup-simplify]: Simplify 0 into 0 6.882 * [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) 6.884 * [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) 6.884 * [approximate]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) in (n k) around 0 6.884 * [taylor]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) in k 6.884 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 6.884 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 6.884 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 6.884 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 6.884 * [taylor]: Taking taylor expansion of 0.25 in k 6.884 * [backup-simplify]: Simplify 0.25 into 0.25 6.884 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.884 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.884 * [taylor]: Taking taylor expansion of k in k 6.884 * [backup-simplify]: Simplify 0 into 0 6.884 * [backup-simplify]: Simplify 1 into 1 6.885 * [backup-simplify]: Simplify (/ 1 1) into 1 6.885 * [taylor]: Taking taylor expansion of 1.0 in k 6.885 * [backup-simplify]: Simplify 1.0 into 1.0 6.885 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 6.885 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 6.885 * [taylor]: Taking taylor expansion of -2.0 in k 6.885 * [backup-simplify]: Simplify -2.0 into -2.0 6.885 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.885 * [taylor]: Taking taylor expansion of PI in k 6.885 * [backup-simplify]: Simplify PI into PI 6.885 * [taylor]: Taking taylor expansion of n in k 6.885 * [backup-simplify]: Simplify n into n 6.885 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.885 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 6.885 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 6.886 * [backup-simplify]: Simplify (+ 1 0) into 1 6.886 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 6.886 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 6.887 * [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)))))) 6.887 * [taylor]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) in n 6.887 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 6.887 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.887 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.887 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 6.887 * [taylor]: Taking taylor expansion of 0.25 in n 6.887 * [backup-simplify]: Simplify 0.25 into 0.25 6.887 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.887 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.887 * [taylor]: Taking taylor expansion of k in n 6.887 * [backup-simplify]: Simplify k into k 6.887 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.887 * [taylor]: Taking taylor expansion of 1.0 in n 6.887 * [backup-simplify]: Simplify 1.0 into 1.0 6.887 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.887 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.887 * [taylor]: Taking taylor expansion of -2.0 in n 6.887 * [backup-simplify]: Simplify -2.0 into -2.0 6.887 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.887 * [taylor]: Taking taylor expansion of PI in n 6.887 * [backup-simplify]: Simplify PI into PI 6.887 * [taylor]: Taking taylor expansion of n in n 6.887 * [backup-simplify]: Simplify 0 into 0 6.887 * [backup-simplify]: Simplify 1 into 1 6.888 * [backup-simplify]: Simplify (/ PI 1) into PI 6.888 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.890 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.890 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.890 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 6.891 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.892 * [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)))) 6.894 * [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))))) 6.894 * [taylor]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) in n 6.894 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 6.894 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.894 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.894 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 6.894 * [taylor]: Taking taylor expansion of 0.25 in n 6.894 * [backup-simplify]: Simplify 0.25 into 0.25 6.894 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.894 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.894 * [taylor]: Taking taylor expansion of k in n 6.894 * [backup-simplify]: Simplify k into k 6.894 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.894 * [taylor]: Taking taylor expansion of 1.0 in n 6.894 * [backup-simplify]: Simplify 1.0 into 1.0 6.894 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.894 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.894 * [taylor]: Taking taylor expansion of -2.0 in n 6.894 * [backup-simplify]: Simplify -2.0 into -2.0 6.894 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.894 * [taylor]: Taking taylor expansion of PI in n 6.894 * [backup-simplify]: Simplify PI into PI 6.894 * [taylor]: Taking taylor expansion of n in n 6.894 * [backup-simplify]: Simplify 0 into 0 6.895 * [backup-simplify]: Simplify 1 into 1 6.895 * [backup-simplify]: Simplify (/ PI 1) into PI 6.895 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.897 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.897 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.897 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 6.898 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.899 * [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)))) 6.901 * [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))))) 6.903 * [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) 6.903 * [taylor]: Taking taylor expansion of (pow (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2) in k 6.903 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 6.903 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 6.904 * [taylor]: Taking taylor expansion of 0.25 in k 6.904 * [backup-simplify]: Simplify 0.25 into 0.25 6.904 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 6.904 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.904 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.904 * [taylor]: Taking taylor expansion of k in k 6.904 * [backup-simplify]: Simplify 0 into 0 6.904 * [backup-simplify]: Simplify 1 into 1 6.904 * [backup-simplify]: Simplify (/ 1 1) into 1 6.904 * [taylor]: Taking taylor expansion of 1.0 in k 6.904 * [backup-simplify]: Simplify 1.0 into 1.0 6.904 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 6.905 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 6.905 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 6.905 * [taylor]: Taking taylor expansion of -2.0 in k 6.905 * [backup-simplify]: Simplify -2.0 into -2.0 6.905 * [taylor]: Taking taylor expansion of PI in k 6.905 * [backup-simplify]: Simplify PI into PI 6.905 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.906 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.906 * [taylor]: Taking taylor expansion of (log n) in k 6.906 * [taylor]: Taking taylor expansion of n in k 6.906 * [backup-simplify]: Simplify n into n 6.906 * [backup-simplify]: Simplify (log n) into (log n) 6.907 * [backup-simplify]: Simplify (+ 1 0) into 1 6.907 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.908 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 6.909 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 6.910 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 6.912 * [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))))) 6.914 * [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) 6.915 * [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) 6.916 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.917 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 6.919 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 6.920 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.920 * [backup-simplify]: Simplify (+ 0 0) into 0 6.920 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 6.922 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.923 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 6.925 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.928 * [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 6.928 * [taylor]: Taking taylor expansion of 0 in k 6.928 * [backup-simplify]: Simplify 0 into 0 6.928 * [backup-simplify]: Simplify 0 into 0 6.930 * [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 6.930 * [backup-simplify]: Simplify 0 into 0 6.931 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.932 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.936 * [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 6.936 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.937 * [backup-simplify]: Simplify (+ 0 0) into 0 6.938 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 6.939 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.941 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 6.943 * [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 6.946 * [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 6.947 * [taylor]: Taking taylor expansion of 0 in k 6.947 * [backup-simplify]: Simplify 0 into 0 6.947 * [backup-simplify]: Simplify 0 into 0 6.947 * [backup-simplify]: Simplify 0 into 0 6.950 * [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 6.950 * [backup-simplify]: Simplify 0 into 0 6.951 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.952 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.959 * [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 6.959 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.960 * [backup-simplify]: Simplify (+ 0 0) into 0 6.961 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 6.963 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.965 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 6.968 * [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 6.978 * [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 6.979 * [taylor]: Taking taylor expansion of 0 in k 6.979 * [backup-simplify]: Simplify 0 into 0 6.979 * [backup-simplify]: Simplify 0 into 0 6.981 * [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) 6.981 * * * [progress]: simplifying candidates 6.990 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 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+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) 7.004 * * [simplify]: Extracting # 0 : cost 0 7.004 * * [simplify]: Extracting # 1 : cost 0 7.004 * * [simplify]: Extracting # 2 : cost 0 7.005 * * [simplify]: Extracting # 3 : cost 0 7.006 * * [simplify]: Extracting # 4 : cost 0 7.006 * * [simplify]: Extracting # 5 : cost 0 7.007 * * [simplify]: Extracting # 6 : cost 0 7.007 * * [simplify]: Extracting # 7 : cost 0 7.008 * * [simplify]: Extracting # 8 : cost 0 7.008 * * [simplify]: Extracting # 9 : cost 0 7.009 * * [simplify]: Extracting # 10 : cost 0 7.010 * * [simplify]: Extracting # 11 : cost 0 7.010 * * [simplify]: Extracting # 12 : cost 0 7.011 * * [simplify]: Extracting # 13 : cost 0 7.011 * * [simplify]: iteration 0 : 379 enodes (cost 5686 ) 7.160 * * [simplify]: Extracting # 0 : cost 0 7.170 * * [simplify]: Extracting # 1 : cost 0 7.172 * * [simplify]: Extracting # 2 : cost 0 7.173 * * [simplify]: Extracting # 3 : cost 0 7.175 * * [simplify]: Extracting # 4 : cost 0 7.177 * * [simplify]: Extracting # 5 : cost 0 7.178 * * [simplify]: Extracting # 6 : cost 0 7.180 * * [simplify]: iteration 1 : 1152 enodes (cost 4768 ) 7.682 * * [simplify]: Extracting # 0 : cost 0 7.689 * * [simplify]: Extracting # 1 : cost 0 7.701 * * [simplify]: Extracting # 2 : cost 0 7.710 * * [simplify]: Extracting # 3 : cost 0 7.723 * * [simplify]: Extracting # 4 : cost 0 7.729 * * [simplify]: Extracting # 5 : cost 0 7.736 * * [simplify]: iteration done: 5000 enodes (cost 4280 ) 7.738 * [simplify]: Simplified to: (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (/ (/ (- 1.0 k) 2.0) 2) (/ (/ (- 1.0 k) 2.0) 2) (/ (/ (- 1.0 k) 2.0) 2) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* 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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)) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (/ (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 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(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))) (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))) (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))) (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))) (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))) (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))) (log (pow (* (* 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))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) 3)) (* (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 (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 4)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (pow 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 (* (* 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 (* (* 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 2.0) 2)) (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 k) 2.0) 2))) (+ (fma (* (pow k 2) (* (pow (* (* 2.0 PI) n) 0.25) (pow (log (* 2.0 PI)) 2))) 0.03125 (pow (* (* 2.0 PI) n) 0.25)) (- (fma (* (* (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.25)) (* (log n) (pow k 2))) 0.0625 (* (* 0.03125 (* (pow (* (* 2.0 PI) n) 0.25) (pow k 2))) (pow (log n) 2))) (* 0.25 (* k (+ (* (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.25)) (* (log n) (pow (* (* 2.0 PI) n) 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))))) (+ (fma (* (pow k 2) (* (pow (* (* 2.0 PI) n) 0.25) (pow (log (* 2.0 PI)) 2))) 0.03125 (pow (* (* 2.0 PI) n) 0.25)) (- (fma (* (* (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.25)) (* (log n) (pow k 2))) 0.0625 (* (* 0.03125 (* (pow (* (* 2.0 PI) n) 0.25) (pow k 2))) (pow (log n) 2))) (* 0.25 (* k (+ (* (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.25)) (* (log n) (pow (* (* 2.0 PI) n) 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) (fma +nan.0 (pow k 2) (- +nan.0)))) (+ (- (/ +nan.0 (pow k 2))) (- (/ +nan.0 k) (/ +nan.0 (pow k 3)))) (+ (- (/ +nan.0 k) +nan.0) (- (/ +nan.0 (pow k 2)))) (- (+ (pow (pow (* (* 2.0 PI) n) 0.25) 2) (fma 0.125 (* (pow k 2) (+ (* (pow (log (* 2.0 PI)) 2) (pow (pow (* (* 2.0 PI) n) 0.25) 2)) (* (pow (log n) 2) (pow (pow (* (* 2.0 PI) n) 0.25) 2)))) (* (* 0.25 (* (pow k 2) (log (* 2.0 PI)))) (* (log n) (pow (pow (* (* 2.0 PI) n) 0.25) 2))))) (* 0.5 (* k (+ (* (pow (pow (* (* 2.0 PI) n) 0.25) 2) (log (* 2.0 PI))) (* (log n) (pow (pow (* (* 2.0 PI) n) 0.25) 2)))))) (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) 7.740 * * * [progress]: adding candidates to table 9.090 * * [progress]: iteration 3 / 4 9.090 * * * [progress]: picking best candidate 9.124 * * * * [pick]: Picked # 9.125 * * * [progress]: localizing error 9.165 * * * [progress]: generating rewritten candidates 9.165 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 9.232 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 9.265 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 9.272 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 9.320 * * * [progress]: generating series expansions 9.320 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 9.321 * [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))) 9.321 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 9.321 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 9.321 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 9.321 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 9.321 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 9.321 * [taylor]: Taking taylor expansion of 0.25 in k 9.321 * [backup-simplify]: Simplify 0.25 into 0.25 9.321 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 9.321 * [taylor]: Taking taylor expansion of 1.0 in k 9.321 * [backup-simplify]: Simplify 1.0 into 1.0 9.321 * [taylor]: Taking taylor expansion of k in k 9.321 * [backup-simplify]: Simplify 0 into 0 9.322 * [backup-simplify]: Simplify 1 into 1 9.322 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 9.322 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 9.322 * [taylor]: Taking taylor expansion of 2.0 in k 9.322 * [backup-simplify]: Simplify 2.0 into 2.0 9.322 * [taylor]: Taking taylor expansion of (* n PI) in k 9.322 * [taylor]: Taking taylor expansion of n in k 9.322 * [backup-simplify]: Simplify n into n 9.322 * [taylor]: Taking taylor expansion of PI in k 9.322 * [backup-simplify]: Simplify PI into PI 9.322 * [backup-simplify]: Simplify (* n PI) into (* n PI) 9.322 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 9.322 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 9.323 * [backup-simplify]: Simplify (- 0) into 0 9.323 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 9.324 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 9.324 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 9.324 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 9.324 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 9.324 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 9.324 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 9.324 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 9.324 * [taylor]: Taking taylor expansion of 0.25 in n 9.324 * [backup-simplify]: Simplify 0.25 into 0.25 9.324 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 9.324 * [taylor]: Taking taylor expansion of 1.0 in n 9.324 * [backup-simplify]: Simplify 1.0 into 1.0 9.324 * [taylor]: Taking taylor expansion of k in n 9.324 * [backup-simplify]: Simplify k into k 9.324 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 9.325 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.325 * [taylor]: Taking taylor expansion of 2.0 in n 9.325 * [backup-simplify]: Simplify 2.0 into 2.0 9.325 * [taylor]: Taking taylor expansion of (* n PI) in n 9.325 * [taylor]: Taking taylor expansion of n in n 9.325 * [backup-simplify]: Simplify 0 into 0 9.325 * [backup-simplify]: Simplify 1 into 1 9.325 * [taylor]: Taking taylor expansion of PI in n 9.325 * [backup-simplify]: Simplify PI into PI 9.325 * [backup-simplify]: Simplify (* 0 PI) into 0 9.326 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.327 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.329 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.330 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.330 * [backup-simplify]: Simplify (- k) into (- k) 9.330 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 9.330 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 9.331 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.332 * [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)))) 9.333 * [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))))) 9.333 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 9.333 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 9.333 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 9.333 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 9.333 * [taylor]: Taking taylor expansion of 0.25 in n 9.333 * [backup-simplify]: Simplify 0.25 into 0.25 9.333 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 9.333 * [taylor]: Taking taylor expansion of 1.0 in n 9.333 * [backup-simplify]: Simplify 1.0 into 1.0 9.333 * [taylor]: Taking taylor expansion of k in n 9.333 * [backup-simplify]: Simplify k into k 9.333 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 9.333 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.333 * [taylor]: Taking taylor expansion of 2.0 in n 9.333 * [backup-simplify]: Simplify 2.0 into 2.0 9.333 * [taylor]: Taking taylor expansion of (* n PI) in n 9.333 * [taylor]: Taking taylor expansion of n in n 9.333 * [backup-simplify]: Simplify 0 into 0 9.333 * [backup-simplify]: Simplify 1 into 1 9.333 * [taylor]: Taking taylor expansion of PI in n 9.333 * [backup-simplify]: Simplify PI into PI 9.334 * [backup-simplify]: Simplify (* 0 PI) into 0 9.334 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.335 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.336 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.336 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.336 * [backup-simplify]: Simplify (- k) into (- k) 9.336 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 9.337 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 9.337 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.338 * [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)))) 9.339 * [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))))) 9.339 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 9.339 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 9.339 * [taylor]: Taking taylor expansion of 0.25 in k 9.339 * [backup-simplify]: Simplify 0.25 into 0.25 9.339 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 9.339 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 9.339 * [taylor]: Taking taylor expansion of 1.0 in k 9.339 * [backup-simplify]: Simplify 1.0 into 1.0 9.339 * [taylor]: Taking taylor expansion of k in k 9.339 * [backup-simplify]: Simplify 0 into 0 9.339 * [backup-simplify]: Simplify 1 into 1 9.339 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 9.339 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 9.339 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 9.339 * [taylor]: Taking taylor expansion of 2.0 in k 9.339 * [backup-simplify]: Simplify 2.0 into 2.0 9.339 * [taylor]: Taking taylor expansion of PI in k 9.339 * [backup-simplify]: Simplify PI into PI 9.340 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.340 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.340 * [taylor]: Taking taylor expansion of (log n) in k 9.340 * [taylor]: Taking taylor expansion of n in k 9.340 * [backup-simplify]: Simplify n into n 9.340 * [backup-simplify]: Simplify (log n) into (log n) 9.341 * [backup-simplify]: Simplify (- 0) into 0 9.341 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 9.342 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 9.342 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 9.343 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 9.344 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 9.345 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 9.345 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 9.346 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 9.347 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.347 * [backup-simplify]: Simplify (- 0) into 0 9.347 * [backup-simplify]: Simplify (+ 0 0) into 0 9.348 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 9.349 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.349 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 9.351 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.351 * [taylor]: Taking taylor expansion of 0 in k 9.351 * [backup-simplify]: Simplify 0 into 0 9.351 * [backup-simplify]: Simplify 0 into 0 9.351 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.352 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.353 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 9.353 * [backup-simplify]: Simplify (+ 0 0) into 0 9.353 * [backup-simplify]: Simplify (- 1) into -1 9.354 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.355 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 9.356 * [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)))) 9.358 * [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)))))) 9.360 * [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)))))) 9.361 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 9.362 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 9.365 * [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 9.366 * [backup-simplify]: Simplify (- 0) into 0 9.366 * [backup-simplify]: Simplify (+ 0 0) into 0 9.367 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 9.368 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.370 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 9.373 * [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 9.373 * [taylor]: Taking taylor expansion of 0 in k 9.373 * [backup-simplify]: Simplify 0 into 0 9.373 * [backup-simplify]: Simplify 0 into 0 9.373 * [backup-simplify]: Simplify 0 into 0 9.374 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.378 * [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 9.380 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 9.380 * [backup-simplify]: Simplify (+ 0 0) into 0 9.381 * [backup-simplify]: Simplify (- 0) into 0 9.381 * [backup-simplify]: Simplify (+ 0 0) into 0 9.383 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 9.386 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 9.390 * [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))))) 9.396 * [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))))) 9.403 * [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)))))) 9.404 * [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)))) 9.404 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 9.404 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 9.404 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 9.404 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 9.404 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 9.404 * [taylor]: Taking taylor expansion of 0.25 in k 9.404 * [backup-simplify]: Simplify 0.25 into 0.25 9.404 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.404 * [taylor]: Taking taylor expansion of 1.0 in k 9.404 * [backup-simplify]: Simplify 1.0 into 1.0 9.404 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.404 * [taylor]: Taking taylor expansion of k in k 9.404 * [backup-simplify]: Simplify 0 into 0 9.404 * [backup-simplify]: Simplify 1 into 1 9.405 * [backup-simplify]: Simplify (/ 1 1) into 1 9.405 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 9.405 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 9.405 * [taylor]: Taking taylor expansion of 2.0 in k 9.405 * [backup-simplify]: Simplify 2.0 into 2.0 9.405 * [taylor]: Taking taylor expansion of (/ PI n) in k 9.405 * [taylor]: Taking taylor expansion of PI in k 9.405 * [backup-simplify]: Simplify PI into PI 9.405 * [taylor]: Taking taylor expansion of n in k 9.405 * [backup-simplify]: Simplify n into n 9.405 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 9.405 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 9.405 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 9.405 * [backup-simplify]: Simplify (- 1) into -1 9.405 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.406 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 9.406 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 9.406 * [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))))) 9.406 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 9.406 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 9.406 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 9.406 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 9.406 * [taylor]: Taking taylor expansion of 0.25 in n 9.406 * [backup-simplify]: Simplify 0.25 into 0.25 9.406 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.406 * [taylor]: Taking taylor expansion of 1.0 in n 9.406 * [backup-simplify]: Simplify 1.0 into 1.0 9.406 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.406 * [taylor]: Taking taylor expansion of k in n 9.406 * [backup-simplify]: Simplify k into k 9.406 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.406 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 9.406 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.406 * [taylor]: Taking taylor expansion of 2.0 in n 9.406 * [backup-simplify]: Simplify 2.0 into 2.0 9.406 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.406 * [taylor]: Taking taylor expansion of PI in n 9.406 * [backup-simplify]: Simplify PI into PI 9.406 * [taylor]: Taking taylor expansion of n in n 9.406 * [backup-simplify]: Simplify 0 into 0 9.406 * [backup-simplify]: Simplify 1 into 1 9.414 * [backup-simplify]: Simplify (/ PI 1) into PI 9.414 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.415 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.415 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.415 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.415 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 9.416 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.417 * [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)))) 9.418 * [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))))) 9.418 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 9.418 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 9.418 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 9.418 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 9.418 * [taylor]: Taking taylor expansion of 0.25 in n 9.418 * [backup-simplify]: Simplify 0.25 into 0.25 9.418 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.418 * [taylor]: Taking taylor expansion of 1.0 in n 9.418 * [backup-simplify]: Simplify 1.0 into 1.0 9.418 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.418 * [taylor]: Taking taylor expansion of k in n 9.418 * [backup-simplify]: Simplify k into k 9.418 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.418 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 9.418 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.418 * [taylor]: Taking taylor expansion of 2.0 in n 9.418 * [backup-simplify]: Simplify 2.0 into 2.0 9.418 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.418 * [taylor]: Taking taylor expansion of PI in n 9.418 * [backup-simplify]: Simplify PI into PI 9.418 * [taylor]: Taking taylor expansion of n in n 9.418 * [backup-simplify]: Simplify 0 into 0 9.418 * [backup-simplify]: Simplify 1 into 1 9.419 * [backup-simplify]: Simplify (/ PI 1) into PI 9.419 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.420 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.420 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.420 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.420 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 9.421 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.422 * [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)))) 9.422 * [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))))) 9.423 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 9.423 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 9.423 * [taylor]: Taking taylor expansion of 0.25 in k 9.423 * [backup-simplify]: Simplify 0.25 into 0.25 9.423 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 9.423 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 9.423 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 9.423 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 9.423 * [taylor]: Taking taylor expansion of 2.0 in k 9.423 * [backup-simplify]: Simplify 2.0 into 2.0 9.423 * [taylor]: Taking taylor expansion of PI in k 9.423 * [backup-simplify]: Simplify PI into PI 9.423 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.424 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.424 * [taylor]: Taking taylor expansion of (log n) in k 9.424 * [taylor]: Taking taylor expansion of n in k 9.424 * [backup-simplify]: Simplify n into n 9.424 * [backup-simplify]: Simplify (log n) into (log n) 9.424 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.424 * [taylor]: Taking taylor expansion of 1.0 in k 9.424 * [backup-simplify]: Simplify 1.0 into 1.0 9.424 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.424 * [taylor]: Taking taylor expansion of k in k 9.424 * [backup-simplify]: Simplify 0 into 0 9.424 * [backup-simplify]: Simplify 1 into 1 9.424 * [backup-simplify]: Simplify (/ 1 1) into 1 9.424 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.425 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 9.425 * [backup-simplify]: Simplify (- 1) into -1 9.425 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.426 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 9.427 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 9.428 * [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))))) 9.428 * [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))))) 9.429 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.429 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.430 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.431 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.431 * [backup-simplify]: Simplify (- 0) into 0 9.431 * [backup-simplify]: Simplify (+ 0 0) into 0 9.431 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 9.432 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.433 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 9.434 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.434 * [taylor]: Taking taylor expansion of 0 in k 9.434 * [backup-simplify]: Simplify 0 into 0 9.434 * [backup-simplify]: Simplify 0 into 0 9.435 * [backup-simplify]: Simplify 0 into 0 9.435 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.436 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.438 * [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 9.438 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.438 * [backup-simplify]: Simplify (- 0) into 0 9.439 * [backup-simplify]: Simplify (+ 0 0) into 0 9.440 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 9.441 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.442 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 9.444 * [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 9.444 * [taylor]: Taking taylor expansion of 0 in k 9.444 * [backup-simplify]: Simplify 0 into 0 9.444 * [backup-simplify]: Simplify 0 into 0 9.444 * [backup-simplify]: Simplify 0 into 0 9.444 * [backup-simplify]: Simplify 0 into 0 9.445 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.445 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.449 * [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 9.449 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.449 * [backup-simplify]: Simplify (- 0) into 0 9.449 * [backup-simplify]: Simplify (+ 0 0) into 0 9.450 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 9.451 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.452 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 9.454 * [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 9.454 * [taylor]: Taking taylor expansion of 0 in k 9.454 * [backup-simplify]: Simplify 0 into 0 9.454 * [backup-simplify]: Simplify 0 into 0 9.455 * [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)))) 9.455 * [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))) 9.455 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 9.455 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 9.455 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 9.455 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 9.455 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 9.456 * [taylor]: Taking taylor expansion of 0.25 in k 9.456 * [backup-simplify]: Simplify 0.25 into 0.25 9.456 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.456 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.456 * [taylor]: Taking taylor expansion of k in k 9.456 * [backup-simplify]: Simplify 0 into 0 9.456 * [backup-simplify]: Simplify 1 into 1 9.456 * [backup-simplify]: Simplify (/ 1 1) into 1 9.456 * [taylor]: Taking taylor expansion of 1.0 in k 9.456 * [backup-simplify]: Simplify 1.0 into 1.0 9.456 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 9.456 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 9.456 * [taylor]: Taking taylor expansion of -2.0 in k 9.456 * [backup-simplify]: Simplify -2.0 into -2.0 9.456 * [taylor]: Taking taylor expansion of (/ PI n) in k 9.456 * [taylor]: Taking taylor expansion of PI in k 9.456 * [backup-simplify]: Simplify PI into PI 9.456 * [taylor]: Taking taylor expansion of n in k 9.456 * [backup-simplify]: Simplify n into n 9.456 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 9.456 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 9.456 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 9.457 * [backup-simplify]: Simplify (+ 1 0) into 1 9.457 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 9.457 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 9.457 * [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)))))) 9.457 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 9.457 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 9.457 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 9.457 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 9.457 * [taylor]: Taking taylor expansion of 0.25 in n 9.457 * [backup-simplify]: Simplify 0.25 into 0.25 9.457 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.457 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.457 * [taylor]: Taking taylor expansion of k in n 9.457 * [backup-simplify]: Simplify k into k 9.457 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.457 * [taylor]: Taking taylor expansion of 1.0 in n 9.457 * [backup-simplify]: Simplify 1.0 into 1.0 9.457 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 9.457 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.457 * [taylor]: Taking taylor expansion of -2.0 in n 9.457 * [backup-simplify]: Simplify -2.0 into -2.0 9.457 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.457 * [taylor]: Taking taylor expansion of PI in n 9.457 * [backup-simplify]: Simplify PI into PI 9.457 * [taylor]: Taking taylor expansion of n in n 9.457 * [backup-simplify]: Simplify 0 into 0 9.457 * [backup-simplify]: Simplify 1 into 1 9.458 * [backup-simplify]: Simplify (/ PI 1) into PI 9.458 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.459 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.459 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.459 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 9.460 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.461 * [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)))) 9.462 * [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))))) 9.462 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 9.462 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 9.462 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 9.462 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 9.462 * [taylor]: Taking taylor expansion of 0.25 in n 9.462 * [backup-simplify]: Simplify 0.25 into 0.25 9.462 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.462 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.462 * [taylor]: Taking taylor expansion of k in n 9.462 * [backup-simplify]: Simplify k into k 9.462 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.462 * [taylor]: Taking taylor expansion of 1.0 in n 9.462 * [backup-simplify]: Simplify 1.0 into 1.0 9.462 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 9.462 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.462 * [taylor]: Taking taylor expansion of -2.0 in n 9.462 * [backup-simplify]: Simplify -2.0 into -2.0 9.462 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.462 * [taylor]: Taking taylor expansion of PI in n 9.462 * [backup-simplify]: Simplify PI into PI 9.462 * [taylor]: Taking taylor expansion of n in n 9.462 * [backup-simplify]: Simplify 0 into 0 9.462 * [backup-simplify]: Simplify 1 into 1 9.462 * [backup-simplify]: Simplify (/ PI 1) into PI 9.463 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.463 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.463 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.464 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 9.464 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.465 * [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)))) 9.466 * [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))))) 9.466 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 9.466 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 9.466 * [taylor]: Taking taylor expansion of 0.25 in k 9.466 * [backup-simplify]: Simplify 0.25 into 0.25 9.466 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 9.466 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.466 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.466 * [taylor]: Taking taylor expansion of k in k 9.466 * [backup-simplify]: Simplify 0 into 0 9.466 * [backup-simplify]: Simplify 1 into 1 9.467 * [backup-simplify]: Simplify (/ 1 1) into 1 9.467 * [taylor]: Taking taylor expansion of 1.0 in k 9.467 * [backup-simplify]: Simplify 1.0 into 1.0 9.467 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 9.467 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 9.467 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 9.467 * [taylor]: Taking taylor expansion of -2.0 in k 9.467 * [backup-simplify]: Simplify -2.0 into -2.0 9.467 * [taylor]: Taking taylor expansion of PI in k 9.467 * [backup-simplify]: Simplify PI into PI 9.468 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.469 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.469 * [taylor]: Taking taylor expansion of (log n) in k 9.469 * [taylor]: Taking taylor expansion of n in k 9.469 * [backup-simplify]: Simplify n into n 9.469 * [backup-simplify]: Simplify (log n) into (log n) 9.469 * [backup-simplify]: Simplify (+ 1 0) into 1 9.469 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.471 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 9.472 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 9.473 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 9.474 * [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))))) 9.476 * [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))))) 9.477 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.477 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 9.479 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 9.480 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.480 * [backup-simplify]: Simplify (+ 0 0) into 0 9.481 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 9.482 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.483 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 9.485 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.486 * [taylor]: Taking taylor expansion of 0 in k 9.486 * [backup-simplify]: Simplify 0 into 0 9.486 * [backup-simplify]: Simplify 0 into 0 9.486 * [backup-simplify]: Simplify 0 into 0 9.487 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.488 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.491 * [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 9.491 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.491 * [backup-simplify]: Simplify (+ 0 0) into 0 9.492 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 9.493 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.494 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 9.495 * [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 9.495 * [taylor]: Taking taylor expansion of 0 in k 9.495 * [backup-simplify]: Simplify 0 into 0 9.495 * [backup-simplify]: Simplify 0 into 0 9.495 * [backup-simplify]: Simplify 0 into 0 9.495 * [backup-simplify]: Simplify 0 into 0 9.496 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.497 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.500 * [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 9.500 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.501 * [backup-simplify]: Simplify (+ 0 0) into 0 9.502 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 9.503 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.504 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 9.506 * [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 9.506 * [taylor]: Taking taylor expansion of 0 in k 9.506 * [backup-simplify]: Simplify 0 into 0 9.506 * [backup-simplify]: Simplify 0 into 0 9.506 * [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)))))) 9.507 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 9.507 * [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))) 9.507 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 9.507 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 9.507 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 9.507 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 9.507 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 9.507 * [taylor]: Taking taylor expansion of 0.25 in k 9.507 * [backup-simplify]: Simplify 0.25 into 0.25 9.507 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 9.507 * [taylor]: Taking taylor expansion of 1.0 in k 9.507 * [backup-simplify]: Simplify 1.0 into 1.0 9.507 * [taylor]: Taking taylor expansion of k in k 9.507 * [backup-simplify]: Simplify 0 into 0 9.507 * [backup-simplify]: Simplify 1 into 1 9.507 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 9.507 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 9.507 * [taylor]: Taking taylor expansion of 2.0 in k 9.507 * [backup-simplify]: Simplify 2.0 into 2.0 9.507 * [taylor]: Taking taylor expansion of (* n PI) in k 9.507 * [taylor]: Taking taylor expansion of n in k 9.507 * [backup-simplify]: Simplify n into n 9.507 * [taylor]: Taking taylor expansion of PI in k 9.507 * [backup-simplify]: Simplify PI into PI 9.508 * [backup-simplify]: Simplify (* n PI) into (* n PI) 9.508 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 9.508 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 9.508 * [backup-simplify]: Simplify (- 0) into 0 9.508 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 9.508 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 9.509 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 9.509 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 9.509 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 9.509 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 9.509 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 9.509 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 9.509 * [taylor]: Taking taylor expansion of 0.25 in n 9.509 * [backup-simplify]: Simplify 0.25 into 0.25 9.509 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 9.509 * [taylor]: Taking taylor expansion of 1.0 in n 9.509 * [backup-simplify]: Simplify 1.0 into 1.0 9.509 * [taylor]: Taking taylor expansion of k in n 9.509 * [backup-simplify]: Simplify k into k 9.509 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 9.509 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.509 * [taylor]: Taking taylor expansion of 2.0 in n 9.509 * [backup-simplify]: Simplify 2.0 into 2.0 9.509 * [taylor]: Taking taylor expansion of (* n PI) in n 9.509 * [taylor]: Taking taylor expansion of n in n 9.509 * [backup-simplify]: Simplify 0 into 0 9.509 * [backup-simplify]: Simplify 1 into 1 9.509 * [taylor]: Taking taylor expansion of PI in n 9.509 * [backup-simplify]: Simplify PI into PI 9.510 * [backup-simplify]: Simplify (* 0 PI) into 0 9.510 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.511 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.512 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.513 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.513 * [backup-simplify]: Simplify (- k) into (- k) 9.513 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 9.513 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 9.514 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.514 * [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)))) 9.515 * [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))))) 9.515 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 9.515 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 9.515 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 9.515 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 9.515 * [taylor]: Taking taylor expansion of 0.25 in n 9.515 * [backup-simplify]: Simplify 0.25 into 0.25 9.515 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 9.515 * [taylor]: Taking taylor expansion of 1.0 in n 9.515 * [backup-simplify]: Simplify 1.0 into 1.0 9.515 * [taylor]: Taking taylor expansion of k in n 9.515 * [backup-simplify]: Simplify k into k 9.515 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 9.515 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.515 * [taylor]: Taking taylor expansion of 2.0 in n 9.516 * [backup-simplify]: Simplify 2.0 into 2.0 9.516 * [taylor]: Taking taylor expansion of (* n PI) in n 9.516 * [taylor]: Taking taylor expansion of n in n 9.516 * [backup-simplify]: Simplify 0 into 0 9.516 * [backup-simplify]: Simplify 1 into 1 9.516 * [taylor]: Taking taylor expansion of PI in n 9.516 * [backup-simplify]: Simplify PI into PI 9.516 * [backup-simplify]: Simplify (* 0 PI) into 0 9.516 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.517 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.525 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.526 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.526 * [backup-simplify]: Simplify (- k) into (- k) 9.526 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 9.527 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 9.528 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.529 * [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)))) 9.531 * [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))))) 9.531 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 9.531 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 9.531 * [taylor]: Taking taylor expansion of 0.25 in k 9.531 * [backup-simplify]: Simplify 0.25 into 0.25 9.531 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 9.531 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 9.531 * [taylor]: Taking taylor expansion of 1.0 in k 9.531 * [backup-simplify]: Simplify 1.0 into 1.0 9.531 * [taylor]: Taking taylor expansion of k in k 9.531 * [backup-simplify]: Simplify 0 into 0 9.531 * [backup-simplify]: Simplify 1 into 1 9.531 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 9.531 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 9.531 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 9.531 * [taylor]: Taking taylor expansion of 2.0 in k 9.531 * [backup-simplify]: Simplify 2.0 into 2.0 9.531 * [taylor]: Taking taylor expansion of PI in k 9.532 * [backup-simplify]: Simplify PI into PI 9.532 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.533 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.533 * [taylor]: Taking taylor expansion of (log n) in k 9.533 * [taylor]: Taking taylor expansion of n in k 9.533 * [backup-simplify]: Simplify n into n 9.533 * [backup-simplify]: Simplify (log n) into (log n) 9.534 * [backup-simplify]: Simplify (- 0) into 0 9.534 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 9.535 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 9.536 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 9.538 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 9.539 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 9.540 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 9.541 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 9.542 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 9.544 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.545 * [backup-simplify]: Simplify (- 0) into 0 9.545 * [backup-simplify]: Simplify (+ 0 0) into 0 9.545 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 9.547 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.548 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 9.550 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.550 * [taylor]: Taking taylor expansion of 0 in k 9.550 * [backup-simplify]: Simplify 0 into 0 9.550 * [backup-simplify]: Simplify 0 into 0 9.551 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.553 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.554 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 9.554 * [backup-simplify]: Simplify (+ 0 0) into 0 9.555 * [backup-simplify]: Simplify (- 1) into -1 9.555 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.557 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 9.560 * [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)))) 9.563 * [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)))))) 9.566 * [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)))))) 9.568 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 9.569 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 9.573 * [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 9.573 * [backup-simplify]: Simplify (- 0) into 0 9.574 * [backup-simplify]: Simplify (+ 0 0) into 0 9.574 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 9.576 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.578 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 9.580 * [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 9.580 * [taylor]: Taking taylor expansion of 0 in k 9.580 * [backup-simplify]: Simplify 0 into 0 9.581 * [backup-simplify]: Simplify 0 into 0 9.581 * [backup-simplify]: Simplify 0 into 0 9.582 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.585 * [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 9.587 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 9.588 * [backup-simplify]: Simplify (+ 0 0) into 0 9.588 * [backup-simplify]: Simplify (- 0) into 0 9.589 * [backup-simplify]: Simplify (+ 0 0) into 0 9.590 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 9.592 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 9.595 * [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))))) 9.598 * [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))))) 9.604 * [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)))))) 9.605 * [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)))) 9.605 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 9.605 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 9.605 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 9.605 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 9.605 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 9.605 * [taylor]: Taking taylor expansion of 0.25 in k 9.605 * [backup-simplify]: Simplify 0.25 into 0.25 9.605 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.605 * [taylor]: Taking taylor expansion of 1.0 in k 9.605 * [backup-simplify]: Simplify 1.0 into 1.0 9.605 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.605 * [taylor]: Taking taylor expansion of k in k 9.605 * [backup-simplify]: Simplify 0 into 0 9.605 * [backup-simplify]: Simplify 1 into 1 9.606 * [backup-simplify]: Simplify (/ 1 1) into 1 9.606 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 9.606 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 9.606 * [taylor]: Taking taylor expansion of 2.0 in k 9.606 * [backup-simplify]: Simplify 2.0 into 2.0 9.606 * [taylor]: Taking taylor expansion of (/ PI n) in k 9.606 * [taylor]: Taking taylor expansion of PI in k 9.606 * [backup-simplify]: Simplify PI into PI 9.606 * [taylor]: Taking taylor expansion of n in k 9.606 * [backup-simplify]: Simplify n into n 9.606 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 9.606 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 9.606 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 9.606 * [backup-simplify]: Simplify (- 1) into -1 9.606 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.607 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 9.607 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 9.607 * [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))))) 9.607 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 9.607 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 9.607 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 9.607 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 9.607 * [taylor]: Taking taylor expansion of 0.25 in n 9.607 * [backup-simplify]: Simplify 0.25 into 0.25 9.607 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.607 * [taylor]: Taking taylor expansion of 1.0 in n 9.607 * [backup-simplify]: Simplify 1.0 into 1.0 9.607 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.607 * [taylor]: Taking taylor expansion of k in n 9.607 * [backup-simplify]: Simplify k into k 9.607 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.607 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 9.607 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.607 * [taylor]: Taking taylor expansion of 2.0 in n 9.607 * [backup-simplify]: Simplify 2.0 into 2.0 9.607 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.607 * [taylor]: Taking taylor expansion of PI in n 9.607 * [backup-simplify]: Simplify PI into PI 9.607 * [taylor]: Taking taylor expansion of n in n 9.607 * [backup-simplify]: Simplify 0 into 0 9.607 * [backup-simplify]: Simplify 1 into 1 9.608 * [backup-simplify]: Simplify (/ PI 1) into PI 9.608 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.609 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.609 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.609 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.609 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 9.610 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.611 * [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)))) 9.612 * [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))))) 9.612 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 9.612 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 9.612 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 9.612 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 9.612 * [taylor]: Taking taylor expansion of 0.25 in n 9.612 * [backup-simplify]: Simplify 0.25 into 0.25 9.612 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.612 * [taylor]: Taking taylor expansion of 1.0 in n 9.612 * [backup-simplify]: Simplify 1.0 into 1.0 9.612 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.612 * [taylor]: Taking taylor expansion of k in n 9.612 * [backup-simplify]: Simplify k into k 9.612 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.612 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 9.612 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.612 * [taylor]: Taking taylor expansion of 2.0 in n 9.612 * [backup-simplify]: Simplify 2.0 into 2.0 9.612 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.612 * [taylor]: Taking taylor expansion of PI in n 9.612 * [backup-simplify]: Simplify PI into PI 9.612 * [taylor]: Taking taylor expansion of n in n 9.612 * [backup-simplify]: Simplify 0 into 0 9.612 * [backup-simplify]: Simplify 1 into 1 9.612 * [backup-simplify]: Simplify (/ PI 1) into PI 9.613 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.613 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.614 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.614 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.614 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 9.615 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.615 * [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)))) 9.616 * [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))))) 9.616 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 9.616 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 9.616 * [taylor]: Taking taylor expansion of 0.25 in k 9.616 * [backup-simplify]: Simplify 0.25 into 0.25 9.616 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 9.616 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 9.616 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 9.616 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 9.617 * [taylor]: Taking taylor expansion of 2.0 in k 9.617 * [backup-simplify]: Simplify 2.0 into 2.0 9.617 * [taylor]: Taking taylor expansion of PI in k 9.617 * [backup-simplify]: Simplify PI into PI 9.617 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.618 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.618 * [taylor]: Taking taylor expansion of (log n) in k 9.618 * [taylor]: Taking taylor expansion of n in k 9.618 * [backup-simplify]: Simplify n into n 9.618 * [backup-simplify]: Simplify (log n) into (log n) 9.618 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.618 * [taylor]: Taking taylor expansion of 1.0 in k 9.618 * [backup-simplify]: Simplify 1.0 into 1.0 9.618 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.618 * [taylor]: Taking taylor expansion of k in k 9.618 * [backup-simplify]: Simplify 0 into 0 9.618 * [backup-simplify]: Simplify 1 into 1 9.618 * [backup-simplify]: Simplify (/ 1 1) into 1 9.618 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.619 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 9.619 * [backup-simplify]: Simplify (- 1) into -1 9.619 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.620 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 9.621 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 9.622 * [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))))) 9.623 * [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))))) 9.623 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.624 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.625 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.625 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.625 * [backup-simplify]: Simplify (- 0) into 0 9.625 * [backup-simplify]: Simplify (+ 0 0) into 0 9.626 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 9.626 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.627 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 9.628 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.629 * [taylor]: Taking taylor expansion of 0 in k 9.629 * [backup-simplify]: Simplify 0 into 0 9.629 * [backup-simplify]: Simplify 0 into 0 9.629 * [backup-simplify]: Simplify 0 into 0 9.629 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.630 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.632 * [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 9.632 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.632 * [backup-simplify]: Simplify (- 0) into 0 9.632 * [backup-simplify]: Simplify (+ 0 0) into 0 9.633 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 9.634 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.635 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 9.638 * [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 9.638 * [taylor]: Taking taylor expansion of 0 in k 9.638 * [backup-simplify]: Simplify 0 into 0 9.638 * [backup-simplify]: Simplify 0 into 0 9.638 * [backup-simplify]: Simplify 0 into 0 9.638 * [backup-simplify]: Simplify 0 into 0 9.639 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.641 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.647 * [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 9.647 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.647 * [backup-simplify]: Simplify (- 0) into 0 9.648 * [backup-simplify]: Simplify (+ 0 0) into 0 9.658 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 9.660 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.662 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 9.665 * [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 9.665 * [taylor]: Taking taylor expansion of 0 in k 9.665 * [backup-simplify]: Simplify 0 into 0 9.665 * [backup-simplify]: Simplify 0 into 0 9.666 * [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)))) 9.667 * [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))) 9.667 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 9.667 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 9.667 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 9.667 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 9.667 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 9.667 * [taylor]: Taking taylor expansion of 0.25 in k 9.667 * [backup-simplify]: Simplify 0.25 into 0.25 9.667 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.667 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.667 * [taylor]: Taking taylor expansion of k in k 9.667 * [backup-simplify]: Simplify 0 into 0 9.667 * [backup-simplify]: Simplify 1 into 1 9.668 * [backup-simplify]: Simplify (/ 1 1) into 1 9.668 * [taylor]: Taking taylor expansion of 1.0 in k 9.668 * [backup-simplify]: Simplify 1.0 into 1.0 9.668 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 9.668 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 9.668 * [taylor]: Taking taylor expansion of -2.0 in k 9.668 * [backup-simplify]: Simplify -2.0 into -2.0 9.668 * [taylor]: Taking taylor expansion of (/ PI n) in k 9.668 * [taylor]: Taking taylor expansion of PI in k 9.668 * [backup-simplify]: Simplify PI into PI 9.668 * [taylor]: Taking taylor expansion of n in k 9.668 * [backup-simplify]: Simplify n into n 9.668 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 9.668 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 9.668 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 9.669 * [backup-simplify]: Simplify (+ 1 0) into 1 9.669 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 9.669 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 9.670 * [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)))))) 9.670 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 9.670 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 9.670 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 9.670 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 9.670 * [taylor]: Taking taylor expansion of 0.25 in n 9.670 * [backup-simplify]: Simplify 0.25 into 0.25 9.670 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.671 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.671 * [taylor]: Taking taylor expansion of k in n 9.671 * [backup-simplify]: Simplify k into k 9.671 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.671 * [taylor]: Taking taylor expansion of 1.0 in n 9.671 * [backup-simplify]: Simplify 1.0 into 1.0 9.671 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 9.671 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.671 * [taylor]: Taking taylor expansion of -2.0 in n 9.671 * [backup-simplify]: Simplify -2.0 into -2.0 9.671 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.671 * [taylor]: Taking taylor expansion of PI in n 9.671 * [backup-simplify]: Simplify PI into PI 9.671 * [taylor]: Taking taylor expansion of n in n 9.671 * [backup-simplify]: Simplify 0 into 0 9.671 * [backup-simplify]: Simplify 1 into 1 9.672 * [backup-simplify]: Simplify (/ PI 1) into PI 9.672 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.673 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.673 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.673 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 9.675 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.676 * [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)))) 9.678 * [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))))) 9.678 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 9.678 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 9.678 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 9.678 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 9.678 * [taylor]: Taking taylor expansion of 0.25 in n 9.678 * [backup-simplify]: Simplify 0.25 into 0.25 9.678 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.678 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.678 * [taylor]: Taking taylor expansion of k in n 9.678 * [backup-simplify]: Simplify k into k 9.678 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.678 * [taylor]: Taking taylor expansion of 1.0 in n 9.678 * [backup-simplify]: Simplify 1.0 into 1.0 9.678 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 9.678 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.678 * [taylor]: Taking taylor expansion of -2.0 in n 9.678 * [backup-simplify]: Simplify -2.0 into -2.0 9.678 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.678 * [taylor]: Taking taylor expansion of PI in n 9.678 * [backup-simplify]: Simplify PI into PI 9.678 * [taylor]: Taking taylor expansion of n in n 9.678 * [backup-simplify]: Simplify 0 into 0 9.678 * [backup-simplify]: Simplify 1 into 1 9.679 * [backup-simplify]: Simplify (/ PI 1) into PI 9.679 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.681 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.681 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.681 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 9.682 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.683 * [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)))) 9.685 * [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))))) 9.685 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 9.685 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 9.685 * [taylor]: Taking taylor expansion of 0.25 in k 9.685 * [backup-simplify]: Simplify 0.25 into 0.25 9.685 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 9.685 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.685 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.685 * [taylor]: Taking taylor expansion of k in k 9.685 * [backup-simplify]: Simplify 0 into 0 9.686 * [backup-simplify]: Simplify 1 into 1 9.686 * [backup-simplify]: Simplify (/ 1 1) into 1 9.686 * [taylor]: Taking taylor expansion of 1.0 in k 9.686 * [backup-simplify]: Simplify 1.0 into 1.0 9.686 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 9.686 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 9.686 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 9.686 * [taylor]: Taking taylor expansion of -2.0 in k 9.686 * [backup-simplify]: Simplify -2.0 into -2.0 9.686 * [taylor]: Taking taylor expansion of PI in k 9.686 * [backup-simplify]: Simplify PI into PI 9.686 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.687 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.687 * [taylor]: Taking taylor expansion of (log n) in k 9.687 * [taylor]: Taking taylor expansion of n in k 9.687 * [backup-simplify]: Simplify n into n 9.687 * [backup-simplify]: Simplify (log n) into (log n) 9.687 * [backup-simplify]: Simplify (+ 1 0) into 1 9.687 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.688 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 9.689 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 9.690 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 9.690 * [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))))) 9.691 * [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))))) 9.692 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.692 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 9.693 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 9.693 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.694 * [backup-simplify]: Simplify (+ 0 0) into 0 9.694 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 9.695 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.696 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 9.697 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.697 * [taylor]: Taking taylor expansion of 0 in k 9.697 * [backup-simplify]: Simplify 0 into 0 9.697 * [backup-simplify]: Simplify 0 into 0 9.697 * [backup-simplify]: Simplify 0 into 0 9.698 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.698 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.700 * [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 9.700 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.700 * [backup-simplify]: Simplify (+ 0 0) into 0 9.701 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 9.702 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.703 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 9.704 * [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 9.704 * [taylor]: Taking taylor expansion of 0 in k 9.704 * [backup-simplify]: Simplify 0 into 0 9.704 * [backup-simplify]: Simplify 0 into 0 9.705 * [backup-simplify]: Simplify 0 into 0 9.705 * [backup-simplify]: Simplify 0 into 0 9.705 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.706 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.709 * [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 9.709 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.710 * [backup-simplify]: Simplify (+ 0 0) into 0 9.710 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 9.711 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.712 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 9.714 * [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 9.715 * [taylor]: Taking taylor expansion of 0 in k 9.715 * [backup-simplify]: Simplify 0 into 0 9.715 * [backup-simplify]: Simplify 0 into 0 9.716 * [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)))))) 9.716 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 9.716 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 9.716 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 9.716 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 9.716 * [taylor]: Taking taylor expansion of 1.0 in k 9.716 * [backup-simplify]: Simplify 1.0 into 1.0 9.716 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 9.716 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.717 * [taylor]: Taking taylor expansion of k in k 9.717 * [backup-simplify]: Simplify 0 into 0 9.717 * [backup-simplify]: Simplify 1 into 1 9.717 * [backup-simplify]: Simplify (/ 1 1) into 1 9.717 * [backup-simplify]: Simplify (sqrt 0) into 0 9.719 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.719 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 9.719 * [taylor]: Taking taylor expansion of 1.0 in k 9.719 * [backup-simplify]: Simplify 1.0 into 1.0 9.719 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 9.719 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.719 * [taylor]: Taking taylor expansion of k in k 9.719 * [backup-simplify]: Simplify 0 into 0 9.719 * [backup-simplify]: Simplify 1 into 1 9.720 * [backup-simplify]: Simplify (/ 1 1) into 1 9.720 * [backup-simplify]: Simplify (sqrt 0) into 0 9.721 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.721 * [backup-simplify]: Simplify (* 1.0 0) into 0 9.721 * [backup-simplify]: Simplify 0 into 0 9.722 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 9.722 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.723 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 9.725 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.726 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 9.726 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.726 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.729 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.730 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 9.730 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.731 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 9.731 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 9.731 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 9.732 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 9.732 * [taylor]: Taking taylor expansion of 1.0 in k 9.732 * [backup-simplify]: Simplify 1.0 into 1.0 9.732 * [taylor]: Taking taylor expansion of (sqrt k) in k 9.732 * [taylor]: Taking taylor expansion of k in k 9.732 * [backup-simplify]: Simplify 0 into 0 9.732 * [backup-simplify]: Simplify 1 into 1 9.732 * [backup-simplify]: Simplify (sqrt 0) into 0 9.733 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.733 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 9.733 * [taylor]: Taking taylor expansion of 1.0 in k 9.733 * [backup-simplify]: Simplify 1.0 into 1.0 9.733 * [taylor]: Taking taylor expansion of (sqrt k) in k 9.733 * [taylor]: Taking taylor expansion of k in k 9.733 * [backup-simplify]: Simplify 0 into 0 9.733 * [backup-simplify]: Simplify 1 into 1 9.733 * [backup-simplify]: Simplify (sqrt 0) into 0 9.734 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.734 * [backup-simplify]: Simplify (* 1.0 0) into 0 9.734 * [backup-simplify]: Simplify 0 into 0 9.735 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 9.736 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.737 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.738 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 9.739 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.741 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.742 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 9.742 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.743 * [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)))))))) 9.744 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 9.744 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 9.744 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 9.744 * [taylor]: Taking taylor expansion of 1.0 in k 9.744 * [backup-simplify]: Simplify 1.0 into 1.0 9.744 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 9.744 * [taylor]: Taking taylor expansion of (/ -1 k) in k 9.744 * [taylor]: Taking taylor expansion of -1 in k 9.744 * [backup-simplify]: Simplify -1 into -1 9.744 * [taylor]: Taking taylor expansion of k in k 9.744 * [backup-simplify]: Simplify 0 into 0 9.744 * [backup-simplify]: Simplify 1 into 1 9.744 * [backup-simplify]: Simplify (/ -1 1) into -1 9.744 * [backup-simplify]: Simplify (sqrt 0) into 0 9.745 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 9.745 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 9.745 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 9.745 * [taylor]: Taking taylor expansion of 1.0 in k 9.745 * [backup-simplify]: Simplify 1.0 into 1.0 9.745 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 9.745 * [taylor]: Taking taylor expansion of (/ -1 k) in k 9.745 * [taylor]: Taking taylor expansion of -1 in k 9.745 * [backup-simplify]: Simplify -1 into -1 9.745 * [taylor]: Taking taylor expansion of k in k 9.746 * [backup-simplify]: Simplify 0 into 0 9.746 * [backup-simplify]: Simplify 1 into 1 9.746 * [backup-simplify]: Simplify (/ -1 1) into -1 9.746 * [backup-simplify]: Simplify (sqrt 0) into 0 9.747 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 9.747 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 9.747 * [backup-simplify]: Simplify +nan.0 into +nan.0 9.748 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 9.750 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.752 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 9.752 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.754 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.757 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.762 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 9.762 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.763 * [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))))) 9.763 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 9.764 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 9.764 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 9.764 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.764 * [taylor]: Taking taylor expansion of 2.0 in n 9.764 * [backup-simplify]: Simplify 2.0 into 2.0 9.764 * [taylor]: Taking taylor expansion of (* n PI) in n 9.764 * [taylor]: Taking taylor expansion of n in n 9.764 * [backup-simplify]: Simplify 0 into 0 9.764 * [backup-simplify]: Simplify 1 into 1 9.764 * [taylor]: Taking taylor expansion of PI in n 9.764 * [backup-simplify]: Simplify PI into PI 9.764 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.764 * [taylor]: Taking taylor expansion of 2.0 in n 9.764 * [backup-simplify]: Simplify 2.0 into 2.0 9.764 * [taylor]: Taking taylor expansion of (* n PI) in n 9.764 * [taylor]: Taking taylor expansion of n in n 9.764 * [backup-simplify]: Simplify 0 into 0 9.764 * [backup-simplify]: Simplify 1 into 1 9.764 * [taylor]: Taking taylor expansion of PI in n 9.765 * [backup-simplify]: Simplify PI into PI 9.765 * [backup-simplify]: Simplify (* 0 PI) into 0 9.765 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.765 * [backup-simplify]: Simplify 0 into 0 9.774 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.775 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.775 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.776 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 9.777 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 9.777 * [backup-simplify]: Simplify 0 into 0 9.777 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 9.778 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 9.778 * [backup-simplify]: Simplify 0 into 0 9.779 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.780 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 9.780 * [backup-simplify]: Simplify 0 into 0 9.781 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 9.782 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 9.782 * [backup-simplify]: Simplify 0 into 0 9.783 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 9.784 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 9.784 * [backup-simplify]: Simplify 0 into 0 9.785 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 9.786 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 9.786 * [backup-simplify]: Simplify 0 into 0 9.786 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 9.787 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 9.787 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 9.787 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.787 * [taylor]: Taking taylor expansion of 2.0 in n 9.787 * [backup-simplify]: Simplify 2.0 into 2.0 9.787 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.787 * [taylor]: Taking taylor expansion of PI in n 9.787 * [backup-simplify]: Simplify PI into PI 9.787 * [taylor]: Taking taylor expansion of n in n 9.787 * [backup-simplify]: Simplify 0 into 0 9.787 * [backup-simplify]: Simplify 1 into 1 9.787 * [backup-simplify]: Simplify (/ PI 1) into PI 9.787 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.787 * [taylor]: Taking taylor expansion of 2.0 in n 9.787 * [backup-simplify]: Simplify 2.0 into 2.0 9.787 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.787 * [taylor]: Taking taylor expansion of PI in n 9.787 * [backup-simplify]: Simplify PI into PI 9.787 * [taylor]: Taking taylor expansion of n in n 9.787 * [backup-simplify]: Simplify 0 into 0 9.787 * [backup-simplify]: Simplify 1 into 1 9.788 * [backup-simplify]: Simplify (/ PI 1) into PI 9.788 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.788 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.789 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.789 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.790 * [backup-simplify]: Simplify 0 into 0 9.790 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.791 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.791 * [backup-simplify]: Simplify 0 into 0 9.791 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.792 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.792 * [backup-simplify]: Simplify 0 into 0 9.793 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.793 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.793 * [backup-simplify]: Simplify 0 into 0 9.794 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.795 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 9.795 * [backup-simplify]: Simplify 0 into 0 9.796 * [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 9.796 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 9.796 * [backup-simplify]: Simplify 0 into 0 9.797 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 9.797 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 9.797 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 9.797 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.797 * [taylor]: Taking taylor expansion of -2.0 in n 9.797 * [backup-simplify]: Simplify -2.0 into -2.0 9.797 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.797 * [taylor]: Taking taylor expansion of PI in n 9.797 * [backup-simplify]: Simplify PI into PI 9.797 * [taylor]: Taking taylor expansion of n in n 9.797 * [backup-simplify]: Simplify 0 into 0 9.797 * [backup-simplify]: Simplify 1 into 1 9.798 * [backup-simplify]: Simplify (/ PI 1) into PI 9.798 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.798 * [taylor]: Taking taylor expansion of -2.0 in n 9.798 * [backup-simplify]: Simplify -2.0 into -2.0 9.798 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.798 * [taylor]: Taking taylor expansion of PI in n 9.798 * [backup-simplify]: Simplify PI into PI 9.798 * [taylor]: Taking taylor expansion of n in n 9.798 * [backup-simplify]: Simplify 0 into 0 9.798 * [backup-simplify]: Simplify 1 into 1 9.798 * [backup-simplify]: Simplify (/ PI 1) into PI 9.799 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.799 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.799 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.800 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 9.800 * [backup-simplify]: Simplify 0 into 0 9.801 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.801 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.801 * [backup-simplify]: Simplify 0 into 0 9.802 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.802 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.802 * [backup-simplify]: Simplify 0 into 0 9.803 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.804 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.804 * [backup-simplify]: Simplify 0 into 0 9.804 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.805 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 9.805 * [backup-simplify]: Simplify 0 into 0 9.806 * [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 9.807 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 9.807 * [backup-simplify]: Simplify 0 into 0 9.807 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 9.807 * * * [progress]: simplifying candidates 9.811 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) 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n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 9.819 * * [simplify]: Extracting # 0 : cost 0 9.819 * * [simplify]: Extracting # 1 : cost 0 9.819 * * [simplify]: Extracting # 2 : cost 0 9.820 * * [simplify]: Extracting # 3 : cost 0 9.820 * * [simplify]: Extracting # 4 : cost 0 9.821 * * [simplify]: Extracting # 5 : cost 0 9.821 * * [simplify]: Extracting # 6 : cost 0 9.822 * * [simplify]: Extracting # 7 : cost 0 9.822 * * [simplify]: Extracting # 8 : cost 0 9.823 * * [simplify]: Extracting # 9 : cost 0 9.823 * * [simplify]: Extracting # 10 : cost 0 9.824 * * [simplify]: Extracting # 11 : cost 0 9.824 * * [simplify]: Extracting # 12 : cost 0 9.825 * * [simplify]: Extracting # 13 : cost 0 9.825 * * [simplify]: Extracting # 14 : cost 0 9.826 * * [simplify]: iteration 0 : 332 enodes (cost 3588 ) 9.984 * * [simplify]: Extracting # 0 : cost 0 9.987 * * [simplify]: Extracting # 1 : cost 0 9.989 * * [simplify]: Extracting # 2 : cost 0 9.992 * * [simplify]: Extracting # 3 : cost 0 9.996 * * [simplify]: Extracting # 4 : cost 0 9.998 * * [simplify]: Extracting # 5 : cost 0 10.001 * * [simplify]: Extracting # 6 : cost 0 10.004 * * [simplify]: Extracting # 7 : cost 0 10.007 * * [simplify]: iteration 1 : 979 enodes (cost 3316 ) 10.840 * * [simplify]: Extracting # 0 : cost 0 10.853 * * [simplify]: Extracting # 1 : cost 0 10.859 * * [simplify]: Extracting # 2 : cost 0 10.865 * * [simplify]: Extracting # 3 : cost 0 10.870 * * [simplify]: Extracting # 4 : cost 0 10.876 * * [simplify]: iteration 2 : 4191 enodes (cost 3202 ) 12.175 * * [simplify]: Extracting # 0 : cost 0 12.182 * * [simplify]: Extracting # 1 : cost 0 12.189 * * [simplify]: Extracting # 2 : cost 0 12.196 * * [simplify]: Extracting # 3 : cost 0 12.204 * * [simplify]: iteration done: 5000 enodes (cost 3197 ) 12.208 * [simplify]: Simplified to: (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (/ (/ (- 1.0 k) 2.0) 2) (/ (/ (- 1.0 k) 2.0) 2) (/ (/ (- 1.0 k) 2.0) 2) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 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(- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2))) (pow (* n (* 2.0 PI)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (sqrt 2))) (pow (* n (* 2.0 PI)) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 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2)) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* n (* 2.0 PI)) (/ (/ (- 1.0 k) 2.0) 4)) (pow (* n (* 2.0 PI)) (/ (/ (- 1.0 k) 2.0) 4)) (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (/ (/ (- 1.0 k) 2.0) 2) (/ (/ (- 1.0 k) 2.0) 2) (/ (/ (- 1.0 k) 2.0) 2) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (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 (- 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(pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2))) (pow (* n (* 2.0 PI)) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* n (* PI 2.0)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* n (* PI 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* n (* 2.0 PI)) (- 1.0 k)) (* n (* PI 2.0)) (pow (* n (* 2.0 PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* n (* 2.0 PI)) (/ (/ (- 1.0 k) 2.0) 4)) (pow (* n (* 2.0 PI)) (/ (/ (- 1.0 k) 2.0) 4)) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (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) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* n (* PI 2.0)) (* n (* PI 2.0)) (log (* n (* 2.0 PI))) (log (* n (* 2.0 PI))) (log (* n (* 2.0 PI))) (exp (* (* 2.0 PI) n)) (pow (* n (* 2.0 PI)) 3) (pow (* n (* 2.0 PI)) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* n (* 2.0 PI)) 3) (sqrt (* n (* 2.0 PI))) (sqrt (* n (* 2.0 PI))) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* PI n) (- (fma (* 0.03125 (* (pow (* n (* 2.0 PI)) 0.25) (pow (log (* 2.0 PI)) 2))) (pow k 2) (fma 0.03125 (* (* (pow (log n) 2) (pow (* n (* 2.0 PI)) 0.25)) (pow k 2)) (fma (* (* (log n) (pow (* n (* 2.0 PI)) 0.25)) (log (* 2.0 PI))) (* 0.0625 (pow k 2)) (pow (* n (* 2.0 PI)) 0.25)))) (* 0.25 (* k (fma (pow (* n (* 2.0 PI)) 0.25) (log (* 2.0 PI)) (* (log n) (pow (* n (* 2.0 PI)) 0.25)))))) (pow (pow (* n (* 2.0 PI)) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (fma (* 0.03125 (* (pow (* n (* 2.0 PI)) 0.25) (pow (log (* 2.0 PI)) 2))) (pow k 2) (fma 0.03125 (* (* (pow (log n) 2) (pow (* n (* 2.0 PI)) 0.25)) (pow k 2)) (fma (* (* (log n) (pow (* n (* 2.0 PI)) 0.25)) (log (* 2.0 PI))) (* 0.0625 (pow k 2)) (pow (* n (* 2.0 PI)) 0.25)))) (* 0.25 (* k (fma (pow (* n (* 2.0 PI)) 0.25) (log (* 2.0 PI)) (* (log n) (pow (* n (* 2.0 PI)) 0.25)))))) (pow (pow (* n (* 2.0 PI)) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (fma +nan.0 (- k) (fma (pow k 2) +nan.0 (- +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)) (* n (* PI 2.0)) (* n (* PI 2.0)) (* n (* PI 2.0)) 12.211 * * * [progress]: adding candidates to table 13.483 * * [progress]: iteration 4 / 4 13.483 * * * [progress]: picking best candidate 13.515 * * * * [pick]: Picked # 13.515 * * * [progress]: localizing error 13.559 * * * [progress]: generating rewritten candidates 13.559 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1 2) 13.611 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2) 13.625 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 13.632 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 2 1) 13.678 * * * [progress]: generating series expansions 13.678 * * * * [progress]: [ 1 / 4 ] generating series at (2 1 2) 13.679 * [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))) 13.679 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 13.679 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 13.679 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 13.679 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 13.679 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 13.679 * [taylor]: Taking taylor expansion of 0.25 in k 13.679 * [backup-simplify]: Simplify 0.25 into 0.25 13.679 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 13.679 * [taylor]: Taking taylor expansion of 1.0 in k 13.679 * [backup-simplify]: Simplify 1.0 into 1.0 13.679 * [taylor]: Taking taylor expansion of k in k 13.679 * [backup-simplify]: Simplify 0 into 0 13.679 * [backup-simplify]: Simplify 1 into 1 13.679 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 13.679 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 13.679 * [taylor]: Taking taylor expansion of 2.0 in k 13.679 * [backup-simplify]: Simplify 2.0 into 2.0 13.679 * [taylor]: Taking taylor expansion of (* n PI) in k 13.679 * [taylor]: Taking taylor expansion of n in k 13.679 * [backup-simplify]: Simplify n into n 13.679 * [taylor]: Taking taylor expansion of PI in k 13.679 * [backup-simplify]: Simplify PI into PI 13.679 * [backup-simplify]: Simplify (* n PI) into (* n PI) 13.679 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 13.679 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 13.680 * [backup-simplify]: Simplify (- 0) into 0 13.680 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 13.680 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 13.680 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 13.680 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 13.681 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 13.681 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 13.681 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 13.681 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 13.681 * [taylor]: Taking taylor expansion of 0.25 in n 13.681 * [backup-simplify]: Simplify 0.25 into 0.25 13.681 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 13.681 * [taylor]: Taking taylor expansion of 1.0 in n 13.681 * [backup-simplify]: Simplify 1.0 into 1.0 13.681 * [taylor]: Taking taylor expansion of k in n 13.681 * [backup-simplify]: Simplify k into k 13.681 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 13.681 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 13.681 * [taylor]: Taking taylor expansion of 2.0 in n 13.681 * [backup-simplify]: Simplify 2.0 into 2.0 13.681 * [taylor]: Taking taylor expansion of (* n PI) in n 13.681 * [taylor]: Taking taylor expansion of n in n 13.681 * [backup-simplify]: Simplify 0 into 0 13.681 * [backup-simplify]: Simplify 1 into 1 13.681 * [taylor]: Taking taylor expansion of PI in n 13.681 * [backup-simplify]: Simplify PI into PI 13.681 * [backup-simplify]: Simplify (* 0 PI) into 0 13.681 * [backup-simplify]: Simplify (* 2.0 0) into 0 13.683 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.685 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 13.686 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.686 * [backup-simplify]: Simplify (- k) into (- k) 13.686 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 13.686 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 13.687 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.688 * [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)))) 13.690 * [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))))) 13.690 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 13.690 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 13.690 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 13.690 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 13.690 * [taylor]: Taking taylor expansion of 0.25 in n 13.690 * [backup-simplify]: Simplify 0.25 into 0.25 13.690 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 13.690 * [taylor]: Taking taylor expansion of 1.0 in n 13.690 * [backup-simplify]: Simplify 1.0 into 1.0 13.690 * [taylor]: Taking taylor expansion of k in n 13.690 * [backup-simplify]: Simplify k into k 13.690 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 13.690 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 13.690 * [taylor]: Taking taylor expansion of 2.0 in n 13.690 * [backup-simplify]: Simplify 2.0 into 2.0 13.690 * [taylor]: Taking taylor expansion of (* n PI) in n 13.690 * [taylor]: Taking taylor expansion of n in n 13.690 * [backup-simplify]: Simplify 0 into 0 13.690 * [backup-simplify]: Simplify 1 into 1 13.690 * [taylor]: Taking taylor expansion of PI in n 13.690 * [backup-simplify]: Simplify PI into PI 13.691 * [backup-simplify]: Simplify (* 0 PI) into 0 13.691 * [backup-simplify]: Simplify (* 2.0 0) into 0 13.693 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.694 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 13.696 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.696 * [backup-simplify]: Simplify (- k) into (- k) 13.696 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 13.696 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 13.697 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.699 * [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)))) 13.700 * [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))))) 13.700 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 13.700 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 13.700 * [taylor]: Taking taylor expansion of 0.25 in k 13.700 * [backup-simplify]: Simplify 0.25 into 0.25 13.700 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 13.700 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 13.700 * [taylor]: Taking taylor expansion of 1.0 in k 13.700 * [backup-simplify]: Simplify 1.0 into 1.0 13.700 * [taylor]: Taking taylor expansion of k in k 13.700 * [backup-simplify]: Simplify 0 into 0 13.700 * [backup-simplify]: Simplify 1 into 1 13.700 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 13.700 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 13.700 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 13.700 * [taylor]: Taking taylor expansion of 2.0 in k 13.700 * [backup-simplify]: Simplify 2.0 into 2.0 13.700 * [taylor]: Taking taylor expansion of PI in k 13.700 * [backup-simplify]: Simplify PI into PI 13.701 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.702 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.702 * [taylor]: Taking taylor expansion of (log n) in k 13.702 * [taylor]: Taking taylor expansion of n in k 13.702 * [backup-simplify]: Simplify n into n 13.702 * [backup-simplify]: Simplify (log n) into (log n) 13.703 * [backup-simplify]: Simplify (- 0) into 0 13.703 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 13.704 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 13.705 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 13.706 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 13.708 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 13.709 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 13.710 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.711 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 13.713 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 13.713 * [backup-simplify]: Simplify (- 0) into 0 13.714 * [backup-simplify]: Simplify (+ 0 0) into 0 13.714 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 13.716 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.717 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 13.719 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.719 * [taylor]: Taking taylor expansion of 0 in k 13.719 * [backup-simplify]: Simplify 0 into 0 13.719 * [backup-simplify]: Simplify 0 into 0 13.720 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 13.722 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 13.723 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 13.723 * [backup-simplify]: Simplify (+ 0 0) into 0 13.724 * [backup-simplify]: Simplify (- 1) into -1 13.724 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.726 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 13.728 * [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)))) 13.732 * [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)))))) 13.735 * [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)))))) 13.737 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 13.738 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 13.740 * [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 13.740 * [backup-simplify]: Simplify (- 0) into 0 13.741 * [backup-simplify]: Simplify (+ 0 0) into 0 13.741 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 13.742 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.743 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 13.745 * [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 13.745 * [taylor]: Taking taylor expansion of 0 in k 13.745 * [backup-simplify]: Simplify 0 into 0 13.745 * [backup-simplify]: Simplify 0 into 0 13.745 * [backup-simplify]: Simplify 0 into 0 13.745 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.747 * [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 13.749 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 13.749 * [backup-simplify]: Simplify (+ 0 0) into 0 13.749 * [backup-simplify]: Simplify (- 0) into 0 13.749 * [backup-simplify]: Simplify (+ 0 0) into 0 13.750 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 13.752 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 13.755 * [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))))) 13.758 * [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))))) 13.764 * [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)))))) 13.765 * [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)))) 13.765 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 13.765 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 13.765 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 13.765 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 13.765 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 13.765 * [taylor]: Taking taylor expansion of 0.25 in k 13.765 * [backup-simplify]: Simplify 0.25 into 0.25 13.765 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.765 * [taylor]: Taking taylor expansion of 1.0 in k 13.765 * [backup-simplify]: Simplify 1.0 into 1.0 13.765 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.765 * [taylor]: Taking taylor expansion of k in k 13.765 * [backup-simplify]: Simplify 0 into 0 13.765 * [backup-simplify]: Simplify 1 into 1 13.765 * [backup-simplify]: Simplify (/ 1 1) into 1 13.765 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 13.765 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 13.765 * [taylor]: Taking taylor expansion of 2.0 in k 13.765 * [backup-simplify]: Simplify 2.0 into 2.0 13.766 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.766 * [taylor]: Taking taylor expansion of PI in k 13.766 * [backup-simplify]: Simplify PI into PI 13.766 * [taylor]: Taking taylor expansion of n in k 13.766 * [backup-simplify]: Simplify n into n 13.766 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.766 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 13.766 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 13.766 * [backup-simplify]: Simplify (- 1) into -1 13.767 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.767 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 13.767 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 13.768 * [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))))) 13.768 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 13.768 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 13.768 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 13.768 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 13.768 * [taylor]: Taking taylor expansion of 0.25 in n 13.768 * [backup-simplify]: Simplify 0.25 into 0.25 13.768 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 13.768 * [taylor]: Taking taylor expansion of 1.0 in n 13.768 * [backup-simplify]: Simplify 1.0 into 1.0 13.768 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.768 * [taylor]: Taking taylor expansion of k in n 13.768 * [backup-simplify]: Simplify k into k 13.768 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.768 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 13.768 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.768 * [taylor]: Taking taylor expansion of 2.0 in n 13.768 * [backup-simplify]: Simplify 2.0 into 2.0 13.768 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.768 * [taylor]: Taking taylor expansion of PI in n 13.768 * [backup-simplify]: Simplify PI into PI 13.768 * [taylor]: Taking taylor expansion of n in n 13.768 * [backup-simplify]: Simplify 0 into 0 13.768 * [backup-simplify]: Simplify 1 into 1 13.769 * [backup-simplify]: Simplify (/ PI 1) into PI 13.769 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.771 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.771 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 13.771 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 13.771 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 13.772 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.774 * [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)))) 13.775 * [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))))) 13.775 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 13.775 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 13.775 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 13.775 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 13.775 * [taylor]: Taking taylor expansion of 0.25 in n 13.775 * [backup-simplify]: Simplify 0.25 into 0.25 13.775 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 13.775 * [taylor]: Taking taylor expansion of 1.0 in n 13.775 * [backup-simplify]: Simplify 1.0 into 1.0 13.775 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.775 * [taylor]: Taking taylor expansion of k in n 13.775 * [backup-simplify]: Simplify k into k 13.776 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.776 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 13.776 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.776 * [taylor]: Taking taylor expansion of 2.0 in n 13.776 * [backup-simplify]: Simplify 2.0 into 2.0 13.776 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.776 * [taylor]: Taking taylor expansion of PI in n 13.776 * [backup-simplify]: Simplify PI into PI 13.776 * [taylor]: Taking taylor expansion of n in n 13.776 * [backup-simplify]: Simplify 0 into 0 13.776 * [backup-simplify]: Simplify 1 into 1 13.776 * [backup-simplify]: Simplify (/ PI 1) into PI 13.777 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.778 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.778 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 13.778 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 13.778 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 13.780 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.781 * [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)))) 13.782 * [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))))) 13.783 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 13.783 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 13.783 * [taylor]: Taking taylor expansion of 0.25 in k 13.783 * [backup-simplify]: Simplify 0.25 into 0.25 13.783 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 13.783 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 13.783 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 13.783 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 13.783 * [taylor]: Taking taylor expansion of 2.0 in k 13.783 * [backup-simplify]: Simplify 2.0 into 2.0 13.783 * [taylor]: Taking taylor expansion of PI in k 13.783 * [backup-simplify]: Simplify PI into PI 13.784 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.785 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.785 * [taylor]: Taking taylor expansion of (log n) in k 13.785 * [taylor]: Taking taylor expansion of n in k 13.785 * [backup-simplify]: Simplify n into n 13.785 * [backup-simplify]: Simplify (log n) into (log n) 13.785 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.785 * [taylor]: Taking taylor expansion of 1.0 in k 13.785 * [backup-simplify]: Simplify 1.0 into 1.0 13.785 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.785 * [taylor]: Taking taylor expansion of k in k 13.785 * [backup-simplify]: Simplify 0 into 0 13.785 * [backup-simplify]: Simplify 1 into 1 13.785 * [backup-simplify]: Simplify (/ 1 1) into 1 13.785 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.787 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 13.787 * [backup-simplify]: Simplify (- 1) into -1 13.787 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.789 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 13.790 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 13.791 * [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))))) 13.793 * [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))))) 13.794 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.795 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 13.797 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 13.797 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.807 * [backup-simplify]: Simplify (- 0) into 0 13.807 * [backup-simplify]: Simplify (+ 0 0) into 0 13.808 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 13.810 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.811 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 13.813 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.814 * [taylor]: Taking taylor expansion of 0 in k 13.814 * [backup-simplify]: Simplify 0 into 0 13.814 * [backup-simplify]: Simplify 0 into 0 13.814 * [backup-simplify]: Simplify 0 into 0 13.815 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.816 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.820 * [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 13.821 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.821 * [backup-simplify]: Simplify (- 0) into 0 13.821 * [backup-simplify]: Simplify (+ 0 0) into 0 13.822 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 13.824 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.826 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 13.829 * [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 13.829 * [taylor]: Taking taylor expansion of 0 in k 13.829 * [backup-simplify]: Simplify 0 into 0 13.829 * [backup-simplify]: Simplify 0 into 0 13.829 * [backup-simplify]: Simplify 0 into 0 13.829 * [backup-simplify]: Simplify 0 into 0 13.830 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.831 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.837 * [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 13.838 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.838 * [backup-simplify]: Simplify (- 0) into 0 13.838 * [backup-simplify]: Simplify (+ 0 0) into 0 13.840 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 13.841 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.843 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 13.846 * [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 13.846 * [taylor]: Taking taylor expansion of 0 in k 13.846 * [backup-simplify]: Simplify 0 into 0 13.846 * [backup-simplify]: Simplify 0 into 0 13.848 * [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)))) 13.848 * [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))) 13.849 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 13.849 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 13.849 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 13.849 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 13.849 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 13.849 * [taylor]: Taking taylor expansion of 0.25 in k 13.849 * [backup-simplify]: Simplify 0.25 into 0.25 13.849 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.849 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.849 * [taylor]: Taking taylor expansion of k in k 13.849 * [backup-simplify]: Simplify 0 into 0 13.849 * [backup-simplify]: Simplify 1 into 1 13.849 * [backup-simplify]: Simplify (/ 1 1) into 1 13.849 * [taylor]: Taking taylor expansion of 1.0 in k 13.849 * [backup-simplify]: Simplify 1.0 into 1.0 13.849 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 13.849 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 13.849 * [taylor]: Taking taylor expansion of -2.0 in k 13.849 * [backup-simplify]: Simplify -2.0 into -2.0 13.850 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.850 * [taylor]: Taking taylor expansion of PI in k 13.850 * [backup-simplify]: Simplify PI into PI 13.850 * [taylor]: Taking taylor expansion of n in k 13.850 * [backup-simplify]: Simplify n into n 13.850 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.850 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 13.850 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 13.850 * [backup-simplify]: Simplify (+ 1 0) into 1 13.851 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 13.851 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 13.851 * [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)))))) 13.851 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 13.851 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 13.851 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 13.851 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 13.852 * [taylor]: Taking taylor expansion of 0.25 in n 13.852 * [backup-simplify]: Simplify 0.25 into 0.25 13.852 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 13.852 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.852 * [taylor]: Taking taylor expansion of k in n 13.852 * [backup-simplify]: Simplify k into k 13.852 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.852 * [taylor]: Taking taylor expansion of 1.0 in n 13.852 * [backup-simplify]: Simplify 1.0 into 1.0 13.852 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 13.852 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.852 * [taylor]: Taking taylor expansion of -2.0 in n 13.852 * [backup-simplify]: Simplify -2.0 into -2.0 13.852 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.852 * [taylor]: Taking taylor expansion of PI in n 13.852 * [backup-simplify]: Simplify PI into PI 13.852 * [taylor]: Taking taylor expansion of n in n 13.852 * [backup-simplify]: Simplify 0 into 0 13.852 * [backup-simplify]: Simplify 1 into 1 13.853 * [backup-simplify]: Simplify (/ PI 1) into PI 13.853 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.855 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.855 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 13.855 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 13.856 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.858 * [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)))) 13.859 * [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))))) 13.859 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 13.859 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 13.859 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 13.859 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 13.859 * [taylor]: Taking taylor expansion of 0.25 in n 13.859 * [backup-simplify]: Simplify 0.25 into 0.25 13.859 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 13.859 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.859 * [taylor]: Taking taylor expansion of k in n 13.859 * [backup-simplify]: Simplify k into k 13.859 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.859 * [taylor]: Taking taylor expansion of 1.0 in n 13.860 * [backup-simplify]: Simplify 1.0 into 1.0 13.860 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 13.860 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.860 * [taylor]: Taking taylor expansion of -2.0 in n 13.860 * [backup-simplify]: Simplify -2.0 into -2.0 13.860 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.860 * [taylor]: Taking taylor expansion of PI in n 13.860 * [backup-simplify]: Simplify PI into PI 13.860 * [taylor]: Taking taylor expansion of n in n 13.860 * [backup-simplify]: Simplify 0 into 0 13.860 * [backup-simplify]: Simplify 1 into 1 13.860 * [backup-simplify]: Simplify (/ PI 1) into PI 13.861 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.862 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.862 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 13.862 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 13.864 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.865 * [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)))) 13.866 * [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))))) 13.866 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 13.867 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 13.867 * [taylor]: Taking taylor expansion of 0.25 in k 13.867 * [backup-simplify]: Simplify 0.25 into 0.25 13.867 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 13.867 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.867 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.867 * [taylor]: Taking taylor expansion of k in k 13.867 * [backup-simplify]: Simplify 0 into 0 13.867 * [backup-simplify]: Simplify 1 into 1 13.867 * [backup-simplify]: Simplify (/ 1 1) into 1 13.867 * [taylor]: Taking taylor expansion of 1.0 in k 13.867 * [backup-simplify]: Simplify 1.0 into 1.0 13.867 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 13.867 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 13.867 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 13.867 * [taylor]: Taking taylor expansion of -2.0 in k 13.867 * [backup-simplify]: Simplify -2.0 into -2.0 13.867 * [taylor]: Taking taylor expansion of PI in k 13.867 * [backup-simplify]: Simplify PI into PI 13.868 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.869 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.869 * [taylor]: Taking taylor expansion of (log n) in k 13.869 * [taylor]: Taking taylor expansion of n in k 13.869 * [backup-simplify]: Simplify n into n 13.869 * [backup-simplify]: Simplify (log n) into (log n) 13.870 * [backup-simplify]: Simplify (+ 1 0) into 1 13.870 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.871 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 13.872 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 13.873 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 13.875 * [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))))) 13.876 * [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))))) 13.877 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.878 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 13.880 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 13.880 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.880 * [backup-simplify]: Simplify (+ 0 0) into 0 13.881 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 13.882 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.884 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 13.886 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.886 * [taylor]: Taking taylor expansion of 0 in k 13.886 * [backup-simplify]: Simplify 0 into 0 13.886 * [backup-simplify]: Simplify 0 into 0 13.886 * [backup-simplify]: Simplify 0 into 0 13.887 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.888 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.892 * [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 13.892 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.893 * [backup-simplify]: Simplify (+ 0 0) into 0 13.894 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 13.896 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.897 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 13.900 * [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 13.900 * [taylor]: Taking taylor expansion of 0 in k 13.900 * [backup-simplify]: Simplify 0 into 0 13.900 * [backup-simplify]: Simplify 0 into 0 13.900 * [backup-simplify]: Simplify 0 into 0 13.900 * [backup-simplify]: Simplify 0 into 0 13.901 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.902 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.909 * [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 13.909 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.910 * [backup-simplify]: Simplify (+ 0 0) into 0 13.911 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 13.913 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.915 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 13.918 * [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 13.918 * [taylor]: Taking taylor expansion of 0 in k 13.918 * [backup-simplify]: Simplify 0 into 0 13.918 * [backup-simplify]: Simplify 0 into 0 13.919 * [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)))))) 13.919 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2) 13.919 * [backup-simplify]: Simplify (pow n (/ (/ (- 1.0 k) 2.0) 2)) into (pow n (* 0.25 (- 1.0 k))) 13.919 * [approximate]: Taking taylor expansion of (pow n (* 0.25 (- 1.0 k))) in (n k) around 0 13.919 * [taylor]: Taking taylor expansion of (pow n (* 0.25 (- 1.0 k))) in k 13.919 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log n))) in k 13.919 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log n)) in k 13.919 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 13.919 * [taylor]: Taking taylor expansion of 0.25 in k 13.919 * [backup-simplify]: Simplify 0.25 into 0.25 13.919 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 13.919 * [taylor]: Taking taylor expansion of 1.0 in k 13.919 * [backup-simplify]: Simplify 1.0 into 1.0 13.919 * [taylor]: Taking taylor expansion of k in k 13.920 * [backup-simplify]: Simplify 0 into 0 13.920 * [backup-simplify]: Simplify 1 into 1 13.920 * [taylor]: Taking taylor expansion of (log n) in k 13.920 * [taylor]: Taking taylor expansion of n in k 13.920 * [backup-simplify]: Simplify n into n 13.920 * [backup-simplify]: Simplify (log n) into (log n) 13.920 * [backup-simplify]: Simplify (- 0) into 0 13.920 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 13.920 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 13.921 * [backup-simplify]: Simplify (* 0.25 (log n)) into (* 0.25 (log n)) 13.921 * [backup-simplify]: Simplify (exp (* 0.25 (log n))) into (pow n 0.25) 13.921 * [taylor]: Taking taylor expansion of (pow n (* 0.25 (- 1.0 k))) in n 13.921 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log n))) in n 13.921 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log n)) in n 13.921 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 13.921 * [taylor]: Taking taylor expansion of 0.25 in n 13.921 * [backup-simplify]: Simplify 0.25 into 0.25 13.921 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 13.921 * [taylor]: Taking taylor expansion of 1.0 in n 13.921 * [backup-simplify]: Simplify 1.0 into 1.0 13.921 * [taylor]: Taking taylor expansion of k in n 13.921 * [backup-simplify]: Simplify k into k 13.921 * [taylor]: Taking taylor expansion of (log n) in n 13.921 * [taylor]: Taking taylor expansion of n in n 13.921 * [backup-simplify]: Simplify 0 into 0 13.921 * [backup-simplify]: Simplify 1 into 1 13.921 * [backup-simplify]: Simplify (log 1) into 0 13.921 * [backup-simplify]: Simplify (- k) into (- k) 13.921 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 13.921 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 13.922 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 13.922 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (log n)) into (* 0.25 (* (- 1.0 k) (log n))) 13.922 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (log n)))) into (exp (* 0.25 (* (- 1.0 k) (log n)))) 13.922 * [taylor]: Taking taylor expansion of (pow n (* 0.25 (- 1.0 k))) in n 13.922 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log n))) in n 13.922 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log n)) in n 13.922 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 13.922 * [taylor]: Taking taylor expansion of 0.25 in n 13.922 * [backup-simplify]: Simplify 0.25 into 0.25 13.922 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 13.922 * [taylor]: Taking taylor expansion of 1.0 in n 13.922 * [backup-simplify]: Simplify 1.0 into 1.0 13.922 * [taylor]: Taking taylor expansion of k in n 13.922 * [backup-simplify]: Simplify k into k 13.922 * [taylor]: Taking taylor expansion of (log n) in n 13.922 * [taylor]: Taking taylor expansion of n in n 13.922 * [backup-simplify]: Simplify 0 into 0 13.922 * [backup-simplify]: Simplify 1 into 1 13.922 * [backup-simplify]: Simplify (log 1) into 0 13.922 * [backup-simplify]: Simplify (- k) into (- k) 13.923 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 13.923 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 13.923 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 13.923 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (log n)) into (* 0.25 (* (- 1.0 k) (log n))) 13.923 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (log n)))) into (exp (* 0.25 (* (- 1.0 k) (log n)))) 13.923 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (log n)))) in k 13.923 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (log n))) in k 13.923 * [taylor]: Taking taylor expansion of 0.25 in k 13.923 * [backup-simplify]: Simplify 0.25 into 0.25 13.923 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (log n)) in k 13.923 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 13.923 * [taylor]: Taking taylor expansion of 1.0 in k 13.923 * [backup-simplify]: Simplify 1.0 into 1.0 13.923 * [taylor]: Taking taylor expansion of k in k 13.923 * [backup-simplify]: Simplify 0 into 0 13.923 * [backup-simplify]: Simplify 1 into 1 13.923 * [taylor]: Taking taylor expansion of (log n) in k 13.923 * [taylor]: Taking taylor expansion of n in k 13.923 * [backup-simplify]: Simplify n into n 13.923 * [backup-simplify]: Simplify (log n) into (log n) 13.924 * [backup-simplify]: Simplify (- 0) into 0 13.924 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 13.924 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 13.924 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (log n))) into (* 0.25 (log n)) 13.924 * [backup-simplify]: Simplify (exp (* 0.25 (log n))) into (pow n 0.25) 13.924 * [backup-simplify]: Simplify (pow n 0.25) into (pow n 0.25) 13.926 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 13.926 * [backup-simplify]: Simplify (- 0) into 0 13.926 * [backup-simplify]: Simplify (+ 0 0) into 0 13.927 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 13.927 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 13.927 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (log n))) into 0 13.928 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 13.928 * [taylor]: Taking taylor expansion of 0 in k 13.928 * [backup-simplify]: Simplify 0 into 0 13.928 * [backup-simplify]: Simplify 0 into 0 13.929 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 13.929 * [backup-simplify]: Simplify (- 1) into -1 13.929 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.930 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (log n))) into (- (log n)) 13.930 * [backup-simplify]: Simplify (+ (* 0.25 (- (log n))) (* 0 (* 1.0 (log n)))) into (- (* 0.25 (log n))) 13.930 * [backup-simplify]: Simplify (* (exp (* 0.25 (log n))) (+ (* (/ (pow (- (* 0.25 (log n))) 1) 1)))) into (* -0.25 (* (pow (pow n 1.0) 0.25) (log n))) 13.930 * [backup-simplify]: Simplify (* -0.25 (* (pow (pow n 1.0) 0.25) (log n))) into (* -0.25 (* (pow (pow n 1.0) 0.25) (log n))) 13.932 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 13.932 * [backup-simplify]: Simplify (- 0) into 0 13.933 * [backup-simplify]: Simplify (+ 0 0) into 0 13.933 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 13.934 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 13.934 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0 13.935 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.935 * [taylor]: Taking taylor expansion of 0 in k 13.935 * [backup-simplify]: Simplify 0 into 0 13.935 * [backup-simplify]: Simplify 0 into 0 13.935 * [backup-simplify]: Simplify 0 into 0 13.936 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 13.936 * [backup-simplify]: Simplify (- 0) into 0 13.937 * [backup-simplify]: Simplify (+ 0 0) into 0 13.937 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (log n)))) into 0 13.938 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (log n))) (* 0 (* 1.0 (log n))))) into 0 13.938 * [backup-simplify]: Simplify (* (exp (* 0.25 (log n))) (+ (* (/ (pow (- (* 0.25 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.03125 (* (pow (pow n 1.0) 0.25) (pow (log n) 2))) 13.939 * [backup-simplify]: Simplify (* 0.03125 (* (pow (pow n 1.0) 0.25) (pow (log n) 2))) into (* 0.03125 (* (pow (pow n 1.0) 0.25) (pow (log n) 2))) 13.939 * [backup-simplify]: Simplify (+ (* (* 0.03125 (* (pow (pow n 1.0) 0.25) (pow (log n) 2))) (pow (* k 1) 2)) (+ (* (* -0.25 (* (pow (pow n 1.0) 0.25) (log n))) (* k 1)) (pow n 0.25))) into (- (+ (* 0.03125 (* (* (pow k 2) (pow (log n) 2)) (pow (pow n 1.0) 0.25))) (pow n 0.25)) (* 0.25 (* (* k (log n)) (pow (pow n 1.0) 0.25)))) 13.940 * [backup-simplify]: Simplify (pow (/ 1 n) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (/ 1 n) (* 0.25 (- 1.0 (/ 1 k)))) 13.940 * [approximate]: Taking taylor expansion of (pow (/ 1 n) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 13.940 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 0.25 (- 1.0 (/ 1 k)))) in k 13.940 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (/ 1 n)))) in k 13.940 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (/ 1 n))) in k 13.940 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 13.940 * [taylor]: Taking taylor expansion of 0.25 in k 13.940 * [backup-simplify]: Simplify 0.25 into 0.25 13.940 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.940 * [taylor]: Taking taylor expansion of 1.0 in k 13.940 * [backup-simplify]: Simplify 1.0 into 1.0 13.940 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.940 * [taylor]: Taking taylor expansion of k in k 13.940 * [backup-simplify]: Simplify 0 into 0 13.940 * [backup-simplify]: Simplify 1 into 1 13.940 * [backup-simplify]: Simplify (/ 1 1) into 1 13.940 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k 13.940 * [taylor]: Taking taylor expansion of (/ 1 n) in k 13.940 * [taylor]: Taking taylor expansion of n in k 13.940 * [backup-simplify]: Simplify n into n 13.940 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n) 13.940 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n)) 13.941 * [backup-simplify]: Simplify (- 1) into -1 13.941 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.941 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 13.941 * [backup-simplify]: Simplify (* -0.25 (log (/ 1 n))) into (* -0.25 (log (/ 1 n))) 13.941 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (/ 1 n)))) into (exp (* 0.25 (* (log (/ 1 n)) (- 1.0 (/ 1 k))))) 13.941 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 0.25 (- 1.0 (/ 1 k)))) in n 13.941 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (/ 1 n)))) in n 13.941 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (/ 1 n))) in n 13.941 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 13.941 * [taylor]: Taking taylor expansion of 0.25 in n 13.941 * [backup-simplify]: Simplify 0.25 into 0.25 13.942 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 13.942 * [taylor]: Taking taylor expansion of 1.0 in n 13.942 * [backup-simplify]: Simplify 1.0 into 1.0 13.942 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.942 * [taylor]: Taking taylor expansion of k in n 13.942 * [backup-simplify]: Simplify k into k 13.942 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.942 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 13.942 * [taylor]: Taking taylor expansion of (/ 1 n) in n 13.942 * [taylor]: Taking taylor expansion of n in n 13.942 * [backup-simplify]: Simplify 0 into 0 13.942 * [backup-simplify]: Simplify 1 into 1 13.942 * [backup-simplify]: Simplify (/ 1 1) into 1 13.942 * [backup-simplify]: Simplify (log 1) into 0 13.942 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 13.942 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 13.942 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 13.943 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.943 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log n))) into (* -0.25 (* (log n) (- 1.0 (/ 1 k)))) 13.943 * [backup-simplify]: Simplify (exp (* -0.25 (* (log n) (- 1.0 (/ 1 k))))) into (exp (* -0.25 (* (log n) (- 1.0 (/ 1 k))))) 13.943 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 0.25 (- 1.0 (/ 1 k)))) in n 13.943 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (/ 1 n)))) in n 13.943 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (/ 1 n))) in n 13.943 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 13.943 * [taylor]: Taking taylor expansion of 0.25 in n 13.943 * [backup-simplify]: Simplify 0.25 into 0.25 13.943 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 13.943 * [taylor]: Taking taylor expansion of 1.0 in n 13.943 * [backup-simplify]: Simplify 1.0 into 1.0 13.943 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.943 * [taylor]: Taking taylor expansion of k in n 13.943 * [backup-simplify]: Simplify k into k 13.943 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.943 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 13.943 * [taylor]: Taking taylor expansion of (/ 1 n) in n 13.943 * [taylor]: Taking taylor expansion of n in n 13.943 * [backup-simplify]: Simplify 0 into 0 13.943 * [backup-simplify]: Simplify 1 into 1 13.944 * [backup-simplify]: Simplify (/ 1 1) into 1 13.944 * [backup-simplify]: Simplify (log 1) into 0 13.944 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 13.944 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 13.944 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 13.944 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.944 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log n))) into (* -0.25 (* (log n) (- 1.0 (/ 1 k)))) 13.945 * [backup-simplify]: Simplify (exp (* -0.25 (* (log n) (- 1.0 (/ 1 k))))) into (exp (* -0.25 (* (log n) (- 1.0 (/ 1 k))))) 13.945 * [taylor]: Taking taylor expansion of (exp (* -0.25 (* (log n) (- 1.0 (/ 1 k))))) in k 13.945 * [taylor]: Taking taylor expansion of (* -0.25 (* (log n) (- 1.0 (/ 1 k)))) in k 13.945 * [taylor]: Taking taylor expansion of -0.25 in k 13.945 * [backup-simplify]: Simplify -0.25 into -0.25 13.945 * [taylor]: Taking taylor expansion of (* (log n) (- 1.0 (/ 1 k))) in k 13.945 * [taylor]: Taking taylor expansion of (log n) in k 13.945 * [taylor]: Taking taylor expansion of n in k 13.945 * [backup-simplify]: Simplify n into n 13.945 * [backup-simplify]: Simplify (log n) into (log n) 13.945 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.945 * [taylor]: Taking taylor expansion of 1.0 in k 13.945 * [backup-simplify]: Simplify 1.0 into 1.0 13.945 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.945 * [taylor]: Taking taylor expansion of k in k 13.945 * [backup-simplify]: Simplify 0 into 0 13.945 * [backup-simplify]: Simplify 1 into 1 13.945 * [backup-simplify]: Simplify (/ 1 1) into 1 13.945 * [backup-simplify]: Simplify (- 1) into -1 13.946 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.946 * [backup-simplify]: Simplify (* (log n) -1) into (* -1 (log n)) 13.946 * [backup-simplify]: Simplify (* -0.25 (* -1 (log n))) into (* 0.25 (log n)) 13.946 * [backup-simplify]: Simplify (exp (* -0.25 (* (log n) (- 1.0 (/ 1 k))))) into (exp (* -0.25 (* (log n) (- 1.0 (/ 1 k))))) 13.946 * [backup-simplify]: Simplify (exp (* -0.25 (* (log n) (- 1.0 (/ 1 k))))) into (exp (* -0.25 (* (log n) (- 1.0 (/ 1 k))))) 13.947 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 13.947 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 13.947 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.948 * [backup-simplify]: Simplify (- 0) into 0 13.948 * [backup-simplify]: Simplify (+ 0 0) into 0 13.948 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 13.949 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.949 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 13.949 * [backup-simplify]: Simplify (* (exp (* -0.25 (* (log n) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.949 * [taylor]: Taking taylor expansion of 0 in k 13.949 * [backup-simplify]: Simplify 0 into 0 13.949 * [backup-simplify]: Simplify 0 into 0 13.949 * [backup-simplify]: Simplify 0 into 0 13.956 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.958 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 13.958 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.958 * [backup-simplify]: Simplify (- 0) into 0 13.958 * [backup-simplify]: Simplify (+ 0 0) into 0 13.959 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 13.959 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.960 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 13.960 * [backup-simplify]: Simplify (* (exp (* -0.25 (* (log n) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.960 * [taylor]: Taking taylor expansion of 0 in k 13.960 * [backup-simplify]: Simplify 0 into 0 13.961 * [backup-simplify]: Simplify 0 into 0 13.961 * [backup-simplify]: Simplify 0 into 0 13.961 * [backup-simplify]: Simplify 0 into 0 13.961 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.964 * [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 13.964 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.964 * [backup-simplify]: Simplify (- 0) into 0 13.965 * [backup-simplify]: Simplify (+ 0 0) into 0 13.965 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 13.966 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.967 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 13.968 * [backup-simplify]: Simplify (* (exp (* -0.25 (* (log n) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.968 * [taylor]: Taking taylor expansion of 0 in k 13.968 * [backup-simplify]: Simplify 0 into 0 13.969 * [backup-simplify]: Simplify 0 into 0 13.969 * [backup-simplify]: Simplify (exp (* -0.25 (* (log (/ 1 n)) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* -0.25 (* (- 1.0 k) (log (/ 1 n))))) 13.969 * [backup-simplify]: Simplify (pow (/ 1 (- n)) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (/ -1 n) (* 0.25 (+ (/ 1 k) 1.0))) 13.969 * [approximate]: Taking taylor expansion of (pow (/ -1 n) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 13.969 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 0.25 (+ (/ 1 k) 1.0))) in k 13.969 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) in k 13.969 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (/ -1 n))) in k 13.969 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 13.969 * [taylor]: Taking taylor expansion of 0.25 in k 13.969 * [backup-simplify]: Simplify 0.25 into 0.25 13.969 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.969 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.969 * [taylor]: Taking taylor expansion of k in k 13.970 * [backup-simplify]: Simplify 0 into 0 13.970 * [backup-simplify]: Simplify 1 into 1 13.970 * [backup-simplify]: Simplify (/ 1 1) into 1 13.970 * [taylor]: Taking taylor expansion of 1.0 in k 13.970 * [backup-simplify]: Simplify 1.0 into 1.0 13.970 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k 13.970 * [taylor]: Taking taylor expansion of (/ -1 n) in k 13.970 * [taylor]: Taking taylor expansion of -1 in k 13.970 * [backup-simplify]: Simplify -1 into -1 13.970 * [taylor]: Taking taylor expansion of n in k 13.970 * [backup-simplify]: Simplify n into n 13.970 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n) 13.970 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n)) 13.971 * [backup-simplify]: Simplify (+ 1 0) into 1 13.971 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 13.971 * [backup-simplify]: Simplify (* 0.25 (log (/ -1 n))) into (* 0.25 (log (/ -1 n))) 13.972 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (/ -1 n))))) 13.972 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 0.25 (+ (/ 1 k) 1.0))) in n 13.972 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) in n 13.972 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (/ -1 n))) in n 13.972 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 13.972 * [taylor]: Taking taylor expansion of 0.25 in n 13.972 * [backup-simplify]: Simplify 0.25 into 0.25 13.972 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 13.972 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.972 * [taylor]: Taking taylor expansion of k in n 13.972 * [backup-simplify]: Simplify k into k 13.972 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.972 * [taylor]: Taking taylor expansion of 1.0 in n 13.972 * [backup-simplify]: Simplify 1.0 into 1.0 13.972 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 13.972 * [taylor]: Taking taylor expansion of (/ -1 n) in n 13.972 * [taylor]: Taking taylor expansion of -1 in n 13.972 * [backup-simplify]: Simplify -1 into -1 13.972 * [taylor]: Taking taylor expansion of n in n 13.972 * [backup-simplify]: Simplify 0 into 0 13.972 * [backup-simplify]: Simplify 1 into 1 13.973 * [backup-simplify]: Simplify (/ -1 1) into -1 13.973 * [backup-simplify]: Simplify (log -1) into (log -1) 13.973 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 13.973 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 13.974 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 13.975 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log -1) (log n))) into (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0))) 13.975 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 13.975 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 0.25 (+ (/ 1 k) 1.0))) in n 13.976 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) in n 13.976 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (/ -1 n))) in n 13.976 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 13.976 * [taylor]: Taking taylor expansion of 0.25 in n 13.976 * [backup-simplify]: Simplify 0.25 into 0.25 13.976 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 13.976 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.976 * [taylor]: Taking taylor expansion of k in n 13.976 * [backup-simplify]: Simplify k into k 13.976 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.976 * [taylor]: Taking taylor expansion of 1.0 in n 13.976 * [backup-simplify]: Simplify 1.0 into 1.0 13.976 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 13.976 * [taylor]: Taking taylor expansion of (/ -1 n) in n 13.976 * [taylor]: Taking taylor expansion of -1 in n 13.976 * [backup-simplify]: Simplify -1 into -1 13.976 * [taylor]: Taking taylor expansion of n in n 13.976 * [backup-simplify]: Simplify 0 into 0 13.976 * [backup-simplify]: Simplify 1 into 1 13.977 * [backup-simplify]: Simplify (/ -1 1) into -1 13.977 * [backup-simplify]: Simplify (log -1) into (log -1) 13.977 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 13.977 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 13.978 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 13.979 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log -1) (log n))) into (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0))) 13.979 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 13.979 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) in k 13.980 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0))) in k 13.980 * [taylor]: Taking taylor expansion of 0.25 in k 13.980 * [backup-simplify]: Simplify 0.25 into 0.25 13.980 * [taylor]: Taking taylor expansion of (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)) in k 13.980 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k 13.980 * [taylor]: Taking taylor expansion of (log -1) in k 13.980 * [taylor]: Taking taylor expansion of -1 in k 13.980 * [backup-simplify]: Simplify -1 into -1 13.980 * [backup-simplify]: Simplify (log -1) into (log -1) 13.980 * [taylor]: Taking taylor expansion of (log n) in k 13.980 * [taylor]: Taking taylor expansion of n in k 13.980 * [backup-simplify]: Simplify n into n 13.980 * [backup-simplify]: Simplify (log n) into (log n) 13.980 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.980 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.980 * [taylor]: Taking taylor expansion of k in k 13.980 * [backup-simplify]: Simplify 0 into 0 13.980 * [backup-simplify]: Simplify 1 into 1 13.981 * [backup-simplify]: Simplify (/ 1 1) into 1 13.981 * [taylor]: Taking taylor expansion of 1.0 in k 13.981 * [backup-simplify]: Simplify 1.0 into 1.0 13.981 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.981 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n)) 13.982 * [backup-simplify]: Simplify (+ 1 0) into 1 13.982 * [backup-simplify]: Simplify (* (- (log -1) (log n)) 1) into (- (log -1) (log n)) 13.983 * [backup-simplify]: Simplify (* 0.25 (- (log -1) (log n))) into (* 0.25 (- (log -1) (log n))) 13.983 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 13.984 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 13.985 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 13.986 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 13.986 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.987 * [backup-simplify]: Simplify (+ 0 0) into 0 13.987 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 13.988 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 13.989 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log -1) (log n)))) into 0 13.990 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 13.990 * [taylor]: Taking taylor expansion of 0 in k 13.990 * [backup-simplify]: Simplify 0 into 0 13.990 * [backup-simplify]: Simplify 0 into 0 13.990 * [backup-simplify]: Simplify 0 into 0 13.991 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.994 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0 13.994 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.994 * [backup-simplify]: Simplify (+ 0 0) into 0 13.995 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 13.995 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 13.996 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0 13.997 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.997 * [taylor]: Taking taylor expansion of 0 in k 13.997 * [backup-simplify]: Simplify 0 into 0 13.997 * [backup-simplify]: Simplify 0 into 0 13.997 * [backup-simplify]: Simplify 0 into 0 13.997 * [backup-simplify]: Simplify 0 into 0 13.998 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.001 * [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 14.001 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 14.001 * [backup-simplify]: Simplify (+ 0 0) into 0 14.002 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 14.003 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 14.003 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -1) (log n)))))) into 0 14.005 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 14.005 * [taylor]: Taking taylor expansion of 0 in k 14.005 * [backup-simplify]: Simplify 0 into 0 14.005 * [backup-simplify]: Simplify 0 into 0 14.005 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log -1) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.25 (* (- 1.0 k) (- (log -1) (log (/ -1 n)))))) 14.005 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 14.005 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 14.005 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 14.005 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 14.005 * [taylor]: Taking taylor expansion of 1.0 in k 14.005 * [backup-simplify]: Simplify 1.0 into 1.0 14.006 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 14.006 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.006 * [taylor]: Taking taylor expansion of k in k 14.006 * [backup-simplify]: Simplify 0 into 0 14.006 * [backup-simplify]: Simplify 1 into 1 14.006 * [backup-simplify]: Simplify (/ 1 1) into 1 14.006 * [backup-simplify]: Simplify (sqrt 0) into 0 14.007 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.007 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 14.007 * [taylor]: Taking taylor expansion of 1.0 in k 14.007 * [backup-simplify]: Simplify 1.0 into 1.0 14.007 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 14.007 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.007 * [taylor]: Taking taylor expansion of k in k 14.007 * [backup-simplify]: Simplify 0 into 0 14.007 * [backup-simplify]: Simplify 1 into 1 14.007 * [backup-simplify]: Simplify (/ 1 1) into 1 14.008 * [backup-simplify]: Simplify (sqrt 0) into 0 14.008 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.009 * [backup-simplify]: Simplify (* 1.0 0) into 0 14.009 * [backup-simplify]: Simplify 0 into 0 14.010 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 14.010 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.010 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 14.012 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 14.013 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 14.014 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.014 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.017 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 14.018 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 14.018 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.019 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 14.019 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 14.019 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 14.019 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 14.020 * [taylor]: Taking taylor expansion of 1.0 in k 14.020 * [backup-simplify]: Simplify 1.0 into 1.0 14.020 * [taylor]: Taking taylor expansion of (sqrt k) in k 14.020 * [taylor]: Taking taylor expansion of k in k 14.020 * [backup-simplify]: Simplify 0 into 0 14.020 * [backup-simplify]: Simplify 1 into 1 14.020 * [backup-simplify]: Simplify (sqrt 0) into 0 14.021 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.021 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 14.021 * [taylor]: Taking taylor expansion of 1.0 in k 14.021 * [backup-simplify]: Simplify 1.0 into 1.0 14.021 * [taylor]: Taking taylor expansion of (sqrt k) in k 14.021 * [taylor]: Taking taylor expansion of k in k 14.021 * [backup-simplify]: Simplify 0 into 0 14.021 * [backup-simplify]: Simplify 1 into 1 14.021 * [backup-simplify]: Simplify (sqrt 0) into 0 14.022 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.023 * [backup-simplify]: Simplify (* 1.0 0) into 0 14.023 * [backup-simplify]: Simplify 0 into 0 14.024 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 14.024 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.026 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 14.027 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 14.027 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.029 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 14.031 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 14.031 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.032 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 14.032 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 14.032 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 14.032 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 14.032 * [taylor]: Taking taylor expansion of 1.0 in k 14.032 * [backup-simplify]: Simplify 1.0 into 1.0 14.032 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 14.032 * [taylor]: Taking taylor expansion of (/ -1 k) in k 14.032 * [taylor]: Taking taylor expansion of -1 in k 14.032 * [backup-simplify]: Simplify -1 into -1 14.032 * [taylor]: Taking taylor expansion of k in k 14.032 * [backup-simplify]: Simplify 0 into 0 14.032 * [backup-simplify]: Simplify 1 into 1 14.032 * [backup-simplify]: Simplify (/ -1 1) into -1 14.033 * [backup-simplify]: Simplify (sqrt 0) into 0 14.033 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 14.034 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 14.034 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 14.034 * [taylor]: Taking taylor expansion of 1.0 in k 14.034 * [backup-simplify]: Simplify 1.0 into 1.0 14.034 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 14.034 * [taylor]: Taking taylor expansion of (/ -1 k) in k 14.034 * [taylor]: Taking taylor expansion of -1 in k 14.034 * [backup-simplify]: Simplify -1 into -1 14.034 * [taylor]: Taking taylor expansion of k in k 14.034 * [backup-simplify]: Simplify 0 into 0 14.034 * [backup-simplify]: Simplify 1 into 1 14.034 * [backup-simplify]: Simplify (/ -1 1) into -1 14.034 * [backup-simplify]: Simplify (sqrt 0) into 0 14.035 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 14.036 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 14.036 * [backup-simplify]: Simplify +nan.0 into +nan.0 14.036 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 14.038 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 14.039 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 14.040 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.040 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.042 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 14.045 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 14.045 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.046 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 14.046 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 2 1) 14.046 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 14.046 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 14.046 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 14.046 * [taylor]: Taking taylor expansion of 2.0 in n 14.046 * [backup-simplify]: Simplify 2.0 into 2.0 14.046 * [taylor]: Taking taylor expansion of (* n PI) in n 14.046 * [taylor]: Taking taylor expansion of n in n 14.046 * [backup-simplify]: Simplify 0 into 0 14.046 * [backup-simplify]: Simplify 1 into 1 14.046 * [taylor]: Taking taylor expansion of PI in n 14.046 * [backup-simplify]: Simplify PI into PI 14.046 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 14.046 * [taylor]: Taking taylor expansion of 2.0 in n 14.046 * [backup-simplify]: Simplify 2.0 into 2.0 14.046 * [taylor]: Taking taylor expansion of (* n PI) in n 14.046 * [taylor]: Taking taylor expansion of n in n 14.046 * [backup-simplify]: Simplify 0 into 0 14.046 * [backup-simplify]: Simplify 1 into 1 14.046 * [taylor]: Taking taylor expansion of PI in n 14.047 * [backup-simplify]: Simplify PI into PI 14.047 * [backup-simplify]: Simplify (* 0 PI) into 0 14.047 * [backup-simplify]: Simplify (* 2.0 0) into 0 14.047 * [backup-simplify]: Simplify 0 into 0 14.048 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 14.049 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 14.049 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.050 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 14.050 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 14.050 * [backup-simplify]: Simplify 0 into 0 14.051 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 14.052 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 14.052 * [backup-simplify]: Simplify 0 into 0 14.053 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 14.053 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 14.053 * [backup-simplify]: Simplify 0 into 0 14.055 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 14.065 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 14.065 * [backup-simplify]: Simplify 0 into 0 14.067 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 14.069 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 14.069 * [backup-simplify]: Simplify 0 into 0 14.071 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 14.073 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 14.073 * [backup-simplify]: Simplify 0 into 0 14.074 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 14.074 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 14.074 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 14.074 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 14.074 * [taylor]: Taking taylor expansion of 2.0 in n 14.075 * [backup-simplify]: Simplify 2.0 into 2.0 14.075 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.075 * [taylor]: Taking taylor expansion of PI in n 14.075 * [backup-simplify]: Simplify PI into PI 14.075 * [taylor]: Taking taylor expansion of n in n 14.075 * [backup-simplify]: Simplify 0 into 0 14.075 * [backup-simplify]: Simplify 1 into 1 14.075 * [backup-simplify]: Simplify (/ PI 1) into PI 14.075 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 14.075 * [taylor]: Taking taylor expansion of 2.0 in n 14.075 * [backup-simplify]: Simplify 2.0 into 2.0 14.075 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.075 * [taylor]: Taking taylor expansion of PI in n 14.075 * [backup-simplify]: Simplify PI into PI 14.075 * [taylor]: Taking taylor expansion of n in n 14.075 * [backup-simplify]: Simplify 0 into 0 14.075 * [backup-simplify]: Simplify 1 into 1 14.076 * [backup-simplify]: Simplify (/ PI 1) into PI 14.076 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.077 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.078 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 14.078 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 14.079 * [backup-simplify]: Simplify 0 into 0 14.080 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.081 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 14.081 * [backup-simplify]: Simplify 0 into 0 14.082 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.083 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 14.083 * [backup-simplify]: Simplify 0 into 0 14.084 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.085 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 14.085 * [backup-simplify]: Simplify 0 into 0 14.086 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.088 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 14.088 * [backup-simplify]: Simplify 0 into 0 14.089 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.090 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 14.090 * [backup-simplify]: Simplify 0 into 0 14.091 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 14.092 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 14.092 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 14.092 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 14.092 * [taylor]: Taking taylor expansion of -2.0 in n 14.092 * [backup-simplify]: Simplify -2.0 into -2.0 14.092 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.092 * [taylor]: Taking taylor expansion of PI in n 14.092 * [backup-simplify]: Simplify PI into PI 14.092 * [taylor]: Taking taylor expansion of n in n 14.092 * [backup-simplify]: Simplify 0 into 0 14.092 * [backup-simplify]: Simplify 1 into 1 14.092 * [backup-simplify]: Simplify (/ PI 1) into PI 14.092 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 14.092 * [taylor]: Taking taylor expansion of -2.0 in n 14.093 * [backup-simplify]: Simplify -2.0 into -2.0 14.093 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.093 * [taylor]: Taking taylor expansion of PI in n 14.093 * [backup-simplify]: Simplify PI into PI 14.093 * [taylor]: Taking taylor expansion of n in n 14.093 * [backup-simplify]: Simplify 0 into 0 14.093 * [backup-simplify]: Simplify 1 into 1 14.093 * [backup-simplify]: Simplify (/ PI 1) into PI 14.094 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 14.094 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 14.095 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 14.096 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 14.096 * [backup-simplify]: Simplify 0 into 0 14.097 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.098 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 14.098 * [backup-simplify]: Simplify 0 into 0 14.099 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.100 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 14.100 * [backup-simplify]: Simplify 0 into 0 14.101 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.102 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 14.103 * [backup-simplify]: Simplify 0 into 0 14.104 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.105 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 14.105 * [backup-simplify]: Simplify 0 into 0 14.106 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.108 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 14.108 * [backup-simplify]: Simplify 0 into 0 14.108 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 14.109 * * * [progress]: simplifying candidates 14.115 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (expm1 (pow n (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow n (/ (/ (- 1.0 k) 2.0) 2))) (* (log n) (/ (/ (- 1.0 k) 2.0) 2)) (* (log n) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ 1.0 2.0) 2)) (pow n (/ (/ k 2.0) 2)) (pow n (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow n (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow n (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow n (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow n (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 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1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (* (pow k 2) (pow (log n) 2)) (pow (pow n 1.0) 0.25))) (pow n 0.25)) (* 0.25 (* (* k (log n)) (pow (pow n 1.0) 0.25)))) (exp (* -0.25 (* (- 1.0 k) (log (/ 1 n))))) (exp (* 0.25 (* (- 1.0 k) (- (log -1) (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)) 14.126 * * [simplify]: Extracting # 0 : cost 0 14.126 * * [simplify]: Extracting # 1 : cost 0 14.128 * * [simplify]: Extracting # 2 : cost 0 14.129 * * [simplify]: Extracting # 3 : cost 0 14.130 * * [simplify]: Extracting # 4 : cost 0 14.131 * * [simplify]: Extracting # 5 : cost 0 14.133 * * [simplify]: Extracting # 6 : cost 0 14.134 * * [simplify]: Extracting # 7 : cost 0 14.135 * * [simplify]: Extracting # 8 : cost 0 14.137 * * [simplify]: Extracting # 9 : cost 0 14.138 * * [simplify]: Extracting # 10 : cost 0 14.139 * * [simplify]: Extracting # 11 : cost 0 14.140 * * [simplify]: Extracting # 12 : cost 0 14.142 * * [simplify]: Extracting # 13 : cost 0 14.143 * * [simplify]: Extracting # 14 : cost 0 14.145 * * [simplify]: iteration 0 : 421 enodes (cost 3171 ) 14.423 * * [simplify]: Extracting # 0 : cost 0 14.425 * * [simplify]: Extracting # 1 : cost 0 14.427 * * [simplify]: Extracting # 2 : cost 0 14.429 * * [simplify]: Extracting # 3 : cost 0 14.431 * * [simplify]: Extracting # 4 : cost 0 14.433 * * [simplify]: Extracting # 5 : cost 0 14.436 * * [simplify]: iteration 1 : 1322 enodes (cost 2913 ) 14.908 * * [simplify]: Extracting # 0 : cost 0 14.914 * * [simplify]: Extracting # 1 : cost 0 14.921 * * [simplify]: Extracting # 2 : cost 0 14.929 * * [simplify]: Extracting # 3 : cost 0 14.940 * * [simplify]: Extracting # 4 : cost 0 14.961 * * [simplify]: iteration done: 5001 enodes (cost 2825 ) 14.964 * [simplify]: Simplified to: (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (/ (/ (- 1.0 k) 2.0) 2) (/ (/ (- 1.0 k) 2.0) 2) (/ (/ (- 1.0 k) 2.0) 2) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) 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(+ (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))) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* 2.0 PI) n) (- 1.0 k)) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 4)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 4)) (expm1 (pow n (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow n (/ (/ (- 1.0 k) 2.0) 2))) (* (log n) (/ (/ (- 1.0 k) 2.0) 2)) (* (log n) (/ (/ (- 1.0 k) 2.0) 2)) (/ (/ (- 1.0 k) 2.0) 2) (pow n (/ (/ 1.0 2.0) 2)) (pow n (/ (/ k 2.0) 2)) (pow n (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow n (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow n (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow n (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow n (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow n (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow n (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow n (sqrt (/ (- 1.0 k) 2.0))) (pow n (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow n (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow n (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow n (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow n (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow n (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2) (cbrt 2)))) (pow n (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2))) (pow n (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow n (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow n (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow n (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow n (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow n (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow n (/ (sqrt (- 1.0 k)) (* (cbrt 2) (cbrt 2)))) (pow n (/ (sqrt (- 1.0 k)) (sqrt 2))) (pow n (sqrt (- 1.0 k))) (pow n (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow n (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow n (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow n (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow n (/ 1 (sqrt 2.0))) (pow n (/ 1 (* (cbrt 2) (cbrt 2)))) (pow n (/ 1 (sqrt 2))) n (pow n (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow n (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow n (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow n (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow n (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow n (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow n (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2))) (pow n (+ (sqrt 1.0) (sqrt k))) (pow n (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow n (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow n (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow n (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow n (/ 1 (sqrt 2.0))) (pow n (/ 1 (* (cbrt 2) (cbrt 2)))) (pow n (/ 1 (sqrt 2))) n (pow n (/ 1 (* (cbrt 2) (cbrt 2)))) (pow n (/ 1 (sqrt 2))) n (pow n (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow n (/ (- 1.0 k) (sqrt 2))) (pow n (- 1.0 k)) n (pow n (/ (- 1.0 k) 2.0)) (pow (* (cbrt n) (cbrt n)) (/ (/ (- 1.0 k) 2.0) 2)) (pow (cbrt n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (sqrt n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (sqrt n) (/ (/ (- 1.0 k) 2.0) 2)) 1 (pow n (/ (/ (- 1.0 k) 2.0) 2)) (log (pow n (/ (/ (- 1.0 k) 2.0) 2))) (exp (pow n (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow n (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow n (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow n (/ (/ (- 1.0 k) 2.0) 2))) (pow (pow n (/ (/ (- 1.0 k) 2.0) 2)) 3) (sqrt (pow n (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow n (/ (/ (- 1.0 k) 2.0) 2))) (pow n (/ (/ (- 1.0 k) 2.0) 4)) (pow n (/ (/ (- 1.0 k) 2.0) 4)) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (/ (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) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (pow 2.0 3) (* (pow PI 3) (pow n 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) (* PI n) (+ (fma (* 0.03125 (pow k 2)) (* (pow (* (* 2.0 PI) n) 0.25) (pow (log (* 2.0 PI)) 2)) (pow (* (* 2.0 PI) n) 0.25)) (- (fma (* 0.0625 (pow k 2)) (* (* (pow (* (* 2.0 PI) n) 0.25) (log n)) (log (* 2.0 PI))) (* (* 0.03125 (* (pow k 2) (pow (* (* 2.0 PI) n) 0.25))) (pow (log n) 2))) (* 0.25 (* k (+ (* (pow (* (* 2.0 PI) n) 0.25) (log (* 2.0 PI))) (* (pow (* (* 2.0 PI) n) 0.25) (log n))))))) (pow (pow (* (* 2.0 PI) n) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (fma 0.03125 (* (* (pow k 2) (pow (log n) 2)) (pow (pow n 1.0) 0.25)) (pow n 0.25)) (* 0.25 (* (* k (log n)) (pow (pow n 1.0) 0.25)))) (exp (* -0.25 (* (- (log n)) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log -1) (log (/ -1 n)))))) (- (fma +nan.0 k (- (fma +nan.0 (pow k 2) (- +nan.0))))) (- (- (/ +nan.0 (pow k 2)) (- (/ +nan.0 k) (/ +nan.0 (pow k 3))))) (+ (- (/ +nan.0 k) +nan.0) (- (/ +nan.0 (pow k 2)))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 14.967 * * * [progress]: adding candidates to table 16.517 * [progress]: [Phase 3 of 3] Extracting. 16.518 * * [regime]: Finding splitpoints for: (# # # # # # #) 16.524 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 16.524 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # #) 16.576 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # #) 16.616 * * * * [regimes]: Trying to branch on n from (# # # # # # #) 16.680 * * * * [regimes]: Trying to branch on k from (# # # # # # #) 16.746 * * * [regime]: Found split indices: #