52.177 * [progress]: [Phase 1 of 3] Setting up. 0.002 * * * [progress]: [1/2] Preparing points 0.220 * * * [progress]: [2/2] Setting up program. 0.225 * [progress]: [Phase 2 of 3] Improving. 0.226 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.226 * * [simplify]: Extracting # 0 : cost 0 0.226 * * [simplify]: Extracting # 1 : cost 0 0.226 * * [simplify]: Extracting # 2 : cost 0 0.226 * * [simplify]: Extracting # 3 : cost 0 0.226 * * [simplify]: Extracting # 4 : cost 0 0.226 * * [simplify]: Extracting # 5 : cost 0 0.226 * * [simplify]: Extracting # 6 : cost 0 0.227 * * [simplify]: Extracting # 7 : cost 0 0.227 * * [simplify]: iteration 0 : 13 enodes (cost 16 ) 0.233 * * [simplify]: Extracting # 0 : cost 0 0.233 * * [simplify]: Extracting # 1 : cost 0 0.233 * * [simplify]: Extracting # 2 : cost 0 0.233 * * [simplify]: Extracting # 3 : cost 0 0.233 * * [simplify]: Extracting # 4 : cost 0 0.234 * * [simplify]: Extracting # 5 : cost 0 0.234 * * [simplify]: iteration 1 : 29 enodes (cost 16 ) 0.246 * * [simplify]: Extracting # 0 : cost 0 0.246 * * [simplify]: Extracting # 1 : cost 0 0.246 * * [simplify]: Extracting # 2 : cost 0 0.247 * * [simplify]: Extracting # 3 : cost 0 0.247 * * [simplify]: Extracting # 4 : cost 0 0.247 * * [simplify]: iteration 2 : 59 enodes (cost 16 ) 0.272 * * [simplify]: Extracting # 0 : cost 0 0.272 * * [simplify]: Extracting # 1 : cost 0 0.272 * * [simplify]: Extracting # 2 : cost 0 0.273 * * [simplify]: Extracting # 3 : cost 0 0.273 * * [simplify]: Extracting # 4 : cost 0 0.273 * * [simplify]: iteration 3 : 120 enodes (cost 16 ) 0.351 * * [simplify]: Extracting # 0 : cost 0 0.352 * * [simplify]: Extracting # 1 : cost 0 0.352 * * [simplify]: Extracting # 2 : cost 0 0.353 * * [simplify]: Extracting # 3 : cost 0 0.355 * * [simplify]: Extracting # 4 : cost 0 0.356 * * [simplify]: iteration 4 : 330 enodes (cost 16 ) 0.632 * * [simplify]: Extracting # 0 : cost 0 0.635 * * [simplify]: Extracting # 1 : cost 0 0.638 * * [simplify]: Extracting # 2 : cost 0 0.641 * * [simplify]: Extracting # 3 : cost 0 0.643 * * [simplify]: Extracting # 4 : cost 0 0.647 * * [simplify]: Extracting # 5 : cost 0 0.649 * * [simplify]: iteration 5 : 1555 enodes (cost 16 ) 1.530 * * [simplify]: Extracting # 0 : cost 0 1.572 * * [simplify]: Extracting # 1 : cost 0 1.578 * * [simplify]: Extracting # 2 : cost 0 1.585 * * [simplify]: Extracting # 3 : cost 0 1.597 * * [simplify]: Extracting # 4 : cost 0 1.609 * * [simplify]: iteration done: 5001 enodes (cost 16 ) 1.609 * [simplify]: Simplified to: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1.610 * * [progress]: iteration 1 / 4 1.610 * * * [progress]: picking best candidate 1.619 * * * * [pick]: Picked # 1.619 * * * [progress]: localizing error 1.652 * * * [progress]: generating rewritten candidates 1.652 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 1.699 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 1.713 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 1.751 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 1.830 * * * [progress]: generating series expansions 1.830 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 1.831 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 1.831 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 1.831 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.831 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.831 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.831 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.831 * [taylor]: Taking taylor expansion of 0.5 in k 1.831 * [backup-simplify]: Simplify 0.5 into 0.5 1.831 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.832 * [taylor]: Taking taylor expansion of 1.0 in k 1.832 * [backup-simplify]: Simplify 1.0 into 1.0 1.832 * [taylor]: Taking taylor expansion of k in k 1.832 * [backup-simplify]: Simplify 0 into 0 1.832 * [backup-simplify]: Simplify 1 into 1 1.832 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.832 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.832 * [taylor]: Taking taylor expansion of 2.0 in k 1.832 * [backup-simplify]: Simplify 2.0 into 2.0 1.832 * [taylor]: Taking taylor expansion of (* n PI) in k 1.832 * [taylor]: Taking taylor expansion of n in k 1.832 * [backup-simplify]: Simplify n into n 1.832 * [taylor]: Taking taylor expansion of PI in k 1.832 * [backup-simplify]: Simplify PI into PI 1.832 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.832 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.832 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.833 * [backup-simplify]: Simplify (- 0) into 0 1.833 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.834 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 1.834 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 1.834 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 1.834 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.834 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.834 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.834 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.834 * [taylor]: Taking taylor expansion of 0.5 in n 1.834 * [backup-simplify]: Simplify 0.5 into 0.5 1.834 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.834 * [taylor]: Taking taylor expansion of 1.0 in n 1.834 * [backup-simplify]: Simplify 1.0 into 1.0 1.834 * [taylor]: Taking taylor expansion of k in n 1.834 * [backup-simplify]: Simplify k into k 1.834 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.834 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.834 * [taylor]: Taking taylor expansion of 2.0 in n 1.834 * [backup-simplify]: Simplify 2.0 into 2.0 1.834 * [taylor]: Taking taylor expansion of (* n PI) in n 1.834 * [taylor]: Taking taylor expansion of n in n 1.835 * [backup-simplify]: Simplify 0 into 0 1.835 * [backup-simplify]: Simplify 1 into 1 1.835 * [taylor]: Taking taylor expansion of PI in n 1.835 * [backup-simplify]: Simplify PI into PI 1.835 * [backup-simplify]: Simplify (* 0 PI) into 0 1.836 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.837 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.839 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.840 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.840 * [backup-simplify]: Simplify (- k) into (- k) 1.840 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.840 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.842 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.843 * [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)))) 1.844 * [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))))) 1.844 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.844 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.844 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.844 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.844 * [taylor]: Taking taylor expansion of 0.5 in n 1.845 * [backup-simplify]: Simplify 0.5 into 0.5 1.845 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.845 * [taylor]: Taking taylor expansion of 1.0 in n 1.845 * [backup-simplify]: Simplify 1.0 into 1.0 1.845 * [taylor]: Taking taylor expansion of k in n 1.845 * [backup-simplify]: Simplify k into k 1.845 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.845 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.845 * [taylor]: Taking taylor expansion of 2.0 in n 1.845 * [backup-simplify]: Simplify 2.0 into 2.0 1.845 * [taylor]: Taking taylor expansion of (* n PI) in n 1.845 * [taylor]: Taking taylor expansion of n in n 1.845 * [backup-simplify]: Simplify 0 into 0 1.845 * [backup-simplify]: Simplify 1 into 1 1.845 * [taylor]: Taking taylor expansion of PI in n 1.845 * [backup-simplify]: Simplify PI into PI 1.845 * [backup-simplify]: Simplify (* 0 PI) into 0 1.846 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.847 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.849 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.850 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.850 * [backup-simplify]: Simplify (- k) into (- k) 1.850 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.850 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.851 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.853 * [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)))) 1.854 * [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))))) 1.854 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.854 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.854 * [taylor]: Taking taylor expansion of 0.5 in k 1.854 * [backup-simplify]: Simplify 0.5 into 0.5 1.854 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.854 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.854 * [taylor]: Taking taylor expansion of 1.0 in k 1.854 * [backup-simplify]: Simplify 1.0 into 1.0 1.854 * [taylor]: Taking taylor expansion of k in k 1.854 * [backup-simplify]: Simplify 0 into 0 1.854 * [backup-simplify]: Simplify 1 into 1 1.854 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.854 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.854 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.854 * [taylor]: Taking taylor expansion of 2.0 in k 1.854 * [backup-simplify]: Simplify 2.0 into 2.0 1.854 * [taylor]: Taking taylor expansion of PI in k 1.854 * [backup-simplify]: Simplify PI into PI 1.855 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.856 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.856 * [taylor]: Taking taylor expansion of (log n) in k 1.856 * [taylor]: Taking taylor expansion of n in k 1.856 * [backup-simplify]: Simplify n into n 1.856 * [backup-simplify]: Simplify (log n) into (log n) 1.856 * [backup-simplify]: Simplify (- 0) into 0 1.857 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.858 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 1.859 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 1.860 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 1.861 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.863 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.864 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.865 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.867 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.867 * [backup-simplify]: Simplify (- 0) into 0 1.867 * [backup-simplify]: Simplify (+ 0 0) into 0 1.868 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 1.869 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.870 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 1.872 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.872 * [taylor]: Taking taylor expansion of 0 in k 1.872 * [backup-simplify]: Simplify 0 into 0 1.872 * [backup-simplify]: Simplify 0 into 0 1.878 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.880 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.880 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.881 * [backup-simplify]: Simplify (+ 0 0) into 0 1.881 * [backup-simplify]: Simplify (- 1) into -1 1.881 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.882 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 1.884 * [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)))) 1.885 * [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)))))) 1.887 * [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)))))) 1.888 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.889 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.891 * [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 1.891 * [backup-simplify]: Simplify (- 0) into 0 1.892 * [backup-simplify]: Simplify (+ 0 0) into 0 1.892 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 1.893 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.894 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.896 * [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 1.896 * [taylor]: Taking taylor expansion of 0 in k 1.896 * [backup-simplify]: Simplify 0 into 0 1.896 * [backup-simplify]: Simplify 0 into 0 1.896 * [backup-simplify]: Simplify 0 into 0 1.896 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.898 * [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 1.900 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.900 * [backup-simplify]: Simplify (+ 0 0) into 0 1.900 * [backup-simplify]: Simplify (- 0) into 0 1.900 * [backup-simplify]: Simplify (+ 0 0) into 0 1.901 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.903 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 1.905 * [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)))))) 1.909 * [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)))))) 1.915 * [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)))))) 1.916 * [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)))) 1.916 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 1.916 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.916 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.916 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.916 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.916 * [taylor]: Taking taylor expansion of 0.5 in k 1.916 * [backup-simplify]: Simplify 0.5 into 0.5 1.916 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.916 * [taylor]: Taking taylor expansion of 1.0 in k 1.916 * [backup-simplify]: Simplify 1.0 into 1.0 1.916 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.916 * [taylor]: Taking taylor expansion of k in k 1.916 * [backup-simplify]: Simplify 0 into 0 1.916 * [backup-simplify]: Simplify 1 into 1 1.916 * [backup-simplify]: Simplify (/ 1 1) into 1 1.916 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.917 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.917 * [taylor]: Taking taylor expansion of 2.0 in k 1.917 * [backup-simplify]: Simplify 2.0 into 2.0 1.917 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.917 * [taylor]: Taking taylor expansion of PI in k 1.917 * [backup-simplify]: Simplify PI into PI 1.917 * [taylor]: Taking taylor expansion of n in k 1.917 * [backup-simplify]: Simplify n into n 1.917 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.917 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.917 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.917 * [backup-simplify]: Simplify (- 1) into -1 1.917 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.918 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 1.918 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 1.918 * [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))))) 1.918 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.918 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.918 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.918 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.918 * [taylor]: Taking taylor expansion of 0.5 in n 1.918 * [backup-simplify]: Simplify 0.5 into 0.5 1.918 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.918 * [taylor]: Taking taylor expansion of 1.0 in n 1.918 * [backup-simplify]: Simplify 1.0 into 1.0 1.918 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.918 * [taylor]: Taking taylor expansion of k in n 1.918 * [backup-simplify]: Simplify k into k 1.918 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.918 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.918 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.918 * [taylor]: Taking taylor expansion of 2.0 in n 1.918 * [backup-simplify]: Simplify 2.0 into 2.0 1.918 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.918 * [taylor]: Taking taylor expansion of PI in n 1.918 * [backup-simplify]: Simplify PI into PI 1.918 * [taylor]: Taking taylor expansion of n in n 1.918 * [backup-simplify]: Simplify 0 into 0 1.918 * [backup-simplify]: Simplify 1 into 1 1.919 * [backup-simplify]: Simplify (/ PI 1) into PI 1.919 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.920 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.920 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.920 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.920 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.921 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.921 * [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)))) 1.922 * [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))))) 1.922 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.922 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.922 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.922 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.922 * [taylor]: Taking taylor expansion of 0.5 in n 1.922 * [backup-simplify]: Simplify 0.5 into 0.5 1.922 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.922 * [taylor]: Taking taylor expansion of 1.0 in n 1.922 * [backup-simplify]: Simplify 1.0 into 1.0 1.922 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.922 * [taylor]: Taking taylor expansion of k in n 1.922 * [backup-simplify]: Simplify k into k 1.923 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.923 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.923 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.923 * [taylor]: Taking taylor expansion of 2.0 in n 1.923 * [backup-simplify]: Simplify 2.0 into 2.0 1.923 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.923 * [taylor]: Taking taylor expansion of PI in n 1.923 * [backup-simplify]: Simplify PI into PI 1.923 * [taylor]: Taking taylor expansion of n in n 1.923 * [backup-simplify]: Simplify 0 into 0 1.923 * [backup-simplify]: Simplify 1 into 1 1.923 * [backup-simplify]: Simplify (/ PI 1) into PI 1.923 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.924 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.924 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.924 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.924 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.925 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.926 * [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)))) 1.926 * [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))))) 1.927 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.927 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.927 * [taylor]: Taking taylor expansion of 0.5 in k 1.927 * [backup-simplify]: Simplify 0.5 into 0.5 1.927 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.927 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.927 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.927 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.927 * [taylor]: Taking taylor expansion of 2.0 in k 1.927 * [backup-simplify]: Simplify 2.0 into 2.0 1.927 * [taylor]: Taking taylor expansion of PI in k 1.927 * [backup-simplify]: Simplify PI into PI 1.927 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.928 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.928 * [taylor]: Taking taylor expansion of (log n) in k 1.928 * [taylor]: Taking taylor expansion of n in k 1.928 * [backup-simplify]: Simplify n into n 1.928 * [backup-simplify]: Simplify (log n) into (log n) 1.928 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.928 * [taylor]: Taking taylor expansion of 1.0 in k 1.928 * [backup-simplify]: Simplify 1.0 into 1.0 1.928 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.928 * [taylor]: Taking taylor expansion of k in k 1.928 * [backup-simplify]: Simplify 0 into 0 1.928 * [backup-simplify]: Simplify 1 into 1 1.928 * [backup-simplify]: Simplify (/ 1 1) into 1 1.928 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.929 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 1.929 * [backup-simplify]: Simplify (- 1) into -1 1.929 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.930 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 1.931 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 1.932 * [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))))) 1.932 * [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))))) 1.933 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.933 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.934 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.935 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.935 * [backup-simplify]: Simplify (- 0) into 0 1.935 * [backup-simplify]: Simplify (+ 0 0) into 0 1.935 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 1.936 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.937 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 1.938 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.938 * [taylor]: Taking taylor expansion of 0 in k 1.938 * [backup-simplify]: Simplify 0 into 0 1.938 * [backup-simplify]: Simplify 0 into 0 1.938 * [backup-simplify]: Simplify 0 into 0 1.939 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.939 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.941 * [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 1.941 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.942 * [backup-simplify]: Simplify (- 0) into 0 1.942 * [backup-simplify]: Simplify (+ 0 0) into 0 1.942 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 1.943 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.944 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 1.946 * [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 1.946 * [taylor]: Taking taylor expansion of 0 in k 1.946 * [backup-simplify]: Simplify 0 into 0 1.946 * [backup-simplify]: Simplify 0 into 0 1.946 * [backup-simplify]: Simplify 0 into 0 1.946 * [backup-simplify]: Simplify 0 into 0 1.947 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.948 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.951 * [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 1.951 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.951 * [backup-simplify]: Simplify (- 0) into 0 1.952 * [backup-simplify]: Simplify (+ 0 0) into 0 1.953 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 1.954 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.955 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 1.956 * [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 1.957 * [taylor]: Taking taylor expansion of 0 in k 1.957 * [backup-simplify]: Simplify 0 into 0 1.957 * [backup-simplify]: Simplify 0 into 0 1.957 * [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)))) 1.958 * [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))) 1.958 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 1.958 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.958 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.958 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.958 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.958 * [taylor]: Taking taylor expansion of 0.5 in k 1.958 * [backup-simplify]: Simplify 0.5 into 0.5 1.958 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.958 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.958 * [taylor]: Taking taylor expansion of k in k 1.958 * [backup-simplify]: Simplify 0 into 0 1.958 * [backup-simplify]: Simplify 1 into 1 1.958 * [backup-simplify]: Simplify (/ 1 1) into 1 1.958 * [taylor]: Taking taylor expansion of 1.0 in k 1.958 * [backup-simplify]: Simplify 1.0 into 1.0 1.958 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.958 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.959 * [taylor]: Taking taylor expansion of -2.0 in k 1.959 * [backup-simplify]: Simplify -2.0 into -2.0 1.959 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.959 * [taylor]: Taking taylor expansion of PI in k 1.959 * [backup-simplify]: Simplify PI into PI 1.959 * [taylor]: Taking taylor expansion of n in k 1.959 * [backup-simplify]: Simplify n into n 1.959 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.959 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.959 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.959 * [backup-simplify]: Simplify (+ 1 0) into 1 1.959 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 1.959 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 1.960 * [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)))))) 1.960 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.960 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.960 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.960 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.960 * [taylor]: Taking taylor expansion of 0.5 in n 1.960 * [backup-simplify]: Simplify 0.5 into 0.5 1.960 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.960 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.960 * [taylor]: Taking taylor expansion of k in n 1.960 * [backup-simplify]: Simplify k into k 1.960 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.960 * [taylor]: Taking taylor expansion of 1.0 in n 1.960 * [backup-simplify]: Simplify 1.0 into 1.0 1.960 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.960 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.960 * [taylor]: Taking taylor expansion of -2.0 in n 1.960 * [backup-simplify]: Simplify -2.0 into -2.0 1.960 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.960 * [taylor]: Taking taylor expansion of PI in n 1.960 * [backup-simplify]: Simplify PI into PI 1.960 * [taylor]: Taking taylor expansion of n in n 1.960 * [backup-simplify]: Simplify 0 into 0 1.960 * [backup-simplify]: Simplify 1 into 1 1.960 * [backup-simplify]: Simplify (/ PI 1) into PI 1.961 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.961 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.961 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.961 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.962 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.963 * [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)))) 1.964 * [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))))) 1.964 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.964 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.964 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.964 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.964 * [taylor]: Taking taylor expansion of 0.5 in n 1.964 * [backup-simplify]: Simplify 0.5 into 0.5 1.964 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.964 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.964 * [taylor]: Taking taylor expansion of k in n 1.964 * [backup-simplify]: Simplify k into k 1.964 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.964 * [taylor]: Taking taylor expansion of 1.0 in n 1.964 * [backup-simplify]: Simplify 1.0 into 1.0 1.964 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.964 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.964 * [taylor]: Taking taylor expansion of -2.0 in n 1.964 * [backup-simplify]: Simplify -2.0 into -2.0 1.964 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.964 * [taylor]: Taking taylor expansion of PI in n 1.964 * [backup-simplify]: Simplify PI into PI 1.964 * [taylor]: Taking taylor expansion of n in n 1.964 * [backup-simplify]: Simplify 0 into 0 1.964 * [backup-simplify]: Simplify 1 into 1 1.965 * [backup-simplify]: Simplify (/ PI 1) into PI 1.965 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.966 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.966 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.966 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.967 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.967 * [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)))) 1.968 * [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))))) 1.968 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.968 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.968 * [taylor]: Taking taylor expansion of 0.5 in k 1.968 * [backup-simplify]: Simplify 0.5 into 0.5 1.968 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.968 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.968 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.968 * [taylor]: Taking taylor expansion of k in k 1.968 * [backup-simplify]: Simplify 0 into 0 1.968 * [backup-simplify]: Simplify 1 into 1 1.972 * [backup-simplify]: Simplify (/ 1 1) into 1 1.972 * [taylor]: Taking taylor expansion of 1.0 in k 1.972 * [backup-simplify]: Simplify 1.0 into 1.0 1.972 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.972 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.972 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.972 * [taylor]: Taking taylor expansion of -2.0 in k 1.972 * [backup-simplify]: Simplify -2.0 into -2.0 1.972 * [taylor]: Taking taylor expansion of PI in k 1.972 * [backup-simplify]: Simplify PI into PI 1.972 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.973 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.973 * [taylor]: Taking taylor expansion of (log n) in k 1.973 * [taylor]: Taking taylor expansion of n in k 1.973 * [backup-simplify]: Simplify n into n 1.973 * [backup-simplify]: Simplify (log n) into (log n) 1.974 * [backup-simplify]: Simplify (+ 1 0) into 1 1.974 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.974 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 1.975 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 1.976 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 1.977 * [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))))) 1.977 * [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))))) 1.978 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.978 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.979 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 1.979 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.980 * [backup-simplify]: Simplify (+ 0 0) into 0 1.980 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 1.981 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.982 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 1.983 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.983 * [taylor]: Taking taylor expansion of 0 in k 1.983 * [backup-simplify]: Simplify 0 into 0 1.983 * [backup-simplify]: Simplify 0 into 0 1.983 * [backup-simplify]: Simplify 0 into 0 1.983 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.984 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.986 * [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 1.986 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.986 * [backup-simplify]: Simplify (+ 0 0) into 0 1.987 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 1.988 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.989 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 1.990 * [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 1.990 * [taylor]: Taking taylor expansion of 0 in k 1.990 * [backup-simplify]: Simplify 0 into 0 1.990 * [backup-simplify]: Simplify 0 into 0 1.990 * [backup-simplify]: Simplify 0 into 0 1.990 * [backup-simplify]: Simplify 0 into 0 1.991 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.991 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.995 * [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 1.995 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.995 * [backup-simplify]: Simplify (+ 0 0) into 0 1.996 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 1.997 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.998 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.000 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.000 * [taylor]: Taking taylor expansion of 0 in k 2.000 * [backup-simplify]: Simplify 0 into 0 2.000 * [backup-simplify]: Simplify 0 into 0 2.001 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 2.001 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 2.001 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 2.001 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 2.001 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 2.001 * [taylor]: Taking taylor expansion of 1.0 in k 2.001 * [backup-simplify]: Simplify 1.0 into 1.0 2.001 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.001 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.002 * [taylor]: Taking taylor expansion of k in k 2.002 * [backup-simplify]: Simplify 0 into 0 2.002 * [backup-simplify]: Simplify 1 into 1 2.002 * [backup-simplify]: Simplify (/ 1 1) into 1 2.002 * [backup-simplify]: Simplify (sqrt 0) into 0 2.004 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.004 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 2.004 * [taylor]: Taking taylor expansion of 1.0 in k 2.004 * [backup-simplify]: Simplify 1.0 into 1.0 2.004 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.004 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.004 * [taylor]: Taking taylor expansion of k in k 2.004 * [backup-simplify]: Simplify 0 into 0 2.004 * [backup-simplify]: Simplify 1 into 1 2.005 * [backup-simplify]: Simplify (/ 1 1) into 1 2.005 * [backup-simplify]: Simplify (sqrt 0) into 0 2.006 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.007 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.007 * [backup-simplify]: Simplify 0 into 0 2.008 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 2.009 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.010 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.013 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.016 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 2.016 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.017 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.021 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.023 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 2.024 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.025 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 2.025 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 2.025 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 2.026 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 2.026 * [taylor]: Taking taylor expansion of 1.0 in k 2.026 * [backup-simplify]: Simplify 1.0 into 1.0 2.026 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.026 * [taylor]: Taking taylor expansion of k in k 2.026 * [backup-simplify]: Simplify 0 into 0 2.026 * [backup-simplify]: Simplify 1 into 1 2.026 * [backup-simplify]: Simplify (sqrt 0) into 0 2.027 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.027 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 2.027 * [taylor]: Taking taylor expansion of 1.0 in k 2.027 * [backup-simplify]: Simplify 1.0 into 1.0 2.027 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.027 * [taylor]: Taking taylor expansion of k in k 2.028 * [backup-simplify]: Simplify 0 into 0 2.028 * [backup-simplify]: Simplify 1 into 1 2.028 * [backup-simplify]: Simplify (sqrt 0) into 0 2.029 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.030 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.030 * [backup-simplify]: Simplify 0 into 0 2.031 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 2.031 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.034 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.036 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 2.037 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.040 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.043 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 2.043 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.045 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 2.045 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 2.045 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 2.045 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 2.045 * [taylor]: Taking taylor expansion of 1.0 in k 2.045 * [backup-simplify]: Simplify 1.0 into 1.0 2.045 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.045 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.045 * [taylor]: Taking taylor expansion of -1 in k 2.045 * [backup-simplify]: Simplify -1 into -1 2.045 * [taylor]: Taking taylor expansion of k in k 2.045 * [backup-simplify]: Simplify 0 into 0 2.045 * [backup-simplify]: Simplify 1 into 1 2.046 * [backup-simplify]: Simplify (/ -1 1) into -1 2.046 * [backup-simplify]: Simplify (sqrt 0) into 0 2.047 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.048 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 2.048 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 2.048 * [taylor]: Taking taylor expansion of 1.0 in k 2.048 * [backup-simplify]: Simplify 1.0 into 1.0 2.048 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.048 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.048 * [taylor]: Taking taylor expansion of -1 in k 2.048 * [backup-simplify]: Simplify -1 into -1 2.048 * [taylor]: Taking taylor expansion of k in k 2.048 * [backup-simplify]: Simplify 0 into 0 2.048 * [backup-simplify]: Simplify 1 into 1 2.049 * [backup-simplify]: Simplify (/ -1 1) into -1 2.049 * [backup-simplify]: Simplify (sqrt 0) into 0 2.050 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.051 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 2.051 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.052 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.055 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.057 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 2.058 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.059 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.063 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.067 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 2.068 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.069 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 2.069 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 2.070 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.070 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 2.070 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.070 * [taylor]: Taking taylor expansion of 2.0 in n 2.070 * [backup-simplify]: Simplify 2.0 into 2.0 2.070 * [taylor]: Taking taylor expansion of (* n PI) in n 2.070 * [taylor]: Taking taylor expansion of n in n 2.070 * [backup-simplify]: Simplify 0 into 0 2.070 * [backup-simplify]: Simplify 1 into 1 2.070 * [taylor]: Taking taylor expansion of PI in n 2.070 * [backup-simplify]: Simplify PI into PI 2.070 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.070 * [taylor]: Taking taylor expansion of 2.0 in n 2.070 * [backup-simplify]: Simplify 2.0 into 2.0 2.070 * [taylor]: Taking taylor expansion of (* n PI) in n 2.070 * [taylor]: Taking taylor expansion of n in n 2.070 * [backup-simplify]: Simplify 0 into 0 2.070 * [backup-simplify]: Simplify 1 into 1 2.070 * [taylor]: Taking taylor expansion of PI in n 2.070 * [backup-simplify]: Simplify PI into PI 2.071 * [backup-simplify]: Simplify (* 0 PI) into 0 2.071 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.071 * [backup-simplify]: Simplify 0 into 0 2.073 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.074 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.075 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.076 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.076 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.076 * [backup-simplify]: Simplify 0 into 0 2.077 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.077 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.078 * [backup-simplify]: Simplify 0 into 0 2.078 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.079 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.079 * [backup-simplify]: Simplify 0 into 0 2.080 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.081 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 2.081 * [backup-simplify]: Simplify 0 into 0 2.082 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.082 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 2.082 * [backup-simplify]: Simplify 0 into 0 2.084 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.085 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.085 * [backup-simplify]: Simplify 0 into 0 2.085 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.085 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 2.085 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 2.085 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.085 * [taylor]: Taking taylor expansion of 2.0 in n 2.085 * [backup-simplify]: Simplify 2.0 into 2.0 2.085 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.085 * [taylor]: Taking taylor expansion of PI in n 2.085 * [backup-simplify]: Simplify PI into PI 2.085 * [taylor]: Taking taylor expansion of n in n 2.086 * [backup-simplify]: Simplify 0 into 0 2.086 * [backup-simplify]: Simplify 1 into 1 2.086 * [backup-simplify]: Simplify (/ PI 1) into PI 2.086 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.086 * [taylor]: Taking taylor expansion of 2.0 in n 2.086 * [backup-simplify]: Simplify 2.0 into 2.0 2.086 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.086 * [taylor]: Taking taylor expansion of PI in n 2.086 * [backup-simplify]: Simplify PI into PI 2.086 * [taylor]: Taking taylor expansion of n in n 2.086 * [backup-simplify]: Simplify 0 into 0 2.086 * [backup-simplify]: Simplify 1 into 1 2.086 * [backup-simplify]: Simplify (/ PI 1) into PI 2.087 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.087 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.087 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.088 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.088 * [backup-simplify]: Simplify 0 into 0 2.092 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.093 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.093 * [backup-simplify]: Simplify 0 into 0 2.094 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.094 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.094 * [backup-simplify]: Simplify 0 into 0 2.095 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.096 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.096 * [backup-simplify]: Simplify 0 into 0 2.096 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.097 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.097 * [backup-simplify]: Simplify 0 into 0 2.098 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.099 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.099 * [backup-simplify]: Simplify 0 into 0 2.099 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 2.100 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 2.100 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 2.100 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.100 * [taylor]: Taking taylor expansion of -2.0 in n 2.100 * [backup-simplify]: Simplify -2.0 into -2.0 2.100 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.100 * [taylor]: Taking taylor expansion of PI in n 2.100 * [backup-simplify]: Simplify PI into PI 2.100 * [taylor]: Taking taylor expansion of n in n 2.100 * [backup-simplify]: Simplify 0 into 0 2.100 * [backup-simplify]: Simplify 1 into 1 2.100 * [backup-simplify]: Simplify (/ PI 1) into PI 2.100 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.100 * [taylor]: Taking taylor expansion of -2.0 in n 2.100 * [backup-simplify]: Simplify -2.0 into -2.0 2.100 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.100 * [taylor]: Taking taylor expansion of PI in n 2.100 * [backup-simplify]: Simplify PI into PI 2.100 * [taylor]: Taking taylor expansion of n in n 2.100 * [backup-simplify]: Simplify 0 into 0 2.100 * [backup-simplify]: Simplify 1 into 1 2.101 * [backup-simplify]: Simplify (/ PI 1) into PI 2.101 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.101 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.102 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.102 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.102 * [backup-simplify]: Simplify 0 into 0 2.103 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.103 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.103 * [backup-simplify]: Simplify 0 into 0 2.104 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.105 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.105 * [backup-simplify]: Simplify 0 into 0 2.105 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.106 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.106 * [backup-simplify]: Simplify 0 into 0 2.107 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.108 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.108 * [backup-simplify]: Simplify 0 into 0 2.108 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.109 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.109 * [backup-simplify]: Simplify 0 into 0 2.110 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 2.110 * * * * [progress]: [ 4 / 4 ] generating series at (2) 2.110 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) 2.110 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in (k n) around 0 2.110 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 2.110 * [taylor]: Taking taylor expansion of 1.0 in n 2.110 * [backup-simplify]: Simplify 1.0 into 1.0 2.110 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 2.110 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.110 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.110 * [taylor]: Taking taylor expansion of k in n 2.110 * [backup-simplify]: Simplify k into k 2.110 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.110 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 2.111 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.111 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 2.111 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.111 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.111 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.111 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.111 * [taylor]: Taking taylor expansion of 0.5 in n 2.111 * [backup-simplify]: Simplify 0.5 into 0.5 2.111 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.111 * [taylor]: Taking taylor expansion of 1.0 in n 2.111 * [backup-simplify]: Simplify 1.0 into 1.0 2.111 * [taylor]: Taking taylor expansion of k in n 2.111 * [backup-simplify]: Simplify k into k 2.111 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.111 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.111 * [taylor]: Taking taylor expansion of 2.0 in n 2.111 * [backup-simplify]: Simplify 2.0 into 2.0 2.111 * [taylor]: Taking taylor expansion of (* n PI) in n 2.111 * [taylor]: Taking taylor expansion of n in n 2.111 * [backup-simplify]: Simplify 0 into 0 2.111 * [backup-simplify]: Simplify 1 into 1 2.111 * [taylor]: Taking taylor expansion of PI in n 2.111 * [backup-simplify]: Simplify PI into PI 2.111 * [backup-simplify]: Simplify (* 0 PI) into 0 2.112 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.112 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.113 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.114 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.114 * [backup-simplify]: Simplify (- k) into (- k) 2.114 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.114 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.115 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.116 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.117 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.117 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 2.117 * [taylor]: Taking taylor expansion of 1.0 in k 2.117 * [backup-simplify]: Simplify 1.0 into 1.0 2.117 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 2.117 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.117 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.117 * [taylor]: Taking taylor expansion of k in k 2.117 * [backup-simplify]: Simplify 0 into 0 2.117 * [backup-simplify]: Simplify 1 into 1 2.117 * [backup-simplify]: Simplify (/ 1 1) into 1 2.117 * [backup-simplify]: Simplify (sqrt 0) into 0 2.118 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.118 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.118 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.118 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.118 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.118 * [taylor]: Taking taylor expansion of 0.5 in k 2.118 * [backup-simplify]: Simplify 0.5 into 0.5 2.118 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.118 * [taylor]: Taking taylor expansion of 1.0 in k 2.118 * [backup-simplify]: Simplify 1.0 into 1.0 2.118 * [taylor]: Taking taylor expansion of k in k 2.118 * [backup-simplify]: Simplify 0 into 0 2.118 * [backup-simplify]: Simplify 1 into 1 2.118 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.118 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.118 * [taylor]: Taking taylor expansion of 2.0 in k 2.118 * [backup-simplify]: Simplify 2.0 into 2.0 2.118 * [taylor]: Taking taylor expansion of (* n PI) in k 2.118 * [taylor]: Taking taylor expansion of n in k 2.118 * [backup-simplify]: Simplify n into n 2.118 * [taylor]: Taking taylor expansion of PI in k 2.118 * [backup-simplify]: Simplify PI into PI 2.118 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.119 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.119 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.119 * [backup-simplify]: Simplify (- 0) into 0 2.119 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.119 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.119 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.120 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.120 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 2.120 * [taylor]: Taking taylor expansion of 1.0 in k 2.120 * [backup-simplify]: Simplify 1.0 into 1.0 2.120 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 2.120 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.120 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.120 * [taylor]: Taking taylor expansion of k in k 2.120 * [backup-simplify]: Simplify 0 into 0 2.120 * [backup-simplify]: Simplify 1 into 1 2.120 * [backup-simplify]: Simplify (/ 1 1) into 1 2.120 * [backup-simplify]: Simplify (sqrt 0) into 0 2.121 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.121 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.121 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.121 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.121 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.121 * [taylor]: Taking taylor expansion of 0.5 in k 2.121 * [backup-simplify]: Simplify 0.5 into 0.5 2.121 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.121 * [taylor]: Taking taylor expansion of 1.0 in k 2.121 * [backup-simplify]: Simplify 1.0 into 1.0 2.121 * [taylor]: Taking taylor expansion of k in k 2.121 * [backup-simplify]: Simplify 0 into 0 2.121 * [backup-simplify]: Simplify 1 into 1 2.121 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.121 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.121 * [taylor]: Taking taylor expansion of 2.0 in k 2.121 * [backup-simplify]: Simplify 2.0 into 2.0 2.121 * [taylor]: Taking taylor expansion of (* n PI) in k 2.121 * [taylor]: Taking taylor expansion of n in k 2.121 * [backup-simplify]: Simplify n into n 2.121 * [taylor]: Taking taylor expansion of PI in k 2.121 * [backup-simplify]: Simplify PI into PI 2.121 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.121 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.121 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.122 * [backup-simplify]: Simplify (- 0) into 0 2.122 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.122 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.122 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.122 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.123 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 2.123 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.123 * [taylor]: Taking taylor expansion of 0 in n 2.123 * [backup-simplify]: Simplify 0 into 0 2.123 * [backup-simplify]: Simplify 0 into 0 2.123 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 2.124 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 2.125 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 2.125 * [backup-simplify]: Simplify (- 1) into -1 2.125 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.127 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 2.128 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 2.129 * [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))) 2.131 * [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))) 2.133 * [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))) 2.133 * [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 2.133 * [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 2.133 * [taylor]: Taking taylor expansion of +nan.0 in n 2.133 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.133 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 2.133 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.133 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.133 * [taylor]: Taking taylor expansion of 0.5 in n 2.134 * [backup-simplify]: Simplify 0.5 into 0.5 2.134 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.134 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.134 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.134 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.134 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.134 * [taylor]: Taking taylor expansion of 1.0 in n 2.134 * [backup-simplify]: Simplify 1.0 into 1.0 2.134 * [taylor]: Taking taylor expansion of (log PI) in n 2.134 * [taylor]: Taking taylor expansion of PI in n 2.134 * [backup-simplify]: Simplify PI into PI 2.134 * [backup-simplify]: Simplify (log PI) into (log PI) 2.135 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.137 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.137 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.137 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.137 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.137 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.137 * [taylor]: Taking taylor expansion of 1.0 in n 2.137 * [backup-simplify]: Simplify 1.0 into 1.0 2.137 * [taylor]: Taking taylor expansion of (log n) in n 2.137 * [taylor]: Taking taylor expansion of n in n 2.137 * [backup-simplify]: Simplify 0 into 0 2.137 * [backup-simplify]: Simplify 1 into 1 2.138 * [backup-simplify]: Simplify (log 1) into 0 2.138 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.138 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.138 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.138 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.138 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.138 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.139 * [taylor]: Taking taylor expansion of 1.0 in n 2.139 * [backup-simplify]: Simplify 1.0 into 1.0 2.139 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.139 * [taylor]: Taking taylor expansion of 2.0 in n 2.139 * [backup-simplify]: Simplify 2.0 into 2.0 2.139 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.140 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.141 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.142 * [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) 2.143 * [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) 2.145 * [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)) 2.146 * [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))) 2.148 * [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) 2.149 * [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)) 2.151 * [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))) 2.152 * [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))) 2.152 * [backup-simplify]: Simplify 0 into 0 2.153 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 2.154 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 2.156 * [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 2.156 * [backup-simplify]: Simplify (- 0) into 0 2.157 * [backup-simplify]: Simplify (+ 0 0) into 0 2.158 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 2.159 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 2.160 * [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))) 2.161 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.164 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.168 * [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)))))))) 2.174 * [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)))))))) 2.174 * [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 2.174 * [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 2.174 * [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 2.174 * [taylor]: Taking taylor expansion of +nan.0 in n 2.174 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.174 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 2.174 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.174 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.174 * [taylor]: Taking taylor expansion of 0.5 in n 2.174 * [backup-simplify]: Simplify 0.5 into 0.5 2.174 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.174 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.174 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.174 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.174 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.174 * [taylor]: Taking taylor expansion of 1.0 in n 2.174 * [backup-simplify]: Simplify 1.0 into 1.0 2.174 * [taylor]: Taking taylor expansion of (log PI) in n 2.175 * [taylor]: Taking taylor expansion of PI in n 2.175 * [backup-simplify]: Simplify PI into PI 2.175 * [backup-simplify]: Simplify (log PI) into (log PI) 2.176 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.178 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.178 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.178 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.178 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.178 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.178 * [taylor]: Taking taylor expansion of 1.0 in n 2.178 * [backup-simplify]: Simplify 1.0 into 1.0 2.178 * [taylor]: Taking taylor expansion of (log n) in n 2.178 * [taylor]: Taking taylor expansion of n in n 2.178 * [backup-simplify]: Simplify 0 into 0 2.178 * [backup-simplify]: Simplify 1 into 1 2.179 * [backup-simplify]: Simplify (log 1) into 0 2.179 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.179 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.179 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.179 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.179 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.179 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.179 * [taylor]: Taking taylor expansion of 1.0 in n 2.179 * [backup-simplify]: Simplify 1.0 into 1.0 2.179 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.179 * [taylor]: Taking taylor expansion of 2.0 in n 2.179 * [backup-simplify]: Simplify 2.0 into 2.0 2.180 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.181 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.182 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.183 * [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) 2.184 * [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) 2.186 * [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)) 2.187 * [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))) 2.188 * [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) 2.189 * [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 2.189 * [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 2.189 * [taylor]: Taking taylor expansion of +nan.0 in n 2.189 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.189 * [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 2.189 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 2.189 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 2.189 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 2.189 * [taylor]: Taking taylor expansion of 0.5 in n 2.189 * [backup-simplify]: Simplify 0.5 into 0.5 2.189 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 2.189 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 2.189 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.189 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.189 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.189 * [taylor]: Taking taylor expansion of 1.0 in n 2.189 * [backup-simplify]: Simplify 1.0 into 1.0 2.189 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.189 * [taylor]: Taking taylor expansion of 2.0 in n 2.189 * [backup-simplify]: Simplify 2.0 into 2.0 2.190 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.191 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.192 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.192 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 2.192 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.192 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.192 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.192 * [taylor]: Taking taylor expansion of 1.0 in n 2.192 * [backup-simplify]: Simplify 1.0 into 1.0 2.192 * [taylor]: Taking taylor expansion of (log PI) in n 2.192 * [taylor]: Taking taylor expansion of PI in n 2.192 * [backup-simplify]: Simplify PI into PI 2.193 * [backup-simplify]: Simplify (log PI) into (log PI) 2.194 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.196 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.196 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.196 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.196 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.196 * [taylor]: Taking taylor expansion of 1.0 in n 2.196 * [backup-simplify]: Simplify 1.0 into 1.0 2.196 * [taylor]: Taking taylor expansion of (log n) in n 2.196 * [taylor]: Taking taylor expansion of n in n 2.196 * [backup-simplify]: Simplify 0 into 0 2.196 * [backup-simplify]: Simplify 1 into 1 2.196 * [backup-simplify]: Simplify (log 1) into 0 2.197 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.197 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.197 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.198 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.199 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 2.200 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 2.202 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 2.203 * [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) 2.203 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.203 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.203 * [taylor]: Taking taylor expansion of 2.0 in n 2.203 * [backup-simplify]: Simplify 2.0 into 2.0 2.203 * [taylor]: Taking taylor expansion of (* n PI) in n 2.203 * [taylor]: Taking taylor expansion of n in n 2.203 * [backup-simplify]: Simplify 0 into 0 2.203 * [backup-simplify]: Simplify 1 into 1 2.203 * [taylor]: Taking taylor expansion of PI in n 2.204 * [backup-simplify]: Simplify PI into PI 2.204 * [backup-simplify]: Simplify (* 0 PI) into 0 2.205 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.206 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.208 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.209 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.211 * [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)) 2.213 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.216 * [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)) 2.218 * [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))) 2.221 * [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)))))) 2.227 * [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)))))))) 2.238 * [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)))))))) 2.245 * [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)))))))) 2.247 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 2.247 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 2.249 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 2.250 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.251 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.251 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 2.252 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.253 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 2.255 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 2.256 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 2.257 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 2.259 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 2.261 * [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 2.263 * [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 2.264 * [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 2.266 * [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 2.266 * [backup-simplify]: Simplify (- 0) into 0 2.266 * [backup-simplify]: Simplify 0 into 0 2.266 * [backup-simplify]: Simplify 0 into 0 2.267 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.268 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 2.269 * [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 2.270 * [backup-simplify]: Simplify (- 0) into 0 2.270 * [backup-simplify]: Simplify (+ 0 0) into 0 2.271 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 2.272 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 2.273 * [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))) 2.273 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.276 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.279 * [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)))))))) 2.285 * [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)))))))) 2.285 * [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 2.285 * [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 2.286 * [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 2.286 * [taylor]: Taking taylor expansion of +nan.0 in n 2.286 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.286 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 2.286 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 2.286 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 2.286 * [taylor]: Taking taylor expansion of 0.5 in n 2.286 * [backup-simplify]: Simplify 0.5 into 0.5 2.286 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 2.286 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 2.286 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.286 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.286 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.286 * [taylor]: Taking taylor expansion of 1.0 in n 2.286 * [backup-simplify]: Simplify 1.0 into 1.0 2.286 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.286 * [taylor]: Taking taylor expansion of 2.0 in n 2.286 * [backup-simplify]: Simplify 2.0 into 2.0 2.286 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.287 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.288 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.288 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 2.288 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.288 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.288 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.288 * [taylor]: Taking taylor expansion of 1.0 in n 2.288 * [backup-simplify]: Simplify 1.0 into 1.0 2.288 * [taylor]: Taking taylor expansion of (log n) in n 2.288 * [taylor]: Taking taylor expansion of n in n 2.288 * [backup-simplify]: Simplify 0 into 0 2.288 * [backup-simplify]: Simplify 1 into 1 2.288 * [backup-simplify]: Simplify (log 1) into 0 2.288 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.288 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.288 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.288 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.288 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.288 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.288 * [taylor]: Taking taylor expansion of 1.0 in n 2.288 * [backup-simplify]: Simplify 1.0 into 1.0 2.288 * [taylor]: Taking taylor expansion of (log PI) in n 2.288 * [taylor]: Taking taylor expansion of PI in n 2.288 * [backup-simplify]: Simplify PI into PI 2.289 * [backup-simplify]: Simplify (log PI) into (log PI) 2.289 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.290 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.291 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.291 * [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) 2.292 * [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)) 2.293 * [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))) 2.294 * [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) 2.294 * [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 2.294 * [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 2.294 * [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 2.294 * [taylor]: Taking taylor expansion of +nan.0 in n 2.294 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.294 * [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 2.294 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 2.294 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 2.294 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 2.294 * [taylor]: Taking taylor expansion of 0.5 in n 2.294 * [backup-simplify]: Simplify 0.5 into 0.5 2.294 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 2.294 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 2.294 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.294 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.294 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.294 * [taylor]: Taking taylor expansion of 1.0 in n 2.294 * [backup-simplify]: Simplify 1.0 into 1.0 2.294 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.294 * [taylor]: Taking taylor expansion of 2.0 in n 2.294 * [backup-simplify]: Simplify 2.0 into 2.0 2.295 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.295 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.297 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.297 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 2.297 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.297 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.297 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.297 * [taylor]: Taking taylor expansion of 1.0 in n 2.297 * [backup-simplify]: Simplify 1.0 into 1.0 2.297 * [taylor]: Taking taylor expansion of (log PI) in n 2.297 * [taylor]: Taking taylor expansion of PI in n 2.297 * [backup-simplify]: Simplify PI into PI 2.297 * [backup-simplify]: Simplify (log PI) into (log PI) 2.298 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.300 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.300 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.300 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.300 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.300 * [taylor]: Taking taylor expansion of 1.0 in n 2.300 * [backup-simplify]: Simplify 1.0 into 1.0 2.300 * [taylor]: Taking taylor expansion of (log n) in n 2.300 * [taylor]: Taking taylor expansion of n in n 2.300 * [backup-simplify]: Simplify 0 into 0 2.300 * [backup-simplify]: Simplify 1 into 1 2.301 * [backup-simplify]: Simplify (log 1) into 0 2.301 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.301 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.301 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.302 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.303 * [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) 2.305 * [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)) 2.306 * [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))) 2.308 * [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) 2.308 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.308 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.308 * [taylor]: Taking taylor expansion of 2.0 in n 2.308 * [backup-simplify]: Simplify 2.0 into 2.0 2.308 * [taylor]: Taking taylor expansion of (* n PI) in n 2.308 * [taylor]: Taking taylor expansion of n in n 2.308 * [backup-simplify]: Simplify 0 into 0 2.308 * [backup-simplify]: Simplify 1 into 1 2.308 * [taylor]: Taking taylor expansion of PI in n 2.308 * [backup-simplify]: Simplify PI into PI 2.308 * [backup-simplify]: Simplify (* 0 PI) into 0 2.309 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.310 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.312 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.313 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.313 * [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 2.313 * [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 2.313 * [taylor]: Taking taylor expansion of +nan.0 in n 2.313 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.313 * [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 2.313 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 2.313 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 2.313 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 2.314 * [taylor]: Taking taylor expansion of 0.5 in n 2.314 * [backup-simplify]: Simplify 0.5 into 0.5 2.314 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 2.314 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 2.314 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.314 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.314 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.314 * [taylor]: Taking taylor expansion of 1.0 in n 2.314 * [backup-simplify]: Simplify 1.0 into 1.0 2.314 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.314 * [taylor]: Taking taylor expansion of 2.0 in n 2.314 * [backup-simplify]: Simplify 2.0 into 2.0 2.314 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.315 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.317 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.317 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 2.317 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.317 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.317 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) 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 (log PI) in n 2.317 * [taylor]: Taking taylor expansion of PI in n 2.317 * [backup-simplify]: Simplify PI into PI 2.318 * [backup-simplify]: Simplify (log PI) into (log PI) 2.319 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.320 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.320 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.320 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.320 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.320 * [taylor]: Taking taylor expansion of 1.0 in n 2.320 * [backup-simplify]: Simplify 1.0 into 1.0 2.320 * [taylor]: Taking taylor expansion of (log n) in n 2.321 * [taylor]: Taking taylor expansion of n in n 2.321 * [backup-simplify]: Simplify 0 into 0 2.321 * [backup-simplify]: Simplify 1 into 1 2.321 * [backup-simplify]: Simplify (log 1) into 0 2.321 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.321 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.322 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.322 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.324 * [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) 2.325 * [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)) 2.326 * [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))) 2.328 * [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) 2.328 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 2.328 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.328 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.328 * [taylor]: Taking taylor expansion of 2.0 in n 2.328 * [backup-simplify]: Simplify 2.0 into 2.0 2.328 * [taylor]: Taking taylor expansion of (* n PI) in n 2.328 * [taylor]: Taking taylor expansion of n in n 2.328 * [backup-simplify]: Simplify 0 into 0 2.328 * [backup-simplify]: Simplify 1 into 1 2.328 * [taylor]: Taking taylor expansion of PI in n 2.328 * [backup-simplify]: Simplify PI into PI 2.329 * [backup-simplify]: Simplify (* 0 PI) into 0 2.329 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.331 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.332 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.334 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.335 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.337 * [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)) 2.338 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.341 * [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)) 2.344 * [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))) 2.345 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.347 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.349 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 2.352 * [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)) 2.355 * [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))) 2.358 * [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)))))))) 2.376 * [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)))))))))))) 2.392 * [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)))))))))))) 2.401 * [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)))))))))))))) 2.411 * [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)))))))))))))) 2.423 * [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)))))))))))))) 2.444 * [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)))))))))))))))))))))) 2.445 * [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)))))) 2.445 * [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 2.445 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 2.445 * [taylor]: Taking taylor expansion of 1.0 in n 2.445 * [backup-simplify]: Simplify 1.0 into 1.0 2.445 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 2.445 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.445 * [taylor]: Taking taylor expansion of k in n 2.445 * [backup-simplify]: Simplify k into k 2.445 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.445 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.445 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.445 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.445 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.445 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.445 * [taylor]: Taking taylor expansion of 0.5 in n 2.445 * [backup-simplify]: Simplify 0.5 into 0.5 2.445 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.445 * [taylor]: Taking taylor expansion of 1.0 in n 2.445 * [backup-simplify]: Simplify 1.0 into 1.0 2.445 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.445 * [taylor]: Taking taylor expansion of k in n 2.445 * [backup-simplify]: Simplify k into k 2.445 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.445 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.445 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.445 * [taylor]: Taking taylor expansion of 2.0 in n 2.445 * [backup-simplify]: Simplify 2.0 into 2.0 2.445 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.445 * [taylor]: Taking taylor expansion of PI in n 2.445 * [backup-simplify]: Simplify PI into PI 2.446 * [taylor]: Taking taylor expansion of n in n 2.446 * [backup-simplify]: Simplify 0 into 0 2.446 * [backup-simplify]: Simplify 1 into 1 2.446 * [backup-simplify]: Simplify (/ PI 1) into PI 2.446 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.447 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.447 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.447 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.447 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.448 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.449 * [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)))) 2.449 * [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))))) 2.449 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 2.449 * [taylor]: Taking taylor expansion of 1.0 in k 2.450 * [backup-simplify]: Simplify 1.0 into 1.0 2.450 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 2.450 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.450 * [taylor]: Taking taylor expansion of k in k 2.450 * [backup-simplify]: Simplify 0 into 0 2.450 * [backup-simplify]: Simplify 1 into 1 2.450 * [backup-simplify]: Simplify (sqrt 0) into 0 2.451 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.451 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.451 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.451 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.451 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.451 * [taylor]: Taking taylor expansion of 0.5 in k 2.451 * [backup-simplify]: Simplify 0.5 into 0.5 2.451 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.451 * [taylor]: Taking taylor expansion of 1.0 in k 2.451 * [backup-simplify]: Simplify 1.0 into 1.0 2.451 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.451 * [taylor]: Taking taylor expansion of k in k 2.451 * [backup-simplify]: Simplify 0 into 0 2.451 * [backup-simplify]: Simplify 1 into 1 2.451 * [backup-simplify]: Simplify (/ 1 1) into 1 2.451 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.451 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.451 * [taylor]: Taking taylor expansion of 2.0 in k 2.451 * [backup-simplify]: Simplify 2.0 into 2.0 2.451 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.451 * [taylor]: Taking taylor expansion of PI in k 2.451 * [backup-simplify]: Simplify PI into PI 2.451 * [taylor]: Taking taylor expansion of n in k 2.451 * [backup-simplify]: Simplify n into n 2.451 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.451 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.452 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.452 * [backup-simplify]: Simplify (- 1) into -1 2.452 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.452 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.452 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.453 * [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))))) 2.453 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 2.453 * [taylor]: Taking taylor expansion of 1.0 in k 2.453 * [backup-simplify]: Simplify 1.0 into 1.0 2.453 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 2.453 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.453 * [taylor]: Taking taylor expansion of k in k 2.453 * [backup-simplify]: Simplify 0 into 0 2.453 * [backup-simplify]: Simplify 1 into 1 2.453 * [backup-simplify]: Simplify (sqrt 0) into 0 2.454 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.454 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.454 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.454 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.454 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.454 * [taylor]: Taking taylor expansion of 0.5 in k 2.454 * [backup-simplify]: Simplify 0.5 into 0.5 2.454 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.454 * [taylor]: Taking taylor expansion of 1.0 in k 2.454 * [backup-simplify]: Simplify 1.0 into 1.0 2.454 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.454 * [taylor]: Taking taylor expansion of k in k 2.454 * [backup-simplify]: Simplify 0 into 0 2.454 * [backup-simplify]: Simplify 1 into 1 2.454 * [backup-simplify]: Simplify (/ 1 1) into 1 2.454 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.454 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.454 * [taylor]: Taking taylor expansion of 2.0 in k 2.454 * [backup-simplify]: Simplify 2.0 into 2.0 2.454 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.454 * [taylor]: Taking taylor expansion of PI in k 2.454 * [backup-simplify]: Simplify PI into PI 2.454 * [taylor]: Taking taylor expansion of n in k 2.454 * [backup-simplify]: Simplify n into n 2.454 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.455 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.455 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.455 * [backup-simplify]: Simplify (- 1) into -1 2.455 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.455 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.456 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.456 * [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))))) 2.456 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 2.456 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.456 * [taylor]: Taking taylor expansion of 0 in n 2.456 * [backup-simplify]: Simplify 0 into 0 2.456 * [backup-simplify]: Simplify 0 into 0 2.457 * [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))))))) 2.457 * [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))))))) 2.457 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 2.457 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 2.457 * [taylor]: Taking taylor expansion of +nan.0 in n 2.457 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.457 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 2.457 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 2.457 * [taylor]: Taking taylor expansion of 0.5 in n 2.457 * [backup-simplify]: Simplify 0.5 into 0.5 2.457 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 2.457 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.457 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.457 * [taylor]: Taking taylor expansion of 2.0 in n 2.457 * [backup-simplify]: Simplify 2.0 into 2.0 2.458 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.458 * [taylor]: Taking taylor expansion of PI in n 2.458 * [backup-simplify]: Simplify PI into PI 2.458 * [taylor]: Taking taylor expansion of n in n 2.458 * [backup-simplify]: Simplify 0 into 0 2.458 * [backup-simplify]: Simplify 1 into 1 2.458 * [backup-simplify]: Simplify (/ PI 1) into PI 2.458 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.459 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.459 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.459 * [taylor]: Taking taylor expansion of 1.0 in n 2.459 * [backup-simplify]: Simplify 1.0 into 1.0 2.459 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.459 * [taylor]: Taking taylor expansion of k in n 2.459 * [backup-simplify]: Simplify k into k 2.459 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.460 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.460 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.460 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.461 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 2.462 * [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)))) 2.463 * [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))))) 2.463 * [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)))))) 2.464 * [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))))))) 2.465 * [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))))))) 2.465 * [backup-simplify]: Simplify 0 into 0 2.467 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.468 * [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))))))) 2.469 * [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))))))) 2.470 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 2.470 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 2.470 * [taylor]: Taking taylor expansion of +nan.0 in n 2.470 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.470 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 2.470 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 2.470 * [taylor]: Taking taylor expansion of 0.5 in n 2.470 * [backup-simplify]: Simplify 0.5 into 0.5 2.470 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 2.470 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.470 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.470 * [taylor]: Taking taylor expansion of 2.0 in n 2.470 * [backup-simplify]: Simplify 2.0 into 2.0 2.470 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.470 * [taylor]: Taking taylor expansion of PI in n 2.470 * [backup-simplify]: Simplify PI into PI 2.470 * [taylor]: Taking taylor expansion of n in n 2.470 * [backup-simplify]: Simplify 0 into 0 2.470 * [backup-simplify]: Simplify 1 into 1 2.471 * [backup-simplify]: Simplify (/ PI 1) into PI 2.471 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.472 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.472 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.472 * [taylor]: Taking taylor expansion of 1.0 in n 2.472 * [backup-simplify]: Simplify 1.0 into 1.0 2.472 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.472 * [taylor]: Taking taylor expansion of k in n 2.472 * [backup-simplify]: Simplify k into k 2.472 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.474 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.474 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.474 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.475 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 2.477 * [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)))) 2.478 * [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))))) 2.479 * [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)))))) 2.481 * [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))))))) 2.482 * [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))))))) 2.489 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.489 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.489 * [backup-simplify]: Simplify (- 0) into 0 2.490 * [backup-simplify]: Simplify (+ 0 0) into 0 2.491 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.492 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.493 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.495 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.496 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 2.498 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.500 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 2.500 * [backup-simplify]: Simplify (- 0) into 0 2.500 * [backup-simplify]: Simplify 0 into 0 2.501 * [backup-simplify]: Simplify 0 into 0 2.505 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.506 * [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))))))) 2.508 * [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))))))) 2.508 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 2.508 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 2.508 * [taylor]: Taking taylor expansion of +nan.0 in n 2.508 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.508 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 2.508 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 2.508 * [taylor]: Taking taylor expansion of 0.5 in n 2.508 * [backup-simplify]: Simplify 0.5 into 0.5 2.508 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 2.508 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.508 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.508 * [taylor]: Taking taylor expansion of 2.0 in n 2.508 * [backup-simplify]: Simplify 2.0 into 2.0 2.508 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.508 * [taylor]: Taking taylor expansion of PI in n 2.508 * [backup-simplify]: Simplify PI into PI 2.508 * [taylor]: Taking taylor expansion of n in n 2.508 * [backup-simplify]: Simplify 0 into 0 2.508 * [backup-simplify]: Simplify 1 into 1 2.509 * [backup-simplify]: Simplify (/ PI 1) into PI 2.510 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.511 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.511 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.511 * [taylor]: Taking taylor expansion of 1.0 in n 2.511 * [backup-simplify]: Simplify 1.0 into 1.0 2.511 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.511 * [taylor]: Taking taylor expansion of k in n 2.511 * [backup-simplify]: Simplify k into k 2.511 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.512 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.512 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.512 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.513 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 2.513 * [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)))) 2.514 * [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))))) 2.515 * [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)))))) 2.516 * [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))))))) 2.516 * [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))))))) 2.519 * [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)))))))) 2.520 * [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)))) 2.520 * [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 2.520 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 2.520 * [taylor]: Taking taylor expansion of 1.0 in n 2.520 * [backup-simplify]: Simplify 1.0 into 1.0 2.520 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 2.520 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.520 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.520 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.520 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.520 * [taylor]: Taking taylor expansion of 0.5 in n 2.520 * [backup-simplify]: Simplify 0.5 into 0.5 2.520 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.520 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.520 * [taylor]: Taking taylor expansion of k in n 2.520 * [backup-simplify]: Simplify k into k 2.520 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.520 * [taylor]: Taking taylor expansion of 1.0 in n 2.520 * [backup-simplify]: Simplify 1.0 into 1.0 2.520 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.520 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.520 * [taylor]: Taking taylor expansion of -2.0 in n 2.520 * [backup-simplify]: Simplify -2.0 into -2.0 2.520 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.520 * [taylor]: Taking taylor expansion of PI in n 2.520 * [backup-simplify]: Simplify PI into PI 2.520 * [taylor]: Taking taylor expansion of n in n 2.520 * [backup-simplify]: Simplify 0 into 0 2.520 * [backup-simplify]: Simplify 1 into 1 2.521 * [backup-simplify]: Simplify (/ PI 1) into PI 2.521 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.522 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.522 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.522 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.523 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.523 * [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)))) 2.524 * [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))))) 2.524 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.524 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.524 * [taylor]: Taking taylor expansion of -1 in n 2.524 * [backup-simplify]: Simplify -1 into -1 2.524 * [taylor]: Taking taylor expansion of k in n 2.524 * [backup-simplify]: Simplify k into k 2.524 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.524 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.524 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.525 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.525 * [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))) 2.525 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 2.525 * [taylor]: Taking taylor expansion of 1.0 in k 2.525 * [backup-simplify]: Simplify 1.0 into 1.0 2.525 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 2.525 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.525 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.525 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.525 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.525 * [taylor]: Taking taylor expansion of 0.5 in k 2.526 * [backup-simplify]: Simplify 0.5 into 0.5 2.526 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.526 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.526 * [taylor]: Taking taylor expansion of k in k 2.526 * [backup-simplify]: Simplify 0 into 0 2.526 * [backup-simplify]: Simplify 1 into 1 2.526 * [backup-simplify]: Simplify (/ 1 1) into 1 2.526 * [taylor]: Taking taylor expansion of 1.0 in k 2.526 * [backup-simplify]: Simplify 1.0 into 1.0 2.526 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.526 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.526 * [taylor]: Taking taylor expansion of -2.0 in k 2.526 * [backup-simplify]: Simplify -2.0 into -2.0 2.526 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.526 * [taylor]: Taking taylor expansion of PI in k 2.526 * [backup-simplify]: Simplify PI into PI 2.526 * [taylor]: Taking taylor expansion of n in k 2.526 * [backup-simplify]: Simplify n into n 2.526 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.526 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.526 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.527 * [backup-simplify]: Simplify (+ 1 0) into 1 2.527 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.527 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.527 * [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)))))) 2.527 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.527 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.527 * [taylor]: Taking taylor expansion of -1 in k 2.527 * [backup-simplify]: Simplify -1 into -1 2.527 * [taylor]: Taking taylor expansion of k in k 2.527 * [backup-simplify]: Simplify 0 into 0 2.527 * [backup-simplify]: Simplify 1 into 1 2.528 * [backup-simplify]: Simplify (/ -1 1) into -1 2.528 * [backup-simplify]: Simplify (sqrt 0) into 0 2.529 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.529 * [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))))))) 2.529 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 2.529 * [taylor]: Taking taylor expansion of 1.0 in k 2.529 * [backup-simplify]: Simplify 1.0 into 1.0 2.529 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 2.529 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.529 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.529 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.529 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.529 * [taylor]: Taking taylor expansion of 0.5 in k 2.529 * [backup-simplify]: Simplify 0.5 into 0.5 2.529 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.529 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.529 * [taylor]: Taking taylor expansion of k in k 2.529 * [backup-simplify]: Simplify 0 into 0 2.529 * [backup-simplify]: Simplify 1 into 1 2.529 * [backup-simplify]: Simplify (/ 1 1) into 1 2.529 * [taylor]: Taking taylor expansion of 1.0 in k 2.529 * [backup-simplify]: Simplify 1.0 into 1.0 2.529 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.529 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.529 * [taylor]: Taking taylor expansion of -2.0 in k 2.529 * [backup-simplify]: Simplify -2.0 into -2.0 2.529 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.529 * [taylor]: Taking taylor expansion of PI in k 2.529 * [backup-simplify]: Simplify PI into PI 2.529 * [taylor]: Taking taylor expansion of n in k 2.530 * [backup-simplify]: Simplify n into n 2.530 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.530 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.530 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.530 * [backup-simplify]: Simplify (+ 1 0) into 1 2.530 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.530 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.530 * [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)))))) 2.530 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.530 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.531 * [taylor]: Taking taylor expansion of -1 in k 2.531 * [backup-simplify]: Simplify -1 into -1 2.531 * [taylor]: Taking taylor expansion of k in k 2.531 * [backup-simplify]: Simplify 0 into 0 2.531 * [backup-simplify]: Simplify 1 into 1 2.531 * [backup-simplify]: Simplify (/ -1 1) into -1 2.531 * [backup-simplify]: Simplify (sqrt 0) into 0 2.532 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.532 * [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))))))) 2.532 * [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))))))) 2.532 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 2.532 * [taylor]: Taking taylor expansion of +nan.0 in n 2.532 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.532 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 2.532 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 2.532 * [taylor]: Taking taylor expansion of 0.5 in n 2.532 * [backup-simplify]: Simplify 0.5 into 0.5 2.532 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 2.532 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.532 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.532 * [taylor]: Taking taylor expansion of k in n 2.532 * [backup-simplify]: Simplify k into k 2.532 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.532 * [taylor]: Taking taylor expansion of 1.0 in n 2.533 * [backup-simplify]: Simplify 1.0 into 1.0 2.533 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.533 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.533 * [taylor]: Taking taylor expansion of -2.0 in n 2.533 * [backup-simplify]: Simplify -2.0 into -2.0 2.533 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.533 * [taylor]: Taking taylor expansion of PI in n 2.533 * [backup-simplify]: Simplify PI into PI 2.533 * [taylor]: Taking taylor expansion of n in n 2.533 * [backup-simplify]: Simplify 0 into 0 2.533 * [backup-simplify]: Simplify 1 into 1 2.533 * [backup-simplify]: Simplify (/ PI 1) into PI 2.533 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.534 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.534 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.535 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.535 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 2.536 * [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)))) 2.537 * [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))))) 2.538 * [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)))))) 2.538 * [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)))))) 2.539 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.541 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.541 * [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)))))))) 2.542 * [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)))))))) 2.542 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 2.542 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 2.542 * [taylor]: Taking taylor expansion of +nan.0 in n 2.542 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.542 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 2.542 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 2.542 * [taylor]: Taking taylor expansion of 0.5 in n 2.542 * [backup-simplify]: Simplify 0.5 into 0.5 2.542 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 2.542 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.542 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.542 * [taylor]: Taking taylor expansion of k in n 2.542 * [backup-simplify]: Simplify k into k 2.542 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.542 * [taylor]: Taking taylor expansion of 1.0 in n 2.542 * [backup-simplify]: Simplify 1.0 into 1.0 2.542 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.542 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.542 * [taylor]: Taking taylor expansion of -2.0 in n 2.542 * [backup-simplify]: Simplify -2.0 into -2.0 2.542 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.542 * [taylor]: Taking taylor expansion of PI in n 2.542 * [backup-simplify]: Simplify PI into PI 2.542 * [taylor]: Taking taylor expansion of n in n 2.542 * [backup-simplify]: Simplify 0 into 0 2.542 * [backup-simplify]: Simplify 1 into 1 2.543 * [backup-simplify]: Simplify (/ PI 1) into PI 2.543 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.544 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.544 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.545 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.546 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 2.548 * [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)))) 2.549 * [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))))) 2.550 * [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)))))) 2.552 * [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))))))) 2.553 * [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))))))) 2.554 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.555 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.557 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.557 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.557 * [backup-simplify]: Simplify (+ 0 0) into 0 2.559 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.560 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.561 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 2.563 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.565 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 2.565 * [backup-simplify]: Simplify 0 into 0 2.566 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.570 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.572 * [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)))))))) 2.573 * [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)))))))) 2.573 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 2.573 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 2.573 * [taylor]: Taking taylor expansion of +nan.0 in n 2.573 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.573 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 2.573 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 2.573 * [taylor]: Taking taylor expansion of 0.5 in n 2.573 * [backup-simplify]: Simplify 0.5 into 0.5 2.573 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 2.574 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.574 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.574 * [taylor]: Taking taylor expansion of k in n 2.574 * [backup-simplify]: Simplify k into k 2.574 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.574 * [taylor]: Taking taylor expansion of 1.0 in n 2.574 * [backup-simplify]: Simplify 1.0 into 1.0 2.574 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.574 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.574 * [taylor]: Taking taylor expansion of -2.0 in n 2.574 * [backup-simplify]: Simplify -2.0 into -2.0 2.574 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.574 * [taylor]: Taking taylor expansion of PI in n 2.574 * [backup-simplify]: Simplify PI into PI 2.574 * [taylor]: Taking taylor expansion of n in n 2.574 * [backup-simplify]: Simplify 0 into 0 2.574 * [backup-simplify]: Simplify 1 into 1 2.575 * [backup-simplify]: Simplify (/ PI 1) into PI 2.575 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.576 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.576 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.577 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.578 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 2.579 * [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)))) 2.580 * [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))))) 2.580 * [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)))))) 2.581 * [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))))))) 2.582 * [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))))))) 2.585 * [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)))))))))))) 2.585 * * * [progress]: simplifying candidates 2.588 * [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)))))))))))) 2.592 * * [simplify]: Extracting # 0 : cost 0 2.593 * * [simplify]: Extracting # 1 : cost 0 2.593 * * [simplify]: Extracting # 2 : cost 0 2.593 * * [simplify]: Extracting # 3 : cost 0 2.594 * * [simplify]: Extracting # 4 : cost 0 2.594 * * [simplify]: Extracting # 5 : cost 0 2.595 * * [simplify]: Extracting # 6 : cost 0 2.595 * * [simplify]: Extracting # 7 : cost 0 2.596 * * [simplify]: Extracting # 8 : cost 0 2.596 * * [simplify]: Extracting # 9 : cost 0 2.597 * * [simplify]: Extracting # 10 : cost 0 2.597 * * [simplify]: Extracting # 11 : cost 0 2.598 * * [simplify]: Extracting # 12 : cost 0 2.602 * * [simplify]: Extracting # 13 : cost 0 2.603 * * [simplify]: Extracting # 14 : cost 0 2.603 * * [simplify]: Extracting # 15 : cost 0 2.604 * * [simplify]: Extracting # 16 : cost 0 2.604 * * [simplify]: Extracting # 17 : cost 0 2.605 * * [simplify]: Extracting # 18 : cost 0 2.606 * * [simplify]: Extracting # 19 : cost 0 2.606 * * [simplify]: Extracting # 20 : cost 0 2.607 * * [simplify]: Extracting # 21 : cost 0 2.607 * * [simplify]: Extracting # 22 : cost 0 2.608 * * [simplify]: Extracting # 23 : cost 0 2.609 * * [simplify]: Extracting # 24 : cost 0 2.610 * * [simplify]: Extracting # 25 : cost 0 2.611 * * [simplify]: Extracting # 26 : cost 0 2.612 * * [simplify]: Extracting # 27 : cost 0 2.614 * * [simplify]: Extracting # 28 : cost 0 2.615 * * [simplify]: Extracting # 29 : cost 0 2.616 * * [simplify]: Extracting # 30 : cost 0 2.617 * * [simplify]: Extracting # 31 : cost 0 2.618 * * [simplify]: Extracting # 32 : cost 0 2.619 * * [simplify]: iteration 0 : 369 enodes (cost 2880 ) 2.777 * * [simplify]: Extracting # 0 : cost 0 2.780 * * [simplify]: Extracting # 1 : cost 0 2.783 * * [simplify]: Extracting # 2 : cost 0 2.787 * * [simplify]: Extracting # 3 : cost 0 2.790 * * [simplify]: Extracting # 4 : cost 0 2.793 * * [simplify]: Extracting # 5 : cost 0 2.796 * * [simplify]: Extracting # 6 : cost 0 2.799 * * [simplify]: iteration 1 : 1037 enodes (cost 2720 ) 3.561 * * [simplify]: Extracting # 0 : cost 0 3.567 * * [simplify]: Extracting # 1 : cost 0 3.576 * * [simplify]: Extracting # 2 : cost 0 3.595 * * [simplify]: Extracting # 3 : cost 0 3.605 * * [simplify]: Extracting # 4 : cost 0 3.611 * * [simplify]: iteration 2 : 4934 enodes (cost 2550 ) 5.339 * * [simplify]: Extracting # 0 : cost 0 5.351 * * [simplify]: Extracting # 1 : cost 0 5.370 * * [simplify]: Extracting # 2 : cost 0 5.383 * * [simplify]: Extracting # 3 : cost 0 5.395 * * [simplify]: Extracting # 4 : cost 0 5.407 * * [simplify]: iteration done: 5000 enodes (cost 2548 ) 5.410 * [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)))) 5.412 * * * [progress]: adding candidates to table 6.069 * * [progress]: iteration 2 / 4 6.069 * * * [progress]: picking best candidate 6.093 * * * * [pick]: Picked # 6.093 * * * [progress]: localizing error 6.130 * * * [progress]: generating rewritten candidates 6.130 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 6.194 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 6.225 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 6.238 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 6.306 * * * [progress]: generating series expansions 6.306 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 6.308 * [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))) 6.308 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 6.308 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 6.308 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 6.308 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 6.308 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 6.308 * [taylor]: Taking taylor expansion of 0.25 in k 6.308 * [backup-simplify]: Simplify 0.25 into 0.25 6.308 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.308 * [taylor]: Taking taylor expansion of 1.0 in k 6.308 * [backup-simplify]: Simplify 1.0 into 1.0 6.308 * [taylor]: Taking taylor expansion of k in k 6.308 * [backup-simplify]: Simplify 0 into 0 6.308 * [backup-simplify]: Simplify 1 into 1 6.308 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 6.308 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 6.308 * [taylor]: Taking taylor expansion of 2.0 in k 6.308 * [backup-simplify]: Simplify 2.0 into 2.0 6.308 * [taylor]: Taking taylor expansion of (* n PI) in k 6.308 * [taylor]: Taking taylor expansion of n in k 6.308 * [backup-simplify]: Simplify n into n 6.308 * [taylor]: Taking taylor expansion of PI in k 6.308 * [backup-simplify]: Simplify PI into PI 6.308 * [backup-simplify]: Simplify (* n PI) into (* n PI) 6.308 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 6.308 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 6.309 * [backup-simplify]: Simplify (- 0) into 0 6.309 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.310 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 6.310 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 6.310 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 6.310 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 6.310 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.310 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.310 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 6.310 * [taylor]: Taking taylor expansion of 0.25 in n 6.310 * [backup-simplify]: Simplify 0.25 into 0.25 6.310 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.310 * [taylor]: Taking taylor expansion of 1.0 in n 6.310 * [backup-simplify]: Simplify 1.0 into 1.0 6.310 * [taylor]: Taking taylor expansion of k in n 6.310 * [backup-simplify]: Simplify k into k 6.310 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.310 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.310 * [taylor]: Taking taylor expansion of 2.0 in n 6.310 * [backup-simplify]: Simplify 2.0 into 2.0 6.310 * [taylor]: Taking taylor expansion of (* n PI) in n 6.310 * [taylor]: Taking taylor expansion of n in n 6.310 * [backup-simplify]: Simplify 0 into 0 6.310 * [backup-simplify]: Simplify 1 into 1 6.310 * [taylor]: Taking taylor expansion of PI in n 6.310 * [backup-simplify]: Simplify PI into PI 6.311 * [backup-simplify]: Simplify (* 0 PI) into 0 6.311 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.313 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.314 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.315 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.315 * [backup-simplify]: Simplify (- k) into (- k) 6.315 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.316 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 6.317 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.318 * [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)))) 6.319 * [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))))) 6.319 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 6.319 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.319 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.319 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 6.319 * [taylor]: Taking taylor expansion of 0.25 in n 6.319 * [backup-simplify]: Simplify 0.25 into 0.25 6.319 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.319 * [taylor]: Taking taylor expansion of 1.0 in n 6.319 * [backup-simplify]: Simplify 1.0 into 1.0 6.319 * [taylor]: Taking taylor expansion of k in n 6.319 * [backup-simplify]: Simplify k into k 6.319 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.319 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.319 * [taylor]: Taking taylor expansion of 2.0 in n 6.319 * [backup-simplify]: Simplify 2.0 into 2.0 6.319 * [taylor]: Taking taylor expansion of (* n PI) in n 6.320 * [taylor]: Taking taylor expansion of n in n 6.320 * [backup-simplify]: Simplify 0 into 0 6.320 * [backup-simplify]: Simplify 1 into 1 6.320 * [taylor]: Taking taylor expansion of PI in n 6.320 * [backup-simplify]: Simplify PI into PI 6.320 * [backup-simplify]: Simplify (* 0 PI) into 0 6.320 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.321 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.322 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.323 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.323 * [backup-simplify]: Simplify (- k) into (- k) 6.323 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.323 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 6.324 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.324 * [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)))) 6.325 * [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))))) 6.325 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 6.325 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 6.325 * [taylor]: Taking taylor expansion of 0.25 in k 6.325 * [backup-simplify]: Simplify 0.25 into 0.25 6.325 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 6.325 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.325 * [taylor]: Taking taylor expansion of 1.0 in k 6.325 * [backup-simplify]: Simplify 1.0 into 1.0 6.325 * [taylor]: Taking taylor expansion of k in k 6.325 * [backup-simplify]: Simplify 0 into 0 6.325 * [backup-simplify]: Simplify 1 into 1 6.325 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 6.326 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.326 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.326 * [taylor]: Taking taylor expansion of 2.0 in k 6.326 * [backup-simplify]: Simplify 2.0 into 2.0 6.326 * [taylor]: Taking taylor expansion of PI in k 6.326 * [backup-simplify]: Simplify PI into PI 6.326 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.326 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.327 * [taylor]: Taking taylor expansion of (log n) in k 6.327 * [taylor]: Taking taylor expansion of n in k 6.327 * [backup-simplify]: Simplify n into n 6.327 * [backup-simplify]: Simplify (log n) into (log n) 6.327 * [backup-simplify]: Simplify (- 0) into 0 6.327 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.328 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 6.328 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 6.329 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 6.330 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 6.331 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 6.331 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 6.332 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 6.333 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.333 * [backup-simplify]: Simplify (- 0) into 0 6.333 * [backup-simplify]: Simplify (+ 0 0) into 0 6.334 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 6.335 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.336 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 6.337 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.337 * [taylor]: Taking taylor expansion of 0 in k 6.337 * [backup-simplify]: Simplify 0 into 0 6.337 * [backup-simplify]: Simplify 0 into 0 6.337 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.338 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.339 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 6.339 * [backup-simplify]: Simplify (+ 0 0) into 0 6.339 * [backup-simplify]: Simplify (- 1) into -1 6.340 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.340 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 6.342 * [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)))) 6.344 * [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)))))) 6.346 * [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)))))) 6.347 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 6.348 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 6.350 * [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 6.350 * [backup-simplify]: Simplify (- 0) into 0 6.350 * [backup-simplify]: Simplify (+ 0 0) into 0 6.351 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 6.352 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.353 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.354 * [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 6.354 * [taylor]: Taking taylor expansion of 0 in k 6.355 * [backup-simplify]: Simplify 0 into 0 6.355 * [backup-simplify]: Simplify 0 into 0 6.355 * [backup-simplify]: Simplify 0 into 0 6.356 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.359 * [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 6.361 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 6.362 * [backup-simplify]: Simplify (+ 0 0) into 0 6.362 * [backup-simplify]: Simplify (- 0) into 0 6.362 * [backup-simplify]: Simplify (+ 0 0) into 0 6.364 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.367 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 6.369 * [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))))) 6.373 * [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))))) 6.379 * [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)))))) 6.380 * [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)))) 6.380 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 6.380 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 6.380 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 6.380 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 6.380 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 6.380 * [taylor]: Taking taylor expansion of 0.25 in k 6.380 * [backup-simplify]: Simplify 0.25 into 0.25 6.380 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.380 * [taylor]: Taking taylor expansion of 1.0 in k 6.380 * [backup-simplify]: Simplify 1.0 into 1.0 6.380 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.380 * [taylor]: Taking taylor expansion of k in k 6.380 * [backup-simplify]: Simplify 0 into 0 6.380 * [backup-simplify]: Simplify 1 into 1 6.380 * [backup-simplify]: Simplify (/ 1 1) into 1 6.380 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 6.380 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 6.380 * [taylor]: Taking taylor expansion of 2.0 in k 6.380 * [backup-simplify]: Simplify 2.0 into 2.0 6.380 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.380 * [taylor]: Taking taylor expansion of PI in k 6.380 * [backup-simplify]: Simplify PI into PI 6.380 * [taylor]: Taking taylor expansion of n in k 6.380 * [backup-simplify]: Simplify n into n 6.380 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.380 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 6.380 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 6.381 * [backup-simplify]: Simplify (- 1) into -1 6.381 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.381 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 6.381 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 6.381 * [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))))) 6.381 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 6.381 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.381 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.381 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 6.382 * [taylor]: Taking taylor expansion of 0.25 in n 6.382 * [backup-simplify]: Simplify 0.25 into 0.25 6.382 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.382 * [taylor]: Taking taylor expansion of 1.0 in n 6.382 * [backup-simplify]: Simplify 1.0 into 1.0 6.382 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.382 * [taylor]: Taking taylor expansion of k in n 6.382 * [backup-simplify]: Simplify k into k 6.382 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.382 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.382 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.382 * [taylor]: Taking taylor expansion of 2.0 in n 6.382 * [backup-simplify]: Simplify 2.0 into 2.0 6.382 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.382 * [taylor]: Taking taylor expansion of PI in n 6.382 * [backup-simplify]: Simplify PI into PI 6.382 * [taylor]: Taking taylor expansion of n in n 6.382 * [backup-simplify]: Simplify 0 into 0 6.382 * [backup-simplify]: Simplify 1 into 1 6.382 * [backup-simplify]: Simplify (/ PI 1) into PI 6.382 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.383 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.383 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.383 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.383 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 6.384 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.385 * [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)))) 6.386 * [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))))) 6.386 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 6.386 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.386 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.386 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 6.386 * [taylor]: Taking taylor expansion of 0.25 in n 6.386 * [backup-simplify]: Simplify 0.25 into 0.25 6.386 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.386 * [taylor]: Taking taylor expansion of 1.0 in n 6.386 * [backup-simplify]: Simplify 1.0 into 1.0 6.386 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.386 * [taylor]: Taking taylor expansion of k in n 6.386 * [backup-simplify]: Simplify k into k 6.386 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.386 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.386 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.386 * [taylor]: Taking taylor expansion of 2.0 in n 6.386 * [backup-simplify]: Simplify 2.0 into 2.0 6.386 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.386 * [taylor]: Taking taylor expansion of PI in n 6.386 * [backup-simplify]: Simplify PI into PI 6.386 * [taylor]: Taking taylor expansion of n in n 6.386 * [backup-simplify]: Simplify 0 into 0 6.386 * [backup-simplify]: Simplify 1 into 1 6.386 * [backup-simplify]: Simplify (/ PI 1) into PI 6.387 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.387 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.387 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.387 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.387 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 6.388 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.389 * [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)))) 6.390 * [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))))) 6.390 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 6.390 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 6.390 * [taylor]: Taking taylor expansion of 0.25 in k 6.390 * [backup-simplify]: Simplify 0.25 into 0.25 6.390 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 6.390 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 6.390 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.390 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.390 * [taylor]: Taking taylor expansion of 2.0 in k 6.390 * [backup-simplify]: Simplify 2.0 into 2.0 6.390 * [taylor]: Taking taylor expansion of PI in k 6.390 * [backup-simplify]: Simplify PI into PI 6.395 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.396 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.396 * [taylor]: Taking taylor expansion of (log n) in k 6.396 * [taylor]: Taking taylor expansion of n in k 6.396 * [backup-simplify]: Simplify n into n 6.396 * [backup-simplify]: Simplify (log n) into (log n) 6.396 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.396 * [taylor]: Taking taylor expansion of 1.0 in k 6.396 * [backup-simplify]: Simplify 1.0 into 1.0 6.396 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.396 * [taylor]: Taking taylor expansion of k in k 6.396 * [backup-simplify]: Simplify 0 into 0 6.396 * [backup-simplify]: Simplify 1 into 1 6.397 * [backup-simplify]: Simplify (/ 1 1) into 1 6.397 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.397 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 6.397 * [backup-simplify]: Simplify (- 1) into -1 6.398 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.399 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 6.399 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 6.400 * [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))))) 6.401 * [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))))) 6.401 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.402 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.403 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.403 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.403 * [backup-simplify]: Simplify (- 0) into 0 6.404 * [backup-simplify]: Simplify (+ 0 0) into 0 6.404 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 6.405 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.405 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 6.407 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.407 * [taylor]: Taking taylor expansion of 0 in k 6.407 * [backup-simplify]: Simplify 0 into 0 6.407 * [backup-simplify]: Simplify 0 into 0 6.407 * [backup-simplify]: Simplify 0 into 0 6.407 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.408 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.410 * [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 6.410 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.410 * [backup-simplify]: Simplify (- 0) into 0 6.410 * [backup-simplify]: Simplify (+ 0 0) into 0 6.411 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 6.412 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.414 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 6.416 * [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 6.416 * [taylor]: Taking taylor expansion of 0 in k 6.417 * [backup-simplify]: Simplify 0 into 0 6.417 * [backup-simplify]: Simplify 0 into 0 6.417 * [backup-simplify]: Simplify 0 into 0 6.417 * [backup-simplify]: Simplify 0 into 0 6.418 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.419 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.425 * [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 6.426 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.426 * [backup-simplify]: Simplify (- 0) into 0 6.426 * [backup-simplify]: Simplify (+ 0 0) into 0 6.428 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 6.430 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.432 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 6.435 * [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 6.435 * [taylor]: Taking taylor expansion of 0 in k 6.435 * [backup-simplify]: Simplify 0 into 0 6.435 * [backup-simplify]: Simplify 0 into 0 6.436 * [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)))) 6.437 * [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))) 6.437 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 6.437 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 6.437 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 6.437 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 6.437 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 6.437 * [taylor]: Taking taylor expansion of 0.25 in k 6.437 * [backup-simplify]: Simplify 0.25 into 0.25 6.437 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.437 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.437 * [taylor]: Taking taylor expansion of k in k 6.437 * [backup-simplify]: Simplify 0 into 0 6.437 * [backup-simplify]: Simplify 1 into 1 6.438 * [backup-simplify]: Simplify (/ 1 1) into 1 6.438 * [taylor]: Taking taylor expansion of 1.0 in k 6.438 * [backup-simplify]: Simplify 1.0 into 1.0 6.438 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 6.438 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 6.438 * [taylor]: Taking taylor expansion of -2.0 in k 6.438 * [backup-simplify]: Simplify -2.0 into -2.0 6.438 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.438 * [taylor]: Taking taylor expansion of PI in k 6.438 * [backup-simplify]: Simplify PI into PI 6.438 * [taylor]: Taking taylor expansion of n in k 6.438 * [backup-simplify]: Simplify n into n 6.438 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.438 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 6.438 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 6.439 * [backup-simplify]: Simplify (+ 1 0) into 1 6.439 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 6.439 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 6.440 * [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)))))) 6.440 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 6.440 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.440 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.440 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 6.440 * [taylor]: Taking taylor expansion of 0.25 in n 6.440 * [backup-simplify]: Simplify 0.25 into 0.25 6.440 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.440 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.440 * [taylor]: Taking taylor expansion of k in n 6.440 * [backup-simplify]: Simplify k into k 6.440 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.440 * [taylor]: Taking taylor expansion of 1.0 in n 6.440 * [backup-simplify]: Simplify 1.0 into 1.0 6.440 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.440 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.440 * [taylor]: Taking taylor expansion of -2.0 in n 6.440 * [backup-simplify]: Simplify -2.0 into -2.0 6.440 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.440 * [taylor]: Taking taylor expansion of PI in n 6.440 * [backup-simplify]: Simplify PI into PI 6.440 * [taylor]: Taking taylor expansion of n in n 6.440 * [backup-simplify]: Simplify 0 into 0 6.440 * [backup-simplify]: Simplify 1 into 1 6.441 * [backup-simplify]: Simplify (/ PI 1) into PI 6.442 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.443 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.443 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.443 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 6.444 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.446 * [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)))) 6.447 * [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))))) 6.447 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 6.447 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.447 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.447 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 6.447 * [taylor]: Taking taylor expansion of 0.25 in n 6.447 * [backup-simplify]: Simplify 0.25 into 0.25 6.447 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.447 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.447 * [taylor]: Taking taylor expansion of k in n 6.447 * [backup-simplify]: Simplify k into k 6.447 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.447 * [taylor]: Taking taylor expansion of 1.0 in n 6.447 * [backup-simplify]: Simplify 1.0 into 1.0 6.447 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.448 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.448 * [taylor]: Taking taylor expansion of -2.0 in n 6.448 * [backup-simplify]: Simplify -2.0 into -2.0 6.448 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.448 * [taylor]: Taking taylor expansion of PI in n 6.448 * [backup-simplify]: Simplify PI into PI 6.448 * [taylor]: Taking taylor expansion of n in n 6.448 * [backup-simplify]: Simplify 0 into 0 6.448 * [backup-simplify]: Simplify 1 into 1 6.449 * [backup-simplify]: Simplify (/ PI 1) into PI 6.449 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.450 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.450 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.450 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 6.452 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.453 * [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)))) 6.454 * [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))))) 6.454 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 6.454 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 6.454 * [taylor]: Taking taylor expansion of 0.25 in k 6.454 * [backup-simplify]: Simplify 0.25 into 0.25 6.454 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 6.455 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.455 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.455 * [taylor]: Taking taylor expansion of k in k 6.455 * [backup-simplify]: Simplify 0 into 0 6.455 * [backup-simplify]: Simplify 1 into 1 6.455 * [backup-simplify]: Simplify (/ 1 1) into 1 6.455 * [taylor]: Taking taylor expansion of 1.0 in k 6.455 * [backup-simplify]: Simplify 1.0 into 1.0 6.455 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 6.455 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 6.455 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 6.455 * [taylor]: Taking taylor expansion of -2.0 in k 6.455 * [backup-simplify]: Simplify -2.0 into -2.0 6.455 * [taylor]: Taking taylor expansion of PI in k 6.455 * [backup-simplify]: Simplify PI into PI 6.456 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.457 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.457 * [taylor]: Taking taylor expansion of (log n) in k 6.457 * [taylor]: Taking taylor expansion of n in k 6.457 * [backup-simplify]: Simplify n into n 6.457 * [backup-simplify]: Simplify (log n) into (log n) 6.457 * [backup-simplify]: Simplify (+ 1 0) into 1 6.457 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.459 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 6.460 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 6.461 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 6.462 * [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))))) 6.463 * [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))))) 6.464 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.465 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 6.467 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 6.467 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.467 * [backup-simplify]: Simplify (+ 0 0) into 0 6.468 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 6.469 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.471 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 6.473 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.473 * [taylor]: Taking taylor expansion of 0 in k 6.473 * [backup-simplify]: Simplify 0 into 0 6.473 * [backup-simplify]: Simplify 0 into 0 6.473 * [backup-simplify]: Simplify 0 into 0 6.474 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.475 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.479 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 6.479 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.479 * [backup-simplify]: Simplify (+ 0 0) into 0 6.480 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 6.482 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.483 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 6.486 * [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 6.486 * [taylor]: Taking taylor expansion of 0 in k 6.486 * [backup-simplify]: Simplify 0 into 0 6.486 * [backup-simplify]: Simplify 0 into 0 6.486 * [backup-simplify]: Simplify 0 into 0 6.486 * [backup-simplify]: Simplify 0 into 0 6.487 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.488 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.495 * [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 6.495 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.496 * [backup-simplify]: Simplify (+ 0 0) into 0 6.498 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 6.499 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.502 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 6.505 * [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 6.505 * [taylor]: Taking taylor expansion of 0 in k 6.505 * [backup-simplify]: Simplify 0 into 0 6.505 * [backup-simplify]: Simplify 0 into 0 6.506 * [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)))))) 6.506 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 6.507 * [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))) 6.507 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 6.507 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 6.507 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 6.507 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 6.507 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 6.507 * [taylor]: Taking taylor expansion of 0.25 in k 6.507 * [backup-simplify]: Simplify 0.25 into 0.25 6.507 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.507 * [taylor]: Taking taylor expansion of 1.0 in k 6.508 * [backup-simplify]: Simplify 1.0 into 1.0 6.508 * [taylor]: Taking taylor expansion of k in k 6.508 * [backup-simplify]: Simplify 0 into 0 6.508 * [backup-simplify]: Simplify 1 into 1 6.508 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 6.508 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 6.508 * [taylor]: Taking taylor expansion of 2.0 in k 6.508 * [backup-simplify]: Simplify 2.0 into 2.0 6.508 * [taylor]: Taking taylor expansion of (* n PI) in k 6.508 * [taylor]: Taking taylor expansion of n in k 6.508 * [backup-simplify]: Simplify n into n 6.508 * [taylor]: Taking taylor expansion of PI in k 6.508 * [backup-simplify]: Simplify PI into PI 6.508 * [backup-simplify]: Simplify (* n PI) into (* n PI) 6.508 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 6.508 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 6.509 * [backup-simplify]: Simplify (- 0) into 0 6.509 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.509 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 6.510 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 6.510 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 6.510 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 6.510 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.510 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.510 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 6.510 * [taylor]: Taking taylor expansion of 0.25 in n 6.510 * [backup-simplify]: Simplify 0.25 into 0.25 6.510 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.510 * [taylor]: Taking taylor expansion of 1.0 in n 6.510 * [backup-simplify]: Simplify 1.0 into 1.0 6.510 * [taylor]: Taking taylor expansion of k in n 6.510 * [backup-simplify]: Simplify k into k 6.510 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.510 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.510 * [taylor]: Taking taylor expansion of 2.0 in n 6.510 * [backup-simplify]: Simplify 2.0 into 2.0 6.510 * [taylor]: Taking taylor expansion of (* n PI) in n 6.510 * [taylor]: Taking taylor expansion of n in n 6.510 * [backup-simplify]: Simplify 0 into 0 6.510 * [backup-simplify]: Simplify 1 into 1 6.510 * [taylor]: Taking taylor expansion of PI in n 6.510 * [backup-simplify]: Simplify PI into PI 6.511 * [backup-simplify]: Simplify (* 0 PI) into 0 6.511 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.513 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.514 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.515 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.516 * [backup-simplify]: Simplify (- k) into (- k) 6.516 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.516 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 6.517 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.518 * [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)))) 6.520 * [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))))) 6.520 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 6.520 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.520 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.520 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 6.520 * [taylor]: Taking taylor expansion of 0.25 in n 6.520 * [backup-simplify]: Simplify 0.25 into 0.25 6.520 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.520 * [taylor]: Taking taylor expansion of 1.0 in n 6.520 * [backup-simplify]: Simplify 1.0 into 1.0 6.520 * [taylor]: Taking taylor expansion of k in n 6.520 * [backup-simplify]: Simplify k into k 6.520 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.520 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.520 * [taylor]: Taking taylor expansion of 2.0 in n 6.520 * [backup-simplify]: Simplify 2.0 into 2.0 6.520 * [taylor]: Taking taylor expansion of (* n PI) in n 6.520 * [taylor]: Taking taylor expansion of n in n 6.520 * [backup-simplify]: Simplify 0 into 0 6.520 * [backup-simplify]: Simplify 1 into 1 6.520 * [taylor]: Taking taylor expansion of PI in n 6.520 * [backup-simplify]: Simplify PI into PI 6.521 * [backup-simplify]: Simplify (* 0 PI) into 0 6.521 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.523 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.524 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.525 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.525 * [backup-simplify]: Simplify (- k) into (- k) 6.526 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.526 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 6.527 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.528 * [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)))) 6.529 * [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))))) 6.530 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 6.530 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (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 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 6.530 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.530 * [taylor]: Taking taylor expansion of 1.0 in k 6.530 * [backup-simplify]: Simplify 1.0 into 1.0 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 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 6.530 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.530 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.530 * [taylor]: Taking taylor expansion of 2.0 in k 6.530 * [backup-simplify]: Simplify 2.0 into 2.0 6.530 * [taylor]: Taking taylor expansion of PI in k 6.530 * [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) 6.532 * [backup-simplify]: Simplify (- 0) into 0 6.533 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.534 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 6.535 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 6.536 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 6.542 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 6.543 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 6.544 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 6.545 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 6.547 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.548 * [backup-simplify]: Simplify (- 0) into 0 6.548 * [backup-simplify]: Simplify (+ 0 0) into 0 6.548 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 6.550 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.552 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 6.554 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.554 * [taylor]: Taking taylor expansion of 0 in k 6.554 * [backup-simplify]: Simplify 0 into 0 6.554 * [backup-simplify]: Simplify 0 into 0 6.555 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.557 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.558 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 6.558 * [backup-simplify]: Simplify (+ 0 0) into 0 6.558 * [backup-simplify]: Simplify (- 1) into -1 6.559 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.560 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 6.563 * [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)))) 6.566 * [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)))))) 6.568 * [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)))))) 6.569 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 6.570 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 6.572 * [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 6.572 * [backup-simplify]: Simplify (- 0) into 0 6.572 * [backup-simplify]: Simplify (+ 0 0) into 0 6.573 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 6.573 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.574 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.576 * [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 6.576 * [taylor]: Taking taylor expansion of 0 in k 6.576 * [backup-simplify]: Simplify 0 into 0 6.576 * [backup-simplify]: Simplify 0 into 0 6.576 * [backup-simplify]: Simplify 0 into 0 6.576 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.578 * [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 6.579 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 6.580 * [backup-simplify]: Simplify (+ 0 0) into 0 6.580 * [backup-simplify]: Simplify (- 0) into 0 6.580 * [backup-simplify]: Simplify (+ 0 0) into 0 6.581 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.583 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 6.585 * [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))))) 6.588 * [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))))) 6.595 * [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)))))) 6.595 * [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)))) 6.595 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 6.595 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 6.595 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 6.595 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 6.595 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 6.595 * [taylor]: Taking taylor expansion of 0.25 in k 6.595 * [backup-simplify]: Simplify 0.25 into 0.25 6.595 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.595 * [taylor]: Taking taylor expansion of 1.0 in k 6.595 * [backup-simplify]: Simplify 1.0 into 1.0 6.595 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.596 * [taylor]: Taking taylor expansion of k in k 6.596 * [backup-simplify]: Simplify 0 into 0 6.596 * [backup-simplify]: Simplify 1 into 1 6.596 * [backup-simplify]: Simplify (/ 1 1) into 1 6.596 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 6.596 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 6.596 * [taylor]: Taking taylor expansion of 2.0 in k 6.596 * [backup-simplify]: Simplify 2.0 into 2.0 6.596 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.596 * [taylor]: Taking taylor expansion of PI in k 6.596 * [backup-simplify]: Simplify PI into PI 6.596 * [taylor]: Taking taylor expansion of n in k 6.596 * [backup-simplify]: Simplify n into n 6.596 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.596 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 6.596 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 6.597 * [backup-simplify]: Simplify (- 1) into -1 6.597 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.598 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 6.598 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 6.598 * [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))))) 6.598 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 6.598 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.598 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.598 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 6.598 * [taylor]: Taking taylor expansion of 0.25 in n 6.598 * [backup-simplify]: Simplify 0.25 into 0.25 6.598 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.598 * [taylor]: Taking taylor expansion of 1.0 in n 6.598 * [backup-simplify]: Simplify 1.0 into 1.0 6.598 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.598 * [taylor]: Taking taylor expansion of k in n 6.598 * [backup-simplify]: Simplify k into k 6.598 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.598 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.598 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.599 * [taylor]: Taking taylor expansion of 2.0 in n 6.599 * [backup-simplify]: Simplify 2.0 into 2.0 6.599 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.599 * [taylor]: Taking taylor expansion of PI in n 6.599 * [backup-simplify]: Simplify PI into PI 6.599 * [taylor]: Taking taylor expansion of n in n 6.599 * [backup-simplify]: Simplify 0 into 0 6.599 * [backup-simplify]: Simplify 1 into 1 6.599 * [backup-simplify]: Simplify (/ PI 1) into PI 6.600 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.601 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.601 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.601 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.601 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 6.602 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.603 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 6.605 * [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))))) 6.605 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 6.605 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.605 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.605 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 6.605 * [taylor]: Taking taylor expansion of 0.25 in n 6.605 * [backup-simplify]: Simplify 0.25 into 0.25 6.605 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.605 * [taylor]: Taking taylor expansion of 1.0 in n 6.605 * [backup-simplify]: Simplify 1.0 into 1.0 6.605 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.605 * [taylor]: Taking taylor expansion of k in n 6.605 * [backup-simplify]: Simplify k into k 6.605 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.605 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.605 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.605 * [taylor]: Taking taylor expansion of 2.0 in n 6.605 * [backup-simplify]: Simplify 2.0 into 2.0 6.605 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.605 * [taylor]: Taking taylor expansion of PI in n 6.605 * [backup-simplify]: Simplify PI into PI 6.605 * [taylor]: Taking taylor expansion of n in n 6.605 * [backup-simplify]: Simplify 0 into 0 6.605 * [backup-simplify]: Simplify 1 into 1 6.606 * [backup-simplify]: Simplify (/ PI 1) into PI 6.606 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.607 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.607 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.607 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.608 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 6.609 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.610 * [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)))) 6.611 * [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))))) 6.612 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 6.612 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 6.612 * [taylor]: Taking taylor expansion of 0.25 in k 6.612 * [backup-simplify]: Simplify 0.25 into 0.25 6.612 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 6.612 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 6.612 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.612 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.612 * [taylor]: Taking taylor expansion of 2.0 in k 6.612 * [backup-simplify]: Simplify 2.0 into 2.0 6.612 * [taylor]: Taking taylor expansion of PI in k 6.612 * [backup-simplify]: Simplify PI into PI 6.612 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.613 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.613 * [taylor]: Taking taylor expansion of (log n) in k 6.613 * [taylor]: Taking taylor expansion of n in k 6.613 * [backup-simplify]: Simplify n into n 6.613 * [backup-simplify]: Simplify (log n) into (log n) 6.613 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.613 * [taylor]: Taking taylor expansion of 1.0 in k 6.613 * [backup-simplify]: Simplify 1.0 into 1.0 6.613 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.613 * [taylor]: Taking taylor expansion of k in k 6.613 * [backup-simplify]: Simplify 0 into 0 6.613 * [backup-simplify]: Simplify 1 into 1 6.613 * [backup-simplify]: Simplify (/ 1 1) into 1 6.613 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.614 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 6.614 * [backup-simplify]: Simplify (- 1) into -1 6.614 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.615 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 6.616 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 6.616 * [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))))) 6.617 * [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))))) 6.618 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.618 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.619 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.619 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.620 * [backup-simplify]: Simplify (- 0) into 0 6.620 * [backup-simplify]: Simplify (+ 0 0) into 0 6.620 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 6.621 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.622 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 6.623 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.623 * [taylor]: Taking taylor expansion of 0 in k 6.623 * [backup-simplify]: Simplify 0 into 0 6.623 * [backup-simplify]: Simplify 0 into 0 6.623 * [backup-simplify]: Simplify 0 into 0 6.624 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.624 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.626 * [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 6.626 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.626 * [backup-simplify]: Simplify (- 0) into 0 6.627 * [backup-simplify]: Simplify (+ 0 0) into 0 6.627 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 6.628 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.629 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 6.630 * [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 6.631 * [taylor]: Taking taylor expansion of 0 in k 6.631 * [backup-simplify]: Simplify 0 into 0 6.631 * [backup-simplify]: Simplify 0 into 0 6.631 * [backup-simplify]: Simplify 0 into 0 6.631 * [backup-simplify]: Simplify 0 into 0 6.631 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.632 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.635 * [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 6.636 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.636 * [backup-simplify]: Simplify (- 0) into 0 6.636 * [backup-simplify]: Simplify (+ 0 0) into 0 6.637 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 6.638 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.639 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 6.640 * [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 6.640 * [taylor]: Taking taylor expansion of 0 in k 6.640 * [backup-simplify]: Simplify 0 into 0 6.640 * [backup-simplify]: Simplify 0 into 0 6.641 * [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)))) 6.642 * [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))) 6.642 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 6.642 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 6.642 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 6.642 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 6.642 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 6.642 * [taylor]: Taking taylor expansion of 0.25 in k 6.642 * [backup-simplify]: Simplify 0.25 into 0.25 6.642 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.642 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.642 * [taylor]: Taking taylor expansion of k in k 6.642 * [backup-simplify]: Simplify 0 into 0 6.642 * [backup-simplify]: Simplify 1 into 1 6.642 * [backup-simplify]: Simplify (/ 1 1) into 1 6.642 * [taylor]: Taking taylor expansion of 1.0 in k 6.642 * [backup-simplify]: Simplify 1.0 into 1.0 6.642 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 6.642 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 6.642 * [taylor]: Taking taylor expansion of -2.0 in k 6.642 * [backup-simplify]: Simplify -2.0 into -2.0 6.642 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.642 * [taylor]: Taking taylor expansion of PI in k 6.642 * [backup-simplify]: Simplify PI into PI 6.642 * [taylor]: Taking taylor expansion of n in k 6.642 * [backup-simplify]: Simplify n into n 6.642 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.643 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 6.643 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 6.643 * [backup-simplify]: Simplify (+ 1 0) into 1 6.643 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 6.643 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 6.644 * [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)))))) 6.644 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 6.644 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.644 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.644 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 6.644 * [taylor]: Taking taylor expansion of 0.25 in n 6.644 * [backup-simplify]: Simplify 0.25 into 0.25 6.644 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.644 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.644 * [taylor]: Taking taylor expansion of k in n 6.644 * [backup-simplify]: Simplify k into k 6.644 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.644 * [taylor]: Taking taylor expansion of 1.0 in n 6.644 * [backup-simplify]: Simplify 1.0 into 1.0 6.644 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.644 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.644 * [taylor]: Taking taylor expansion of -2.0 in n 6.644 * [backup-simplify]: Simplify -2.0 into -2.0 6.644 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.644 * [taylor]: Taking taylor expansion of PI in n 6.644 * [backup-simplify]: Simplify PI into PI 6.644 * [taylor]: Taking taylor expansion of n in n 6.644 * [backup-simplify]: Simplify 0 into 0 6.644 * [backup-simplify]: Simplify 1 into 1 6.650 * [backup-simplify]: Simplify (/ PI 1) into PI 6.650 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.651 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.652 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.652 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 6.653 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.654 * [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)))) 6.655 * [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))))) 6.655 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 6.655 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.655 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.656 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 6.656 * [taylor]: Taking taylor expansion of 0.25 in n 6.656 * [backup-simplify]: Simplify 0.25 into 0.25 6.656 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.656 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.656 * [taylor]: Taking taylor expansion of k in n 6.656 * [backup-simplify]: Simplify k into k 6.656 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.656 * [taylor]: Taking taylor expansion of 1.0 in n 6.656 * [backup-simplify]: Simplify 1.0 into 1.0 6.656 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.656 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.656 * [taylor]: Taking taylor expansion of -2.0 in n 6.656 * [backup-simplify]: Simplify -2.0 into -2.0 6.656 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.656 * [taylor]: Taking taylor expansion of PI in n 6.656 * [backup-simplify]: Simplify PI into PI 6.656 * [taylor]: Taking taylor expansion of n in n 6.656 * [backup-simplify]: Simplify 0 into 0 6.656 * [backup-simplify]: Simplify 1 into 1 6.657 * [backup-simplify]: Simplify (/ PI 1) into PI 6.657 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.658 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.658 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.658 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 6.660 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.661 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 6.662 * [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))))) 6.662 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 6.662 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 6.662 * [taylor]: Taking taylor expansion of 0.25 in k 6.662 * [backup-simplify]: Simplify 0.25 into 0.25 6.662 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 6.662 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.662 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.662 * [taylor]: Taking taylor expansion of k in k 6.662 * [backup-simplify]: Simplify 0 into 0 6.662 * [backup-simplify]: Simplify 1 into 1 6.663 * [backup-simplify]: Simplify (/ 1 1) into 1 6.663 * [taylor]: Taking taylor expansion of 1.0 in k 6.663 * [backup-simplify]: Simplify 1.0 into 1.0 6.663 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 6.663 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 6.663 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 6.663 * [taylor]: Taking taylor expansion of -2.0 in k 6.663 * [backup-simplify]: Simplify -2.0 into -2.0 6.663 * [taylor]: Taking taylor expansion of PI in k 6.663 * [backup-simplify]: Simplify PI into PI 6.664 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.664 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.665 * [taylor]: Taking taylor expansion of (log n) in k 6.665 * [taylor]: Taking taylor expansion of n in k 6.665 * [backup-simplify]: Simplify n into n 6.665 * [backup-simplify]: Simplify (log n) into (log n) 6.665 * [backup-simplify]: Simplify (+ 1 0) into 1 6.665 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.666 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 6.667 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 6.668 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 6.669 * [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))))) 6.671 * [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))))) 6.671 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.672 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 6.673 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 6.673 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.673 * [backup-simplify]: Simplify (+ 0 0) into 0 6.674 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 6.674 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.675 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 6.676 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.676 * [taylor]: Taking taylor expansion of 0 in k 6.676 * [backup-simplify]: Simplify 0 into 0 6.676 * [backup-simplify]: Simplify 0 into 0 6.676 * [backup-simplify]: Simplify 0 into 0 6.677 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.678 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.679 * [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 6.680 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.680 * [backup-simplify]: Simplify (+ 0 0) into 0 6.680 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 6.681 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.682 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 6.684 * [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 6.684 * [taylor]: Taking taylor expansion of 0 in k 6.684 * [backup-simplify]: Simplify 0 into 0 6.684 * [backup-simplify]: Simplify 0 into 0 6.684 * [backup-simplify]: Simplify 0 into 0 6.684 * [backup-simplify]: Simplify 0 into 0 6.685 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.685 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.689 * [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 6.689 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.689 * [backup-simplify]: Simplify (+ 0 0) into 0 6.690 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 6.691 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.692 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 6.694 * [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 6.694 * [taylor]: Taking taylor expansion of 0 in k 6.694 * [backup-simplify]: Simplify 0 into 0 6.694 * [backup-simplify]: Simplify 0 into 0 6.695 * [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)))))) 6.695 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 6.695 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 6.695 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 6.695 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 6.695 * [taylor]: Taking taylor expansion of 1.0 in k 6.695 * [backup-simplify]: Simplify 1.0 into 1.0 6.695 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 6.695 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.695 * [taylor]: Taking taylor expansion of k in k 6.695 * [backup-simplify]: Simplify 0 into 0 6.695 * [backup-simplify]: Simplify 1 into 1 6.695 * [backup-simplify]: Simplify (/ 1 1) into 1 6.695 * [backup-simplify]: Simplify (sqrt 0) into 0 6.696 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.696 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 6.696 * [taylor]: Taking taylor expansion of 1.0 in k 6.696 * [backup-simplify]: Simplify 1.0 into 1.0 6.696 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 6.696 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.696 * [taylor]: Taking taylor expansion of k in k 6.696 * [backup-simplify]: Simplify 0 into 0 6.696 * [backup-simplify]: Simplify 1 into 1 6.697 * [backup-simplify]: Simplify (/ 1 1) into 1 6.697 * [backup-simplify]: Simplify (sqrt 0) into 0 6.698 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.698 * [backup-simplify]: Simplify (* 1.0 0) into 0 6.698 * [backup-simplify]: Simplify 0 into 0 6.699 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 6.699 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.699 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 6.701 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 6.702 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 6.703 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.703 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.705 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 6.707 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 6.707 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.708 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 6.708 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 6.708 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 6.708 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 6.708 * [taylor]: Taking taylor expansion of 1.0 in k 6.708 * [backup-simplify]: Simplify 1.0 into 1.0 6.708 * [taylor]: Taking taylor expansion of (sqrt k) in k 6.708 * [taylor]: Taking taylor expansion of k in k 6.708 * [backup-simplify]: Simplify 0 into 0 6.709 * [backup-simplify]: Simplify 1 into 1 6.709 * [backup-simplify]: Simplify (sqrt 0) into 0 6.711 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.711 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 6.711 * [taylor]: Taking taylor expansion of 1.0 in k 6.711 * [backup-simplify]: Simplify 1.0 into 1.0 6.711 * [taylor]: Taking taylor expansion of (sqrt k) in k 6.711 * [taylor]: Taking taylor expansion of k in k 6.711 * [backup-simplify]: Simplify 0 into 0 6.711 * [backup-simplify]: Simplify 1 into 1 6.711 * [backup-simplify]: Simplify (sqrt 0) into 0 6.712 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.713 * [backup-simplify]: Simplify (* 1.0 0) into 0 6.713 * [backup-simplify]: Simplify 0 into 0 6.714 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 6.715 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.717 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 6.718 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 6.718 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.720 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 6.722 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 6.722 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.723 * [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)))))))) 6.723 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 6.723 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 6.723 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 6.724 * [taylor]: Taking taylor expansion of 1.0 in k 6.724 * [backup-simplify]: Simplify 1.0 into 1.0 6.724 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 6.724 * [taylor]: Taking taylor expansion of (/ -1 k) in k 6.724 * [taylor]: Taking taylor expansion of -1 in k 6.724 * [backup-simplify]: Simplify -1 into -1 6.724 * [taylor]: Taking taylor expansion of k in k 6.724 * [backup-simplify]: Simplify 0 into 0 6.724 * [backup-simplify]: Simplify 1 into 1 6.724 * [backup-simplify]: Simplify (/ -1 1) into -1 6.724 * [backup-simplify]: Simplify (sqrt 0) into 0 6.725 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 6.725 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 6.725 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 6.725 * [taylor]: Taking taylor expansion of 1.0 in k 6.725 * [backup-simplify]: Simplify 1.0 into 1.0 6.725 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 6.725 * [taylor]: Taking taylor expansion of (/ -1 k) in k 6.725 * [taylor]: Taking taylor expansion of -1 in k 6.725 * [backup-simplify]: Simplify -1 into -1 6.725 * [taylor]: Taking taylor expansion of k in k 6.725 * [backup-simplify]: Simplify 0 into 0 6.725 * [backup-simplify]: Simplify 1 into 1 6.726 * [backup-simplify]: Simplify (/ -1 1) into -1 6.726 * [backup-simplify]: Simplify (sqrt 0) into 0 6.727 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 6.727 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 6.727 * [backup-simplify]: Simplify +nan.0 into +nan.0 6.728 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 6.729 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 6.731 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 6.731 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.732 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.734 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 6.737 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 6.737 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 6.738 * [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))))) 6.738 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 6.738 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 6.738 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 6.738 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.738 * [taylor]: Taking taylor expansion of 2.0 in n 6.738 * [backup-simplify]: Simplify 2.0 into 2.0 6.738 * [taylor]: Taking taylor expansion of (* n PI) in n 6.738 * [taylor]: Taking taylor expansion of n in n 6.738 * [backup-simplify]: Simplify 0 into 0 6.738 * [backup-simplify]: Simplify 1 into 1 6.738 * [taylor]: Taking taylor expansion of PI in n 6.738 * [backup-simplify]: Simplify PI into PI 6.738 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.738 * [taylor]: Taking taylor expansion of 2.0 in n 6.739 * [backup-simplify]: Simplify 2.0 into 2.0 6.739 * [taylor]: Taking taylor expansion of (* n PI) in n 6.739 * [taylor]: Taking taylor expansion of n in n 6.739 * [backup-simplify]: Simplify 0 into 0 6.739 * [backup-simplify]: Simplify 1 into 1 6.739 * [taylor]: Taking taylor expansion of PI in n 6.739 * [backup-simplify]: Simplify PI into PI 6.739 * [backup-simplify]: Simplify (* 0 PI) into 0 6.739 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.739 * [backup-simplify]: Simplify 0 into 0 6.740 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.741 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.741 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.742 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 6.743 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 6.743 * [backup-simplify]: Simplify 0 into 0 6.743 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 6.744 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 6.744 * [backup-simplify]: Simplify 0 into 0 6.745 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 6.746 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 6.746 * [backup-simplify]: Simplify 0 into 0 6.746 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 6.750 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 6.750 * [backup-simplify]: Simplify 0 into 0 6.751 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 6.753 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 6.753 * [backup-simplify]: Simplify 0 into 0 6.755 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 6.757 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 6.757 * [backup-simplify]: Simplify 0 into 0 6.758 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 6.759 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 6.759 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 6.759 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.759 * [taylor]: Taking taylor expansion of 2.0 in n 6.759 * [backup-simplify]: Simplify 2.0 into 2.0 6.759 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.759 * [taylor]: Taking taylor expansion of PI in n 6.759 * [backup-simplify]: Simplify PI into PI 6.759 * [taylor]: Taking taylor expansion of n in n 6.759 * [backup-simplify]: Simplify 0 into 0 6.759 * [backup-simplify]: Simplify 1 into 1 6.759 * [backup-simplify]: Simplify (/ PI 1) into PI 6.759 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.759 * [taylor]: Taking taylor expansion of 2.0 in n 6.760 * [backup-simplify]: Simplify 2.0 into 2.0 6.760 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.760 * [taylor]: Taking taylor expansion of PI in n 6.760 * [backup-simplify]: Simplify PI into PI 6.760 * [taylor]: Taking taylor expansion of n in n 6.760 * [backup-simplify]: Simplify 0 into 0 6.760 * [backup-simplify]: Simplify 1 into 1 6.760 * [backup-simplify]: Simplify (/ PI 1) into PI 6.761 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.762 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.762 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.763 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.763 * [backup-simplify]: Simplify 0 into 0 6.764 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.765 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.765 * [backup-simplify]: Simplify 0 into 0 6.767 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.768 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.768 * [backup-simplify]: Simplify 0 into 0 6.769 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.770 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 6.770 * [backup-simplify]: Simplify 0 into 0 6.771 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.772 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 6.772 * [backup-simplify]: Simplify 0 into 0 6.773 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.774 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 6.774 * [backup-simplify]: Simplify 0 into 0 6.774 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 6.775 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 6.775 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 6.775 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.775 * [taylor]: Taking taylor expansion of -2.0 in n 6.775 * [backup-simplify]: Simplify -2.0 into -2.0 6.775 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.775 * [taylor]: Taking taylor expansion of PI in n 6.775 * [backup-simplify]: Simplify PI into PI 6.775 * [taylor]: Taking taylor expansion of n in n 6.775 * [backup-simplify]: Simplify 0 into 0 6.775 * [backup-simplify]: Simplify 1 into 1 6.775 * [backup-simplify]: Simplify (/ PI 1) into PI 6.775 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.775 * [taylor]: Taking taylor expansion of -2.0 in n 6.775 * [backup-simplify]: Simplify -2.0 into -2.0 6.775 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.775 * [taylor]: Taking taylor expansion of PI in n 6.775 * [backup-simplify]: Simplify PI into PI 6.775 * [taylor]: Taking taylor expansion of n in n 6.775 * [backup-simplify]: Simplify 0 into 0 6.775 * [backup-simplify]: Simplify 1 into 1 6.776 * [backup-simplify]: Simplify (/ PI 1) into PI 6.776 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.776 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.777 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.777 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 6.777 * [backup-simplify]: Simplify 0 into 0 6.778 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.779 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.779 * [backup-simplify]: Simplify 0 into 0 6.779 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.780 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.780 * [backup-simplify]: Simplify 0 into 0 6.780 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.781 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 6.781 * [backup-simplify]: Simplify 0 into 0 6.782 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.783 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 6.783 * [backup-simplify]: Simplify 0 into 0 6.783 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.784 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 6.784 * [backup-simplify]: Simplify 0 into 0 6.785 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 6.785 * * * [progress]: simplifying candidates 6.788 * [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 (* 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(log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 6.793 * * [simplify]: Extracting # 0 : cost 0 6.794 * * [simplify]: Extracting # 1 : cost 0 6.794 * * [simplify]: Extracting # 2 : cost 0 6.794 * * [simplify]: Extracting # 3 : cost 0 6.795 * * [simplify]: Extracting # 4 : cost 0 6.795 * * [simplify]: Extracting # 5 : cost 0 6.796 * * [simplify]: Extracting # 6 : cost 0 6.796 * * [simplify]: Extracting # 7 : cost 0 6.797 * * [simplify]: Extracting # 8 : cost 0 6.797 * * [simplify]: Extracting # 9 : cost 0 6.798 * * [simplify]: Extracting # 10 : cost 0 6.798 * * [simplify]: Extracting # 11 : cost 0 6.799 * * [simplify]: Extracting # 12 : cost 0 6.799 * * [simplify]: Extracting # 13 : cost 0 6.800 * * [simplify]: Extracting # 14 : cost 0 6.800 * * [simplify]: iteration 0 : 332 enodes (cost 3588 ) 6.922 * * [simplify]: Extracting # 0 : cost 0 6.923 * * [simplify]: Extracting # 1 : cost 0 6.925 * * [simplify]: Extracting # 2 : cost 0 6.926 * * [simplify]: Extracting # 3 : cost 0 6.928 * * [simplify]: Extracting # 4 : cost 0 6.929 * * [simplify]: Extracting # 5 : cost 0 6.931 * * [simplify]: Extracting # 6 : cost 0 6.932 * * [simplify]: Extracting # 7 : cost 0 6.933 * * [simplify]: iteration 1 : 979 enodes (cost 3316 ) 7.761 * * [simplify]: Extracting # 0 : cost 0 7.766 * * [simplify]: Extracting # 1 : cost 0 7.777 * * [simplify]: Extracting # 2 : cost 0 7.782 * * [simplify]: Extracting # 3 : cost 0 7.791 * * [simplify]: Extracting # 4 : cost 0 7.802 * * [simplify]: iteration 2 : 4191 enodes (cost 3202 ) 9.455 * * [simplify]: Extracting # 0 : cost 0 9.470 * * [simplify]: Extracting # 1 : cost 0 9.477 * * [simplify]: Extracting # 2 : cost 0 9.484 * * [simplify]: Extracting # 3 : cost 0 9.490 * * [simplify]: iteration done: 5000 enodes (cost 3197 ) 9.493 * [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) (/ (* (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 (/ (- 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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 (- 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 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) (/ (/ (+ (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 (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2))) (pow (* n (* 2.0 PI)) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 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)) 9.498 * * * [progress]: adding candidates to table 10.806 * * [progress]: iteration 3 / 4 10.806 * * * [progress]: picking best candidate 10.847 * * * * [pick]: Picked # 10.847 * * * [progress]: localizing error 10.866 * * * [progress]: generating rewritten candidates 10.866 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 10.918 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1 1) 10.929 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 10.937 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 2 1) 10.970 * * * [progress]: generating series expansions 10.970 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 10.972 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 10.972 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 10.972 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 10.972 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 10.972 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 10.972 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 10.972 * [taylor]: Taking taylor expansion of 0.5 in k 10.972 * [backup-simplify]: Simplify 0.5 into 0.5 10.972 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 10.972 * [taylor]: Taking taylor expansion of 1.0 in k 10.972 * [backup-simplify]: Simplify 1.0 into 1.0 10.972 * [taylor]: Taking taylor expansion of k in k 10.972 * [backup-simplify]: Simplify 0 into 0 10.972 * [backup-simplify]: Simplify 1 into 1 10.972 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 10.972 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 10.972 * [taylor]: Taking taylor expansion of 2.0 in k 10.972 * [backup-simplify]: Simplify 2.0 into 2.0 10.972 * [taylor]: Taking taylor expansion of (* n PI) in k 10.972 * [taylor]: Taking taylor expansion of n in k 10.972 * [backup-simplify]: Simplify n into n 10.973 * [taylor]: Taking taylor expansion of PI in k 10.973 * [backup-simplify]: Simplify PI into PI 10.973 * [backup-simplify]: Simplify (* n PI) into (* n PI) 10.973 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 10.973 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 10.973 * [backup-simplify]: Simplify (- 0) into 0 10.974 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 10.974 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 10.974 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 10.974 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 10.975 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 10.975 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 10.975 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 10.975 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 10.975 * [taylor]: Taking taylor expansion of 0.5 in n 10.975 * [backup-simplify]: Simplify 0.5 into 0.5 10.975 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 10.975 * [taylor]: Taking taylor expansion of 1.0 in n 10.975 * [backup-simplify]: Simplify 1.0 into 1.0 10.975 * [taylor]: Taking taylor expansion of k in n 10.975 * [backup-simplify]: Simplify k into k 10.975 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 10.975 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 10.975 * [taylor]: Taking taylor expansion of 2.0 in n 10.975 * [backup-simplify]: Simplify 2.0 into 2.0 10.975 * [taylor]: Taking taylor expansion of (* n PI) in n 10.975 * [taylor]: Taking taylor expansion of n in n 10.975 * [backup-simplify]: Simplify 0 into 0 10.975 * [backup-simplify]: Simplify 1 into 1 10.975 * [taylor]: Taking taylor expansion of PI in n 10.975 * [backup-simplify]: Simplify PI into PI 10.976 * [backup-simplify]: Simplify (* 0 PI) into 0 10.976 * [backup-simplify]: Simplify (* 2.0 0) into 0 10.978 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.979 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 10.980 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.980 * [backup-simplify]: Simplify (- k) into (- k) 10.981 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 10.981 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 10.982 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.983 * [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)))) 10.984 * [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))))) 10.984 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 10.985 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 10.985 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 10.985 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 10.985 * [taylor]: Taking taylor expansion of 0.5 in n 10.985 * [backup-simplify]: Simplify 0.5 into 0.5 10.985 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 10.985 * [taylor]: Taking taylor expansion of 1.0 in n 10.985 * [backup-simplify]: Simplify 1.0 into 1.0 10.985 * [taylor]: Taking taylor expansion of k in n 10.985 * [backup-simplify]: Simplify k into k 10.985 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 10.985 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 10.985 * [taylor]: Taking taylor expansion of 2.0 in n 10.985 * [backup-simplify]: Simplify 2.0 into 2.0 10.985 * [taylor]: Taking taylor expansion of (* n PI) in n 10.985 * [taylor]: Taking taylor expansion of n in n 10.985 * [backup-simplify]: Simplify 0 into 0 10.985 * [backup-simplify]: Simplify 1 into 1 10.985 * [taylor]: Taking taylor expansion of PI in n 10.985 * [backup-simplify]: Simplify PI into PI 10.986 * [backup-simplify]: Simplify (* 0 PI) into 0 10.986 * [backup-simplify]: Simplify (* 2.0 0) into 0 10.988 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.989 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 10.990 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.990 * [backup-simplify]: Simplify (- k) into (- k) 10.990 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 10.991 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 10.992 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.993 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 10.995 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 10.995 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 10.995 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 10.995 * [taylor]: Taking taylor expansion of 0.5 in k 10.995 * [backup-simplify]: Simplify 0.5 into 0.5 10.995 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 10.995 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 10.995 * [taylor]: Taking taylor expansion of 1.0 in k 10.995 * [backup-simplify]: Simplify 1.0 into 1.0 10.995 * [taylor]: Taking taylor expansion of k in k 10.995 * [backup-simplify]: Simplify 0 into 0 10.995 * [backup-simplify]: Simplify 1 into 1 10.995 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 10.995 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 10.995 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 10.995 * [taylor]: Taking taylor expansion of 2.0 in k 10.996 * [backup-simplify]: Simplify 2.0 into 2.0 10.996 * [taylor]: Taking taylor expansion of PI in k 10.996 * [backup-simplify]: Simplify PI into PI 10.996 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.997 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.997 * [taylor]: Taking taylor expansion of (log n) in k 10.997 * [taylor]: Taking taylor expansion of n in k 10.997 * [backup-simplify]: Simplify n into n 10.997 * [backup-simplify]: Simplify (log n) into (log n) 10.998 * [backup-simplify]: Simplify (- 0) into 0 10.998 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 10.999 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 11.000 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 11.001 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 11.003 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 11.004 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 11.005 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.006 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 11.008 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 11.008 * [backup-simplify]: Simplify (- 0) into 0 11.008 * [backup-simplify]: Simplify (+ 0 0) into 0 11.009 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 11.011 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.012 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 11.014 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.014 * [taylor]: Taking taylor expansion of 0 in k 11.014 * [backup-simplify]: Simplify 0 into 0 11.014 * [backup-simplify]: Simplify 0 into 0 11.015 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 11.017 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 11.018 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 11.018 * [backup-simplify]: Simplify (+ 0 0) into 0 11.019 * [backup-simplify]: Simplify (- 1) into -1 11.019 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.020 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 11.029 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 11.032 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 11.035 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 11.036 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 11.037 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 11.039 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 11.039 * [backup-simplify]: Simplify (- 0) into 0 11.039 * [backup-simplify]: Simplify (+ 0 0) into 0 11.040 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 11.040 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.041 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 11.043 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.043 * [taylor]: Taking taylor expansion of 0 in k 11.043 * [backup-simplify]: Simplify 0 into 0 11.043 * [backup-simplify]: Simplify 0 into 0 11.043 * [backup-simplify]: Simplify 0 into 0 11.043 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.045 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 11.046 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 11.047 * [backup-simplify]: Simplify (+ 0 0) into 0 11.047 * [backup-simplify]: Simplify (- 0) into 0 11.047 * [backup-simplify]: Simplify (+ 0 0) into 0 11.048 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 11.050 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 11.052 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 11.055 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 11.066 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 11.067 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 11.067 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 11.067 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 11.067 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 11.067 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 11.067 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 11.067 * [taylor]: Taking taylor expansion of 0.5 in k 11.067 * [backup-simplify]: Simplify 0.5 into 0.5 11.067 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 11.067 * [taylor]: Taking taylor expansion of 1.0 in k 11.067 * [backup-simplify]: Simplify 1.0 into 1.0 11.067 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.067 * [taylor]: Taking taylor expansion of k in k 11.067 * [backup-simplify]: Simplify 0 into 0 11.067 * [backup-simplify]: Simplify 1 into 1 11.068 * [backup-simplify]: Simplify (/ 1 1) into 1 11.068 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 11.068 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 11.068 * [taylor]: Taking taylor expansion of 2.0 in k 11.068 * [backup-simplify]: Simplify 2.0 into 2.0 11.068 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.068 * [taylor]: Taking taylor expansion of PI in k 11.068 * [backup-simplify]: Simplify PI into PI 11.068 * [taylor]: Taking taylor expansion of n in k 11.068 * [backup-simplify]: Simplify n into n 11.068 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.068 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 11.068 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 11.069 * [backup-simplify]: Simplify (- 1) into -1 11.069 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.070 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 11.070 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 11.070 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 11.070 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 11.070 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 11.070 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 11.070 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 11.070 * [taylor]: Taking taylor expansion of 0.5 in n 11.070 * [backup-simplify]: Simplify 0.5 into 0.5 11.070 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 11.070 * [taylor]: Taking taylor expansion of 1.0 in n 11.070 * [backup-simplify]: Simplify 1.0 into 1.0 11.070 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.070 * [taylor]: Taking taylor expansion of k in n 11.070 * [backup-simplify]: Simplify k into k 11.070 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.070 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 11.071 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 11.071 * [taylor]: Taking taylor expansion of 2.0 in n 11.071 * [backup-simplify]: Simplify 2.0 into 2.0 11.071 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.071 * [taylor]: Taking taylor expansion of PI in n 11.071 * [backup-simplify]: Simplify PI into PI 11.071 * [taylor]: Taking taylor expansion of n in n 11.071 * [backup-simplify]: Simplify 0 into 0 11.071 * [backup-simplify]: Simplify 1 into 1 11.071 * [backup-simplify]: Simplify (/ PI 1) into PI 11.072 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.073 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.073 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.073 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 11.073 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 11.075 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.076 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 11.077 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 11.077 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 11.077 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 11.077 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 11.077 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 11.077 * [taylor]: Taking taylor expansion of 0.5 in n 11.077 * [backup-simplify]: Simplify 0.5 into 0.5 11.077 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 11.077 * [taylor]: Taking taylor expansion of 1.0 in n 11.077 * [backup-simplify]: Simplify 1.0 into 1.0 11.077 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.077 * [taylor]: Taking taylor expansion of k in n 11.077 * [backup-simplify]: Simplify k into k 11.078 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.078 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 11.078 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 11.078 * [taylor]: Taking taylor expansion of 2.0 in n 11.078 * [backup-simplify]: Simplify 2.0 into 2.0 11.078 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.078 * [taylor]: Taking taylor expansion of PI in n 11.078 * [backup-simplify]: Simplify PI into PI 11.078 * [taylor]: Taking taylor expansion of n in n 11.078 * [backup-simplify]: Simplify 0 into 0 11.078 * [backup-simplify]: Simplify 1 into 1 11.078 * [backup-simplify]: Simplify (/ PI 1) into PI 11.079 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.080 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.080 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.080 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 11.080 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 11.082 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.083 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 11.085 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 11.085 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 11.085 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 11.085 * [taylor]: Taking taylor expansion of 0.5 in k 11.085 * [backup-simplify]: Simplify 0.5 into 0.5 11.085 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 11.085 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 11.085 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 11.085 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 11.085 * [taylor]: Taking taylor expansion of 2.0 in k 11.085 * [backup-simplify]: Simplify 2.0 into 2.0 11.085 * [taylor]: Taking taylor expansion of PI in k 11.085 * [backup-simplify]: Simplify PI into PI 11.086 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.087 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.087 * [taylor]: Taking taylor expansion of (log n) in k 11.087 * [taylor]: Taking taylor expansion of n in k 11.087 * [backup-simplify]: Simplify n into n 11.087 * [backup-simplify]: Simplify (log n) into (log n) 11.087 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 11.087 * [taylor]: Taking taylor expansion of 1.0 in k 11.087 * [backup-simplify]: Simplify 1.0 into 1.0 11.087 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.087 * [taylor]: Taking taylor expansion of k in k 11.087 * [backup-simplify]: Simplify 0 into 0 11.087 * [backup-simplify]: Simplify 1 into 1 11.087 * [backup-simplify]: Simplify (/ 1 1) into 1 11.087 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 11.089 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 11.089 * [backup-simplify]: Simplify (- 1) into -1 11.089 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.090 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 11.092 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 11.093 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 11.094 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 11.095 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.096 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 11.098 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 11.098 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.098 * [backup-simplify]: Simplify (- 0) into 0 11.099 * [backup-simplify]: Simplify (+ 0 0) into 0 11.099 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 11.101 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.102 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 11.104 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.104 * [taylor]: Taking taylor expansion of 0 in k 11.104 * [backup-simplify]: Simplify 0 into 0 11.104 * [backup-simplify]: Simplify 0 into 0 11.104 * [backup-simplify]: Simplify 0 into 0 11.105 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.106 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.110 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 11.110 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.111 * [backup-simplify]: Simplify (- 0) into 0 11.111 * [backup-simplify]: Simplify (+ 0 0) into 0 11.112 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 11.113 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.115 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 11.118 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.118 * [taylor]: Taking taylor expansion of 0 in k 11.118 * [backup-simplify]: Simplify 0 into 0 11.118 * [backup-simplify]: Simplify 0 into 0 11.118 * [backup-simplify]: Simplify 0 into 0 11.118 * [backup-simplify]: Simplify 0 into 0 11.119 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.121 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.127 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 11.127 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.128 * [backup-simplify]: Simplify (- 0) into 0 11.128 * [backup-simplify]: Simplify (+ 0 0) into 0 11.129 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 11.130 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.132 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 11.134 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 11.135 * [taylor]: Taking taylor expansion of 0 in k 11.135 * [backup-simplify]: Simplify 0 into 0 11.135 * [backup-simplify]: Simplify 0 into 0 11.136 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 11.136 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 11.137 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 11.137 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 11.137 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 11.137 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 11.137 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 11.137 * [taylor]: Taking taylor expansion of 0.5 in k 11.137 * [backup-simplify]: Simplify 0.5 into 0.5 11.137 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 11.137 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.137 * [taylor]: Taking taylor expansion of k in k 11.137 * [backup-simplify]: Simplify 0 into 0 11.137 * [backup-simplify]: Simplify 1 into 1 11.137 * [backup-simplify]: Simplify (/ 1 1) into 1 11.137 * [taylor]: Taking taylor expansion of 1.0 in k 11.137 * [backup-simplify]: Simplify 1.0 into 1.0 11.137 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 11.137 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 11.137 * [taylor]: Taking taylor expansion of -2.0 in k 11.137 * [backup-simplify]: Simplify -2.0 into -2.0 11.137 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.137 * [taylor]: Taking taylor expansion of PI in k 11.137 * [backup-simplify]: Simplify PI into PI 11.137 * [taylor]: Taking taylor expansion of n in k 11.137 * [backup-simplify]: Simplify n into n 11.138 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.138 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 11.138 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 11.138 * [backup-simplify]: Simplify (+ 1 0) into 1 11.139 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 11.139 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 11.139 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 11.139 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 11.139 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 11.139 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 11.139 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 11.139 * [taylor]: Taking taylor expansion of 0.5 in n 11.139 * [backup-simplify]: Simplify 0.5 into 0.5 11.139 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 11.139 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.139 * [taylor]: Taking taylor expansion of k in n 11.139 * [backup-simplify]: Simplify k into k 11.139 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.139 * [taylor]: Taking taylor expansion of 1.0 in n 11.139 * [backup-simplify]: Simplify 1.0 into 1.0 11.139 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 11.139 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 11.139 * [taylor]: Taking taylor expansion of -2.0 in n 11.139 * [backup-simplify]: Simplify -2.0 into -2.0 11.139 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.139 * [taylor]: Taking taylor expansion of PI in n 11.140 * [backup-simplify]: Simplify PI into PI 11.140 * [taylor]: Taking taylor expansion of n in n 11.140 * [backup-simplify]: Simplify 0 into 0 11.140 * [backup-simplify]: Simplify 1 into 1 11.140 * [backup-simplify]: Simplify (/ PI 1) into PI 11.141 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.142 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 11.142 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 11.142 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 11.143 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.144 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 11.145 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 11.146 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 11.146 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 11.146 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 11.146 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 11.146 * [taylor]: Taking taylor expansion of 0.5 in n 11.146 * [backup-simplify]: Simplify 0.5 into 0.5 11.146 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 11.146 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.146 * [taylor]: Taking taylor expansion of k in n 11.146 * [backup-simplify]: Simplify k into k 11.146 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.146 * [taylor]: Taking taylor expansion of 1.0 in n 11.146 * [backup-simplify]: Simplify 1.0 into 1.0 11.146 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 11.146 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 11.146 * [taylor]: Taking taylor expansion of -2.0 in n 11.146 * [backup-simplify]: Simplify -2.0 into -2.0 11.146 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.146 * [taylor]: Taking taylor expansion of PI in n 11.146 * [backup-simplify]: Simplify PI into PI 11.146 * [taylor]: Taking taylor expansion of n in n 11.146 * [backup-simplify]: Simplify 0 into 0 11.146 * [backup-simplify]: Simplify 1 into 1 11.147 * [backup-simplify]: Simplify (/ PI 1) into PI 11.147 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.148 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 11.148 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 11.148 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 11.149 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.151 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 11.152 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 11.152 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 11.152 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 11.152 * [taylor]: Taking taylor expansion of 0.5 in k 11.152 * [backup-simplify]: Simplify 0.5 into 0.5 11.152 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 11.152 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 11.152 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.152 * [taylor]: Taking taylor expansion of k in k 11.152 * [backup-simplify]: Simplify 0 into 0 11.152 * [backup-simplify]: Simplify 1 into 1 11.152 * [backup-simplify]: Simplify (/ 1 1) into 1 11.153 * [taylor]: Taking taylor expansion of 1.0 in k 11.153 * [backup-simplify]: Simplify 1.0 into 1.0 11.153 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 11.153 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 11.153 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 11.153 * [taylor]: Taking taylor expansion of -2.0 in k 11.153 * [backup-simplify]: Simplify -2.0 into -2.0 11.153 * [taylor]: Taking taylor expansion of PI in k 11.153 * [backup-simplify]: Simplify PI into PI 11.153 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.154 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 11.154 * [taylor]: Taking taylor expansion of (log n) in k 11.154 * [taylor]: Taking taylor expansion of n in k 11.154 * [backup-simplify]: Simplify n into n 11.154 * [backup-simplify]: Simplify (log n) into (log n) 11.155 * [backup-simplify]: Simplify (+ 1 0) into 1 11.155 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 11.156 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 11.157 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 11.158 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 11.160 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 11.171 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 11.172 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.173 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 11.175 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 11.175 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.176 * [backup-simplify]: Simplify (+ 0 0) into 0 11.176 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 11.178 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.179 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 11.181 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.181 * [taylor]: Taking taylor expansion of 0 in k 11.181 * [backup-simplify]: Simplify 0 into 0 11.181 * [backup-simplify]: Simplify 0 into 0 11.181 * [backup-simplify]: Simplify 0 into 0 11.182 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.183 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.187 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 11.187 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.187 * [backup-simplify]: Simplify (+ 0 0) into 0 11.188 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 11.190 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.191 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 11.194 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.194 * [taylor]: Taking taylor expansion of 0 in k 11.194 * [backup-simplify]: Simplify 0 into 0 11.194 * [backup-simplify]: Simplify 0 into 0 11.194 * [backup-simplify]: Simplify 0 into 0 11.194 * [backup-simplify]: Simplify 0 into 0 11.195 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.197 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.203 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 11.203 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.204 * [backup-simplify]: Simplify (+ 0 0) into 0 11.205 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 11.206 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.208 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 11.211 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 11.211 * [taylor]: Taking taylor expansion of 0 in k 11.211 * [backup-simplify]: Simplify 0 into 0 11.211 * [backup-simplify]: Simplify 0 into 0 11.213 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 11.213 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1 1) 11.213 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 11.213 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 11.213 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 11.213 * [taylor]: Taking taylor expansion of 1.0 in k 11.213 * [backup-simplify]: Simplify 1.0 into 1.0 11.213 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.213 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.213 * [taylor]: Taking taylor expansion of k in k 11.213 * [backup-simplify]: Simplify 0 into 0 11.213 * [backup-simplify]: Simplify 1 into 1 11.213 * [backup-simplify]: Simplify (/ 1 1) into 1 11.214 * [backup-simplify]: Simplify (sqrt 0) into 0 11.215 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.215 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 11.215 * [taylor]: Taking taylor expansion of 1.0 in k 11.215 * [backup-simplify]: Simplify 1.0 into 1.0 11.215 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.215 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.215 * [taylor]: Taking taylor expansion of k in k 11.215 * [backup-simplify]: Simplify 0 into 0 11.215 * [backup-simplify]: Simplify 1 into 1 11.216 * [backup-simplify]: Simplify (/ 1 1) into 1 11.216 * [backup-simplify]: Simplify (sqrt 0) into 0 11.217 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.218 * [backup-simplify]: Simplify (* 1.0 0) into 0 11.218 * [backup-simplify]: Simplify 0 into 0 11.219 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 11.220 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.220 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 11.223 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.225 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 11.226 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.226 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.230 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.232 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 11.233 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.234 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 11.235 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 11.235 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 11.235 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 11.235 * [taylor]: Taking taylor expansion of 1.0 in k 11.235 * [backup-simplify]: Simplify 1.0 into 1.0 11.235 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.235 * [taylor]: Taking taylor expansion of k in k 11.235 * [backup-simplify]: Simplify 0 into 0 11.235 * [backup-simplify]: Simplify 1 into 1 11.235 * [backup-simplify]: Simplify (sqrt 0) into 0 11.237 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.237 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 11.237 * [taylor]: Taking taylor expansion of 1.0 in k 11.237 * [backup-simplify]: Simplify 1.0 into 1.0 11.237 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.237 * [taylor]: Taking taylor expansion of k in k 11.237 * [backup-simplify]: Simplify 0 into 0 11.237 * [backup-simplify]: Simplify 1 into 1 11.237 * [backup-simplify]: Simplify (sqrt 0) into 0 11.239 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.239 * [backup-simplify]: Simplify (* 1.0 0) into 0 11.239 * [backup-simplify]: Simplify 0 into 0 11.241 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 11.241 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.244 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.246 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 11.246 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.250 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.252 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 11.252 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.254 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 11.254 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 11.254 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 11.254 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 11.254 * [taylor]: Taking taylor expansion of 1.0 in k 11.254 * [backup-simplify]: Simplify 1.0 into 1.0 11.254 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.254 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.254 * [taylor]: Taking taylor expansion of -1 in k 11.254 * [backup-simplify]: Simplify -1 into -1 11.254 * [taylor]: Taking taylor expansion of k in k 11.254 * [backup-simplify]: Simplify 0 into 0 11.254 * [backup-simplify]: Simplify 1 into 1 11.255 * [backup-simplify]: Simplify (/ -1 1) into -1 11.255 * [backup-simplify]: Simplify (sqrt 0) into 0 11.256 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.257 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 11.257 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 11.257 * [taylor]: Taking taylor expansion of 1.0 in k 11.257 * [backup-simplify]: Simplify 1.0 into 1.0 11.257 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.257 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.257 * [taylor]: Taking taylor expansion of -1 in k 11.257 * [backup-simplify]: Simplify -1 into -1 11.257 * [taylor]: Taking taylor expansion of k in k 11.257 * [backup-simplify]: Simplify 0 into 0 11.257 * [backup-simplify]: Simplify 1 into 1 11.257 * [backup-simplify]: Simplify (/ -1 1) into -1 11.258 * [backup-simplify]: Simplify (sqrt 0) into 0 11.259 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.260 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 11.260 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.260 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 11.263 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.266 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 11.266 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.267 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.271 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.275 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 11.275 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.276 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 11.276 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 11.277 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 11.277 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 11.277 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 11.277 * [taylor]: Taking taylor expansion of 1.0 in k 11.277 * [backup-simplify]: Simplify 1.0 into 1.0 11.277 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.277 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.277 * [taylor]: Taking taylor expansion of k in k 11.277 * [backup-simplify]: Simplify 0 into 0 11.277 * [backup-simplify]: Simplify 1 into 1 11.277 * [backup-simplify]: Simplify (/ 1 1) into 1 11.278 * [backup-simplify]: Simplify (sqrt 0) into 0 11.279 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.279 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 11.279 * [taylor]: Taking taylor expansion of 1.0 in k 11.279 * [backup-simplify]: Simplify 1.0 into 1.0 11.279 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.279 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.279 * [taylor]: Taking taylor expansion of k in k 11.279 * [backup-simplify]: Simplify 0 into 0 11.279 * [backup-simplify]: Simplify 1 into 1 11.280 * [backup-simplify]: Simplify (/ 1 1) into 1 11.280 * [backup-simplify]: Simplify (sqrt 0) into 0 11.282 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.282 * [backup-simplify]: Simplify (* 1.0 0) into 0 11.282 * [backup-simplify]: Simplify 0 into 0 11.284 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 11.284 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.285 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 11.288 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.290 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 11.291 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.292 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.295 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.298 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 11.298 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.300 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 11.300 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 11.300 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 11.300 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 11.300 * [taylor]: Taking taylor expansion of 1.0 in k 11.300 * [backup-simplify]: Simplify 1.0 into 1.0 11.300 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.300 * [taylor]: Taking taylor expansion of k in k 11.300 * [backup-simplify]: Simplify 0 into 0 11.300 * [backup-simplify]: Simplify 1 into 1 11.300 * [backup-simplify]: Simplify (sqrt 0) into 0 11.302 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.302 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 11.302 * [taylor]: Taking taylor expansion of 1.0 in k 11.302 * [backup-simplify]: Simplify 1.0 into 1.0 11.302 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.302 * [taylor]: Taking taylor expansion of k in k 11.302 * [backup-simplify]: Simplify 0 into 0 11.302 * [backup-simplify]: Simplify 1 into 1 11.302 * [backup-simplify]: Simplify (sqrt 0) into 0 11.304 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.304 * [backup-simplify]: Simplify (* 1.0 0) into 0 11.304 * [backup-simplify]: Simplify 0 into 0 11.306 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 11.306 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.309 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.311 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 11.312 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.322 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.324 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 11.324 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.326 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 11.326 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 11.326 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 11.326 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 11.326 * [taylor]: Taking taylor expansion of 1.0 in k 11.326 * [backup-simplify]: Simplify 1.0 into 1.0 11.326 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.326 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.326 * [taylor]: Taking taylor expansion of -1 in k 11.326 * [backup-simplify]: Simplify -1 into -1 11.326 * [taylor]: Taking taylor expansion of k in k 11.326 * [backup-simplify]: Simplify 0 into 0 11.326 * [backup-simplify]: Simplify 1 into 1 11.327 * [backup-simplify]: Simplify (/ -1 1) into -1 11.327 * [backup-simplify]: Simplify (sqrt 0) into 0 11.328 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.329 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 11.329 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 11.329 * [taylor]: Taking taylor expansion of 1.0 in k 11.329 * [backup-simplify]: Simplify 1.0 into 1.0 11.329 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.329 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.329 * [taylor]: Taking taylor expansion of -1 in k 11.329 * [backup-simplify]: Simplify -1 into -1 11.329 * [taylor]: Taking taylor expansion of k in k 11.329 * [backup-simplify]: Simplify 0 into 0 11.329 * [backup-simplify]: Simplify 1 into 1 11.329 * [backup-simplify]: Simplify (/ -1 1) into -1 11.330 * [backup-simplify]: Simplify (sqrt 0) into 0 11.331 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.331 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 11.331 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.332 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 11.335 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.337 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 11.337 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.338 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.341 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.345 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 11.345 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.346 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 11.346 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 2 1) 11.347 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 11.347 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 11.347 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 11.347 * [taylor]: Taking taylor expansion of 2.0 in n 11.347 * [backup-simplify]: Simplify 2.0 into 2.0 11.347 * [taylor]: Taking taylor expansion of (* n PI) in n 11.347 * [taylor]: Taking taylor expansion of n in n 11.347 * [backup-simplify]: Simplify 0 into 0 11.347 * [backup-simplify]: Simplify 1 into 1 11.347 * [taylor]: Taking taylor expansion of PI in n 11.347 * [backup-simplify]: Simplify PI into PI 11.347 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 11.347 * [taylor]: Taking taylor expansion of 2.0 in n 11.347 * [backup-simplify]: Simplify 2.0 into 2.0 11.347 * [taylor]: Taking taylor expansion of (* n PI) in n 11.347 * [taylor]: Taking taylor expansion of n in n 11.347 * [backup-simplify]: Simplify 0 into 0 11.347 * [backup-simplify]: Simplify 1 into 1 11.347 * [taylor]: Taking taylor expansion of PI in n 11.347 * [backup-simplify]: Simplify PI into PI 11.348 * [backup-simplify]: Simplify (* 0 PI) into 0 11.348 * [backup-simplify]: Simplify (* 2.0 0) into 0 11.348 * [backup-simplify]: Simplify 0 into 0 11.350 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.351 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 11.352 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.353 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.354 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 11.354 * [backup-simplify]: Simplify 0 into 0 11.355 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 11.356 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 11.356 * [backup-simplify]: Simplify 0 into 0 11.357 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.358 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 11.358 * [backup-simplify]: Simplify 0 into 0 11.360 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.361 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 11.361 * [backup-simplify]: Simplify 0 into 0 11.363 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.364 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 11.364 * [backup-simplify]: Simplify 0 into 0 11.366 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 11.368 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 11.368 * [backup-simplify]: Simplify 0 into 0 11.368 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 11.369 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 11.369 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 11.369 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 11.369 * [taylor]: Taking taylor expansion of 2.0 in n 11.369 * [backup-simplify]: Simplify 2.0 into 2.0 11.369 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.369 * [taylor]: Taking taylor expansion of PI in n 11.369 * [backup-simplify]: Simplify PI into PI 11.369 * [taylor]: Taking taylor expansion of n in n 11.369 * [backup-simplify]: Simplify 0 into 0 11.369 * [backup-simplify]: Simplify 1 into 1 11.370 * [backup-simplify]: Simplify (/ PI 1) into PI 11.370 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 11.370 * [taylor]: Taking taylor expansion of 2.0 in n 11.370 * [backup-simplify]: Simplify 2.0 into 2.0 11.370 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.370 * [taylor]: Taking taylor expansion of PI in n 11.370 * [backup-simplify]: Simplify PI into PI 11.370 * [taylor]: Taking taylor expansion of n in n 11.370 * [backup-simplify]: Simplify 0 into 0 11.370 * [backup-simplify]: Simplify 1 into 1 11.370 * [backup-simplify]: Simplify (/ PI 1) into PI 11.371 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.372 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.373 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.373 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 11.373 * [backup-simplify]: Simplify 0 into 0 11.374 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.376 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.376 * [backup-simplify]: Simplify 0 into 0 11.377 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.378 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.378 * [backup-simplify]: Simplify 0 into 0 11.379 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.381 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.381 * [backup-simplify]: Simplify 0 into 0 11.382 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.384 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.384 * [backup-simplify]: Simplify 0 into 0 11.385 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.387 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.387 * [backup-simplify]: Simplify 0 into 0 11.388 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 11.389 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 11.389 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 11.389 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 11.389 * [taylor]: Taking taylor expansion of -2.0 in n 11.389 * [backup-simplify]: Simplify -2.0 into -2.0 11.389 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.389 * [taylor]: Taking taylor expansion of PI in n 11.389 * [backup-simplify]: Simplify PI into PI 11.389 * [taylor]: Taking taylor expansion of n in n 11.389 * [backup-simplify]: Simplify 0 into 0 11.389 * [backup-simplify]: Simplify 1 into 1 11.390 * [backup-simplify]: Simplify (/ PI 1) into PI 11.390 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 11.390 * [taylor]: Taking taylor expansion of -2.0 in n 11.390 * [backup-simplify]: Simplify -2.0 into -2.0 11.390 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.390 * [taylor]: Taking taylor expansion of PI in n 11.390 * [backup-simplify]: Simplify PI into PI 11.390 * [taylor]: Taking taylor expansion of n in n 11.390 * [backup-simplify]: Simplify 0 into 0 11.390 * [backup-simplify]: Simplify 1 into 1 11.391 * [backup-simplify]: Simplify (/ PI 1) into PI 11.391 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.392 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.393 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.394 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 11.394 * [backup-simplify]: Simplify 0 into 0 11.395 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.396 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.396 * [backup-simplify]: Simplify 0 into 0 11.397 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.398 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.398 * [backup-simplify]: Simplify 0 into 0 11.400 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.401 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.401 * [backup-simplify]: Simplify 0 into 0 11.402 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.404 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.404 * [backup-simplify]: Simplify 0 into 0 11.405 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.407 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.407 * [backup-simplify]: Simplify 0 into 0 11.408 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 11.408 * * * [progress]: simplifying candidates 11.412 * [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 (/ 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) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 11.418 * * [simplify]: Extracting # 0 : cost 0 11.418 * * [simplify]: Extracting # 1 : cost 0 11.418 * * [simplify]: Extracting # 2 : cost 0 11.419 * * [simplify]: Extracting # 3 : cost 0 11.419 * * [simplify]: Extracting # 4 : cost 0 11.420 * * [simplify]: Extracting # 5 : cost 0 11.421 * * [simplify]: Extracting # 6 : cost 0 11.421 * * [simplify]: Extracting # 7 : cost 0 11.422 * * [simplify]: Extracting # 8 : cost 0 11.422 * * [simplify]: Extracting # 9 : cost 0 11.423 * * [simplify]: Extracting # 10 : cost 0 11.424 * * [simplify]: Extracting # 11 : cost 0 11.424 * * [simplify]: Extracting # 12 : cost 0 11.425 * * [simplify]: Extracting # 13 : cost 0 11.425 * * [simplify]: iteration 0 : 240 enodes (cost 1698 ) 11.529 * * [simplify]: Extracting # 0 : cost 0 11.531 * * [simplify]: Extracting # 1 : cost 0 11.532 * * [simplify]: Extracting # 2 : cost 0 11.534 * * [simplify]: Extracting # 3 : cost 0 11.536 * * [simplify]: Extracting # 4 : cost 0 11.537 * * [simplify]: Extracting # 5 : cost 0 11.539 * * [simplify]: Extracting # 6 : cost 0 11.541 * * [simplify]: iteration 1 : 616 enodes (cost 1560 ) 11.947 * * [simplify]: Extracting # 0 : cost 0 11.950 * * [simplify]: Extracting # 1 : cost 0 11.954 * * [simplify]: Extracting # 2 : cost 0 11.958 * * [simplify]: Extracting # 3 : cost 0 11.961 * * [simplify]: Extracting # 4 : cost 0 11.972 * * [simplify]: Extracting # 5 : cost 0 11.979 * * [simplify]: iteration 2 : 2748 enodes (cost 1456 ) 13.391 * * [simplify]: Extracting # 0 : cost 0 13.410 * * [simplify]: Extracting # 1 : cost 0 13.422 * * [simplify]: Extracting # 2 : cost 0 13.442 * * [simplify]: Extracting # 3 : cost 0 13.454 * * [simplify]: Extracting # 4 : cost 0 13.466 * * [simplify]: iteration done: 5000 enodes (cost 1451 ) 13.468 * [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 (* n PI)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (pow (* 2.0 (* n PI)) (- 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) (* (sqrt k) k)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (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) (* (sqrt k) k)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* (cbrt n) (cbrt n)) (* 2.0 PI)) (* (sqrt n) (* 2.0 PI)) (* PI 2.0) (* PI n) (fma (- 0.5) (* k (fma (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.5) (* (log n) (pow (* (* 2.0 PI) n) 0.5)))) (fma (* 0.125 (pow k 2)) (fma (pow (* (* 2.0 PI) n) 0.5) (pow (log (* 2.0 PI)) 2) (* (pow (* (* 2.0 PI) n) 0.5) (pow (log n) 2))) (fma (* (* (log n) (pow (* (* 2.0 PI) n) 0.5)) (* (pow k 2) (log (* 2.0 PI)))) 0.25 (pow (* (* 2.0 PI) n) 0.5)))) (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (fma (- k) +nan.0 (- (* +nan.0 (pow k 2)) +nan.0)) (+ (- (/ +nan.0 (pow k 2))) (- (/ +nan.0 k) (/ +nan.0 (pow k 3)))) (- (- (/ +nan.0 (pow k 2)) (- (/ +nan.0 k) +nan.0))) (fma (- k) +nan.0 (- (* +nan.0 (pow k 2)) +nan.0)) (+ (- (/ +nan.0 (pow k 2))) (- (/ +nan.0 k) (/ +nan.0 (pow k 3)))) (- (- (/ +nan.0 (pow k 2)) (- (/ +nan.0 k) +nan.0))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 13.469 * * * [progress]: adding candidates to table 14.233 * * [progress]: iteration 4 / 4 14.233 * * * [progress]: picking best candidate 14.288 * * * * [pick]: Picked # 14.288 * * * [progress]: localizing error 14.327 * * * [progress]: generating rewritten candidates 14.327 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 14.364 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 14.408 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 14.416 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 14.481 * * * [progress]: generating series expansions 14.481 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 14.483 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 14.483 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 14.483 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 14.483 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 14.483 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 14.483 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 14.483 * [taylor]: Taking taylor expansion of 0.5 in k 14.483 * [backup-simplify]: Simplify 0.5 into 0.5 14.483 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 14.483 * [taylor]: Taking taylor expansion of 1.0 in k 14.483 * [backup-simplify]: Simplify 1.0 into 1.0 14.483 * [taylor]: Taking taylor expansion of k in k 14.483 * [backup-simplify]: Simplify 0 into 0 14.483 * [backup-simplify]: Simplify 1 into 1 14.483 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 14.483 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 14.483 * [taylor]: Taking taylor expansion of 2.0 in k 14.483 * [backup-simplify]: Simplify 2.0 into 2.0 14.483 * [taylor]: Taking taylor expansion of (* n PI) in k 14.483 * [taylor]: Taking taylor expansion of n in k 14.483 * [backup-simplify]: Simplify n into n 14.483 * [taylor]: Taking taylor expansion of PI in k 14.483 * [backup-simplify]: Simplify PI into PI 14.483 * [backup-simplify]: Simplify (* n PI) into (* n PI) 14.483 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 14.483 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 14.484 * [backup-simplify]: Simplify (- 0) into 0 14.484 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 14.485 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 14.485 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 14.485 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 14.485 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 14.485 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 14.485 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 14.485 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 14.485 * [taylor]: Taking taylor expansion of 0.5 in n 14.485 * [backup-simplify]: Simplify 0.5 into 0.5 14.485 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 14.485 * [taylor]: Taking taylor expansion of 1.0 in n 14.486 * [backup-simplify]: Simplify 1.0 into 1.0 14.486 * [taylor]: Taking taylor expansion of k in n 14.486 * [backup-simplify]: Simplify k into k 14.486 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 14.486 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 14.486 * [taylor]: Taking taylor expansion of 2.0 in n 14.486 * [backup-simplify]: Simplify 2.0 into 2.0 14.486 * [taylor]: Taking taylor expansion of (* n PI) in n 14.486 * [taylor]: Taking taylor expansion of n in n 14.486 * [backup-simplify]: Simplify 0 into 0 14.486 * [backup-simplify]: Simplify 1 into 1 14.486 * [taylor]: Taking taylor expansion of PI in n 14.486 * [backup-simplify]: Simplify PI into PI 14.486 * [backup-simplify]: Simplify (* 0 PI) into 0 14.487 * [backup-simplify]: Simplify (* 2.0 0) into 0 14.488 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 14.490 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 14.491 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.491 * [backup-simplify]: Simplify (- k) into (- k) 14.491 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 14.491 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 14.492 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.493 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 14.494 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 14.494 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 14.494 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 14.494 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 14.494 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 14.494 * [taylor]: Taking taylor expansion of 0.5 in n 14.494 * [backup-simplify]: Simplify 0.5 into 0.5 14.494 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 14.494 * [taylor]: Taking taylor expansion of 1.0 in n 14.494 * [backup-simplify]: Simplify 1.0 into 1.0 14.494 * [taylor]: Taking taylor expansion of k in n 14.494 * [backup-simplify]: Simplify k into k 14.494 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 14.494 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 14.494 * [taylor]: Taking taylor expansion of 2.0 in n 14.494 * [backup-simplify]: Simplify 2.0 into 2.0 14.494 * [taylor]: Taking taylor expansion of (* n PI) in n 14.494 * [taylor]: Taking taylor expansion of n in n 14.494 * [backup-simplify]: Simplify 0 into 0 14.494 * [backup-simplify]: Simplify 1 into 1 14.494 * [taylor]: Taking taylor expansion of PI in n 14.494 * [backup-simplify]: Simplify PI into PI 14.494 * [backup-simplify]: Simplify (* 0 PI) into 0 14.495 * [backup-simplify]: Simplify (* 2.0 0) into 0 14.495 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 14.496 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 14.497 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.497 * [backup-simplify]: Simplify (- k) into (- k) 14.497 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 14.497 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 14.498 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.499 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 14.500 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 14.500 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 14.500 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 14.500 * [taylor]: Taking taylor expansion of 0.5 in k 14.500 * [backup-simplify]: Simplify 0.5 into 0.5 14.500 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 14.500 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 14.500 * [taylor]: Taking taylor expansion of 1.0 in k 14.500 * [backup-simplify]: Simplify 1.0 into 1.0 14.500 * [taylor]: Taking taylor expansion of k in k 14.500 * [backup-simplify]: Simplify 0 into 0 14.500 * [backup-simplify]: Simplify 1 into 1 14.500 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 14.500 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 14.500 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 14.500 * [taylor]: Taking taylor expansion of 2.0 in k 14.500 * [backup-simplify]: Simplify 2.0 into 2.0 14.500 * [taylor]: Taking taylor expansion of PI in k 14.500 * [backup-simplify]: Simplify PI into PI 14.500 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.501 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.501 * [taylor]: Taking taylor expansion of (log n) in k 14.501 * [taylor]: Taking taylor expansion of n in k 14.501 * [backup-simplify]: Simplify n into n 14.501 * [backup-simplify]: Simplify (log n) into (log n) 14.502 * [backup-simplify]: Simplify (- 0) into 0 14.502 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 14.503 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 14.503 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 14.504 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 14.505 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 14.506 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 14.506 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 14.507 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 14.508 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 14.508 * [backup-simplify]: Simplify (- 0) into 0 14.509 * [backup-simplify]: Simplify (+ 0 0) into 0 14.509 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 14.510 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.517 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 14.519 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 14.519 * [taylor]: Taking taylor expansion of 0 in k 14.519 * [backup-simplify]: Simplify 0 into 0 14.519 * [backup-simplify]: Simplify 0 into 0 14.520 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 14.522 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 14.523 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 14.523 * [backup-simplify]: Simplify (+ 0 0) into 0 14.523 * [backup-simplify]: Simplify (- 1) into -1 14.524 * [backup-simplify]: Simplify (+ 0 -1) into -1 14.525 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 14.528 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 14.531 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 14.534 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 14.535 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 14.536 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 14.538 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 14.538 * [backup-simplify]: Simplify (- 0) into 0 14.539 * [backup-simplify]: Simplify (+ 0 0) into 0 14.539 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 14.540 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.541 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 14.542 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.542 * [taylor]: Taking taylor expansion of 0 in k 14.543 * [backup-simplify]: Simplify 0 into 0 14.543 * [backup-simplify]: Simplify 0 into 0 14.543 * [backup-simplify]: Simplify 0 into 0 14.543 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 14.545 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 14.546 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 14.546 * [backup-simplify]: Simplify (+ 0 0) into 0 14.547 * [backup-simplify]: Simplify (- 0) into 0 14.547 * [backup-simplify]: Simplify (+ 0 0) into 0 14.548 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 14.550 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 14.552 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 14.556 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 14.562 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 14.562 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 14.562 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 14.562 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 14.562 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 14.562 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 14.562 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 14.562 * [taylor]: Taking taylor expansion of 0.5 in k 14.563 * [backup-simplify]: Simplify 0.5 into 0.5 14.563 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 14.563 * [taylor]: Taking taylor expansion of 1.0 in k 14.563 * [backup-simplify]: Simplify 1.0 into 1.0 14.563 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.563 * [taylor]: Taking taylor expansion of k in k 14.563 * [backup-simplify]: Simplify 0 into 0 14.563 * [backup-simplify]: Simplify 1 into 1 14.563 * [backup-simplify]: Simplify (/ 1 1) into 1 14.563 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 14.563 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 14.563 * [taylor]: Taking taylor expansion of 2.0 in k 14.563 * [backup-simplify]: Simplify 2.0 into 2.0 14.563 * [taylor]: Taking taylor expansion of (/ PI n) in k 14.563 * [taylor]: Taking taylor expansion of PI in k 14.563 * [backup-simplify]: Simplify PI into PI 14.563 * [taylor]: Taking taylor expansion of n in k 14.563 * [backup-simplify]: Simplify n into n 14.563 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 14.563 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 14.563 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 14.564 * [backup-simplify]: Simplify (- 1) into -1 14.564 * [backup-simplify]: Simplify (+ 0 -1) into -1 14.564 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 14.565 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 14.565 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 14.565 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 14.565 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 14.565 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 14.565 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 14.565 * [taylor]: Taking taylor expansion of 0.5 in n 14.565 * [backup-simplify]: Simplify 0.5 into 0.5 14.565 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 14.565 * [taylor]: Taking taylor expansion of 1.0 in n 14.565 * [backup-simplify]: Simplify 1.0 into 1.0 14.565 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.565 * [taylor]: Taking taylor expansion of k in n 14.565 * [backup-simplify]: Simplify k into k 14.565 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.565 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 14.565 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 14.565 * [taylor]: Taking taylor expansion of 2.0 in n 14.565 * [backup-simplify]: Simplify 2.0 into 2.0 14.565 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.565 * [taylor]: Taking taylor expansion of PI in n 14.565 * [backup-simplify]: Simplify PI into PI 14.565 * [taylor]: Taking taylor expansion of n in n 14.565 * [backup-simplify]: Simplify 0 into 0 14.566 * [backup-simplify]: Simplify 1 into 1 14.566 * [backup-simplify]: Simplify (/ PI 1) into PI 14.566 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.567 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.568 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 14.568 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 14.568 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 14.569 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 14.570 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 14.571 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 14.572 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 14.572 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 14.572 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 14.572 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 14.572 * [taylor]: Taking taylor expansion of 0.5 in n 14.572 * [backup-simplify]: Simplify 0.5 into 0.5 14.572 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 14.572 * [taylor]: Taking taylor expansion of 1.0 in n 14.572 * [backup-simplify]: Simplify 1.0 into 1.0 14.572 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.572 * [taylor]: Taking taylor expansion of k in n 14.572 * [backup-simplify]: Simplify k into k 14.572 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.572 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 14.572 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 14.572 * [taylor]: Taking taylor expansion of 2.0 in n 14.572 * [backup-simplify]: Simplify 2.0 into 2.0 14.572 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.572 * [taylor]: Taking taylor expansion of PI in n 14.572 * [backup-simplify]: Simplify PI into PI 14.572 * [taylor]: Taking taylor expansion of n in n 14.572 * [backup-simplify]: Simplify 0 into 0 14.572 * [backup-simplify]: Simplify 1 into 1 14.573 * [backup-simplify]: Simplify (/ PI 1) into PI 14.573 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.574 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.574 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 14.574 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 14.574 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 14.576 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 14.577 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 14.578 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 14.578 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 14.578 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 14.578 * [taylor]: Taking taylor expansion of 0.5 in k 14.578 * [backup-simplify]: Simplify 0.5 into 0.5 14.578 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 14.578 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 14.578 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 14.578 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 14.579 * [taylor]: Taking taylor expansion of 2.0 in k 14.579 * [backup-simplify]: Simplify 2.0 into 2.0 14.579 * [taylor]: Taking taylor expansion of PI in k 14.579 * [backup-simplify]: Simplify PI into PI 14.579 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.580 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.580 * [taylor]: Taking taylor expansion of (log n) in k 14.580 * [taylor]: Taking taylor expansion of n in k 14.580 * [backup-simplify]: Simplify n into n 14.580 * [backup-simplify]: Simplify (log n) into (log n) 14.580 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 14.580 * [taylor]: Taking taylor expansion of 1.0 in k 14.580 * [backup-simplify]: Simplify 1.0 into 1.0 14.580 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.580 * [taylor]: Taking taylor expansion of k in k 14.580 * [backup-simplify]: Simplify 0 into 0 14.580 * [backup-simplify]: Simplify 1 into 1 14.581 * [backup-simplify]: Simplify (/ 1 1) into 1 14.581 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 14.582 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 14.582 * [backup-simplify]: Simplify (- 1) into -1 14.583 * [backup-simplify]: Simplify (+ 0 -1) into -1 14.584 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 14.585 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 14.586 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 14.588 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 14.589 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 14.589 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 14.591 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 14.592 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 14.592 * [backup-simplify]: Simplify (- 0) into 0 14.592 * [backup-simplify]: Simplify (+ 0 0) into 0 14.593 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 14.595 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 14.596 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 14.597 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 14.597 * [taylor]: Taking taylor expansion of 0 in k 14.597 * [backup-simplify]: Simplify 0 into 0 14.597 * [backup-simplify]: Simplify 0 into 0 14.597 * [backup-simplify]: Simplify 0 into 0 14.597 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.598 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 14.600 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 14.600 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 14.601 * [backup-simplify]: Simplify (- 0) into 0 14.601 * [backup-simplify]: Simplify (+ 0 0) into 0 14.602 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 14.603 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 14.604 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 14.605 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.605 * [taylor]: Taking taylor expansion of 0 in k 14.605 * [backup-simplify]: Simplify 0 into 0 14.605 * [backup-simplify]: Simplify 0 into 0 14.605 * [backup-simplify]: Simplify 0 into 0 14.605 * [backup-simplify]: Simplify 0 into 0 14.606 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.606 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 14.610 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 14.610 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 14.610 * [backup-simplify]: Simplify (- 0) into 0 14.610 * [backup-simplify]: Simplify (+ 0 0) into 0 14.611 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 14.612 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 14.613 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 14.615 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 14.615 * [taylor]: Taking taylor expansion of 0 in k 14.615 * [backup-simplify]: Simplify 0 into 0 14.615 * [backup-simplify]: Simplify 0 into 0 14.616 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 14.616 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 14.616 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 14.616 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 14.616 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 14.616 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 14.616 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 14.616 * [taylor]: Taking taylor expansion of 0.5 in k 14.616 * [backup-simplify]: Simplify 0.5 into 0.5 14.616 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 14.616 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.616 * [taylor]: Taking taylor expansion of k in k 14.616 * [backup-simplify]: Simplify 0 into 0 14.616 * [backup-simplify]: Simplify 1 into 1 14.617 * [backup-simplify]: Simplify (/ 1 1) into 1 14.617 * [taylor]: Taking taylor expansion of 1.0 in k 14.617 * [backup-simplify]: Simplify 1.0 into 1.0 14.617 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 14.617 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 14.617 * [taylor]: Taking taylor expansion of -2.0 in k 14.617 * [backup-simplify]: Simplify -2.0 into -2.0 14.617 * [taylor]: Taking taylor expansion of (/ PI n) in k 14.617 * [taylor]: Taking taylor expansion of PI in k 14.617 * [backup-simplify]: Simplify PI into PI 14.617 * [taylor]: Taking taylor expansion of n in k 14.617 * [backup-simplify]: Simplify n into n 14.617 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 14.617 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 14.617 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 14.617 * [backup-simplify]: Simplify (+ 1 0) into 1 14.618 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 14.618 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 14.618 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 14.618 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 14.618 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 14.618 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 14.618 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 14.618 * [taylor]: Taking taylor expansion of 0.5 in n 14.618 * [backup-simplify]: Simplify 0.5 into 0.5 14.618 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 14.618 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.618 * [taylor]: Taking taylor expansion of k in n 14.618 * [backup-simplify]: Simplify k into k 14.618 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.618 * [taylor]: Taking taylor expansion of 1.0 in n 14.618 * [backup-simplify]: Simplify 1.0 into 1.0 14.618 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 14.618 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 14.618 * [taylor]: Taking taylor expansion of -2.0 in n 14.618 * [backup-simplify]: Simplify -2.0 into -2.0 14.618 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.618 * [taylor]: Taking taylor expansion of PI in n 14.618 * [backup-simplify]: Simplify PI into PI 14.618 * [taylor]: Taking taylor expansion of n in n 14.618 * [backup-simplify]: Simplify 0 into 0 14.618 * [backup-simplify]: Simplify 1 into 1 14.618 * [backup-simplify]: Simplify (/ PI 1) into PI 14.619 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 14.619 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 14.619 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 14.620 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 14.620 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 14.621 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 14.622 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 14.622 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 14.622 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 14.622 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 14.622 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 14.622 * [taylor]: Taking taylor expansion of 0.5 in n 14.622 * [backup-simplify]: Simplify 0.5 into 0.5 14.622 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 14.622 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.622 * [taylor]: Taking taylor expansion of k in n 14.622 * [backup-simplify]: Simplify k into k 14.622 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.622 * [taylor]: Taking taylor expansion of 1.0 in n 14.622 * [backup-simplify]: Simplify 1.0 into 1.0 14.622 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 14.622 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 14.622 * [taylor]: Taking taylor expansion of -2.0 in n 14.622 * [backup-simplify]: Simplify -2.0 into -2.0 14.622 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.622 * [taylor]: Taking taylor expansion of PI in n 14.622 * [backup-simplify]: Simplify PI into PI 14.622 * [taylor]: Taking taylor expansion of n in n 14.622 * [backup-simplify]: Simplify 0 into 0 14.622 * [backup-simplify]: Simplify 1 into 1 14.623 * [backup-simplify]: Simplify (/ PI 1) into PI 14.623 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 14.624 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 14.624 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 14.624 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 14.632 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 14.634 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 14.635 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 14.635 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 14.635 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 14.635 * [taylor]: Taking taylor expansion of 0.5 in k 14.635 * [backup-simplify]: Simplify 0.5 into 0.5 14.635 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 14.635 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 14.635 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.635 * [taylor]: Taking taylor expansion of k in k 14.635 * [backup-simplify]: Simplify 0 into 0 14.635 * [backup-simplify]: Simplify 1 into 1 14.636 * [backup-simplify]: Simplify (/ 1 1) into 1 14.636 * [taylor]: Taking taylor expansion of 1.0 in k 14.636 * [backup-simplify]: Simplify 1.0 into 1.0 14.636 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 14.636 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 14.636 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 14.636 * [taylor]: Taking taylor expansion of -2.0 in k 14.636 * [backup-simplify]: Simplify -2.0 into -2.0 14.636 * [taylor]: Taking taylor expansion of PI in k 14.636 * [backup-simplify]: Simplify PI into PI 14.636 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 14.637 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 14.637 * [taylor]: Taking taylor expansion of (log n) in k 14.637 * [taylor]: Taking taylor expansion of n in k 14.638 * [backup-simplify]: Simplify n into n 14.638 * [backup-simplify]: Simplify (log n) into (log n) 14.638 * [backup-simplify]: Simplify (+ 1 0) into 1 14.638 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 14.639 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 14.640 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 14.641 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 14.643 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 14.644 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 14.645 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 14.646 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 14.647 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 14.648 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 14.648 * [backup-simplify]: Simplify (+ 0 0) into 0 14.649 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 14.650 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 14.651 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 14.653 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 14.653 * [taylor]: Taking taylor expansion of 0 in k 14.653 * [backup-simplify]: Simplify 0 into 0 14.654 * [backup-simplify]: Simplify 0 into 0 14.654 * [backup-simplify]: Simplify 0 into 0 14.655 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.655 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 14.657 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 14.658 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 14.658 * [backup-simplify]: Simplify (+ 0 0) into 0 14.659 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 14.660 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 14.660 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 14.662 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.662 * [taylor]: Taking taylor expansion of 0 in k 14.662 * [backup-simplify]: Simplify 0 into 0 14.662 * [backup-simplify]: Simplify 0 into 0 14.662 * [backup-simplify]: Simplify 0 into 0 14.662 * [backup-simplify]: Simplify 0 into 0 14.663 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.663 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 14.667 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 14.667 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 14.667 * [backup-simplify]: Simplify (+ 0 0) into 0 14.668 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 14.669 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 14.670 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 14.672 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 14.672 * [taylor]: Taking taylor expansion of 0 in k 14.672 * [backup-simplify]: Simplify 0 into 0 14.672 * [backup-simplify]: Simplify 0 into 0 14.673 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 14.673 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 14.673 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) into (* 1.0 (sqrt (/ 1 k))) 14.673 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 14.673 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 14.673 * [taylor]: Taking taylor expansion of 1.0 in k 14.673 * [backup-simplify]: Simplify 1.0 into 1.0 14.673 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 14.673 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.674 * [taylor]: Taking taylor expansion of k in k 14.674 * [backup-simplify]: Simplify 0 into 0 14.674 * [backup-simplify]: Simplify 1 into 1 14.674 * [backup-simplify]: Simplify (/ 1 1) into 1 14.674 * [backup-simplify]: Simplify (sqrt 0) into 0 14.675 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.675 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 14.675 * [taylor]: Taking taylor expansion of 1.0 in k 14.675 * [backup-simplify]: Simplify 1.0 into 1.0 14.675 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 14.675 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.675 * [taylor]: Taking taylor expansion of k in k 14.675 * [backup-simplify]: Simplify 0 into 0 14.675 * [backup-simplify]: Simplify 1 into 1 14.675 * [backup-simplify]: Simplify (/ 1 1) into 1 14.675 * [backup-simplify]: Simplify (sqrt 0) into 0 14.676 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.676 * [backup-simplify]: Simplify (* 1.0 0) into 0 14.677 * [backup-simplify]: Simplify 0 into 0 14.677 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 14.678 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.678 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 14.680 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 14.681 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 14.681 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.682 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.684 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 14.687 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 14.687 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.689 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 14.689 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt (/ 1 k)))) (sqrt (sqrt (/ 1 k)))) into (* 1.0 (sqrt k)) 14.689 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 14.689 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 14.689 * [taylor]: Taking taylor expansion of 1.0 in k 14.689 * [backup-simplify]: Simplify 1.0 into 1.0 14.689 * [taylor]: Taking taylor expansion of (sqrt k) in k 14.689 * [taylor]: Taking taylor expansion of k in k 14.689 * [backup-simplify]: Simplify 0 into 0 14.689 * [backup-simplify]: Simplify 1 into 1 14.690 * [backup-simplify]: Simplify (sqrt 0) into 0 14.691 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.691 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 14.691 * [taylor]: Taking taylor expansion of 1.0 in k 14.691 * [backup-simplify]: Simplify 1.0 into 1.0 14.691 * [taylor]: Taking taylor expansion of (sqrt k) in k 14.691 * [taylor]: Taking taylor expansion of k in k 14.691 * [backup-simplify]: Simplify 0 into 0 14.691 * [backup-simplify]: Simplify 1 into 1 14.691 * [backup-simplify]: Simplify (sqrt 0) into 0 14.693 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.693 * [backup-simplify]: Simplify (* 1.0 0) into 0 14.693 * [backup-simplify]: Simplify 0 into 0 14.695 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 14.695 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.698 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 14.700 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 14.700 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.702 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 14.704 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 14.704 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.705 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 14.705 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt (/ 1 (- k))))) (sqrt (sqrt (/ 1 (- k))))) into (/ 1.0 (sqrt (/ -1 k))) 14.705 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 14.705 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 14.705 * [taylor]: Taking taylor expansion of 1.0 in k 14.705 * [backup-simplify]: Simplify 1.0 into 1.0 14.705 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 14.705 * [taylor]: Taking taylor expansion of (/ -1 k) in k 14.705 * [taylor]: Taking taylor expansion of -1 in k 14.705 * [backup-simplify]: Simplify -1 into -1 14.705 * [taylor]: Taking taylor expansion of k in k 14.705 * [backup-simplify]: Simplify 0 into 0 14.705 * [backup-simplify]: Simplify 1 into 1 14.706 * [backup-simplify]: Simplify (/ -1 1) into -1 14.706 * [backup-simplify]: Simplify (sqrt 0) into 0 14.707 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 14.707 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 14.707 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 14.707 * [taylor]: Taking taylor expansion of 1.0 in k 14.707 * [backup-simplify]: Simplify 1.0 into 1.0 14.707 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 14.707 * [taylor]: Taking taylor expansion of (/ -1 k) in k 14.707 * [taylor]: Taking taylor expansion of -1 in k 14.707 * [backup-simplify]: Simplify -1 into -1 14.707 * [taylor]: Taking taylor expansion of k in k 14.707 * [backup-simplify]: Simplify 0 into 0 14.707 * [backup-simplify]: Simplify 1 into 1 14.707 * [backup-simplify]: Simplify (/ -1 1) into -1 14.707 * [backup-simplify]: Simplify (sqrt 0) into 0 14.708 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 14.708 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 14.709 * [backup-simplify]: Simplify +nan.0 into +nan.0 14.709 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 14.711 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 14.712 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 14.712 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.713 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.715 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 14.718 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 14.718 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.719 * [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))))) 14.719 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 14.719 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt k))) into (* 1.0 (pow (/ 1 k) 1/4)) 14.719 * [approximate]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in (k) around 0 14.719 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 14.719 * [taylor]: Taking taylor expansion of 1.0 in k 14.719 * [backup-simplify]: Simplify 1.0 into 1.0 14.719 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 14.719 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 14.719 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 14.719 * [taylor]: Taking taylor expansion of 1/4 in k 14.719 * [backup-simplify]: Simplify 1/4 into 1/4 14.719 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 14.719 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.719 * [taylor]: Taking taylor expansion of k in k 14.719 * [backup-simplify]: Simplify 0 into 0 14.719 * [backup-simplify]: Simplify 1 into 1 14.719 * [backup-simplify]: Simplify (/ 1 1) into 1 14.719 * [backup-simplify]: Simplify (log 1) into 0 14.720 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.720 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 14.720 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 14.720 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 14.720 * [taylor]: Taking taylor expansion of 1.0 in k 14.720 * [backup-simplify]: Simplify 1.0 into 1.0 14.720 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 14.720 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 14.720 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 14.720 * [taylor]: Taking taylor expansion of 1/4 in k 14.720 * [backup-simplify]: Simplify 1/4 into 1/4 14.720 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 14.720 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.720 * [taylor]: Taking taylor expansion of k in k 14.720 * [backup-simplify]: Simplify 0 into 0 14.720 * [backup-simplify]: Simplify 1 into 1 14.720 * [backup-simplify]: Simplify (/ 1 1) into 1 14.721 * [backup-simplify]: Simplify (log 1) into 0 14.721 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.721 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 14.721 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 14.721 * [backup-simplify]: Simplify (* 1.0 (pow k -1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 14.721 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 14.722 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 14.722 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 14.723 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.723 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0 14.723 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 14.724 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (pow k -1/4))) into 0 14.724 * [backup-simplify]: Simplify 0 into 0 14.724 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.726 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 14.726 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.727 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 14.727 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.728 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (pow k -1/4)))) into 0 14.728 * [backup-simplify]: Simplify 0 into 0 14.729 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.735 * [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 14.735 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.737 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0 14.746 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 14.747 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4))))) into 0 14.747 * [backup-simplify]: Simplify 0 into 0 14.748 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.760 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 14.761 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.762 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0 14.765 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.767 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4)))))) into 0 14.767 * [backup-simplify]: Simplify 0 into 0 14.768 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.780 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 14.781 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.782 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0 14.784 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 14.785 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4))))))) into 0 14.785 * [backup-simplify]: Simplify 0 into 0 14.786 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.808 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 14.809 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 14.812 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0 14.818 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.821 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4)))))))) into 0 14.821 * [backup-simplify]: Simplify 0 into 0 14.821 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 14.821 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt (/ 1 k)))) into (* 1.0 (pow k 1/4)) 14.821 * [approximate]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in (k) around 0 14.821 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 14.821 * [taylor]: Taking taylor expansion of 1.0 in k 14.821 * [backup-simplify]: Simplify 1.0 into 1.0 14.821 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 14.821 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 14.821 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 14.821 * [taylor]: Taking taylor expansion of 1/4 in k 14.821 * [backup-simplify]: Simplify 1/4 into 1/4 14.821 * [taylor]: Taking taylor expansion of (log k) in k 14.821 * [taylor]: Taking taylor expansion of k in k 14.821 * [backup-simplify]: Simplify 0 into 0 14.821 * [backup-simplify]: Simplify 1 into 1 14.822 * [backup-simplify]: Simplify (log 1) into 0 14.822 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 14.822 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 14.822 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 14.822 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 14.823 * [taylor]: Taking taylor expansion of 1.0 in k 14.823 * [backup-simplify]: Simplify 1.0 into 1.0 14.823 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 14.823 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 14.823 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 14.823 * [taylor]: Taking taylor expansion of 1/4 in k 14.823 * [backup-simplify]: Simplify 1/4 into 1/4 14.823 * [taylor]: Taking taylor expansion of (log k) in k 14.823 * [taylor]: Taking taylor expansion of k in k 14.823 * [backup-simplify]: Simplify 0 into 0 14.823 * [backup-simplify]: Simplify 1 into 1 14.823 * [backup-simplify]: Simplify (log 1) into 0 14.824 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 14.824 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 14.824 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 14.824 * [backup-simplify]: Simplify (* 1.0 (pow k 1/4)) into (* 1.0 (pow k 1/4)) 14.824 * [backup-simplify]: Simplify (* 1.0 (pow k 1/4)) into (* 1.0 (pow k 1/4)) 14.826 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 14.826 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 14.827 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 14.828 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 14.828 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (pow k 1/4))) into 0 14.828 * [backup-simplify]: Simplify 0 into 0 14.831 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 14.832 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 14.833 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 14.834 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.835 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (pow k 1/4)))) into 0 14.835 * [backup-simplify]: Simplify 0 into 0 14.840 * [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 14.841 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 14.842 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0 14.843 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 14.845 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))) into 0 14.845 * [backup-simplify]: Simplify 0 into 0 14.856 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 14.856 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 14.858 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0 14.861 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.863 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))) into 0 14.863 * [backup-simplify]: Simplify 0 into 0 14.889 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 14.891 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 14.892 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0 14.894 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 14.896 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))))) into 0 14.896 * [backup-simplify]: Simplify 0 into 0 14.914 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 14.914 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 14.916 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0 14.919 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.921 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))))) into 0 14.921 * [backup-simplify]: Simplify 0 into 0 14.921 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 14.922 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt (/ 1 (- k))))) into (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) 14.922 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in (k) around 0 14.922 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 14.922 * [taylor]: Taking taylor expansion of 1.0 in k 14.922 * [backup-simplify]: Simplify 1.0 into 1.0 14.922 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 14.922 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 14.922 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 14.922 * [taylor]: Taking taylor expansion of (/ -1 k) in k 14.922 * [taylor]: Taking taylor expansion of -1 in k 14.922 * [backup-simplify]: Simplify -1 into -1 14.922 * [taylor]: Taking taylor expansion of k in k 14.922 * [backup-simplify]: Simplify 0 into 0 14.922 * [backup-simplify]: Simplify 1 into 1 14.922 * [backup-simplify]: Simplify (/ -1 1) into -1 14.923 * [backup-simplify]: Simplify (sqrt 0) into 0 14.924 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 14.924 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 14.924 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 14.925 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 14.927 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 14.928 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 14.929 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 14.929 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 14.929 * [taylor]: Taking taylor expansion of 1.0 in k 14.929 * [backup-simplify]: Simplify 1.0 into 1.0 14.929 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 14.929 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 14.929 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 14.929 * [taylor]: Taking taylor expansion of (/ -1 k) in k 14.929 * [taylor]: Taking taylor expansion of -1 in k 14.929 * [backup-simplify]: Simplify -1 into -1 14.929 * [taylor]: Taking taylor expansion of k in k 14.929 * [backup-simplify]: Simplify 0 into 0 14.929 * [backup-simplify]: Simplify 1 into 1 14.929 * [backup-simplify]: Simplify (/ -1 1) into -1 14.930 * [backup-simplify]: Simplify (sqrt 0) into 0 14.930 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 14.931 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 14.931 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 14.931 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 14.933 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 14.934 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 14.936 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 14.936 * [backup-simplify]: Simplify (* 1.0 (sqrt +nan.0)) into (* 1.0 (sqrt +nan.0)) 14.937 * [backup-simplify]: Simplify (* 1.0 (sqrt +nan.0)) into (* 1.0 (sqrt +nan.0)) 14.940 * [backup-simplify]: Simplify (+ (* 1.0 (/ +nan.0 (sqrt +nan.0))) (* 0 (sqrt +nan.0))) into (- (* +nan.0 (/ 1 (sqrt +nan.0)))) 14.942 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (sqrt +nan.0)))) into (- (* +nan.0 (/ 1 (sqrt +nan.0)))) 14.943 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.947 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 14.951 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 14.957 * [backup-simplify]: Simplify (/ (- (- +nan.0) (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) 14.970 * [backup-simplify]: Simplify (+ (* 1.0 (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))) (+ (* 0 (/ +nan.0 (sqrt +nan.0))) (* 0 (sqrt +nan.0)))) into (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) 14.978 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) into (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) 14.990 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (/ 1 (sqrt +nan.0)))) (/ 1 (- k))) (* 1.0 (sqrt +nan.0)))) into (- (* 1.0 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2))))))))) 14.990 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 14.991 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 14.991 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 14.991 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 14.991 * [taylor]: Taking taylor expansion of 2.0 in n 14.991 * [backup-simplify]: Simplify 2.0 into 2.0 14.991 * [taylor]: Taking taylor expansion of (* n PI) in n 14.991 * [taylor]: Taking taylor expansion of n in n 14.991 * [backup-simplify]: Simplify 0 into 0 14.991 * [backup-simplify]: Simplify 1 into 1 14.991 * [taylor]: Taking taylor expansion of PI in n 14.991 * [backup-simplify]: Simplify PI into PI 14.991 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 14.991 * [taylor]: Taking taylor expansion of 2.0 in n 14.991 * [backup-simplify]: Simplify 2.0 into 2.0 14.991 * [taylor]: Taking taylor expansion of (* n PI) in n 14.991 * [taylor]: Taking taylor expansion of n in n 14.991 * [backup-simplify]: Simplify 0 into 0 14.991 * [backup-simplify]: Simplify 1 into 1 14.991 * [taylor]: Taking taylor expansion of PI in n 14.991 * [backup-simplify]: Simplify PI into PI 14.992 * [backup-simplify]: Simplify (* 0 PI) into 0 14.993 * [backup-simplify]: Simplify (* 2.0 0) into 0 14.993 * [backup-simplify]: Simplify 0 into 0 14.994 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 14.996 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 14.996 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.997 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 14.997 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 14.997 * [backup-simplify]: Simplify 0 into 0 14.998 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 14.999 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 14.999 * [backup-simplify]: Simplify 0 into 0 14.999 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 15.000 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 15.000 * [backup-simplify]: Simplify 0 into 0 15.007 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 15.008 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 15.008 * [backup-simplify]: Simplify 0 into 0 15.009 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 15.010 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 15.010 * [backup-simplify]: Simplify 0 into 0 15.011 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 15.013 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 15.013 * [backup-simplify]: Simplify 0 into 0 15.013 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 15.013 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 15.013 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 15.013 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 15.013 * [taylor]: Taking taylor expansion of 2.0 in n 15.013 * [backup-simplify]: Simplify 2.0 into 2.0 15.013 * [taylor]: Taking taylor expansion of (/ PI n) in n 15.013 * [taylor]: Taking taylor expansion of PI in n 15.013 * [backup-simplify]: Simplify PI into PI 15.014 * [taylor]: Taking taylor expansion of n in n 15.014 * [backup-simplify]: Simplify 0 into 0 15.014 * [backup-simplify]: Simplify 1 into 1 15.014 * [backup-simplify]: Simplify (/ PI 1) into PI 15.014 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 15.014 * [taylor]: Taking taylor expansion of 2.0 in n 15.014 * [backup-simplify]: Simplify 2.0 into 2.0 15.014 * [taylor]: Taking taylor expansion of (/ PI n) in n 15.014 * [taylor]: Taking taylor expansion of PI in n 15.014 * [backup-simplify]: Simplify PI into PI 15.014 * [taylor]: Taking taylor expansion of n in n 15.014 * [backup-simplify]: Simplify 0 into 0 15.014 * [backup-simplify]: Simplify 1 into 1 15.014 * [backup-simplify]: Simplify (/ PI 1) into PI 15.015 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 15.015 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 15.016 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 15.016 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 15.017 * [backup-simplify]: Simplify 0 into 0 15.018 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.019 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 15.019 * [backup-simplify]: Simplify 0 into 0 15.020 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.021 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 15.021 * [backup-simplify]: Simplify 0 into 0 15.022 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.024 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 15.024 * [backup-simplify]: Simplify 0 into 0 15.025 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.027 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 15.027 * [backup-simplify]: Simplify 0 into 0 15.028 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.030 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 15.030 * [backup-simplify]: Simplify 0 into 0 15.031 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 15.031 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 15.031 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 15.031 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 15.031 * [taylor]: Taking taylor expansion of -2.0 in n 15.031 * [backup-simplify]: Simplify -2.0 into -2.0 15.031 * [taylor]: Taking taylor expansion of (/ PI n) in n 15.031 * [taylor]: Taking taylor expansion of PI in n 15.031 * [backup-simplify]: Simplify PI into PI 15.032 * [taylor]: Taking taylor expansion of n in n 15.032 * [backup-simplify]: Simplify 0 into 0 15.032 * [backup-simplify]: Simplify 1 into 1 15.032 * [backup-simplify]: Simplify (/ PI 1) into PI 15.032 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 15.032 * [taylor]: Taking taylor expansion of -2.0 in n 15.032 * [backup-simplify]: Simplify -2.0 into -2.0 15.032 * [taylor]: Taking taylor expansion of (/ PI n) in n 15.032 * [taylor]: Taking taylor expansion of PI in n 15.032 * [backup-simplify]: Simplify PI into PI 15.032 * [taylor]: Taking taylor expansion of n in n 15.032 * [backup-simplify]: Simplify 0 into 0 15.032 * [backup-simplify]: Simplify 1 into 1 15.033 * [backup-simplify]: Simplify (/ PI 1) into PI 15.033 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 15.034 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 15.035 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 15.036 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 15.036 * [backup-simplify]: Simplify 0 into 0 15.037 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.038 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 15.038 * [backup-simplify]: Simplify 0 into 0 15.039 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.040 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 15.040 * [backup-simplify]: Simplify 0 into 0 15.041 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.043 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 15.043 * [backup-simplify]: Simplify 0 into 0 15.044 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.045 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 15.045 * [backup-simplify]: Simplify 0 into 0 15.047 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.048 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 15.049 * [backup-simplify]: Simplify 0 into 0 15.049 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 15.049 * * * [progress]: simplifying candidates 15.066 * [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 (sqrt k))) (sqrt (sqrt k)))) (log1p (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (- (- (log 1.0) (log (sqrt (sqrt k)))) (log (sqrt (sqrt k)))) (- (log (/ 1.0 (sqrt (sqrt k)))) (log (sqrt (sqrt k)))) (log (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (exp (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (* (* (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt k)))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))) (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (- (/ 1.0 (sqrt (sqrt k)))) (- (sqrt (sqrt k))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt 1))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt 1)) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) 1) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt 1))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt 1)) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) 1) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt 1))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt 1)) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt 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[simplify]: Extracting # 0 : cost 0 15.097 * * [simplify]: Extracting # 1 : cost 0 15.099 * * [simplify]: Extracting # 2 : cost 0 15.101 * * [simplify]: Extracting # 3 : cost 0 15.103 * * [simplify]: Extracting # 4 : cost 0 15.105 * * [simplify]: Extracting # 5 : cost 0 15.107 * * [simplify]: Extracting # 6 : cost 0 15.109 * * [simplify]: Extracting # 7 : cost 0 15.111 * * [simplify]: Extracting # 8 : cost 0 15.113 * * [simplify]: Extracting # 9 : cost 0 15.116 * * [simplify]: Extracting # 10 : cost 0 15.118 * * [simplify]: Extracting # 11 : cost 0 15.128 * * [simplify]: Extracting # 12 : cost 0 15.129 * * [simplify]: Extracting # 13 : cost 0 15.130 * * [simplify]: iteration 0 : 566 enodes (cost 9021 ) 15.307 * * [simplify]: Extracting # 0 : cost 0 15.310 * * [simplify]: Extracting # 1 : cost 0 15.311 * * [simplify]: Extracting # 2 : cost 0 15.313 * * [simplify]: Extracting # 3 : cost 0 15.315 * * [simplify]: Extracting # 4 : cost 0 15.317 * * [simplify]: Extracting # 5 : cost 0 15.318 * * [simplify]: iteration 1 : 1407 enodes (cost 7684 ) 15.789 * * [simplify]: Extracting # 0 : cost 0 15.795 * * [simplify]: Extracting # 1 : cost 0 15.802 * * [simplify]: Extracting # 2 : cost 0 15.809 * * [simplify]: Extracting # 3 : cost 0 15.816 * * [simplify]: Extracting # 4 : cost 0 15.824 * * [simplify]: iteration done: 5001 enodes (cost 7188 ) 15.832 * [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) 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1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ 1 (fabs (cbrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ 1 (sqrt (fabs (cbrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt k)) (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ 1 (fabs (cbrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ 1 (sqrt (fabs (cbrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt k)) (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ 1.0 (fabs (cbrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ 1.0 (sqrt (fabs (cbrt k)))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1.0 (/ 1 (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1.0 (/ 1 (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) 1.0 (/ 1 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (fabs (cbrt (sqrt k)))) (/ 1.0 (* (sqrt (fabs (cbrt k))) (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (cbrt (/ 1.0 (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (sqrt (/ 1.0 (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (cbrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (cbrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (cbrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (cbrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (cbrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ 1.0 (cbrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (cbrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (cbrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k)))) (sqrt k) (sqrt k) (expm1 (/ 1.0 (sqrt (sqrt k)))) (log1p (/ 1.0 (sqrt (sqrt k)))) (log (/ 1.0 (sqrt (sqrt k)))) (log (/ 1.0 (sqrt (sqrt k)))) (exp (/ 1.0 (sqrt (sqrt k)))) (/ (pow 1.0 3) (pow (sqrt (sqrt k)) 3)) (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (cbrt (/ 1.0 (sqrt (sqrt k)))) (pow (/ 1.0 (sqrt (sqrt k))) 3) (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))) (- 1.0) (- (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt (sqrt k)))) (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fabs (cbrt k)))) (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (fabs (cbrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (cbrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (fabs (cbrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ 1.0 (cbrt (sqrt (sqrt k)))) (/ 1 (fabs (cbrt (sqrt k)))) (/ 1.0 (sqrt (cbrt (sqrt k)))) (/ 1 (sqrt (fabs (cbrt k)))) (/ 1.0 (sqrt (sqrt (cbrt k)))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) (/ (sqrt (sqrt k)) 1.0) (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ 1.0 (fabs (cbrt (sqrt k)))) (/ 1.0 (sqrt (fabs (cbrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) 1.0 (/ 1.0 (sqrt (sqrt (sqrt k)))) 1.0 (/ 1.0 (sqrt (sqrt (sqrt k)))) 1.0 (/ (sqrt (sqrt k)) (cbrt 1.0)) (/ (sqrt (sqrt k)) (sqrt 1.0)) (/ (sqrt (sqrt k)) 1.0) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (log (* 2.0 (* n PI))) (log (* 2.0 (* n PI))) (log (* 2.0 (* n PI))) (exp (* (* 2.0 PI) n)) (* (pow PI 3) (* (pow 2.0 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 (* n PI)) 3) (sqrt (* 2.0 (* n PI))) (sqrt (* 2.0 (* n PI))) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* n PI) (- (+ (* (* 0.125 (pow k 2)) (+ (* (pow (log (* 2.0 PI)) 2) (pow (* 2.0 (* n PI)) 0.5)) (* (pow (log n) 2) (pow (* 2.0 (* n PI)) 0.5)))) (fma (* (pow k 2) (* (* (log (* 2.0 PI)) (pow (* 2.0 (* n PI)) 0.5)) (log n))) 0.25 (pow (* 2.0 (* n PI)) 0.5))) (* 0.5 (* k (+ (* (log (* 2.0 PI)) (pow (* 2.0 (* n PI)) 0.5)) (* (pow (* 2.0 (* n PI)) 0.5) (log n)))))) (pow (pow (* 2.0 (* n PI)) 0.5) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (- (* +nan.0 k) (fma +nan.0 (pow k 2) (- +nan.0)))) (+ (- (/ +nan.0 k) (/ +nan.0 (pow k 3))) (- (/ +nan.0 (pow k 2)))) (- (- (/ +nan.0 (pow k 2)) (- (/ +nan.0 k) +nan.0))) (* 1.0 (pow (/ 1 k) 1/4)) (* 1.0 (pow (/ 1 k) 1/4)) (fma 1.0 (sqrt +nan.0) (- (+ (- (/ +nan.0 (* (sqrt +nan.0) (pow k 2))) (/ +nan.0 (* (sqrt +nan.0) k))) (/ +nan.0 (* (pow (sqrt +nan.0) 3) (pow k 2)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 15.840 * * * [progress]: adding candidates to table 17.164 * [progress]: [Phase 3 of 3] Extracting. 17.165 * * [regime]: Finding splitpoints for: (# # # # # # # #) 17.170 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 17.171 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # # #) 17.229 * * * * [regimes]: Trying to branch on n from (# # # # # # # #) 17.304 * * * * [regimes]: Trying to branch on k from (# # # # # # # #) 17.381 * * * [regime]: Found split indices: #