5.139 * [progress]: [Phase 1 of 3] Setting up. 0.002 * * * [progress]: [1/2] Preparing points 0.149 * * * [progress]: [2/2] Setting up program. 0.155 * [progress]: [Phase 2 of 3] Improving. 0.156 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.156 * * [simplify]: Extracting # 0 : cost 0 0.156 * * [simplify]: Extracting # 1 : cost 0 0.156 * * [simplify]: Extracting # 2 : cost 0 0.156 * * [simplify]: Extracting # 3 : cost 0 0.156 * * [simplify]: Extracting # 4 : cost 0 0.156 * * [simplify]: Extracting # 5 : cost 0 0.156 * * [simplify]: Extracting # 6 : cost 0 0.156 * * [simplify]: Extracting # 7 : cost 0 0.156 * * [simplify]: iteration 0 : 13 enodes (cost 16 ) 0.162 * * [simplify]: Extracting # 0 : cost 0 0.162 * * [simplify]: Extracting # 1 : cost 0 0.162 * * [simplify]: Extracting # 2 : cost 0 0.162 * * [simplify]: Extracting # 3 : cost 0 0.162 * * [simplify]: Extracting # 4 : cost 0 0.162 * * [simplify]: Extracting # 5 : cost 0 0.162 * * [simplify]: iteration 1 : 29 enodes (cost 16 ) 0.173 * * [simplify]: Extracting # 0 : cost 0 0.173 * * [simplify]: Extracting # 1 : cost 0 0.173 * * [simplify]: Extracting # 2 : cost 0 0.173 * * [simplify]: Extracting # 3 : cost 0 0.173 * * [simplify]: Extracting # 4 : cost 0 0.173 * * [simplify]: iteration 2 : 59 enodes (cost 16 ) 0.233 * * [simplify]: Extracting # 0 : cost 0 0.233 * * [simplify]: Extracting # 1 : cost 0 0.234 * * [simplify]: Extracting # 2 : cost 0 0.234 * * [simplify]: Extracting # 3 : cost 0 0.234 * * [simplify]: Extracting # 4 : cost 0 0.234 * * [simplify]: iteration 3 : 119 enodes (cost 16 ) 0.284 * * [simplify]: Extracting # 0 : cost 0 0.285 * * [simplify]: Extracting # 1 : cost 0 0.285 * * [simplify]: Extracting # 2 : cost 0 0.285 * * [simplify]: Extracting # 3 : cost 0 0.286 * * [simplify]: Extracting # 4 : cost 0 0.286 * * [simplify]: iteration 4 : 313 enodes (cost 16 ) 0.558 * * [simplify]: Extracting # 0 : cost 0 0.559 * * [simplify]: Extracting # 1 : cost 0 0.560 * * [simplify]: Extracting # 2 : cost 0 0.560 * * [simplify]: Extracting # 3 : cost 0 0.561 * * [simplify]: Extracting # 4 : cost 0 0.562 * * [simplify]: iteration 5 : 843 enodes (cost 16 ) 2.109 * * [simplify]: Extracting # 0 : cost 0 2.114 * * [simplify]: Extracting # 1 : cost 0 2.117 * * [simplify]: Extracting # 2 : cost 0 2.120 * * [simplify]: Extracting # 3 : cost 0 2.123 * * [simplify]: Extracting # 4 : cost 0 2.125 * * [simplify]: iteration 6 : 3221 enodes (cost 16 ) 3.647 * * [simplify]: Extracting # 0 : cost 0 3.658 * * [simplify]: Extracting # 1 : cost 0 3.672 * * [simplify]: Extracting # 2 : cost 0 3.677 * * [simplify]: Extracting # 3 : cost 0 3.682 * * [simplify]: Extracting # 4 : cost 0 3.686 * * [simplify]: iteration done: 5001 enodes (cost 16 ) 3.686 * [simplify]: Simplified to: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3.687 * * [progress]: iteration 1 / 4 3.687 * * * [progress]: picking best candidate 3.689 * * * * [pick]: Picked # 3.689 * * * [progress]: localizing error 3.710 * * * [progress]: generating rewritten candidates 3.710 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 3.754 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 3.774 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 3.810 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 3.900 * * * [progress]: generating series expansions 3.900 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 3.901 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 3.901 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 3.901 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.901 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.901 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.901 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.901 * [taylor]: Taking taylor expansion of 0.5 in k 3.901 * [backup-simplify]: Simplify 0.5 into 0.5 3.901 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.902 * [taylor]: Taking taylor expansion of 1.0 in k 3.902 * [backup-simplify]: Simplify 1.0 into 1.0 3.902 * [taylor]: Taking taylor expansion of k in k 3.902 * [backup-simplify]: Simplify 0 into 0 3.902 * [backup-simplify]: Simplify 1 into 1 3.902 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.902 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.902 * [taylor]: Taking taylor expansion of 2.0 in k 3.902 * [backup-simplify]: Simplify 2.0 into 2.0 3.902 * [taylor]: Taking taylor expansion of (* n PI) in k 3.902 * [taylor]: Taking taylor expansion of n in k 3.902 * [backup-simplify]: Simplify n into n 3.902 * [taylor]: Taking taylor expansion of PI in k 3.902 * [backup-simplify]: Simplify PI into PI 3.902 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.902 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 3.902 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 3.903 * [backup-simplify]: Simplify (- 0) into 0 3.903 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.903 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.903 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 3.903 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 3.903 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.903 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.903 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.904 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.904 * [taylor]: Taking taylor expansion of 0.5 in n 3.904 * [backup-simplify]: Simplify 0.5 into 0.5 3.904 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.904 * [taylor]: Taking taylor expansion of 1.0 in n 3.904 * [backup-simplify]: Simplify 1.0 into 1.0 3.904 * [taylor]: Taking taylor expansion of k in n 3.904 * [backup-simplify]: Simplify k into k 3.904 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.904 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.904 * [taylor]: Taking taylor expansion of 2.0 in n 3.904 * [backup-simplify]: Simplify 2.0 into 2.0 3.904 * [taylor]: Taking taylor expansion of (* n PI) in n 3.904 * [taylor]: Taking taylor expansion of n in n 3.904 * [backup-simplify]: Simplify 0 into 0 3.904 * [backup-simplify]: Simplify 1 into 1 3.904 * [taylor]: Taking taylor expansion of PI in n 3.904 * [backup-simplify]: Simplify PI into PI 3.904 * [backup-simplify]: Simplify (* 0 PI) into 0 3.905 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.906 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.906 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.907 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.907 * [backup-simplify]: Simplify (- k) into (- k) 3.907 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.907 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.908 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.909 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 3.910 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 3.910 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.910 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.910 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.910 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.910 * [taylor]: Taking taylor expansion of 0.5 in n 3.910 * [backup-simplify]: Simplify 0.5 into 0.5 3.910 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.910 * [taylor]: Taking taylor expansion of 1.0 in n 3.910 * [backup-simplify]: Simplify 1.0 into 1.0 3.910 * [taylor]: Taking taylor expansion of k in n 3.910 * [backup-simplify]: Simplify k into k 3.910 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.910 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.910 * [taylor]: Taking taylor expansion of 2.0 in n 3.910 * [backup-simplify]: Simplify 2.0 into 2.0 3.910 * [taylor]: Taking taylor expansion of (* n PI) in n 3.910 * [taylor]: Taking taylor expansion of n in n 3.910 * [backup-simplify]: Simplify 0 into 0 3.910 * [backup-simplify]: Simplify 1 into 1 3.910 * [taylor]: Taking taylor expansion of PI in n 3.910 * [backup-simplify]: Simplify PI into PI 3.911 * [backup-simplify]: Simplify (* 0 PI) into 0 3.911 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.912 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.913 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.913 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.913 * [backup-simplify]: Simplify (- k) into (- k) 3.913 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.913 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.914 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.915 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 3.916 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 3.916 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 3.916 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 3.916 * [taylor]: Taking taylor expansion of 0.5 in k 3.916 * [backup-simplify]: Simplify 0.5 into 0.5 3.916 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 3.916 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.916 * [taylor]: Taking taylor expansion of 1.0 in k 3.916 * [backup-simplify]: Simplify 1.0 into 1.0 3.916 * [taylor]: Taking taylor expansion of k in k 3.916 * [backup-simplify]: Simplify 0 into 0 3.916 * [backup-simplify]: Simplify 1 into 1 3.916 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 3.916 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.916 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.916 * [taylor]: Taking taylor expansion of 2.0 in k 3.916 * [backup-simplify]: Simplify 2.0 into 2.0 3.916 * [taylor]: Taking taylor expansion of PI in k 3.916 * [backup-simplify]: Simplify PI into PI 3.916 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.917 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.917 * [taylor]: Taking taylor expansion of (log n) in k 3.917 * [taylor]: Taking taylor expansion of n in k 3.917 * [backup-simplify]: Simplify n into n 3.917 * [backup-simplify]: Simplify (log n) into (log n) 3.917 * [backup-simplify]: Simplify (- 0) into 0 3.918 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.918 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 3.919 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 3.920 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 3.920 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 3.921 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 3.922 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.923 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 3.924 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.924 * [backup-simplify]: Simplify (- 0) into 0 3.924 * [backup-simplify]: Simplify (+ 0 0) into 0 3.925 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 3.925 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.926 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 3.927 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.927 * [taylor]: Taking taylor expansion of 0 in k 3.927 * [backup-simplify]: Simplify 0 into 0 3.927 * [backup-simplify]: Simplify 0 into 0 3.928 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.929 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.929 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 3.930 * [backup-simplify]: Simplify (+ 0 0) into 0 3.930 * [backup-simplify]: Simplify (- 1) into -1 3.930 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.931 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 3.932 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 3.935 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 3.936 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 3.938 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 3.939 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 3.940 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 3.941 * [backup-simplify]: Simplify (- 0) into 0 3.941 * [backup-simplify]: Simplify (+ 0 0) into 0 3.942 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 3.942 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.943 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 3.945 * [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 3.945 * [taylor]: Taking taylor expansion of 0 in k 3.945 * [backup-simplify]: Simplify 0 into 0 3.945 * [backup-simplify]: Simplify 0 into 0 3.946 * [backup-simplify]: Simplify 0 into 0 3.947 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.950 * [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