42.276 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.175 * * * [progress]: [2/2] Setting up program. 0.178 * [progress]: [Phase 2 of 3] Improving. 0.178 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 2.221 * * [progress]: iteration 1 / 4 2.221 * * * [progress]: picking best candidate 2.224 * * * * [pick]: Picked # 2.224 * * * [progress]: localizing error 2.240 * * * [progress]: generating rewritten candidates 2.240 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 2.276 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 2.718 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 2.725 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 2.794 * * * [progress]: generating series expansions 2.795 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 2.796 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 2.796 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 2.796 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.796 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.796 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.796 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.796 * [taylor]: Taking taylor expansion of 0.5 in k 2.796 * [backup-simplify]: Simplify 0.5 into 0.5 2.796 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.796 * [taylor]: Taking taylor expansion of 1.0 in k 2.796 * [backup-simplify]: Simplify 1.0 into 1.0 2.796 * [taylor]: Taking taylor expansion of k in k 2.796 * [backup-simplify]: Simplify 0 into 0 2.796 * [backup-simplify]: Simplify 1 into 1 2.796 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.796 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.796 * [taylor]: Taking taylor expansion of 2.0 in k 2.796 * [backup-simplify]: Simplify 2.0 into 2.0 2.796 * [taylor]: Taking taylor expansion of (* n PI) in k 2.796 * [taylor]: Taking taylor expansion of n in k 2.796 * [backup-simplify]: Simplify n into n 2.796 * [taylor]: Taking taylor expansion of PI in k 2.796 * [backup-simplify]: Simplify PI into PI 2.796 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.796 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.797 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.797 * [backup-simplify]: Simplify (- 0) into 0 2.797 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.798 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.798 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.798 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.798 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.798 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.798 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.798 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.798 * [taylor]: Taking taylor expansion of 0.5 in n 2.798 * [backup-simplify]: Simplify 0.5 into 0.5 2.798 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.798 * [taylor]: Taking taylor expansion of 1.0 in n 2.798 * [backup-simplify]: Simplify 1.0 into 1.0 2.798 * [taylor]: Taking taylor expansion of k in n 2.798 * [backup-simplify]: Simplify k into k 2.798 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.799 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.799 * [taylor]: Taking taylor expansion of 2.0 in n 2.799 * [backup-simplify]: Simplify 2.0 into 2.0 2.799 * [taylor]: Taking taylor expansion of (* n PI) in n 2.799 * [taylor]: Taking taylor expansion of n in n 2.799 * [backup-simplify]: Simplify 0 into 0 2.799 * [backup-simplify]: Simplify 1 into 1 2.799 * [taylor]: Taking taylor expansion of PI in n 2.799 * [backup-simplify]: Simplify PI into PI 2.799 * [backup-simplify]: Simplify (* 0 PI) into 0 2.800 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.801 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.803 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.804 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.804 * [backup-simplify]: Simplify (- k) into (- k) 2.804 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.804 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.805 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.806 * [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)))) 2.808 * [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))))) 2.808 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.808 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.808 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.808 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.808 * [taylor]: Taking taylor expansion of 0.5 in n 2.808 * [backup-simplify]: Simplify 0.5 into 0.5 2.808 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.808 * [taylor]: Taking taylor expansion of 1.0 in n 2.808 * [backup-simplify]: Simplify 1.0 into 1.0 2.808 * [taylor]: Taking taylor expansion of k in n 2.808 * [backup-simplify]: Simplify k into k 2.808 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.808 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.808 * [taylor]: Taking taylor expansion of 2.0 in n 2.808 * [backup-simplify]: Simplify 2.0 into 2.0 2.808 * [taylor]: Taking taylor expansion of (* n PI) in n 2.808 * [taylor]: Taking taylor expansion of n in n 2.808 * [backup-simplify]: Simplify 0 into 0 2.808 * [backup-simplify]: Simplify 1 into 1 2.808 * [taylor]: Taking taylor expansion of PI in n 2.808 * [backup-simplify]: Simplify PI into PI 2.809 * [backup-simplify]: Simplify (* 0 PI) into 0 2.810 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.811 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.813 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.814 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.814 * [backup-simplify]: Simplify (- k) into (- k) 2.814 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.814 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.815 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.816 * [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)))) 2.817 * [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))))) 2.818 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.818 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.818 * [taylor]: Taking taylor expansion of 0.5 in k 2.818 * [backup-simplify]: Simplify 0.5 into 0.5 2.818 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.818 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.818 * [taylor]: Taking taylor expansion of 1.0 in k 2.818 * [backup-simplify]: Simplify 1.0 into 1.0 2.818 * [taylor]: Taking taylor expansion of k in k 2.818 * [backup-simplify]: Simplify 0 into 0 2.818 * [backup-simplify]: Simplify 1 into 1 2.818 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.818 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.818 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.818 * [taylor]: Taking taylor expansion of 2.0 in k 2.818 * [backup-simplify]: Simplify 2.0 into 2.0 2.818 * [taylor]: Taking taylor expansion of PI in k 2.818 * [backup-simplify]: Simplify PI into PI 2.819 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.820 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.820 * [taylor]: Taking taylor expansion of (log n) in k 2.820 * [taylor]: Taking taylor expansion of n in k 2.820 * [backup-simplify]: Simplify n into n 2.820 * [backup-simplify]: Simplify (log n) into (log n) 2.820 * [backup-simplify]: Simplify (- 0) into 0 2.820 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.822 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.823 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.824 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 2.825 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 2.826 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 2.827 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.828 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.830 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.830 * [backup-simplify]: Simplify (- 0) into 0 2.830 * [backup-simplify]: Simplify (+ 0 0) into 0 2.831 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 2.832 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.833 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.835 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.835 * [taylor]: Taking taylor expansion of 0 in k 2.835 * [backup-simplify]: Simplify 0 into 0 2.835 * [backup-simplify]: Simplify 0 into 0 2.836 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.838 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.839 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.839 * [backup-simplify]: Simplify (+ 0 0) into 0 2.840 * [backup-simplify]: Simplify (- 1) into -1 2.840 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.842 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.844 * [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)))) 2.847 * [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)))))) 2.850 * [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)))))) 2.851 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.852 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.856 * [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 2.856 * [backup-simplify]: Simplify (- 0) into 0 2.857 * [backup-simplify]: Simplify (+ 0 0) into 0 2.858 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.859 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.861 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.863 * [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 2.863 * [taylor]: Taking taylor expansion of 0 in k 2.863 * [backup-simplify]: Simplify 0 into 0 2.863 * [backup-simplify]: Simplify 0 into 0 2.863 * [backup-simplify]: Simplify 0 into 0 2.864 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.868 * [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 2.870 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.870 * [backup-simplify]: Simplify (+ 0 0) into 0 2.870 * [backup-simplify]: Simplify (- 0) into 0 2.871 * [backup-simplify]: Simplify (+ 0 0) into 0 2.873 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.875 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.879 * [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)))))) 2.885 * [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)))))) 2.896 * [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)))))) 2.897 * [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)))) 2.897 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 2.897 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.897 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.897 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.897 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.897 * [taylor]: Taking taylor expansion of 0.5 in k 2.897 * [backup-simplify]: Simplify 0.5 into 0.5 2.897 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.897 * [taylor]: Taking taylor expansion of 1.0 in k 2.898 * [backup-simplify]: Simplify 1.0 into 1.0 2.898 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.898 * [taylor]: Taking taylor expansion of k in k 2.898 * [backup-simplify]: Simplify 0 into 0 2.898 * [backup-simplify]: Simplify 1 into 1 2.898 * [backup-simplify]: Simplify (/ 1 1) into 1 2.898 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.898 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.898 * [taylor]: Taking taylor expansion of 2.0 in k 2.898 * [backup-simplify]: Simplify 2.0 into 2.0 2.898 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.898 * [taylor]: Taking taylor expansion of PI in k 2.898 * [backup-simplify]: Simplify PI into PI 2.898 * [taylor]: Taking taylor expansion of n in k 2.898 * [backup-simplify]: Simplify n into n 2.898 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.899 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.899 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.899 * [backup-simplify]: Simplify (- 1) into -1 2.900 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.900 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.900 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.901 * [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))))) 2.901 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.901 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.901 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.901 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.901 * [taylor]: Taking taylor expansion of 0.5 in n 2.901 * [backup-simplify]: Simplify 0.5 into 0.5 2.901 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.901 * [taylor]: Taking taylor expansion of 1.0 in n 2.901 * [backup-simplify]: Simplify 1.0 into 1.0 2.901 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.901 * [taylor]: Taking taylor expansion of k in n 2.901 * [backup-simplify]: Simplify k into k 2.901 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.901 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.901 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.901 * [taylor]: Taking taylor expansion of 2.0 in n 2.902 * [backup-simplify]: Simplify 2.0 into 2.0 2.902 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.902 * [taylor]: Taking taylor expansion of PI in n 2.902 * [backup-simplify]: Simplify PI into PI 2.902 * [taylor]: Taking taylor expansion of n in n 2.902 * [backup-simplify]: Simplify 0 into 0 2.902 * [backup-simplify]: Simplify 1 into 1 2.902 * [backup-simplify]: Simplify (/ PI 1) into PI 2.903 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.904 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.904 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.904 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.904 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.906 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.907 * [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)))) 2.909 * [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))))) 2.909 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.909 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.909 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.909 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.909 * [taylor]: Taking taylor expansion of 0.5 in n 2.909 * [backup-simplify]: Simplify 0.5 into 0.5 2.909 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.909 * [taylor]: Taking taylor expansion of 1.0 in n 2.909 * [backup-simplify]: Simplify 1.0 into 1.0 2.909 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.909 * [taylor]: Taking taylor expansion of k in n 2.909 * [backup-simplify]: Simplify k into k 2.909 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.909 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.909 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.909 * [taylor]: Taking taylor expansion of 2.0 in n 2.909 * [backup-simplify]: Simplify 2.0 into 2.0 2.909 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.909 * [taylor]: Taking taylor expansion of PI in n 2.909 * [backup-simplify]: Simplify PI into PI 2.910 * [taylor]: Taking taylor expansion of n in n 2.910 * [backup-simplify]: Simplify 0 into 0 2.910 * [backup-simplify]: Simplify 1 into 1 2.910 * [backup-simplify]: Simplify (/ PI 1) into PI 2.911 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.912 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.912 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.912 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.912 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.914 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.915 * [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)))) 2.916 * [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))))) 2.916 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.917 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.917 * [taylor]: Taking taylor expansion of 0.5 in k 2.917 * [backup-simplify]: Simplify 0.5 into 0.5 2.917 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.917 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.917 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.917 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.917 * [taylor]: Taking taylor expansion of 2.0 in k 2.917 * [backup-simplify]: Simplify 2.0 into 2.0 2.917 * [taylor]: Taking taylor expansion of PI in k 2.917 * [backup-simplify]: Simplify PI into PI 2.917 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.918 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.919 * [taylor]: Taking taylor expansion of (log n) in k 2.919 * [taylor]: Taking taylor expansion of n in k 2.919 * [backup-simplify]: Simplify n into n 2.919 * [backup-simplify]: Simplify (log n) into (log n) 2.919 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.919 * [taylor]: Taking taylor expansion of 1.0 in k 2.919 * [backup-simplify]: Simplify 1.0 into 1.0 2.919 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.919 * [taylor]: Taking taylor expansion of k in k 2.919 * [backup-simplify]: Simplify 0 into 0 2.919 * [backup-simplify]: Simplify 1 into 1 2.919 * [backup-simplify]: Simplify (/ 1 1) into 1 2.919 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.926 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.927 * [backup-simplify]: Simplify (- 1) into -1 2.927 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.929 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.930 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 2.931 * [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))))) 2.933 * [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))))) 2.934 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.934 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.936 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.937 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.937 * [backup-simplify]: Simplify (- 0) into 0 2.937 * [backup-simplify]: Simplify (+ 0 0) into 0 2.938 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.939 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.940 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.941 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.941 * [taylor]: Taking taylor expansion of 0 in k 2.941 * [backup-simplify]: Simplify 0 into 0 2.941 * [backup-simplify]: Simplify 0 into 0 2.941 * [backup-simplify]: Simplify 0 into 0 2.942 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.942 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.944 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.945 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.945 * [backup-simplify]: Simplify (- 0) into 0 2.945 * [backup-simplify]: Simplify (+ 0 0) into 0 2.946 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.946 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.947 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.949 * [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 2.949 * [taylor]: Taking taylor expansion of 0 in k 2.949 * [backup-simplify]: Simplify 0 into 0 2.949 * [backup-simplify]: Simplify 0 into 0 2.949 * [backup-simplify]: Simplify 0 into 0 2.949 * [backup-simplify]: Simplify 0 into 0 2.950 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.950 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.954 * [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 2.954 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.954 * [backup-simplify]: Simplify (- 0) into 0 2.954 * [backup-simplify]: Simplify (+ 0 0) into 0 2.955 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.956 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.957 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.959 * [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 2.959 * [taylor]: Taking taylor expansion of 0 in k 2.959 * [backup-simplify]: Simplify 0 into 0 2.959 * [backup-simplify]: Simplify 0 into 0 2.960 * [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)))) 2.960 * [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))) 2.960 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 2.960 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.960 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.960 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.960 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.961 * [taylor]: Taking taylor expansion of 0.5 in k 2.961 * [backup-simplify]: Simplify 0.5 into 0.5 2.961 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.961 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.961 * [taylor]: Taking taylor expansion of k in k 2.961 * [backup-simplify]: Simplify 0 into 0 2.961 * [backup-simplify]: Simplify 1 into 1 2.961 * [backup-simplify]: Simplify (/ 1 1) into 1 2.961 * [taylor]: Taking taylor expansion of 1.0 in k 2.961 * [backup-simplify]: Simplify 1.0 into 1.0 2.961 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.961 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.961 * [taylor]: Taking taylor expansion of -2.0 in k 2.961 * [backup-simplify]: Simplify -2.0 into -2.0 2.961 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.961 * [taylor]: Taking taylor expansion of PI in k 2.961 * [backup-simplify]: Simplify PI into PI 2.961 * [taylor]: Taking taylor expansion of n in k 2.961 * [backup-simplify]: Simplify n into n 2.961 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.961 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.961 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.961 * [backup-simplify]: Simplify (+ 1 0) into 1 2.962 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.962 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.962 * [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)))))) 2.962 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.962 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.962 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.962 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.962 * [taylor]: Taking taylor expansion of 0.5 in n 2.962 * [backup-simplify]: Simplify 0.5 into 0.5 2.962 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.962 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.962 * [taylor]: Taking taylor expansion of k in n 2.962 * [backup-simplify]: Simplify k into k 2.962 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.962 * [taylor]: Taking taylor expansion of 1.0 in n 2.962 * [backup-simplify]: Simplify 1.0 into 1.0 2.962 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.962 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.962 * [taylor]: Taking taylor expansion of -2.0 in n 2.962 * [backup-simplify]: Simplify -2.0 into -2.0 2.962 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.962 * [taylor]: Taking taylor expansion of PI in n 2.962 * [backup-simplify]: Simplify PI into PI 2.962 * [taylor]: Taking taylor expansion of n in n 2.962 * [backup-simplify]: Simplify 0 into 0 2.962 * [backup-simplify]: Simplify 1 into 1 2.963 * [backup-simplify]: Simplify (/ PI 1) into PI 2.963 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.964 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.964 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.964 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.965 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.965 * [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)))) 2.966 * [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))))) 2.966 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.966 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.966 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.966 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.966 * [taylor]: Taking taylor expansion of 0.5 in n 2.966 * [backup-simplify]: Simplify 0.5 into 0.5 2.966 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.966 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.966 * [taylor]: Taking taylor expansion of k in n 2.966 * [backup-simplify]: Simplify k into k 2.966 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.966 * [taylor]: Taking taylor expansion of 1.0 in n 2.966 * [backup-simplify]: Simplify 1.0 into 1.0 2.966 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.966 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.966 * [taylor]: Taking taylor expansion of -2.0 in n 2.966 * [backup-simplify]: Simplify -2.0 into -2.0 2.966 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.967 * [taylor]: Taking taylor expansion of PI in n 2.967 * [backup-simplify]: Simplify PI into PI 2.967 * [taylor]: Taking taylor expansion of n in n 2.967 * [backup-simplify]: Simplify 0 into 0 2.967 * [backup-simplify]: Simplify 1 into 1 2.967 * [backup-simplify]: Simplify (/ PI 1) into PI 2.967 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.968 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.968 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.968 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.969 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.970 * [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)))) 2.970 * [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))))) 2.970 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.970 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.970 * [taylor]: Taking taylor expansion of 0.5 in k 2.970 * [backup-simplify]: Simplify 0.5 into 0.5 2.971 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.971 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.971 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.971 * [taylor]: Taking taylor expansion of k in k 2.971 * [backup-simplify]: Simplify 0 into 0 2.971 * [backup-simplify]: Simplify 1 into 1 2.971 * [backup-simplify]: Simplify (/ 1 1) into 1 2.971 * [taylor]: Taking taylor expansion of 1.0 in k 2.971 * [backup-simplify]: Simplify 1.0 into 1.0 2.971 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.971 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.971 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.971 * [taylor]: Taking taylor expansion of -2.0 in k 2.971 * [backup-simplify]: Simplify -2.0 into -2.0 2.971 * [taylor]: Taking taylor expansion of PI in k 2.971 * [backup-simplify]: Simplify PI into PI 2.971 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.972 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.972 * [taylor]: Taking taylor expansion of (log n) in k 2.972 * [taylor]: Taking taylor expansion of n in k 2.972 * [backup-simplify]: Simplify n into n 2.972 * [backup-simplify]: Simplify (log n) into (log n) 2.972 * [backup-simplify]: Simplify (+ 1 0) into 1 2.972 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.973 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.974 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.974 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 2.975 * [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))))) 2.976 * [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))))) 2.976 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.977 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.978 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.978 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.978 * [backup-simplify]: Simplify (+ 0 0) into 0 2.979 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.979 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.980 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.981 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.981 * [taylor]: Taking taylor expansion of 0 in k 2.981 * [backup-simplify]: Simplify 0 into 0 2.981 * [backup-simplify]: Simplify 0 into 0 2.982 * [backup-simplify]: Simplify 0 into 0 2.982 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.983 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.985 * [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 2.985 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.985 * [backup-simplify]: Simplify (+ 0 0) into 0 2.986 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.987 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.988 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.989 * [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 2.989 * [taylor]: Taking taylor expansion of 0 in k 2.989 * [backup-simplify]: Simplify 0 into 0 2.989 * [backup-simplify]: Simplify 0 into 0 2.989 * [backup-simplify]: Simplify 0 into 0 2.989 * [backup-simplify]: Simplify 0 into 0 2.990 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.991 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.994 * [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 2.994 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.994 * [backup-simplify]: Simplify (+ 0 0) into 0 2.995 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.996 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.997 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.999 * [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 2.999 * [taylor]: Taking taylor expansion of 0 in k 2.999 * [backup-simplify]: Simplify 0 into 0 2.999 * [backup-simplify]: Simplify 0 into 0 3.000 * [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)))))) 3.000 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 3.001 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 3.001 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 3.001 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.001 * [taylor]: Taking taylor expansion of 2.0 in n 3.001 * [backup-simplify]: Simplify 2.0 into 2.0 3.001 * [taylor]: Taking taylor expansion of (* n PI) in n 3.001 * [taylor]: Taking taylor expansion of n in n 3.001 * [backup-simplify]: Simplify 0 into 0 3.001 * [backup-simplify]: Simplify 1 into 1 3.001 * [taylor]: Taking taylor expansion of PI in n 3.001 * [backup-simplify]: Simplify PI into PI 3.001 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.001 * [taylor]: Taking taylor expansion of 2.0 in n 3.001 * [backup-simplify]: Simplify 2.0 into 2.0 3.001 * [taylor]: Taking taylor expansion of (* n PI) in n 3.001 * [taylor]: Taking taylor expansion of n in n 3.001 * [backup-simplify]: Simplify 0 into 0 3.001 * [backup-simplify]: Simplify 1 into 1 3.001 * [taylor]: Taking taylor expansion of PI in n 3.001 * [backup-simplify]: Simplify PI into PI 3.002 * [backup-simplify]: Simplify (* 0 PI) into 0 3.002 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.002 * [backup-simplify]: Simplify 0 into 0 3.004 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.004 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.005 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.005 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.006 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 3.006 * [backup-simplify]: Simplify 0 into 0 3.007 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 3.007 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 3.007 * [backup-simplify]: Simplify 0 into 0 3.008 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.009 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 3.009 * [backup-simplify]: Simplify 0 into 0 3.010 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.011 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 3.011 * [backup-simplify]: Simplify 0 into 0 3.012 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.013 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 3.013 * [backup-simplify]: Simplify 0 into 0 3.014 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 3.015 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 3.015 * [backup-simplify]: Simplify 0 into 0 3.015 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 3.016 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 3.016 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 3.016 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.016 * [taylor]: Taking taylor expansion of 2.0 in n 3.016 * [backup-simplify]: Simplify 2.0 into 2.0 3.016 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.016 * [taylor]: Taking taylor expansion of PI in n 3.016 * [backup-simplify]: Simplify PI into PI 3.016 * [taylor]: Taking taylor expansion of n in n 3.016 * [backup-simplify]: Simplify 0 into 0 3.016 * [backup-simplify]: Simplify 1 into 1 3.016 * [backup-simplify]: Simplify (/ PI 1) into PI 3.016 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.016 * [taylor]: Taking taylor expansion of 2.0 in n 3.016 * [backup-simplify]: Simplify 2.0 into 2.0 3.016 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.016 * [taylor]: Taking taylor expansion of PI in n 3.016 * [backup-simplify]: Simplify PI into PI 3.016 * [taylor]: Taking taylor expansion of n in n 3.016 * [backup-simplify]: Simplify 0 into 0 3.016 * [backup-simplify]: Simplify 1 into 1 3.017 * [backup-simplify]: Simplify (/ PI 1) into PI 3.017 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.017 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.018 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.018 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.018 * [backup-simplify]: Simplify 0 into 0 3.019 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.020 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.020 * [backup-simplify]: Simplify 0 into 0 3.020 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.021 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.021 * [backup-simplify]: Simplify 0 into 0 3.021 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.025 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.026 * [backup-simplify]: Simplify 0 into 0 3.026 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.027 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.027 * [backup-simplify]: Simplify 0 into 0 3.028 * [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 3.029 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.029 * [backup-simplify]: Simplify 0 into 0 3.029 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 3.030 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 3.030 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 3.030 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.030 * [taylor]: Taking taylor expansion of -2.0 in n 3.030 * [backup-simplify]: Simplify -2.0 into -2.0 3.030 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.030 * [taylor]: Taking taylor expansion of PI in n 3.030 * [backup-simplify]: Simplify PI into PI 3.030 * [taylor]: Taking taylor expansion of n in n 3.030 * [backup-simplify]: Simplify 0 into 0 3.030 * [backup-simplify]: Simplify 1 into 1 3.030 * [backup-simplify]: Simplify (/ PI 1) into PI 3.030 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.030 * [taylor]: Taking taylor expansion of -2.0 in n 3.030 * [backup-simplify]: Simplify -2.0 into -2.0 3.030 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.030 * [taylor]: Taking taylor expansion of PI in n 3.030 * [backup-simplify]: Simplify PI into PI 3.030 * [taylor]: Taking taylor expansion of n in n 3.030 * [backup-simplify]: Simplify 0 into 0 3.030 * [backup-simplify]: Simplify 1 into 1 3.031 * [backup-simplify]: Simplify (/ PI 1) into PI 3.031 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.031 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.032 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.032 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.032 * [backup-simplify]: Simplify 0 into 0 3.033 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.033 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.033 * [backup-simplify]: Simplify 0 into 0 3.034 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.035 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.035 * [backup-simplify]: Simplify 0 into 0 3.036 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.037 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.037 * [backup-simplify]: Simplify 0 into 0 3.038 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.040 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.040 * [backup-simplify]: Simplify 0 into 0 3.041 * [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 3.042 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.042 * [backup-simplify]: Simplify 0 into 0 3.043 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 3.043 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 3.043 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 3.043 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 3.043 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 3.043 * [taylor]: Taking taylor expansion of 1.0 in k 3.043 * [backup-simplify]: Simplify 1.0 into 1.0 3.043 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.043 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.043 * [taylor]: Taking taylor expansion of k in k 3.043 * [backup-simplify]: Simplify 0 into 0 3.043 * [backup-simplify]: Simplify 1 into 1 3.044 * [backup-simplify]: Simplify (/ 1 1) into 1 3.044 * [backup-simplify]: Simplify (sqrt 0) into 0 3.046 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.046 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 3.046 * [taylor]: Taking taylor expansion of 1.0 in k 3.046 * [backup-simplify]: Simplify 1.0 into 1.0 3.046 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.046 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.046 * [taylor]: Taking taylor expansion of k in k 3.046 * [backup-simplify]: Simplify 0 into 0 3.046 * [backup-simplify]: Simplify 1 into 1 3.046 * [backup-simplify]: Simplify (/ 1 1) into 1 3.047 * [backup-simplify]: Simplify (sqrt 0) into 0 3.048 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.048 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.048 * [backup-simplify]: Simplify 0 into 0 3.050 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 3.051 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.052 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 3.055 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.056 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 3.056 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.057 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.059 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.060 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 3.060 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.062 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 3.062 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 3.062 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 3.062 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.062 * [taylor]: Taking taylor expansion of 1.0 in k 3.062 * [backup-simplify]: Simplify 1.0 into 1.0 3.062 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.062 * [taylor]: Taking taylor expansion of k in k 3.062 * [backup-simplify]: Simplify 0 into 0 3.062 * [backup-simplify]: Simplify 1 into 1 3.062 * [backup-simplify]: Simplify (sqrt 0) into 0 3.063 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.063 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.063 * [taylor]: Taking taylor expansion of 1.0 in k 3.063 * [backup-simplify]: Simplify 1.0 into 1.0 3.063 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.063 * [taylor]: Taking taylor expansion of k in k 3.063 * [backup-simplify]: Simplify 0 into 0 3.063 * [backup-simplify]: Simplify 1 into 1 3.063 * [backup-simplify]: Simplify (sqrt 0) into 0 3.064 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.064 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.064 * [backup-simplify]: Simplify 0 into 0 3.065 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 3.065 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.067 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.068 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 3.069 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.071 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.072 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 3.072 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.073 * [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)))))))) 3.074 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 3.074 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 3.074 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.074 * [taylor]: Taking taylor expansion of 1.0 in k 3.074 * [backup-simplify]: Simplify 1.0 into 1.0 3.074 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.074 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.074 * [taylor]: Taking taylor expansion of -1 in k 3.074 * [backup-simplify]: Simplify -1 into -1 3.074 * [taylor]: Taking taylor expansion of k in k 3.074 * [backup-simplify]: Simplify 0 into 0 3.074 * [backup-simplify]: Simplify 1 into 1 3.074 * [backup-simplify]: Simplify (/ -1 1) into -1 3.074 * [backup-simplify]: Simplify (sqrt 0) into 0 3.075 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.075 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 3.075 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.075 * [taylor]: Taking taylor expansion of 1.0 in k 3.075 * [backup-simplify]: Simplify 1.0 into 1.0 3.075 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.075 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.075 * [taylor]: Taking taylor expansion of -1 in k 3.075 * [backup-simplify]: Simplify -1 into -1 3.075 * [taylor]: Taking taylor expansion of k in k 3.075 * [backup-simplify]: Simplify 0 into 0 3.075 * [backup-simplify]: Simplify 1 into 1 3.076 * [backup-simplify]: Simplify (/ -1 1) into -1 3.076 * [backup-simplify]: Simplify (sqrt 0) into 0 3.077 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.077 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 3.077 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.077 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 3.079 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.081 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 3.081 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.081 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.084 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.086 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 3.086 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.087 * [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))))) 3.087 * * * * [progress]: [ 4 / 4 ] generating series at (2) 3.088 * [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))))) 3.088 * [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 3.088 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 3.088 * [taylor]: Taking taylor expansion of 1.0 in n 3.088 * [backup-simplify]: Simplify 1.0 into 1.0 3.088 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 3.088 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 3.088 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.088 * [taylor]: Taking taylor expansion of k in n 3.088 * [backup-simplify]: Simplify k into k 3.088 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.088 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 3.088 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.089 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 3.089 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.089 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.089 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.089 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.089 * [taylor]: Taking taylor expansion of 0.5 in n 3.089 * [backup-simplify]: Simplify 0.5 into 0.5 3.089 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.089 * [taylor]: Taking taylor expansion of 1.0 in n 3.089 * [backup-simplify]: Simplify 1.0 into 1.0 3.089 * [taylor]: Taking taylor expansion of k in n 3.089 * [backup-simplify]: Simplify k into k 3.089 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.089 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.089 * [taylor]: Taking taylor expansion of 2.0 in n 3.089 * [backup-simplify]: Simplify 2.0 into 2.0 3.089 * [taylor]: Taking taylor expansion of (* n PI) in n 3.089 * [taylor]: Taking taylor expansion of n in n 3.089 * [backup-simplify]: Simplify 0 into 0 3.089 * [backup-simplify]: Simplify 1 into 1 3.089 * [taylor]: Taking taylor expansion of PI in n 3.089 * [backup-simplify]: Simplify PI into PI 3.090 * [backup-simplify]: Simplify (* 0 PI) into 0 3.090 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.092 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.093 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.094 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.094 * [backup-simplify]: Simplify (- k) into (- k) 3.094 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.094 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.096 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.097 * [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)))) 3.098 * [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))))) 3.098 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 3.098 * [taylor]: Taking taylor expansion of 1.0 in k 3.099 * [backup-simplify]: Simplify 1.0 into 1.0 3.099 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 3.099 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.099 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.099 * [taylor]: Taking taylor expansion of k in k 3.099 * [backup-simplify]: Simplify 0 into 0 3.099 * [backup-simplify]: Simplify 1 into 1 3.099 * [backup-simplify]: Simplify (/ 1 1) into 1 3.099 * [backup-simplify]: Simplify (sqrt 0) into 0 3.101 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.101 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.101 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.101 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.101 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.101 * [taylor]: Taking taylor expansion of 0.5 in k 3.101 * [backup-simplify]: Simplify 0.5 into 0.5 3.101 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.101 * [taylor]: Taking taylor expansion of 1.0 in k 3.101 * [backup-simplify]: Simplify 1.0 into 1.0 3.101 * [taylor]: Taking taylor expansion of k in k 3.101 * [backup-simplify]: Simplify 0 into 0 3.101 * [backup-simplify]: Simplify 1 into 1 3.101 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.101 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.101 * [taylor]: Taking taylor expansion of 2.0 in k 3.101 * [backup-simplify]: Simplify 2.0 into 2.0 3.101 * [taylor]: Taking taylor expansion of (* n PI) in k 3.101 * [taylor]: Taking taylor expansion of n in k 3.101 * [backup-simplify]: Simplify n into n 3.101 * [taylor]: Taking taylor expansion of PI in k 3.101 * [backup-simplify]: Simplify PI into PI 3.101 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.102 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 3.102 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 3.102 * [backup-simplify]: Simplify (- 0) into 0 3.103 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.103 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.103 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 3.103 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 3.103 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 3.103 * [taylor]: Taking taylor expansion of 1.0 in k 3.103 * [backup-simplify]: Simplify 1.0 into 1.0 3.103 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 3.103 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.103 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.104 * [taylor]: Taking taylor expansion of k in k 3.104 * [backup-simplify]: Simplify 0 into 0 3.104 * [backup-simplify]: Simplify 1 into 1 3.104 * [backup-simplify]: Simplify (/ 1 1) into 1 3.104 * [backup-simplify]: Simplify (sqrt 0) into 0 3.106 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.106 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.106 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.106 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.106 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.106 * [taylor]: Taking taylor expansion of 0.5 in k 3.106 * [backup-simplify]: Simplify 0.5 into 0.5 3.106 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.106 * [taylor]: Taking taylor expansion of 1.0 in k 3.106 * [backup-simplify]: Simplify 1.0 into 1.0 3.106 * [taylor]: Taking taylor expansion of k in k 3.106 * [backup-simplify]: Simplify 0 into 0 3.106 * [backup-simplify]: Simplify 1 into 1 3.106 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.106 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.106 * [taylor]: Taking taylor expansion of 2.0 in k 3.106 * [backup-simplify]: Simplify 2.0 into 2.0 3.106 * [taylor]: Taking taylor expansion of (* n PI) in k 3.106 * [taylor]: Taking taylor expansion of n in k 3.106 * [backup-simplify]: Simplify n into n 3.106 * [taylor]: Taking taylor expansion of PI in k 3.106 * [backup-simplify]: Simplify PI into PI 3.106 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.106 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 3.107 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 3.107 * [backup-simplify]: Simplify (- 0) into 0 3.107 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.108 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.108 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 3.108 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 3.109 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 3.109 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.109 * [taylor]: Taking taylor expansion of 0 in n 3.109 * [backup-simplify]: Simplify 0 into 0 3.109 * [backup-simplify]: Simplify 0 into 0 3.110 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 3.110 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 3.111 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 3.112 * [backup-simplify]: Simplify (- 1) into -1 3.112 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.114 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 3.115 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 3.115 * [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))) 3.116 * [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))) 3.118 * [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))) 3.118 * [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 3.118 * [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 3.118 * [taylor]: Taking taylor expansion of +nan.0 in n 3.118 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.118 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.118 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.118 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.118 * [taylor]: Taking taylor expansion of 0.5 in n 3.118 * [backup-simplify]: Simplify 0.5 into 0.5 3.118 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.118 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.118 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.118 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.118 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.118 * [taylor]: Taking taylor expansion of 1.0 in n 3.118 * [backup-simplify]: Simplify 1.0 into 1.0 3.118 * [taylor]: Taking taylor expansion of (log PI) in n 3.118 * [taylor]: Taking taylor expansion of PI in n 3.118 * [backup-simplify]: Simplify PI into PI 3.118 * [backup-simplify]: Simplify (log PI) into (log PI) 3.119 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.120 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.120 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.120 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.120 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.120 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.120 * [taylor]: Taking taylor expansion of 1.0 in n 3.120 * [backup-simplify]: Simplify 1.0 into 1.0 3.120 * [taylor]: Taking taylor expansion of (log n) in n 3.120 * [taylor]: Taking taylor expansion of n in n 3.120 * [backup-simplify]: Simplify 0 into 0 3.120 * [backup-simplify]: Simplify 1 into 1 3.120 * [backup-simplify]: Simplify (log 1) into 0 3.121 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.121 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.121 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.121 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.121 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.121 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.121 * [taylor]: Taking taylor expansion of 1.0 in n 3.121 * [backup-simplify]: Simplify 1.0 into 1.0 3.121 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.121 * [taylor]: Taking taylor expansion of 2.0 in n 3.121 * [backup-simplify]: Simplify 2.0 into 2.0 3.121 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.122 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.123 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.123 * [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) 3.124 * [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) 3.125 * [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)) 3.125 * [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))) 3.126 * [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) 3.127 * [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)) 3.128 * [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))) 3.129 * [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))) 3.129 * [backup-simplify]: Simplify 0 into 0 3.130 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 3.130 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 3.131 * [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 3.131 * [backup-simplify]: Simplify (- 0) into 0 3.132 * [backup-simplify]: Simplify (+ 0 0) into 0 3.132 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 3.133 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 3.138 * [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))) 3.138 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 3.140 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.142 * [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)))))))) 3.145 * [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)))))))) 3.145 * [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 3.146 * [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 3.146 * [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 3.146 * [taylor]: Taking taylor expansion of +nan.0 in n 3.146 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.146 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.146 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.146 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.146 * [taylor]: Taking taylor expansion of 0.5 in n 3.146 * [backup-simplify]: Simplify 0.5 into 0.5 3.146 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.146 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.146 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.146 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.146 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.146 * [taylor]: Taking taylor expansion of 1.0 in n 3.146 * [backup-simplify]: Simplify 1.0 into 1.0 3.146 * [taylor]: Taking taylor expansion of (log PI) in n 3.146 * [taylor]: Taking taylor expansion of PI in n 3.146 * [backup-simplify]: Simplify PI into PI 3.146 * [backup-simplify]: Simplify (log PI) into (log PI) 3.147 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.148 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.148 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.148 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.148 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.148 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.148 * [taylor]: Taking taylor expansion of 1.0 in n 3.148 * [backup-simplify]: Simplify 1.0 into 1.0 3.148 * [taylor]: Taking taylor expansion of (log n) in n 3.148 * [taylor]: Taking taylor expansion of n in n 3.148 * [backup-simplify]: Simplify 0 into 0 3.148 * [backup-simplify]: Simplify 1 into 1 3.149 * [backup-simplify]: Simplify (log 1) into 0 3.149 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.149 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.149 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.149 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.149 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.149 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.149 * [taylor]: Taking taylor expansion of 1.0 in n 3.150 * [backup-simplify]: Simplify 1.0 into 1.0 3.150 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.150 * [taylor]: Taking taylor expansion of 2.0 in n 3.150 * [backup-simplify]: Simplify 2.0 into 2.0 3.150 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.151 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.152 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.153 * [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) 3.154 * [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) 3.156 * [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)) 3.157 * [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))) 3.159 * [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) 3.159 * [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 3.159 * [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 3.159 * [taylor]: Taking taylor expansion of +nan.0 in n 3.159 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.159 * [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 3.159 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 3.159 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 3.159 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 3.159 * [taylor]: Taking taylor expansion of 0.5 in n 3.159 * [backup-simplify]: Simplify 0.5 into 0.5 3.159 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 3.159 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 3.159 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.159 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.159 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.159 * [taylor]: Taking taylor expansion of 1.0 in n 3.159 * [backup-simplify]: Simplify 1.0 into 1.0 3.159 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.159 * [taylor]: Taking taylor expansion of 2.0 in n 3.159 * [backup-simplify]: Simplify 2.0 into 2.0 3.160 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.161 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.163 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.163 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 3.163 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.163 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.163 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.163 * [taylor]: Taking taylor expansion of 1.0 in n 3.163 * [backup-simplify]: Simplify 1.0 into 1.0 3.163 * [taylor]: Taking taylor expansion of (log PI) in n 3.163 * [taylor]: Taking taylor expansion of PI in n 3.163 * [backup-simplify]: Simplify PI into PI 3.163 * [backup-simplify]: Simplify (log PI) into (log PI) 3.164 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.166 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.166 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.166 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.166 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.166 * [taylor]: Taking taylor expansion of 1.0 in n 3.166 * [backup-simplify]: Simplify 1.0 into 1.0 3.166 * [taylor]: Taking taylor expansion of (log n) in n 3.166 * [taylor]: Taking taylor expansion of n in n 3.166 * [backup-simplify]: Simplify 0 into 0 3.166 * [backup-simplify]: Simplify 1 into 1 3.167 * [backup-simplify]: Simplify (log 1) into 0 3.167 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.167 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.167 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.168 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 3.169 * [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) 3.171 * [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)) 3.172 * [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))) 3.173 * [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) 3.173 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.174 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.174 * [taylor]: Taking taylor expansion of 2.0 in n 3.174 * [backup-simplify]: Simplify 2.0 into 2.0 3.174 * [taylor]: Taking taylor expansion of (* n PI) in n 3.174 * [taylor]: Taking taylor expansion of n in n 3.174 * [backup-simplify]: Simplify 0 into 0 3.174 * [backup-simplify]: Simplify 1 into 1 3.174 * [taylor]: Taking taylor expansion of PI in n 3.174 * [backup-simplify]: Simplify PI into PI 3.174 * [backup-simplify]: Simplify (* 0 PI) into 0 3.175 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.176 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.177 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.177 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.178 * [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)) 3.179 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.181 * [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)) 3.182 * [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))) 3.184 * [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)))))) 3.187 * [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)))))))) 3.191 * [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)))))))) 3.194 * [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)))))))) 3.195 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 3.196 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 3.197 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 3.198 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 3.198 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.198 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 3.199 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 3.199 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 3.200 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 3.201 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 3.202 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 3.203 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 3.204 * [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 3.205 * [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 3.207 * [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 3.208 * [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 3.209 * [backup-simplify]: Simplify (- 0) into 0 3.209 * [backup-simplify]: Simplify 0 into 0 3.209 * [backup-simplify]: Simplify 0 into 0 3.210 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.211 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 3.214 * [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 3.214 * [backup-simplify]: Simplify (- 0) into 0 3.215 * [backup-simplify]: Simplify (+ 0 0) into 0 3.216 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 3.217 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 3.219 * [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))) 3.220 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.224 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.230 * [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)))))))) 3.241 * [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)))))))) 3.241 * [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 3.241 * [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 3.241 * [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 3.241 * [taylor]: Taking taylor expansion of +nan.0 in n 3.241 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.241 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 3.241 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 3.241 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 3.241 * [taylor]: Taking taylor expansion of 0.5 in n 3.241 * [backup-simplify]: Simplify 0.5 into 0.5 3.241 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 3.241 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 3.241 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.241 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.241 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.241 * [taylor]: Taking taylor expansion of 1.0 in n 3.241 * [backup-simplify]: Simplify 1.0 into 1.0 3.241 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.241 * [taylor]: Taking taylor expansion of 2.0 in n 3.241 * [backup-simplify]: Simplify 2.0 into 2.0 3.242 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.243 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.244 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.244 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 3.244 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.244 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.244 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.244 * [taylor]: Taking taylor expansion of 1.0 in n 3.244 * [backup-simplify]: Simplify 1.0 into 1.0 3.245 * [taylor]: Taking taylor expansion of (log n) in n 3.245 * [taylor]: Taking taylor expansion of n in n 3.245 * [backup-simplify]: Simplify 0 into 0 3.245 * [backup-simplify]: Simplify 1 into 1 3.245 * [backup-simplify]: Simplify (log 1) into 0 3.245 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.245 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.246 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.246 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.246 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.246 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.246 * [taylor]: Taking taylor expansion of 1.0 in n 3.246 * [backup-simplify]: Simplify 1.0 into 1.0 3.246 * [taylor]: Taking taylor expansion of (log PI) in n 3.246 * [taylor]: Taking taylor expansion of PI in n 3.246 * [backup-simplify]: Simplify PI into PI 3.246 * [backup-simplify]: Simplify (log PI) into (log PI) 3.247 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.249 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.250 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 3.251 * [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) 3.252 * [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)) 3.254 * [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))) 3.255 * [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) 3.255 * [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 3.255 * [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 3.255 * [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 3.255 * [taylor]: Taking taylor expansion of +nan.0 in n 3.255 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.255 * [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 3.255 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 3.255 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 3.255 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 3.255 * [taylor]: Taking taylor expansion of 0.5 in n 3.256 * [backup-simplify]: Simplify 0.5 into 0.5 3.256 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 3.256 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 3.256 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.256 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.256 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.256 * [taylor]: Taking taylor expansion of 1.0 in n 3.256 * [backup-simplify]: Simplify 1.0 into 1.0 3.256 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.256 * [taylor]: Taking taylor expansion of 2.0 in n 3.256 * [backup-simplify]: Simplify 2.0 into 2.0 3.256 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.257 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.258 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.259 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 3.259 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.259 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.259 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.259 * [taylor]: Taking taylor expansion of 1.0 in n 3.259 * [backup-simplify]: Simplify 1.0 into 1.0 3.259 * [taylor]: Taking taylor expansion of (log PI) in n 3.259 * [taylor]: Taking taylor expansion of PI in n 3.259 * [backup-simplify]: Simplify PI into PI 3.264 * [backup-simplify]: Simplify (log PI) into (log PI) 3.266 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.267 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.267 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.267 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.268 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.268 * [taylor]: Taking taylor expansion of 1.0 in n 3.268 * [backup-simplify]: Simplify 1.0 into 1.0 3.268 * [taylor]: Taking taylor expansion of (log n) in n 3.268 * [taylor]: Taking taylor expansion of n in n 3.268 * [backup-simplify]: Simplify 0 into 0 3.268 * [backup-simplify]: Simplify 1 into 1 3.268 * [backup-simplify]: Simplify (log 1) into 0 3.269 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.269 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.269 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.269 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 3.271 * [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) 3.272 * [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)) 3.274 * [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))) 3.276 * [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) 3.276 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.276 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.276 * [taylor]: Taking taylor expansion of 2.0 in n 3.276 * [backup-simplify]: Simplify 2.0 into 2.0 3.276 * [taylor]: Taking taylor expansion of (* n PI) in n 3.276 * [taylor]: Taking taylor expansion of n in n 3.276 * [backup-simplify]: Simplify 0 into 0 3.276 * [backup-simplify]: Simplify 1 into 1 3.276 * [taylor]: Taking taylor expansion of PI in n 3.276 * [backup-simplify]: Simplify PI into PI 3.276 * [backup-simplify]: Simplify (* 0 PI) into 0 3.277 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.278 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.280 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.281 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.281 * [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 3.281 * [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 3.281 * [taylor]: Taking taylor expansion of +nan.0 in n 3.281 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.281 * [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 3.281 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 3.281 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 3.281 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 3.282 * [taylor]: Taking taylor expansion of 0.5 in n 3.282 * [backup-simplify]: Simplify 0.5 into 0.5 3.282 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 3.282 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 3.282 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.282 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.282 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.282 * [taylor]: Taking taylor expansion of 1.0 in n 3.282 * [backup-simplify]: Simplify 1.0 into 1.0 3.282 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.282 * [taylor]: Taking taylor expansion of 2.0 in n 3.282 * [backup-simplify]: Simplify 2.0 into 2.0 3.282 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.283 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.285 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.285 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 3.285 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.285 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.285 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.285 * [taylor]: Taking taylor expansion of 1.0 in n 3.285 * [backup-simplify]: Simplify 1.0 into 1.0 3.285 * [taylor]: Taking taylor expansion of (log PI) in n 3.285 * [taylor]: Taking taylor expansion of PI in n 3.285 * [backup-simplify]: Simplify PI into PI 3.286 * [backup-simplify]: Simplify (log PI) into (log PI) 3.286 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.288 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.288 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.288 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.288 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.288 * [taylor]: Taking taylor expansion of 1.0 in n 3.288 * [backup-simplify]: Simplify 1.0 into 1.0 3.288 * [taylor]: Taking taylor expansion of (log n) in n 3.288 * [taylor]: Taking taylor expansion of n in n 3.288 * [backup-simplify]: Simplify 0 into 0 3.288 * [backup-simplify]: Simplify 1 into 1 3.289 * [backup-simplify]: Simplify (log 1) into 0 3.289 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.289 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.289 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.290 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 3.291 * [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) 3.293 * [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)) 3.294 * [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))) 3.296 * [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) 3.296 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 3.296 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.296 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.296 * [taylor]: Taking taylor expansion of 2.0 in n 3.296 * [backup-simplify]: Simplify 2.0 into 2.0 3.296 * [taylor]: Taking taylor expansion of (* n PI) in n 3.296 * [taylor]: Taking taylor expansion of n in n 3.296 * [backup-simplify]: Simplify 0 into 0 3.296 * [backup-simplify]: Simplify 1 into 1 3.296 * [taylor]: Taking taylor expansion of PI in n 3.296 * [backup-simplify]: Simplify PI into PI 3.297 * [backup-simplify]: Simplify (* 0 PI) into 0 3.297 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.299 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.300 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.301 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.303 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.305 * [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)) 3.306 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.309 * [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)) 3.312 * [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))) 3.313 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.315 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.317 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 3.320 * [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)) 3.323 * [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))) 3.325 * [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)))))))) 3.332 * [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)))))))))))) 3.341 * [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)))))))))))) 3.350 * [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)))))))))))))) 3.368 * [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)))))))))))))) 3.386 * [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)))))))))))))) 3.408 * [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)))))))))))))))))))))) 3.409 * [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)))))) 3.409 * [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 3.409 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 3.409 * [taylor]: Taking taylor expansion of 1.0 in n 3.409 * [backup-simplify]: Simplify 1.0 into 1.0 3.409 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 3.409 * [taylor]: Taking taylor expansion of (sqrt k) in n 3.409 * [taylor]: Taking taylor expansion of k in n 3.409 * [backup-simplify]: Simplify k into k 3.409 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 3.409 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 3.409 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.409 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.409 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.409 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.409 * [taylor]: Taking taylor expansion of 0.5 in n 3.409 * [backup-simplify]: Simplify 0.5 into 0.5 3.409 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.409 * [taylor]: Taking taylor expansion of 1.0 in n 3.409 * [backup-simplify]: Simplify 1.0 into 1.0 3.409 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.409 * [taylor]: Taking taylor expansion of k in n 3.409 * [backup-simplify]: Simplify k into k 3.409 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.409 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.409 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.409 * [taylor]: Taking taylor expansion of 2.0 in n 3.409 * [backup-simplify]: Simplify 2.0 into 2.0 3.409 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.409 * [taylor]: Taking taylor expansion of PI in n 3.409 * [backup-simplify]: Simplify PI into PI 3.409 * [taylor]: Taking taylor expansion of n in n 3.409 * [backup-simplify]: Simplify 0 into 0 3.409 * [backup-simplify]: Simplify 1 into 1 3.410 * [backup-simplify]: Simplify (/ PI 1) into PI 3.410 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.411 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.411 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.411 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.411 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.412 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.412 * [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)))) 3.413 * [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))))) 3.413 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 3.413 * [taylor]: Taking taylor expansion of 1.0 in k 3.413 * [backup-simplify]: Simplify 1.0 into 1.0 3.413 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 3.413 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.413 * [taylor]: Taking taylor expansion of k in k 3.413 * [backup-simplify]: Simplify 0 into 0 3.413 * [backup-simplify]: Simplify 1 into 1 3.414 * [backup-simplify]: Simplify (sqrt 0) into 0 3.414 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.414 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.415 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.415 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.415 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.415 * [taylor]: Taking taylor expansion of 0.5 in k 3.415 * [backup-simplify]: Simplify 0.5 into 0.5 3.415 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.415 * [taylor]: Taking taylor expansion of 1.0 in k 3.415 * [backup-simplify]: Simplify 1.0 into 1.0 3.415 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.415 * [taylor]: Taking taylor expansion of k in k 3.415 * [backup-simplify]: Simplify 0 into 0 3.415 * [backup-simplify]: Simplify 1 into 1 3.415 * [backup-simplify]: Simplify (/ 1 1) into 1 3.415 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.415 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.415 * [taylor]: Taking taylor expansion of 2.0 in k 3.415 * [backup-simplify]: Simplify 2.0 into 2.0 3.415 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.415 * [taylor]: Taking taylor expansion of PI in k 3.415 * [backup-simplify]: Simplify PI into PI 3.415 * [taylor]: Taking taylor expansion of n in k 3.415 * [backup-simplify]: Simplify n into n 3.415 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.415 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 3.415 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 3.415 * [backup-simplify]: Simplify (- 1) into -1 3.416 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.416 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 3.416 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 3.416 * [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))))) 3.416 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 3.416 * [taylor]: Taking taylor expansion of 1.0 in k 3.416 * [backup-simplify]: Simplify 1.0 into 1.0 3.416 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 3.416 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.416 * [taylor]: Taking taylor expansion of k in k 3.416 * [backup-simplify]: Simplify 0 into 0 3.416 * [backup-simplify]: Simplify 1 into 1 3.417 * [backup-simplify]: Simplify (sqrt 0) into 0 3.417 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.417 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.417 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.417 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.417 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.418 * [taylor]: Taking taylor expansion of 0.5 in k 3.418 * [backup-simplify]: Simplify 0.5 into 0.5 3.418 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.418 * [taylor]: Taking taylor expansion of 1.0 in k 3.418 * [backup-simplify]: Simplify 1.0 into 1.0 3.418 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.418 * [taylor]: Taking taylor expansion of k in k 3.418 * [backup-simplify]: Simplify 0 into 0 3.418 * [backup-simplify]: Simplify 1 into 1 3.418 * [backup-simplify]: Simplify (/ 1 1) into 1 3.418 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.418 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.418 * [taylor]: Taking taylor expansion of 2.0 in k 3.418 * [backup-simplify]: Simplify 2.0 into 2.0 3.418 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.418 * [taylor]: Taking taylor expansion of PI in k 3.418 * [backup-simplify]: Simplify PI into PI 3.418 * [taylor]: Taking taylor expansion of n in k 3.418 * [backup-simplify]: Simplify n into n 3.418 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.418 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 3.418 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 3.418 * [backup-simplify]: Simplify (- 1) into -1 3.419 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.419 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 3.419 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 3.419 * [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))))) 3.419 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 3.420 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.420 * [taylor]: Taking taylor expansion of 0 in n 3.420 * [backup-simplify]: Simplify 0 into 0 3.420 * [backup-simplify]: Simplify 0 into 0 3.420 * [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))))))) 3.421 * [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))))))) 3.421 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 3.421 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 3.421 * [taylor]: Taking taylor expansion of +nan.0 in n 3.421 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.421 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 3.421 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 3.421 * [taylor]: Taking taylor expansion of 0.5 in n 3.421 * [backup-simplify]: Simplify 0.5 into 0.5 3.421 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 3.421 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.421 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.421 * [taylor]: Taking taylor expansion of 2.0 in n 3.421 * [backup-simplify]: Simplify 2.0 into 2.0 3.421 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.421 * [taylor]: Taking taylor expansion of PI in n 3.421 * [backup-simplify]: Simplify PI into PI 3.421 * [taylor]: Taking taylor expansion of n in n 3.421 * [backup-simplify]: Simplify 0 into 0 3.421 * [backup-simplify]: Simplify 1 into 1 3.421 * [backup-simplify]: Simplify (/ PI 1) into PI 3.422 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.422 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.422 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.422 * [taylor]: Taking taylor expansion of 1.0 in n 3.422 * [backup-simplify]: Simplify 1.0 into 1.0 3.422 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.422 * [taylor]: Taking taylor expansion of k in n 3.422 * [backup-simplify]: Simplify k into k 3.422 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.423 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.423 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.423 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.424 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 3.425 * [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)))) 3.425 * [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))))) 3.426 * [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)))))) 3.427 * [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))))))) 3.428 * [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))))))) 3.428 * [backup-simplify]: Simplify 0 into 0 3.431 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.433 * [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))))))) 3.434 * [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))))))) 3.434 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 3.434 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 3.434 * [taylor]: Taking taylor expansion of +nan.0 in n 3.434 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.434 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 3.434 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 3.434 * [taylor]: Taking taylor expansion of 0.5 in n 3.434 * [backup-simplify]: Simplify 0.5 into 0.5 3.434 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 3.434 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.434 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.434 * [taylor]: Taking taylor expansion of 2.0 in n 3.434 * [backup-simplify]: Simplify 2.0 into 2.0 3.434 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.434 * [taylor]: Taking taylor expansion of PI in n 3.434 * [backup-simplify]: Simplify PI into PI 3.434 * [taylor]: Taking taylor expansion of n in n 3.434 * [backup-simplify]: Simplify 0 into 0 3.434 * [backup-simplify]: Simplify 1 into 1 3.435 * [backup-simplify]: Simplify (/ PI 1) into PI 3.436 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.437 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.437 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.437 * [taylor]: Taking taylor expansion of 1.0 in n 3.437 * [backup-simplify]: Simplify 1.0 into 1.0 3.437 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.437 * [taylor]: Taking taylor expansion of k in n 3.437 * [backup-simplify]: Simplify k into k 3.437 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.438 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.438 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.439 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.440 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 3.441 * [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)))) 3.442 * [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))))) 3.444 * [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)))))) 3.445 * [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))))))) 3.447 * [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))))))) 3.448 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.448 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.449 * [backup-simplify]: Simplify (- 0) into 0 3.449 * [backup-simplify]: Simplify (+ 0 0) into 0 3.450 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.451 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.452 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.454 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 3.455 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 3.457 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.459 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 3.459 * [backup-simplify]: Simplify (- 0) into 0 3.459 * [backup-simplify]: Simplify 0 into 0 3.459 * [backup-simplify]: Simplify 0 into 0 3.463 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.465 * [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))))))) 3.466 * [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))))))) 3.466 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 3.466 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 3.466 * [taylor]: Taking taylor expansion of +nan.0 in n 3.466 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.466 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 3.467 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 3.467 * [taylor]: Taking taylor expansion of 0.5 in n 3.467 * [backup-simplify]: Simplify 0.5 into 0.5 3.467 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 3.467 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.467 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.467 * [taylor]: Taking taylor expansion of 2.0 in n 3.467 * [backup-simplify]: Simplify 2.0 into 2.0 3.467 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.467 * [taylor]: Taking taylor expansion of PI in n 3.467 * [backup-simplify]: Simplify PI into PI 3.467 * [taylor]: Taking taylor expansion of n in n 3.467 * [backup-simplify]: Simplify 0 into 0 3.467 * [backup-simplify]: Simplify 1 into 1 3.467 * [backup-simplify]: Simplify (/ PI 1) into PI 3.468 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.469 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.469 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.469 * [taylor]: Taking taylor expansion of 1.0 in n 3.469 * [backup-simplify]: Simplify 1.0 into 1.0 3.469 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.469 * [taylor]: Taking taylor expansion of k in n 3.469 * [backup-simplify]: Simplify k into k 3.469 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.471 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.471 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.471 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.472 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 3.473 * [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)))) 3.474 * [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))))) 3.475 * [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)))))) 3.476 * [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))))))) 3.477 * [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))))))) 3.480 * [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)))))))) 3.480 * [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)))) 3.480 * [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 3.481 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 3.481 * [taylor]: Taking taylor expansion of 1.0 in n 3.481 * [backup-simplify]: Simplify 1.0 into 1.0 3.481 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 3.481 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.481 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.481 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.481 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.481 * [taylor]: Taking taylor expansion of 0.5 in n 3.481 * [backup-simplify]: Simplify 0.5 into 0.5 3.481 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.481 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.481 * [taylor]: Taking taylor expansion of k in n 3.481 * [backup-simplify]: Simplify k into k 3.481 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.481 * [taylor]: Taking taylor expansion of 1.0 in n 3.481 * [backup-simplify]: Simplify 1.0 into 1.0 3.481 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.481 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.481 * [taylor]: Taking taylor expansion of -2.0 in n 3.481 * [backup-simplify]: Simplify -2.0 into -2.0 3.481 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.481 * [taylor]: Taking taylor expansion of PI in n 3.481 * [backup-simplify]: Simplify PI into PI 3.481 * [taylor]: Taking taylor expansion of n in n 3.481 * [backup-simplify]: Simplify 0 into 0 3.481 * [backup-simplify]: Simplify 1 into 1 3.481 * [backup-simplify]: Simplify (/ PI 1) into PI 3.482 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.482 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.482 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.482 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.483 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.484 * [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)))) 3.485 * [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))))) 3.485 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 3.485 * [taylor]: Taking taylor expansion of (/ -1 k) in n 3.485 * [taylor]: Taking taylor expansion of -1 in n 3.485 * [backup-simplify]: Simplify -1 into -1 3.485 * [taylor]: Taking taylor expansion of k in n 3.485 * [backup-simplify]: Simplify k into k 3.485 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 3.485 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 3.485 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 3.485 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 3.486 * [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))) 3.486 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 3.486 * [taylor]: Taking taylor expansion of 1.0 in k 3.486 * [backup-simplify]: Simplify 1.0 into 1.0 3.486 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 3.486 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.486 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.486 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.486 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.486 * [taylor]: Taking taylor expansion of 0.5 in k 3.486 * [backup-simplify]: Simplify 0.5 into 0.5 3.486 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.486 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.486 * [taylor]: Taking taylor expansion of k in k 3.486 * [backup-simplify]: Simplify 0 into 0 3.486 * [backup-simplify]: Simplify 1 into 1 3.486 * [backup-simplify]: Simplify (/ 1 1) into 1 3.486 * [taylor]: Taking taylor expansion of 1.0 in k 3.486 * [backup-simplify]: Simplify 1.0 into 1.0 3.486 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.486 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.486 * [taylor]: Taking taylor expansion of -2.0 in k 3.487 * [backup-simplify]: Simplify -2.0 into -2.0 3.487 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.487 * [taylor]: Taking taylor expansion of PI in k 3.487 * [backup-simplify]: Simplify PI into PI 3.487 * [taylor]: Taking taylor expansion of n in k 3.487 * [backup-simplify]: Simplify n into n 3.487 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.487 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 3.487 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 3.487 * [backup-simplify]: Simplify (+ 1 0) into 1 3.487 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.487 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 3.488 * [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)))))) 3.488 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.488 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.488 * [taylor]: Taking taylor expansion of -1 in k 3.488 * [backup-simplify]: Simplify -1 into -1 3.488 * [taylor]: Taking taylor expansion of k in k 3.488 * [backup-simplify]: Simplify 0 into 0 3.488 * [backup-simplify]: Simplify 1 into 1 3.488 * [backup-simplify]: Simplify (/ -1 1) into -1 3.488 * [backup-simplify]: Simplify (sqrt 0) into 0 3.489 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.489 * [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))))))) 3.489 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 3.489 * [taylor]: Taking taylor expansion of 1.0 in k 3.489 * [backup-simplify]: Simplify 1.0 into 1.0 3.489 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 3.489 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.489 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.489 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.489 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.489 * [taylor]: Taking taylor expansion of 0.5 in k 3.489 * [backup-simplify]: Simplify 0.5 into 0.5 3.489 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.489 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.489 * [taylor]: Taking taylor expansion of k in k 3.489 * [backup-simplify]: Simplify 0 into 0 3.489 * [backup-simplify]: Simplify 1 into 1 3.490 * [backup-simplify]: Simplify (/ 1 1) into 1 3.490 * [taylor]: Taking taylor expansion of 1.0 in k 3.490 * [backup-simplify]: Simplify 1.0 into 1.0 3.490 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.490 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.490 * [taylor]: Taking taylor expansion of -2.0 in k 3.490 * [backup-simplify]: Simplify -2.0 into -2.0 3.490 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.490 * [taylor]: Taking taylor expansion of PI in k 3.490 * [backup-simplify]: Simplify PI into PI 3.490 * [taylor]: Taking taylor expansion of n in k 3.490 * [backup-simplify]: Simplify n into n 3.490 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.490 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 3.490 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 3.490 * [backup-simplify]: Simplify (+ 1 0) into 1 3.490 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.491 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 3.491 * [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)))))) 3.491 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.491 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.491 * [taylor]: Taking taylor expansion of -1 in k 3.491 * [backup-simplify]: Simplify -1 into -1 3.491 * [taylor]: Taking taylor expansion of k in k 3.491 * [backup-simplify]: Simplify 0 into 0 3.491 * [backup-simplify]: Simplify 1 into 1 3.491 * [backup-simplify]: Simplify (/ -1 1) into -1 3.491 * [backup-simplify]: Simplify (sqrt 0) into 0 3.492 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.492 * [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))))))) 3.492 * [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))))))) 3.493 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 3.493 * [taylor]: Taking taylor expansion of +nan.0 in n 3.493 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.493 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 3.493 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 3.493 * [taylor]: Taking taylor expansion of 0.5 in n 3.493 * [backup-simplify]: Simplify 0.5 into 0.5 3.493 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 3.493 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.493 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.493 * [taylor]: Taking taylor expansion of k in n 3.493 * [backup-simplify]: Simplify k into k 3.493 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.493 * [taylor]: Taking taylor expansion of 1.0 in n 3.493 * [backup-simplify]: Simplify 1.0 into 1.0 3.493 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.493 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.493 * [taylor]: Taking taylor expansion of -2.0 in n 3.493 * [backup-simplify]: Simplify -2.0 into -2.0 3.493 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.493 * [taylor]: Taking taylor expansion of PI in n 3.493 * [backup-simplify]: Simplify PI into PI 3.493 * [taylor]: Taking taylor expansion of n in n 3.493 * [backup-simplify]: Simplify 0 into 0 3.493 * [backup-simplify]: Simplify 1 into 1 3.493 * [backup-simplify]: Simplify (/ PI 1) into PI 3.494 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.494 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.494 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.495 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.496 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 3.497 * [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)))) 3.497 * [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))))) 3.498 * [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)))))) 3.499 * [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)))))) 3.499 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 3.501 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.502 * [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)))))))) 3.502 * [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)))))))) 3.503 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 3.503 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 3.503 * [taylor]: Taking taylor expansion of +nan.0 in n 3.503 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.503 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 3.503 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 3.503 * [taylor]: Taking taylor expansion of 0.5 in n 3.503 * [backup-simplify]: Simplify 0.5 into 0.5 3.503 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 3.503 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.503 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.503 * [taylor]: Taking taylor expansion of k in n 3.503 * [backup-simplify]: Simplify k into k 3.503 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.503 * [taylor]: Taking taylor expansion of 1.0 in n 3.503 * [backup-simplify]: Simplify 1.0 into 1.0 3.503 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.503 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.503 * [taylor]: Taking taylor expansion of -2.0 in n 3.503 * [backup-simplify]: Simplify -2.0 into -2.0 3.503 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.503 * [taylor]: Taking taylor expansion of PI in n 3.503 * [backup-simplify]: Simplify PI into PI 3.503 * [taylor]: Taking taylor expansion of n in n 3.503 * [backup-simplify]: Simplify 0 into 0 3.503 * [backup-simplify]: Simplify 1 into 1 3.503 * [backup-simplify]: Simplify (/ PI 1) into PI 3.504 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.504 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.505 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.506 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.506 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 3.507 * [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)))) 3.514 * [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))))) 3.515 * [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)))))) 3.515 * [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))))))) 3.516 * [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))))))) 3.517 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.517 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.518 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 3.518 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.519 * [backup-simplify]: Simplify (+ 0 0) into 0 3.520 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.520 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 3.521 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 3.522 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.523 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 3.523 * [backup-simplify]: Simplify 0 into 0 3.524 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.526 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.527 * [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)))))))) 3.528 * [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)))))))) 3.528 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 3.528 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 3.528 * [taylor]: Taking taylor expansion of +nan.0 in n 3.528 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.528 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 3.528 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 3.528 * [taylor]: Taking taylor expansion of 0.5 in n 3.528 * [backup-simplify]: Simplify 0.5 into 0.5 3.528 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 3.528 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.528 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.528 * [taylor]: Taking taylor expansion of k in n 3.528 * [backup-simplify]: Simplify k into k 3.528 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.528 * [taylor]: Taking taylor expansion of 1.0 in n 3.528 * [backup-simplify]: Simplify 1.0 into 1.0 3.528 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.528 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.528 * [taylor]: Taking taylor expansion of -2.0 in n 3.528 * [backup-simplify]: Simplify -2.0 into -2.0 3.528 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.529 * [taylor]: Taking taylor expansion of PI in n 3.529 * [backup-simplify]: Simplify PI into PI 3.529 * [taylor]: Taking taylor expansion of n in n 3.529 * [backup-simplify]: Simplify 0 into 0 3.529 * [backup-simplify]: Simplify 1 into 1 3.529 * [backup-simplify]: Simplify (/ PI 1) into PI 3.529 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.530 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.530 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.531 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.532 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 3.532 * [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)))) 3.533 * [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))))) 3.534 * [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)))))) 3.535 * [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))))))) 3.536 * [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))))))) 3.538 * [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)))))))))))) 3.538 * * * [progress]: simplifying candidates 3.541 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (+ (- (log 1.0) (log (sqrt k))) (* (+ (+ (log 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)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +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 (* (* (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)))))))))))) 5.393 * * * [progress]: adding candidates to table 5.967 * * [progress]: iteration 2 / 4 5.967 * * * [progress]: picking best candidate 6.007 * * * * [pick]: Picked # 6.007 * * * [progress]: localizing error 6.043 * * * [progress]: generating rewritten candidates 6.043 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 2) 6.064 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 2) 6.101 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 2 1) 6.137 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 2 1) 6.160 * * * [progress]: generating series expansions 6.160 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 2) 6.161 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 6.161 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 6.161 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 6.161 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 6.161 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 6.161 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 6.161 * [taylor]: Taking taylor expansion of 0.5 in k 6.161 * [backup-simplify]: Simplify 0.5 into 0.5 6.161 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.161 * [taylor]: Taking taylor expansion of 1.0 in k 6.161 * [backup-simplify]: Simplify 1.0 into 1.0 6.161 * [taylor]: Taking taylor expansion of k in k 6.161 * [backup-simplify]: Simplify 0 into 0 6.161 * [backup-simplify]: Simplify 1 into 1 6.161 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 6.161 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 6.161 * [taylor]: Taking taylor expansion of 2.0 in k 6.161 * [backup-simplify]: Simplify 2.0 into 2.0 6.161 * [taylor]: Taking taylor expansion of (* n PI) in k 6.161 * [taylor]: Taking taylor expansion of n in k 6.161 * [backup-simplify]: Simplify n into n 6.161 * [taylor]: Taking taylor expansion of PI in k 6.161 * [backup-simplify]: Simplify PI into PI 6.161 * [backup-simplify]: Simplify (* n PI) into (* n PI) 6.161 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 6.161 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 6.162 * [backup-simplify]: Simplify (- 0) into 0 6.162 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.162 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 6.162 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 6.162 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 6.162 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 6.162 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.162 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.162 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 6.162 * [taylor]: Taking taylor expansion of 0.5 in n 6.162 * [backup-simplify]: Simplify 0.5 into 0.5 6.162 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.163 * [taylor]: Taking taylor expansion of 1.0 in n 6.163 * [backup-simplify]: Simplify 1.0 into 1.0 6.163 * [taylor]: Taking taylor expansion of k in n 6.163 * [backup-simplify]: Simplify k into k 6.163 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.163 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.163 * [taylor]: Taking taylor expansion of 2.0 in n 6.163 * [backup-simplify]: Simplify 2.0 into 2.0 6.163 * [taylor]: Taking taylor expansion of (* n PI) in n 6.163 * [taylor]: Taking taylor expansion of n in n 6.163 * [backup-simplify]: Simplify 0 into 0 6.163 * [backup-simplify]: Simplify 1 into 1 6.163 * [taylor]: Taking taylor expansion of PI in n 6.163 * [backup-simplify]: Simplify PI into PI 6.163 * [backup-simplify]: Simplify (* 0 PI) into 0 6.163 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.165 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.166 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.167 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.167 * [backup-simplify]: Simplify (- k) into (- k) 6.167 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.167 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 6.168 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.168 * [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)))) 6.169 * [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))))) 6.169 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 6.169 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.169 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.169 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 6.169 * [taylor]: Taking taylor expansion of 0.5 in n 6.169 * [backup-simplify]: Simplify 0.5 into 0.5 6.169 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.169 * [taylor]: Taking taylor expansion of 1.0 in n 6.169 * [backup-simplify]: Simplify 1.0 into 1.0 6.169 * [taylor]: Taking taylor expansion of k in n 6.169 * [backup-simplify]: Simplify k into k 6.169 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.170 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.170 * [taylor]: Taking taylor expansion of 2.0 in n 6.170 * [backup-simplify]: Simplify 2.0 into 2.0 6.170 * [taylor]: Taking taylor expansion of (* n PI) in n 6.170 * [taylor]: Taking taylor expansion of n in n 6.170 * [backup-simplify]: Simplify 0 into 0 6.170 * [backup-simplify]: Simplify 1 into 1 6.170 * [taylor]: Taking taylor expansion of PI in n 6.170 * [backup-simplify]: Simplify PI into PI 6.170 * [backup-simplify]: Simplify (* 0 PI) into 0 6.170 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.171 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.172 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.173 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.173 * [backup-simplify]: Simplify (- k) into (- k) 6.173 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.173 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 6.174 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.174 * [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)))) 6.175 * [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))))) 6.175 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 6.175 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 6.175 * [taylor]: Taking taylor expansion of 0.5 in k 6.176 * [backup-simplify]: Simplify 0.5 into 0.5 6.176 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 6.176 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.176 * [taylor]: Taking taylor expansion of 1.0 in k 6.176 * [backup-simplify]: Simplify 1.0 into 1.0 6.176 * [taylor]: Taking taylor expansion of k in k 6.176 * [backup-simplify]: Simplify 0 into 0 6.176 * [backup-simplify]: Simplify 1 into 1 6.176 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 6.176 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.176 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.176 * [taylor]: Taking taylor expansion of 2.0 in k 6.176 * [backup-simplify]: Simplify 2.0 into 2.0 6.176 * [taylor]: Taking taylor expansion of PI in k 6.176 * [backup-simplify]: Simplify PI into PI 6.176 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.177 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.177 * [taylor]: Taking taylor expansion of (log n) in k 6.177 * [taylor]: Taking taylor expansion of n in k 6.177 * [backup-simplify]: Simplify n into n 6.177 * [backup-simplify]: Simplify (log n) into (log n) 6.177 * [backup-simplify]: Simplify (- 0) into 0 6.177 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.178 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 6.179 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 6.179 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 6.180 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 6.181 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 6.182 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 6.182 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 6.183 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.183 * [backup-simplify]: Simplify (- 0) into 0 6.184 * [backup-simplify]: Simplify (+ 0 0) into 0 6.184 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 6.185 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.190 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 6.192 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.192 * [taylor]: Taking taylor expansion of 0 in k 6.192 * [backup-simplify]: Simplify 0 into 0 6.192 * [backup-simplify]: Simplify 0 into 0 6.192 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.194 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.194 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 6.194 * [backup-simplify]: Simplify (+ 0 0) into 0 6.195 * [backup-simplify]: Simplify (- 1) into -1 6.195 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.196 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 6.197 * [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)))) 6.200 * [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)))))) 6.202 * [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)))))) 6.204 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 6.205 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 6.208 * [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 6.208 * [backup-simplify]: Simplify (- 0) into 0 6.209 * [backup-simplify]: Simplify (+ 0 0) into 0 6.209 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 6.211 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.212 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.214 * [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 6.214 * [taylor]: Taking taylor expansion of 0 in k 6.214 * [backup-simplify]: Simplify 0 into 0 6.214 * [backup-simplify]: Simplify 0 into 0 6.214 * [backup-simplify]: Simplify 0 into 0 6.215 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.219 * [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 6.221 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 6.221 * [backup-simplify]: Simplify (+ 0 0) into 0 6.221 * [backup-simplify]: Simplify (- 0) into 0 6.222 * [backup-simplify]: Simplify (+ 0 0) into 0 6.224 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.226 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 6.229 * [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)))))) 6.234 * [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)))))) 6.243 * [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)))))) 6.244 * [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)))) 6.244 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 6.244 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 6.244 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 6.244 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 6.245 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 6.245 * [taylor]: Taking taylor expansion of 0.5 in k 6.245 * [backup-simplify]: Simplify 0.5 into 0.5 6.245 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.245 * [taylor]: Taking taylor expansion of 1.0 in k 6.245 * [backup-simplify]: Simplify 1.0 into 1.0 6.245 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.245 * [taylor]: Taking taylor expansion of k in k 6.245 * [backup-simplify]: Simplify 0 into 0 6.245 * [backup-simplify]: Simplify 1 into 1 6.245 * [backup-simplify]: Simplify (/ 1 1) into 1 6.245 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 6.245 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 6.245 * [taylor]: Taking taylor expansion of 2.0 in k 6.245 * [backup-simplify]: Simplify 2.0 into 2.0 6.245 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.245 * [taylor]: Taking taylor expansion of PI in k 6.245 * [backup-simplify]: Simplify PI into PI 6.245 * [taylor]: Taking taylor expansion of n in k 6.245 * [backup-simplify]: Simplify n into n 6.245 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.245 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 6.246 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 6.246 * [backup-simplify]: Simplify (- 1) into -1 6.247 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.247 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 6.247 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 6.247 * [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))))) 6.247 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 6.247 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.247 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.247 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 6.248 * [taylor]: Taking taylor expansion of 0.5 in n 6.248 * [backup-simplify]: Simplify 0.5 into 0.5 6.248 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.248 * [taylor]: Taking taylor expansion of 1.0 in n 6.248 * [backup-simplify]: Simplify 1.0 into 1.0 6.248 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.248 * [taylor]: Taking taylor expansion of k in n 6.248 * [backup-simplify]: Simplify k into k 6.248 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.248 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.248 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.248 * [taylor]: Taking taylor expansion of 2.0 in n 6.248 * [backup-simplify]: Simplify 2.0 into 2.0 6.248 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.248 * [taylor]: Taking taylor expansion of PI in n 6.248 * [backup-simplify]: Simplify PI into PI 6.248 * [taylor]: Taking taylor expansion of n in n 6.248 * [backup-simplify]: Simplify 0 into 0 6.248 * [backup-simplify]: Simplify 1 into 1 6.248 * [backup-simplify]: Simplify (/ PI 1) into PI 6.249 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.250 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.250 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.250 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.250 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 6.251 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.252 * [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)))) 6.253 * [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))))) 6.253 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 6.253 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.253 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.253 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 6.253 * [taylor]: Taking taylor expansion of 0.5 in n 6.253 * [backup-simplify]: Simplify 0.5 into 0.5 6.253 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.253 * [taylor]: Taking taylor expansion of 1.0 in n 6.253 * [backup-simplify]: Simplify 1.0 into 1.0 6.253 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.253 * [taylor]: Taking taylor expansion of k in n 6.253 * [backup-simplify]: Simplify k into k 6.253 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.253 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.253 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.253 * [taylor]: Taking taylor expansion of 2.0 in n 6.253 * [backup-simplify]: Simplify 2.0 into 2.0 6.253 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.253 * [taylor]: Taking taylor expansion of PI in n 6.253 * [backup-simplify]: Simplify PI into PI 6.253 * [taylor]: Taking taylor expansion of n in n 6.253 * [backup-simplify]: Simplify 0 into 0 6.253 * [backup-simplify]: Simplify 1 into 1 6.253 * [backup-simplify]: Simplify (/ PI 1) into PI 6.254 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.254 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.254 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.255 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.255 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 6.256 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.256 * [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)))) 6.257 * [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))))) 6.257 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 6.257 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 6.257 * [taylor]: Taking taylor expansion of 0.5 in k 6.257 * [backup-simplify]: Simplify 0.5 into 0.5 6.257 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 6.257 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 6.257 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.257 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.257 * [taylor]: Taking taylor expansion of 2.0 in k 6.257 * [backup-simplify]: Simplify 2.0 into 2.0 6.257 * [taylor]: Taking taylor expansion of PI in k 6.257 * [backup-simplify]: Simplify PI into PI 6.258 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.258 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.258 * [taylor]: Taking taylor expansion of (log n) in k 6.258 * [taylor]: Taking taylor expansion of n in k 6.258 * [backup-simplify]: Simplify n into n 6.258 * [backup-simplify]: Simplify (log n) into (log n) 6.258 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.258 * [taylor]: Taking taylor expansion of 1.0 in k 6.258 * [backup-simplify]: Simplify 1.0 into 1.0 6.258 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.258 * [taylor]: Taking taylor expansion of k in k 6.258 * [backup-simplify]: Simplify 0 into 0 6.258 * [backup-simplify]: Simplify 1 into 1 6.259 * [backup-simplify]: Simplify (/ 1 1) into 1 6.259 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.259 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 6.260 * [backup-simplify]: Simplify (- 1) into -1 6.260 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.261 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 6.261 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 6.262 * [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))))) 6.263 * [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))))) 6.263 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.264 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.265 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.265 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.265 * [backup-simplify]: Simplify (- 0) into 0 6.265 * [backup-simplify]: Simplify (+ 0 0) into 0 6.266 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 6.267 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.267 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 6.269 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.269 * [taylor]: Taking taylor expansion of 0 in k 6.269 * [backup-simplify]: Simplify 0 into 0 6.269 * [backup-simplify]: Simplify 0 into 0 6.269 * [backup-simplify]: Simplify 0 into 0 6.269 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.270 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.272 * [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 6.272 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.272 * [backup-simplify]: Simplify (- 0) into 0 6.272 * [backup-simplify]: Simplify (+ 0 0) into 0 6.273 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 6.274 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.275 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 6.276 * [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 6.276 * [taylor]: Taking taylor expansion of 0 in k 6.276 * [backup-simplify]: Simplify 0 into 0 6.276 * [backup-simplify]: Simplify 0 into 0 6.276 * [backup-simplify]: Simplify 0 into 0 6.276 * [backup-simplify]: Simplify 0 into 0 6.277 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.278 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.281 * [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 6.281 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.281 * [backup-simplify]: Simplify (- 0) into 0 6.282 * [backup-simplify]: Simplify (+ 0 0) into 0 6.282 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 6.283 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.285 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 6.288 * [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 6.289 * [taylor]: Taking taylor expansion of 0 in k 6.289 * [backup-simplify]: Simplify 0 into 0 6.289 * [backup-simplify]: Simplify 0 into 0 6.290 * [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)))) 6.291 * [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))) 6.291 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 6.291 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 6.291 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 6.291 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 6.291 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 6.291 * [taylor]: Taking taylor expansion of 0.5 in k 6.291 * [backup-simplify]: Simplify 0.5 into 0.5 6.291 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.291 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.291 * [taylor]: Taking taylor expansion of k in k 6.291 * [backup-simplify]: Simplify 0 into 0 6.291 * [backup-simplify]: Simplify 1 into 1 6.292 * [backup-simplify]: Simplify (/ 1 1) into 1 6.292 * [taylor]: Taking taylor expansion of 1.0 in k 6.292 * [backup-simplify]: Simplify 1.0 into 1.0 6.292 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 6.292 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 6.292 * [taylor]: Taking taylor expansion of -2.0 in k 6.292 * [backup-simplify]: Simplify -2.0 into -2.0 6.292 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.292 * [taylor]: Taking taylor expansion of PI in k 6.292 * [backup-simplify]: Simplify PI into PI 6.292 * [taylor]: Taking taylor expansion of n in k 6.292 * [backup-simplify]: Simplify n into n 6.292 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.292 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 6.292 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 6.293 * [backup-simplify]: Simplify (+ 1 0) into 1 6.294 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 6.294 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 6.294 * [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)))))) 6.294 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 6.294 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.294 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.294 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 6.294 * [taylor]: Taking taylor expansion of 0.5 in n 6.294 * [backup-simplify]: Simplify 0.5 into 0.5 6.294 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.294 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.294 * [taylor]: Taking taylor expansion of k in n 6.294 * [backup-simplify]: Simplify k into k 6.294 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.294 * [taylor]: Taking taylor expansion of 1.0 in n 6.295 * [backup-simplify]: Simplify 1.0 into 1.0 6.295 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.295 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.295 * [taylor]: Taking taylor expansion of -2.0 in n 6.295 * [backup-simplify]: Simplify -2.0 into -2.0 6.295 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.295 * [taylor]: Taking taylor expansion of PI in n 6.295 * [backup-simplify]: Simplify PI into PI 6.295 * [taylor]: Taking taylor expansion of n in n 6.295 * [backup-simplify]: Simplify 0 into 0 6.295 * [backup-simplify]: Simplify 1 into 1 6.295 * [backup-simplify]: Simplify (/ PI 1) into PI 6.296 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.297 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.297 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.297 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 6.299 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.300 * [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)))) 6.302 * [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))))) 6.302 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 6.302 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.302 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.302 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 6.302 * [taylor]: Taking taylor expansion of 0.5 in n 6.302 * [backup-simplify]: Simplify 0.5 into 0.5 6.302 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.302 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.302 * [taylor]: Taking taylor expansion of k in n 6.302 * [backup-simplify]: Simplify k into k 6.302 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.302 * [taylor]: Taking taylor expansion of 1.0 in n 6.302 * [backup-simplify]: Simplify 1.0 into 1.0 6.302 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.302 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.302 * [taylor]: Taking taylor expansion of -2.0 in n 6.302 * [backup-simplify]: Simplify -2.0 into -2.0 6.302 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.302 * [taylor]: Taking taylor expansion of PI in n 6.302 * [backup-simplify]: Simplify PI into PI 6.302 * [taylor]: Taking taylor expansion of n in n 6.302 * [backup-simplify]: Simplify 0 into 0 6.302 * [backup-simplify]: Simplify 1 into 1 6.303 * [backup-simplify]: Simplify (/ PI 1) into PI 6.303 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.304 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.305 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.305 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 6.314 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.315 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 6.317 * [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))))) 6.317 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 6.317 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 6.317 * [taylor]: Taking taylor expansion of 0.5 in k 6.317 * [backup-simplify]: Simplify 0.5 into 0.5 6.317 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 6.317 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.317 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.317 * [taylor]: Taking taylor expansion of k in k 6.317 * [backup-simplify]: Simplify 0 into 0 6.317 * [backup-simplify]: Simplify 1 into 1 6.318 * [backup-simplify]: Simplify (/ 1 1) into 1 6.318 * [taylor]: Taking taylor expansion of 1.0 in k 6.318 * [backup-simplify]: Simplify 1.0 into 1.0 6.318 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 6.318 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 6.318 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 6.318 * [taylor]: Taking taylor expansion of -2.0 in k 6.318 * [backup-simplify]: Simplify -2.0 into -2.0 6.318 * [taylor]: Taking taylor expansion of PI in k 6.318 * [backup-simplify]: Simplify PI into PI 6.318 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.320 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.320 * [taylor]: Taking taylor expansion of (log n) in k 6.320 * [taylor]: Taking taylor expansion of n in k 6.320 * [backup-simplify]: Simplify n into n 6.320 * [backup-simplify]: Simplify (log n) into (log n) 6.320 * [backup-simplify]: Simplify (+ 1 0) into 1 6.320 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.322 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 6.323 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 6.324 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 6.325 * [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))))) 6.326 * [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))))) 6.328 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.328 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 6.330 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 6.330 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.331 * [backup-simplify]: Simplify (+ 0 0) into 0 6.331 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 6.333 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.334 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 6.336 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.336 * [taylor]: Taking taylor expansion of 0 in k 6.336 * [backup-simplify]: Simplify 0 into 0 6.336 * [backup-simplify]: Simplify 0 into 0 6.336 * [backup-simplify]: Simplify 0 into 0 6.337 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.338 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.341 * [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 6.341 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.341 * [backup-simplify]: Simplify (+ 0 0) into 0 6.342 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 6.344 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.345 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 6.348 * [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 6.348 * [taylor]: Taking taylor expansion of 0 in k 6.348 * [backup-simplify]: Simplify 0 into 0 6.348 * [backup-simplify]: Simplify 0 into 0 6.348 * [backup-simplify]: Simplify 0 into 0 6.348 * [backup-simplify]: Simplify 0 into 0 6.350 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.351 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.357 * [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 6.357 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.358 * [backup-simplify]: Simplify (+ 0 0) into 0 6.359 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 6.360 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.362 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 6.364 * [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 6.364 * [taylor]: Taking taylor expansion of 0 in k 6.364 * [backup-simplify]: Simplify 0 into 0 6.364 * [backup-simplify]: Simplify 0 into 0 6.365 * [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)))))) 6.365 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 2) 6.366 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 6.366 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 6.366 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 6.366 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 6.366 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 6.366 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 6.366 * [taylor]: Taking taylor expansion of 0.5 in k 6.366 * [backup-simplify]: Simplify 0.5 into 0.5 6.366 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.366 * [taylor]: Taking taylor expansion of 1.0 in k 6.366 * [backup-simplify]: Simplify 1.0 into 1.0 6.366 * [taylor]: Taking taylor expansion of k in k 6.366 * [backup-simplify]: Simplify 0 into 0 6.366 * [backup-simplify]: Simplify 1 into 1 6.366 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 6.366 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 6.366 * [taylor]: Taking taylor expansion of 2.0 in k 6.366 * [backup-simplify]: Simplify 2.0 into 2.0 6.366 * [taylor]: Taking taylor expansion of (* n PI) in k 6.366 * [taylor]: Taking taylor expansion of n in k 6.366 * [backup-simplify]: Simplify n into n 6.366 * [taylor]: Taking taylor expansion of PI in k 6.366 * [backup-simplify]: Simplify PI into PI 6.366 * [backup-simplify]: Simplify (* n PI) into (* n PI) 6.366 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 6.366 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 6.367 * [backup-simplify]: Simplify (- 0) into 0 6.367 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.367 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 6.367 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 6.367 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 6.367 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 6.367 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.367 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.367 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 6.367 * [taylor]: Taking taylor expansion of 0.5 in n 6.367 * [backup-simplify]: Simplify 0.5 into 0.5 6.367 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.367 * [taylor]: Taking taylor expansion of 1.0 in n 6.367 * [backup-simplify]: Simplify 1.0 into 1.0 6.367 * [taylor]: Taking taylor expansion of k in n 6.367 * [backup-simplify]: Simplify k into k 6.367 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.367 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.367 * [taylor]: Taking taylor expansion of 2.0 in n 6.367 * [backup-simplify]: Simplify 2.0 into 2.0 6.368 * [taylor]: Taking taylor expansion of (* n PI) in n 6.368 * [taylor]: Taking taylor expansion of n in n 6.368 * [backup-simplify]: Simplify 0 into 0 6.368 * [backup-simplify]: Simplify 1 into 1 6.368 * [taylor]: Taking taylor expansion of PI in n 6.368 * [backup-simplify]: Simplify PI into PI 6.368 * [backup-simplify]: Simplify (* 0 PI) into 0 6.368 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.369 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.370 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.371 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.371 * [backup-simplify]: Simplify (- k) into (- k) 6.371 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.371 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 6.372 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.372 * [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)))) 6.373 * [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))))) 6.373 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 6.373 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.373 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.373 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 6.373 * [taylor]: Taking taylor expansion of 0.5 in n 6.373 * [backup-simplify]: Simplify 0.5 into 0.5 6.373 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.373 * [taylor]: Taking taylor expansion of 1.0 in n 6.373 * [backup-simplify]: Simplify 1.0 into 1.0 6.373 * [taylor]: Taking taylor expansion of k in n 6.373 * [backup-simplify]: Simplify k into k 6.373 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.373 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.373 * [taylor]: Taking taylor expansion of 2.0 in n 6.373 * [backup-simplify]: Simplify 2.0 into 2.0 6.373 * [taylor]: Taking taylor expansion of (* n PI) in n 6.373 * [taylor]: Taking taylor expansion of n in n 6.373 * [backup-simplify]: Simplify 0 into 0 6.373 * [backup-simplify]: Simplify 1 into 1 6.373 * [taylor]: Taking taylor expansion of PI in n 6.373 * [backup-simplify]: Simplify PI into PI 6.374 * [backup-simplify]: Simplify (* 0 PI) into 0 6.374 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.375 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.376 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.376 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.376 * [backup-simplify]: Simplify (- k) into (- k) 6.376 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.376 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 6.377 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.378 * [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)))) 6.379 * [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))))) 6.379 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 6.379 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 6.379 * [taylor]: Taking taylor expansion of 0.5 in k 6.379 * [backup-simplify]: Simplify 0.5 into 0.5 6.379 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 6.379 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.379 * [taylor]: Taking taylor expansion of 1.0 in k 6.379 * [backup-simplify]: Simplify 1.0 into 1.0 6.379 * [taylor]: Taking taylor expansion of k in k 6.379 * [backup-simplify]: Simplify 0 into 0 6.379 * [backup-simplify]: Simplify 1 into 1 6.379 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 6.379 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.379 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.379 * [taylor]: Taking taylor expansion of 2.0 in k 6.379 * [backup-simplify]: Simplify 2.0 into 2.0 6.379 * [taylor]: Taking taylor expansion of PI in k 6.379 * [backup-simplify]: Simplify PI into PI 6.379 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.380 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.380 * [taylor]: Taking taylor expansion of (log n) in k 6.380 * [taylor]: Taking taylor expansion of n in k 6.380 * [backup-simplify]: Simplify n into n 6.380 * [backup-simplify]: Simplify (log n) into (log n) 6.381 * [backup-simplify]: Simplify (- 0) into 0 6.381 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.382 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 6.382 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 6.383 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 6.384 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 6.384 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 6.385 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 6.386 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 6.387 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.387 * [backup-simplify]: Simplify (- 0) into 0 6.387 * [backup-simplify]: Simplify (+ 0 0) into 0 6.387 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 6.388 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.389 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 6.390 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.390 * [taylor]: Taking taylor expansion of 0 in k 6.390 * [backup-simplify]: Simplify 0 into 0 6.390 * [backup-simplify]: Simplify 0 into 0 6.391 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.392 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.392 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 6.393 * [backup-simplify]: Simplify (+ 0 0) into 0 6.393 * [backup-simplify]: Simplify (- 1) into -1 6.393 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.394 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 6.396 * [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)))) 6.398 * [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)))))) 6.400 * [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)))))) 6.401 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 6.402 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 6.404 * [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 6.404 * [backup-simplify]: Simplify (- 0) into 0 6.404 * [backup-simplify]: Simplify (+ 0 0) into 0 6.405 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 6.405 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.406 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.408 * [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 6.408 * [taylor]: Taking taylor expansion of 0 in k 6.408 * [backup-simplify]: Simplify 0 into 0 6.408 * [backup-simplify]: Simplify 0 into 0 6.408 * [backup-simplify]: Simplify 0 into 0 6.409 * [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 6.412 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 6.412 * [backup-simplify]: Simplify (+ 0 0) into 0 6.412 * [backup-simplify]: Simplify (- 0) into 0 6.413 * [backup-simplify]: Simplify (+ 0 0) into 0 6.415 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.417 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 6.421 * [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)))))) 6.425 * [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)))))) 6.444 * [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)))))) 6.445 * [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)))) 6.445 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 6.445 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 6.445 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 6.445 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 6.445 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 6.445 * [taylor]: Taking taylor expansion of 0.5 in k 6.445 * [backup-simplify]: Simplify 0.5 into 0.5 6.445 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.445 * [taylor]: Taking taylor expansion of 1.0 in k 6.445 * [backup-simplify]: Simplify 1.0 into 1.0 6.445 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.445 * [taylor]: Taking taylor expansion of k in k 6.445 * [backup-simplify]: Simplify 0 into 0 6.445 * [backup-simplify]: Simplify 1 into 1 6.446 * [backup-simplify]: Simplify (/ 1 1) into 1 6.446 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 6.446 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 6.446 * [taylor]: Taking taylor expansion of 2.0 in k 6.446 * [backup-simplify]: Simplify 2.0 into 2.0 6.446 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.446 * [taylor]: Taking taylor expansion of PI in k 6.446 * [backup-simplify]: Simplify PI into PI 6.446 * [taylor]: Taking taylor expansion of n in k 6.446 * [backup-simplify]: Simplify n into n 6.446 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.446 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 6.447 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 6.447 * [backup-simplify]: Simplify (- 1) into -1 6.448 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.448 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 6.448 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 6.448 * [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))))) 6.449 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 6.449 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.449 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.449 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 6.449 * [taylor]: Taking taylor expansion of 0.5 in n 6.449 * [backup-simplify]: Simplify 0.5 into 0.5 6.449 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.449 * [taylor]: Taking taylor expansion of 1.0 in n 6.449 * [backup-simplify]: Simplify 1.0 into 1.0 6.449 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.449 * [taylor]: Taking taylor expansion of k in n 6.449 * [backup-simplify]: Simplify k into k 6.449 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.449 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.449 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.449 * [taylor]: Taking taylor expansion of 2.0 in n 6.449 * [backup-simplify]: Simplify 2.0 into 2.0 6.450 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.450 * [taylor]: Taking taylor expansion of PI in n 6.450 * [backup-simplify]: Simplify PI into PI 6.450 * [taylor]: Taking taylor expansion of n in n 6.450 * [backup-simplify]: Simplify 0 into 0 6.450 * [backup-simplify]: Simplify 1 into 1 6.450 * [backup-simplify]: Simplify (/ PI 1) into PI 6.451 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.452 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.452 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.452 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.452 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 6.453 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.454 * [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)))) 6.455 * [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))))) 6.455 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 6.455 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.455 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.455 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 6.455 * [taylor]: Taking taylor expansion of 0.5 in n 6.455 * [backup-simplify]: Simplify 0.5 into 0.5 6.455 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.455 * [taylor]: Taking taylor expansion of 1.0 in n 6.455 * [backup-simplify]: Simplify 1.0 into 1.0 6.455 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.455 * [taylor]: Taking taylor expansion of k in n 6.455 * [backup-simplify]: Simplify k into k 6.455 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.455 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.455 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.455 * [taylor]: Taking taylor expansion of 2.0 in n 6.455 * [backup-simplify]: Simplify 2.0 into 2.0 6.455 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.455 * [taylor]: Taking taylor expansion of PI in n 6.455 * [backup-simplify]: Simplify PI into PI 6.455 * [taylor]: Taking taylor expansion of n in n 6.455 * [backup-simplify]: Simplify 0 into 0 6.455 * [backup-simplify]: Simplify 1 into 1 6.455 * [backup-simplify]: Simplify (/ PI 1) into PI 6.456 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.456 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.457 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.457 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.457 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 6.458 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.458 * [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)))) 6.459 * [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))))) 6.459 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 6.459 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 6.459 * [taylor]: Taking taylor expansion of 0.5 in k 6.459 * [backup-simplify]: Simplify 0.5 into 0.5 6.459 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 6.459 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 6.459 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.459 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.459 * [taylor]: Taking taylor expansion of 2.0 in k 6.459 * [backup-simplify]: Simplify 2.0 into 2.0 6.459 * [taylor]: Taking taylor expansion of PI in k 6.459 * [backup-simplify]: Simplify PI into PI 6.460 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.460 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.460 * [taylor]: Taking taylor expansion of (log n) in k 6.460 * [taylor]: Taking taylor expansion of n in k 6.460 * [backup-simplify]: Simplify n into n 6.461 * [backup-simplify]: Simplify (log n) into (log n) 6.461 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.461 * [taylor]: Taking taylor expansion of 1.0 in k 6.461 * [backup-simplify]: Simplify 1.0 into 1.0 6.461 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.461 * [taylor]: Taking taylor expansion of k in k 6.461 * [backup-simplify]: Simplify 0 into 0 6.461 * [backup-simplify]: Simplify 1 into 1 6.461 * [backup-simplify]: Simplify (/ 1 1) into 1 6.461 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.462 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 6.462 * [backup-simplify]: Simplify (- 1) into -1 6.462 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.463 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 6.464 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 6.464 * [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))))) 6.465 * [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))))) 6.466 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.466 * [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 6.468 * [backup-simplify]: Simplify (- 0) into 0 6.468 * [backup-simplify]: Simplify (+ 0 0) into 0 6.468 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 6.469 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.470 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 6.471 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.471 * [taylor]: Taking taylor expansion of 0 in k 6.471 * [backup-simplify]: Simplify 0 into 0 6.471 * [backup-simplify]: Simplify 0 into 0 6.471 * [backup-simplify]: Simplify 0 into 0 6.472 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.472 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.474 * [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 6.474 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.474 * [backup-simplify]: Simplify (- 0) into 0 6.475 * [backup-simplify]: Simplify (+ 0 0) into 0 6.475 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 6.476 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.477 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 6.478 * [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 6.479 * [taylor]: Taking taylor expansion of 0 in k 6.479 * [backup-simplify]: Simplify 0 into 0 6.479 * [backup-simplify]: Simplify 0 into 0 6.479 * [backup-simplify]: Simplify 0 into 0 6.479 * [backup-simplify]: Simplify 0 into 0 6.479 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.480 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.483 * [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 6.483 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.484 * [backup-simplify]: Simplify (- 0) into 0 6.484 * [backup-simplify]: Simplify (+ 0 0) into 0 6.485 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 6.487 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.489 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 6.492 * [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 6.492 * [taylor]: Taking taylor expansion of 0 in k 6.492 * [backup-simplify]: Simplify 0 into 0 6.492 * [backup-simplify]: Simplify 0 into 0 6.493 * [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)))) 6.494 * [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))) 6.494 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 6.494 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 6.494 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 6.494 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 6.494 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 6.494 * [taylor]: Taking taylor expansion of 0.5 in k 6.494 * [backup-simplify]: Simplify 0.5 into 0.5 6.494 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.494 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.494 * [taylor]: Taking taylor expansion of k in k 6.494 * [backup-simplify]: Simplify 0 into 0 6.494 * [backup-simplify]: Simplify 1 into 1 6.494 * [backup-simplify]: Simplify (/ 1 1) into 1 6.494 * [taylor]: Taking taylor expansion of 1.0 in k 6.495 * [backup-simplify]: Simplify 1.0 into 1.0 6.495 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 6.495 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 6.495 * [taylor]: Taking taylor expansion of -2.0 in k 6.495 * [backup-simplify]: Simplify -2.0 into -2.0 6.495 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.495 * [taylor]: Taking taylor expansion of PI in k 6.495 * [backup-simplify]: Simplify PI into PI 6.495 * [taylor]: Taking taylor expansion of n in k 6.495 * [backup-simplify]: Simplify n into n 6.495 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.495 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 6.495 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 6.495 * [backup-simplify]: Simplify (+ 1 0) into 1 6.496 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 6.496 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 6.496 * [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)))))) 6.496 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 6.496 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.496 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.496 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 6.497 * [taylor]: Taking taylor expansion of 0.5 in n 6.497 * [backup-simplify]: Simplify 0.5 into 0.5 6.497 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.497 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.497 * [taylor]: Taking taylor expansion of k in n 6.497 * [backup-simplify]: Simplify k into k 6.497 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.497 * [taylor]: Taking taylor expansion of 1.0 in n 6.497 * [backup-simplify]: Simplify 1.0 into 1.0 6.497 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.497 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.497 * [taylor]: Taking taylor expansion of -2.0 in n 6.497 * [backup-simplify]: Simplify -2.0 into -2.0 6.497 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.497 * [taylor]: Taking taylor expansion of PI in n 6.497 * [backup-simplify]: Simplify PI into PI 6.497 * [taylor]: Taking taylor expansion of n in n 6.497 * [backup-simplify]: Simplify 0 into 0 6.497 * [backup-simplify]: Simplify 1 into 1 6.498 * [backup-simplify]: Simplify (/ PI 1) into PI 6.498 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.499 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.499 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.500 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 6.501 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.502 * [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)))) 6.503 * [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))))) 6.504 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 6.504 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.504 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.504 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 6.504 * [taylor]: Taking taylor expansion of 0.5 in n 6.504 * [backup-simplify]: Simplify 0.5 into 0.5 6.504 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.504 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.504 * [taylor]: Taking taylor expansion of k in n 6.504 * [backup-simplify]: Simplify k into k 6.504 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.504 * [taylor]: Taking taylor expansion of 1.0 in n 6.504 * [backup-simplify]: Simplify 1.0 into 1.0 6.504 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.504 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.504 * [taylor]: Taking taylor expansion of -2.0 in n 6.504 * [backup-simplify]: Simplify -2.0 into -2.0 6.504 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.504 * [taylor]: Taking taylor expansion of PI in n 6.504 * [backup-simplify]: Simplify PI into PI 6.504 * [taylor]: Taking taylor expansion of n in n 6.504 * [backup-simplify]: Simplify 0 into 0 6.504 * [backup-simplify]: Simplify 1 into 1 6.505 * [backup-simplify]: Simplify (/ PI 1) into PI 6.505 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.506 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.506 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.507 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 6.508 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.509 * [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)))) 6.511 * [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))))) 6.511 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 6.511 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 6.511 * [taylor]: Taking taylor expansion of 0.5 in k 6.511 * [backup-simplify]: Simplify 0.5 into 0.5 6.511 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 6.511 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.511 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.511 * [taylor]: Taking taylor expansion of k in k 6.511 * [backup-simplify]: Simplify 0 into 0 6.511 * [backup-simplify]: Simplify 1 into 1 6.511 * [backup-simplify]: Simplify (/ 1 1) into 1 6.511 * [taylor]: Taking taylor expansion of 1.0 in k 6.512 * [backup-simplify]: Simplify 1.0 into 1.0 6.512 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 6.512 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 6.512 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 6.512 * [taylor]: Taking taylor expansion of -2.0 in k 6.512 * [backup-simplify]: Simplify -2.0 into -2.0 6.512 * [taylor]: Taking taylor expansion of PI in k 6.512 * [backup-simplify]: Simplify PI into PI 6.512 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.513 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.513 * [taylor]: Taking taylor expansion of (log n) in k 6.513 * [taylor]: Taking taylor expansion of n in k 6.513 * [backup-simplify]: Simplify n into n 6.513 * [backup-simplify]: Simplify (log n) into (log n) 6.514 * [backup-simplify]: Simplify (+ 1 0) into 1 6.514 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.515 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 6.516 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 6.517 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 6.518 * [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))))) 6.519 * [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))))) 6.520 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.520 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 6.521 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 6.522 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.522 * [backup-simplify]: Simplify (+ 0 0) into 0 6.522 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 6.523 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.524 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 6.525 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.525 * [taylor]: Taking taylor expansion of 0 in k 6.525 * [backup-simplify]: Simplify 0 into 0 6.525 * [backup-simplify]: Simplify 0 into 0 6.525 * [backup-simplify]: Simplify 0 into 0 6.526 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.526 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.528 * [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 6.528 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.528 * [backup-simplify]: Simplify (+ 0 0) into 0 6.529 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 6.530 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.531 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 6.532 * [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 6.532 * [taylor]: Taking taylor expansion of 0 in k 6.532 * [backup-simplify]: Simplify 0 into 0 6.532 * [backup-simplify]: Simplify 0 into 0 6.532 * [backup-simplify]: Simplify 0 into 0 6.532 * [backup-simplify]: Simplify 0 into 0 6.533 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.534 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.537 * [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 6.537 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.537 * [backup-simplify]: Simplify (+ 0 0) into 0 6.538 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 6.539 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.540 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 6.542 * [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 6.542 * [taylor]: Taking taylor expansion of 0 in k 6.542 * [backup-simplify]: Simplify 0 into 0 6.542 * [backup-simplify]: Simplify 0 into 0 6.543 * [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)))))) 6.543 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 2 1) 6.543 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 6.543 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 6.543 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.543 * [taylor]: Taking taylor expansion of 2.0 in n 6.543 * [backup-simplify]: Simplify 2.0 into 2.0 6.543 * [taylor]: Taking taylor expansion of (* n PI) in n 6.543 * [taylor]: Taking taylor expansion of n in n 6.543 * [backup-simplify]: Simplify 0 into 0 6.543 * [backup-simplify]: Simplify 1 into 1 6.543 * [taylor]: Taking taylor expansion of PI in n 6.543 * [backup-simplify]: Simplify PI into PI 6.543 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.543 * [taylor]: Taking taylor expansion of 2.0 in n 6.543 * [backup-simplify]: Simplify 2.0 into 2.0 6.543 * [taylor]: Taking taylor expansion of (* n PI) in n 6.543 * [taylor]: Taking taylor expansion of n in n 6.543 * [backup-simplify]: Simplify 0 into 0 6.543 * [backup-simplify]: Simplify 1 into 1 6.543 * [taylor]: Taking taylor expansion of PI in n 6.543 * [backup-simplify]: Simplify PI into PI 6.544 * [backup-simplify]: Simplify (* 0 PI) into 0 6.544 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.544 * [backup-simplify]: Simplify 0 into 0 6.551 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.552 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.553 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.553 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 6.554 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 6.554 * [backup-simplify]: Simplify 0 into 0 6.555 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 6.556 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 6.556 * [backup-simplify]: Simplify 0 into 0 6.556 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 6.557 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 6.557 * [backup-simplify]: Simplify 0 into 0 6.558 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 6.559 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 6.559 * [backup-simplify]: Simplify 0 into 0 6.561 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 6.563 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 6.563 * [backup-simplify]: Simplify 0 into 0 6.564 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 6.566 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 6.566 * [backup-simplify]: Simplify 0 into 0 6.567 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 6.568 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 6.568 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 6.568 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.568 * [taylor]: Taking taylor expansion of 2.0 in n 6.568 * [backup-simplify]: Simplify 2.0 into 2.0 6.568 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.568 * [taylor]: Taking taylor expansion of PI in n 6.568 * [backup-simplify]: Simplify PI into PI 6.568 * [taylor]: Taking taylor expansion of n in n 6.568 * [backup-simplify]: Simplify 0 into 0 6.568 * [backup-simplify]: Simplify 1 into 1 6.568 * [backup-simplify]: Simplify (/ PI 1) into PI 6.568 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.568 * [taylor]: Taking taylor expansion of 2.0 in n 6.568 * [backup-simplify]: Simplify 2.0 into 2.0 6.568 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.568 * [taylor]: Taking taylor expansion of PI in n 6.568 * [backup-simplify]: Simplify PI into PI 6.568 * [taylor]: Taking taylor expansion of n in n 6.569 * [backup-simplify]: Simplify 0 into 0 6.569 * [backup-simplify]: Simplify 1 into 1 6.569 * [backup-simplify]: Simplify (/ PI 1) into PI 6.570 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.570 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.571 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.572 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.572 * [backup-simplify]: Simplify 0 into 0 6.573 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.574 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.574 * [backup-simplify]: Simplify 0 into 0 6.575 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.576 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.576 * [backup-simplify]: Simplify 0 into 0 6.577 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.578 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 6.578 * [backup-simplify]: Simplify 0 into 0 6.579 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.581 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 6.581 * [backup-simplify]: Simplify 0 into 0 6.582 * [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 6.584 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 6.584 * [backup-simplify]: Simplify 0 into 0 6.584 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 6.585 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 6.585 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 6.585 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.585 * [taylor]: Taking taylor expansion of -2.0 in n 6.585 * [backup-simplify]: Simplify -2.0 into -2.0 6.585 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.585 * [taylor]: Taking taylor expansion of PI in n 6.585 * [backup-simplify]: Simplify PI into PI 6.585 * [taylor]: Taking taylor expansion of n in n 6.585 * [backup-simplify]: Simplify 0 into 0 6.585 * [backup-simplify]: Simplify 1 into 1 6.586 * [backup-simplify]: Simplify (/ PI 1) into PI 6.586 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.586 * [taylor]: Taking taylor expansion of -2.0 in n 6.586 * [backup-simplify]: Simplify -2.0 into -2.0 6.586 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.586 * [taylor]: Taking taylor expansion of PI in n 6.586 * [backup-simplify]: Simplify PI into PI 6.586 * [taylor]: Taking taylor expansion of n in n 6.586 * [backup-simplify]: Simplify 0 into 0 6.586 * [backup-simplify]: Simplify 1 into 1 6.586 * [backup-simplify]: Simplify (/ PI 1) into PI 6.587 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.587 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.588 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.589 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 6.589 * [backup-simplify]: Simplify 0 into 0 6.590 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.591 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.591 * [backup-simplify]: Simplify 0 into 0 6.592 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.593 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.593 * [backup-simplify]: Simplify 0 into 0 6.594 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.596 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 6.596 * [backup-simplify]: Simplify 0 into 0 6.597 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.598 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 6.598 * [backup-simplify]: Simplify 0 into 0 6.599 * [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 6.601 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 6.601 * [backup-simplify]: Simplify 0 into 0 6.601 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 6.602 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 2 1) 6.602 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 6.602 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 6.602 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.602 * [taylor]: Taking taylor expansion of 2.0 in n 6.602 * [backup-simplify]: Simplify 2.0 into 2.0 6.602 * [taylor]: Taking taylor expansion of (* n PI) in n 6.602 * [taylor]: Taking taylor expansion of n in n 6.602 * [backup-simplify]: Simplify 0 into 0 6.602 * [backup-simplify]: Simplify 1 into 1 6.602 * [taylor]: Taking taylor expansion of PI in n 6.602 * [backup-simplify]: Simplify PI into PI 6.602 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.602 * [taylor]: Taking taylor expansion of 2.0 in n 6.603 * [backup-simplify]: Simplify 2.0 into 2.0 6.603 * [taylor]: Taking taylor expansion of (* n PI) in n 6.603 * [taylor]: Taking taylor expansion of n in n 6.603 * [backup-simplify]: Simplify 0 into 0 6.603 * [backup-simplify]: Simplify 1 into 1 6.603 * [taylor]: Taking taylor expansion of PI in n 6.603 * [backup-simplify]: Simplify PI into PI 6.603 * [backup-simplify]: Simplify (* 0 PI) into 0 6.604 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.604 * [backup-simplify]: Simplify 0 into 0 6.605 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.607 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.607 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.608 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 6.609 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 6.609 * [backup-simplify]: Simplify 0 into 0 6.611 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 6.612 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 6.612 * [backup-simplify]: Simplify 0 into 0 6.613 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 6.615 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 6.615 * [backup-simplify]: Simplify 0 into 0 6.616 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 6.618 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 6.618 * [backup-simplify]: Simplify 0 into 0 6.620 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 6.622 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 6.622 * [backup-simplify]: Simplify 0 into 0 6.624 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 6.626 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 6.626 * [backup-simplify]: Simplify 0 into 0 6.627 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 6.627 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 6.627 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 6.627 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.627 * [taylor]: Taking taylor expansion of 2.0 in n 6.627 * [backup-simplify]: Simplify 2.0 into 2.0 6.627 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.627 * [taylor]: Taking taylor expansion of PI in n 6.628 * [backup-simplify]: Simplify PI into PI 6.628 * [taylor]: Taking taylor expansion of n in n 6.628 * [backup-simplify]: Simplify 0 into 0 6.628 * [backup-simplify]: Simplify 1 into 1 6.628 * [backup-simplify]: Simplify (/ PI 1) into PI 6.628 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.628 * [taylor]: Taking taylor expansion of 2.0 in n 6.628 * [backup-simplify]: Simplify 2.0 into 2.0 6.628 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.628 * [taylor]: Taking taylor expansion of PI in n 6.628 * [backup-simplify]: Simplify PI into PI 6.628 * [taylor]: Taking taylor expansion of n in n 6.628 * [backup-simplify]: Simplify 0 into 0 6.628 * [backup-simplify]: Simplify 1 into 1 6.629 * [backup-simplify]: Simplify (/ PI 1) into PI 6.630 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.630 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.631 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.632 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.632 * [backup-simplify]: Simplify 0 into 0 6.633 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.634 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.634 * [backup-simplify]: Simplify 0 into 0 6.635 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.637 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.637 * [backup-simplify]: Simplify 0 into 0 6.638 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.639 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 6.639 * [backup-simplify]: Simplify 0 into 0 6.640 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.642 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 6.642 * [backup-simplify]: Simplify 0 into 0 6.643 * [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 6.645 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 6.645 * [backup-simplify]: Simplify 0 into 0 6.646 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 6.646 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 6.646 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 6.646 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.646 * [taylor]: Taking taylor expansion of -2.0 in n 6.646 * [backup-simplify]: Simplify -2.0 into -2.0 6.646 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.646 * [taylor]: Taking taylor expansion of PI in n 6.646 * [backup-simplify]: Simplify PI into PI 6.647 * [taylor]: Taking taylor expansion of n in n 6.647 * [backup-simplify]: Simplify 0 into 0 6.647 * [backup-simplify]: Simplify 1 into 1 6.647 * [backup-simplify]: Simplify (/ PI 1) into PI 6.647 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.647 * [taylor]: Taking taylor expansion of -2.0 in n 6.647 * [backup-simplify]: Simplify -2.0 into -2.0 6.647 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.647 * [taylor]: Taking taylor expansion of PI in n 6.647 * [backup-simplify]: Simplify PI into PI 6.647 * [taylor]: Taking taylor expansion of n in n 6.647 * [backup-simplify]: Simplify 0 into 0 6.647 * [backup-simplify]: Simplify 1 into 1 6.648 * [backup-simplify]: Simplify (/ PI 1) into PI 6.648 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.649 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.650 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.651 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 6.651 * [backup-simplify]: Simplify 0 into 0 6.652 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.653 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.653 * [backup-simplify]: Simplify 0 into 0 6.654 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.656 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.656 * [backup-simplify]: Simplify 0 into 0 6.657 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.658 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 6.658 * [backup-simplify]: Simplify 0 into 0 6.660 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.661 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 6.661 * [backup-simplify]: Simplify 0 into 0 6.662 * [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 6.664 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 6.664 * [backup-simplify]: Simplify 0 into 0 6.665 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 6.665 * * * [progress]: simplifying candidates 6.668 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (* 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) (* (* 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)))))) (- (+ (* 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)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 7.511 * * * [progress]: adding candidates to table 8.163 * * [progress]: iteration 3 / 4 8.163 * * * [progress]: picking best candidate 8.222 * * * * [pick]: Picked # 8.222 * * * [progress]: localizing error 8.261 * * * [progress]: generating rewritten candidates 8.261 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 2) 8.303 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 2 2) 8.311 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1 2 1) 8.326 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 2 1) 8.372 * * * [progress]: generating series expansions 8.373 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 2) 8.374 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 8.374 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 8.374 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 8.374 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 8.374 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 8.374 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 8.374 * [taylor]: Taking taylor expansion of 0.5 in k 8.374 * [backup-simplify]: Simplify 0.5 into 0.5 8.374 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.374 * [taylor]: Taking taylor expansion of 1.0 in k 8.374 * [backup-simplify]: Simplify 1.0 into 1.0 8.374 * [taylor]: Taking taylor expansion of k in k 8.374 * [backup-simplify]: Simplify 0 into 0 8.374 * [backup-simplify]: Simplify 1 into 1 8.374 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 8.374 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 8.374 * [taylor]: Taking taylor expansion of 2.0 in k 8.374 * [backup-simplify]: Simplify 2.0 into 2.0 8.374 * [taylor]: Taking taylor expansion of (* n PI) in k 8.374 * [taylor]: Taking taylor expansion of n in k 8.374 * [backup-simplify]: Simplify n into n 8.375 * [taylor]: Taking taylor expansion of PI in k 8.375 * [backup-simplify]: Simplify PI into PI 8.375 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.375 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 8.375 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 8.375 * [backup-simplify]: Simplify (- 0) into 0 8.376 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.376 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 8.376 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 8.377 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 8.377 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 8.377 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.377 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.377 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 8.377 * [taylor]: Taking taylor expansion of 0.5 in n 8.377 * [backup-simplify]: Simplify 0.5 into 0.5 8.377 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.377 * [taylor]: Taking taylor expansion of 1.0 in n 8.377 * [backup-simplify]: Simplify 1.0 into 1.0 8.377 * [taylor]: Taking taylor expansion of k in n 8.377 * [backup-simplify]: Simplify k into k 8.377 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.377 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.377 * [taylor]: Taking taylor expansion of 2.0 in n 8.377 * [backup-simplify]: Simplify 2.0 into 2.0 8.377 * [taylor]: Taking taylor expansion of (* n PI) in n 8.377 * [taylor]: Taking taylor expansion of n in n 8.377 * [backup-simplify]: Simplify 0 into 0 8.377 * [backup-simplify]: Simplify 1 into 1 8.377 * [taylor]: Taking taylor expansion of PI in n 8.377 * [backup-simplify]: Simplify PI into PI 8.378 * [backup-simplify]: Simplify (* 0 PI) into 0 8.378 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.380 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.382 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.383 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.383 * [backup-simplify]: Simplify (- k) into (- k) 8.383 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.383 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 8.384 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.386 * [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)))) 8.387 * [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))))) 8.387 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 8.387 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.387 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.387 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 8.387 * [taylor]: Taking taylor expansion of 0.5 in n 8.387 * [backup-simplify]: Simplify 0.5 into 0.5 8.387 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.387 * [taylor]: Taking taylor expansion of 1.0 in n 8.387 * [backup-simplify]: Simplify 1.0 into 1.0 8.387 * [taylor]: Taking taylor expansion of k in n 8.388 * [backup-simplify]: Simplify k into k 8.388 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.388 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.388 * [taylor]: Taking taylor expansion of 2.0 in n 8.388 * [backup-simplify]: Simplify 2.0 into 2.0 8.388 * [taylor]: Taking taylor expansion of (* n PI) in n 8.388 * [taylor]: Taking taylor expansion of n in n 8.388 * [backup-simplify]: Simplify 0 into 0 8.388 * [backup-simplify]: Simplify 1 into 1 8.388 * [taylor]: Taking taylor expansion of PI in n 8.388 * [backup-simplify]: Simplify PI into PI 8.388 * [backup-simplify]: Simplify (* 0 PI) into 0 8.389 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.391 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.392 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.393 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.393 * [backup-simplify]: Simplify (- k) into (- k) 8.393 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.394 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 8.395 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.396 * [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)))) 8.398 * [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))))) 8.398 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 8.398 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 8.398 * [taylor]: Taking taylor expansion of 0.5 in k 8.398 * [backup-simplify]: Simplify 0.5 into 0.5 8.398 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 8.398 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.398 * [taylor]: Taking taylor expansion of 1.0 in k 8.398 * [backup-simplify]: Simplify 1.0 into 1.0 8.398 * [taylor]: Taking taylor expansion of k in k 8.398 * [backup-simplify]: Simplify 0 into 0 8.398 * [backup-simplify]: Simplify 1 into 1 8.398 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 8.398 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.398 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.398 * [taylor]: Taking taylor expansion of 2.0 in k 8.398 * [backup-simplify]: Simplify 2.0 into 2.0 8.398 * [taylor]: Taking taylor expansion of PI in k 8.398 * [backup-simplify]: Simplify PI into PI 8.399 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.407 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.407 * [taylor]: Taking taylor expansion of (log n) in k 8.407 * [taylor]: Taking taylor expansion of n in k 8.407 * [backup-simplify]: Simplify n into n 8.407 * [backup-simplify]: Simplify (log n) into (log n) 8.408 * [backup-simplify]: Simplify (- 0) into 0 8.408 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.409 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 8.410 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 8.412 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 8.413 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 8.414 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 8.415 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.417 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 8.418 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.419 * [backup-simplify]: Simplify (- 0) into 0 8.419 * [backup-simplify]: Simplify (+ 0 0) into 0 8.420 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 8.421 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.423 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 8.425 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.425 * [taylor]: Taking taylor expansion of 0 in k 8.425 * [backup-simplify]: Simplify 0 into 0 8.425 * [backup-simplify]: Simplify 0 into 0 8.426 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.428 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.428 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 8.429 * [backup-simplify]: Simplify (+ 0 0) into 0 8.429 * [backup-simplify]: Simplify (- 1) into -1 8.430 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.431 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 8.434 * [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)))) 8.436 * [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)))))) 8.438 * [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)))))) 8.439 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 8.440 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 8.441 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.442 * [backup-simplify]: Simplify (- 0) into 0 8.442 * [backup-simplify]: Simplify (+ 0 0) into 0 8.443 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 8.443 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.444 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.446 * [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 8.446 * [taylor]: Taking taylor expansion of 0 in k 8.446 * [backup-simplify]: Simplify 0 into 0 8.446 * [backup-simplify]: Simplify 0 into 0 8.446 * [backup-simplify]: Simplify 0 into 0 8.447 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.449 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.450 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 8.450 * [backup-simplify]: Simplify (+ 0 0) into 0 8.451 * [backup-simplify]: Simplify (- 0) into 0 8.451 * [backup-simplify]: Simplify (+ 0 0) into 0 8.452 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.454 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 8.456 * [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)))))) 8.460 * [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)))))) 8.468 * [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)))))) 8.469 * [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)))) 8.469 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 8.469 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 8.469 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 8.469 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 8.469 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 8.469 * [taylor]: Taking taylor expansion of 0.5 in k 8.469 * [backup-simplify]: Simplify 0.5 into 0.5 8.469 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.469 * [taylor]: Taking taylor expansion of 1.0 in k 8.469 * [backup-simplify]: Simplify 1.0 into 1.0 8.469 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.469 * [taylor]: Taking taylor expansion of k in k 8.469 * [backup-simplify]: Simplify 0 into 0 8.469 * [backup-simplify]: Simplify 1 into 1 8.470 * [backup-simplify]: Simplify (/ 1 1) into 1 8.470 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 8.470 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 8.470 * [taylor]: Taking taylor expansion of 2.0 in k 8.470 * [backup-simplify]: Simplify 2.0 into 2.0 8.470 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.470 * [taylor]: Taking taylor expansion of PI in k 8.470 * [backup-simplify]: Simplify PI into PI 8.470 * [taylor]: Taking taylor expansion of n in k 8.470 * [backup-simplify]: Simplify n into n 8.470 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.470 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 8.470 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 8.471 * [backup-simplify]: Simplify (- 1) into -1 8.471 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.471 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 8.472 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 8.472 * [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))))) 8.472 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 8.472 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.472 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.472 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 8.472 * [taylor]: Taking taylor expansion of 0.5 in n 8.472 * [backup-simplify]: Simplify 0.5 into 0.5 8.472 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.472 * [taylor]: Taking taylor expansion of 1.0 in n 8.472 * [backup-simplify]: Simplify 1.0 into 1.0 8.472 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.472 * [taylor]: Taking taylor expansion of k in n 8.472 * [backup-simplify]: Simplify k into k 8.472 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.472 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.472 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.472 * [taylor]: Taking taylor expansion of 2.0 in n 8.472 * [backup-simplify]: Simplify 2.0 into 2.0 8.472 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.472 * [taylor]: Taking taylor expansion of PI in n 8.472 * [backup-simplify]: Simplify PI into PI 8.472 * [taylor]: Taking taylor expansion of n in n 8.472 * [backup-simplify]: Simplify 0 into 0 8.472 * [backup-simplify]: Simplify 1 into 1 8.473 * [backup-simplify]: Simplify (/ PI 1) into PI 8.473 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.475 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.475 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.475 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.475 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 8.476 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.477 * [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)))) 8.479 * [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))))) 8.479 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 8.479 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.479 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.479 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 8.479 * [taylor]: Taking taylor expansion of 0.5 in n 8.479 * [backup-simplify]: Simplify 0.5 into 0.5 8.479 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.479 * [taylor]: Taking taylor expansion of 1.0 in n 8.479 * [backup-simplify]: Simplify 1.0 into 1.0 8.479 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.479 * [taylor]: Taking taylor expansion of k in n 8.479 * [backup-simplify]: Simplify k into k 8.479 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.479 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.479 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.479 * [taylor]: Taking taylor expansion of 2.0 in n 8.479 * [backup-simplify]: Simplify 2.0 into 2.0 8.479 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.479 * [taylor]: Taking taylor expansion of PI in n 8.479 * [backup-simplify]: Simplify PI into PI 8.479 * [taylor]: Taking taylor expansion of n in n 8.479 * [backup-simplify]: Simplify 0 into 0 8.479 * [backup-simplify]: Simplify 1 into 1 8.480 * [backup-simplify]: Simplify (/ PI 1) into PI 8.480 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.481 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.482 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.482 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.482 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 8.483 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.484 * [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)))) 8.486 * [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))))) 8.486 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 8.486 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 8.486 * [taylor]: Taking taylor expansion of 0.5 in k 8.486 * [backup-simplify]: Simplify 0.5 into 0.5 8.486 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 8.486 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 8.486 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.486 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.486 * [taylor]: Taking taylor expansion of 2.0 in k 8.486 * [backup-simplify]: Simplify 2.0 into 2.0 8.486 * [taylor]: Taking taylor expansion of PI in k 8.486 * [backup-simplify]: Simplify PI into PI 8.487 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.488 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.488 * [taylor]: Taking taylor expansion of (log n) in k 8.488 * [taylor]: Taking taylor expansion of n in k 8.488 * [backup-simplify]: Simplify n into n 8.488 * [backup-simplify]: Simplify (log n) into (log n) 8.488 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.488 * [taylor]: Taking taylor expansion of 1.0 in k 8.488 * [backup-simplify]: Simplify 1.0 into 1.0 8.488 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.488 * [taylor]: Taking taylor expansion of k in k 8.488 * [backup-simplify]: Simplify 0 into 0 8.488 * [backup-simplify]: Simplify 1 into 1 8.488 * [backup-simplify]: Simplify (/ 1 1) into 1 8.488 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.489 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 8.490 * [backup-simplify]: Simplify (- 1) into -1 8.490 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.491 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 8.492 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 8.494 * [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))))) 8.495 * [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))))) 8.496 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.497 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.499 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.499 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.499 * [backup-simplify]: Simplify (- 0) into 0 8.500 * [backup-simplify]: Simplify (+ 0 0) into 0 8.500 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 8.502 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.503 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 8.505 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.505 * [taylor]: Taking taylor expansion of 0 in k 8.505 * [backup-simplify]: Simplify 0 into 0 8.505 * [backup-simplify]: Simplify 0 into 0 8.506 * [backup-simplify]: Simplify 0 into 0 8.507 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.508 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.511 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.512 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.512 * [backup-simplify]: Simplify (- 0) into 0 8.513 * [backup-simplify]: Simplify (+ 0 0) into 0 8.513 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 8.515 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.516 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 8.519 * [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 8.519 * [taylor]: Taking taylor expansion of 0 in k 8.519 * [backup-simplify]: Simplify 0 into 0 8.519 * [backup-simplify]: Simplify 0 into 0 8.519 * [backup-simplify]: Simplify 0 into 0 8.519 * [backup-simplify]: Simplify 0 into 0 8.520 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.521 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.524 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 8.524 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.524 * [backup-simplify]: Simplify (- 0) into 0 8.525 * [backup-simplify]: Simplify (+ 0 0) into 0 8.525 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 8.526 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.527 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 8.529 * [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 8.529 * [taylor]: Taking taylor expansion of 0 in k 8.529 * [backup-simplify]: Simplify 0 into 0 8.529 * [backup-simplify]: Simplify 0 into 0 8.535 * [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)))) 8.536 * [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))) 8.536 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 8.536 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 8.536 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 8.536 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 8.536 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 8.536 * [taylor]: Taking taylor expansion of 0.5 in k 8.536 * [backup-simplify]: Simplify 0.5 into 0.5 8.536 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.536 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.536 * [taylor]: Taking taylor expansion of k in k 8.536 * [backup-simplify]: Simplify 0 into 0 8.536 * [backup-simplify]: Simplify 1 into 1 8.536 * [backup-simplify]: Simplify (/ 1 1) into 1 8.536 * [taylor]: Taking taylor expansion of 1.0 in k 8.536 * [backup-simplify]: Simplify 1.0 into 1.0 8.536 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 8.536 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 8.536 * [taylor]: Taking taylor expansion of -2.0 in k 8.536 * [backup-simplify]: Simplify -2.0 into -2.0 8.536 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.536 * [taylor]: Taking taylor expansion of PI in k 8.536 * [backup-simplify]: Simplify PI into PI 8.536 * [taylor]: Taking taylor expansion of n in k 8.536 * [backup-simplify]: Simplify n into n 8.536 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.536 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 8.536 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 8.537 * [backup-simplify]: Simplify (+ 1 0) into 1 8.537 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 8.537 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 8.537 * [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)))))) 8.537 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 8.537 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.537 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.537 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 8.537 * [taylor]: Taking taylor expansion of 0.5 in n 8.537 * [backup-simplify]: Simplify 0.5 into 0.5 8.537 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.537 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.537 * [taylor]: Taking taylor expansion of k in n 8.537 * [backup-simplify]: Simplify k into k 8.537 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.537 * [taylor]: Taking taylor expansion of 1.0 in n 8.537 * [backup-simplify]: Simplify 1.0 into 1.0 8.537 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.538 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.538 * [taylor]: Taking taylor expansion of -2.0 in n 8.538 * [backup-simplify]: Simplify -2.0 into -2.0 8.538 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.538 * [taylor]: Taking taylor expansion of PI in n 8.538 * [backup-simplify]: Simplify PI into PI 8.538 * [taylor]: Taking taylor expansion of n in n 8.538 * [backup-simplify]: Simplify 0 into 0 8.538 * [backup-simplify]: Simplify 1 into 1 8.538 * [backup-simplify]: Simplify (/ PI 1) into PI 8.538 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.539 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.539 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.539 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 8.540 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.541 * [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)))) 8.541 * [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))))) 8.541 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 8.541 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.541 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.541 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 8.541 * [taylor]: Taking taylor expansion of 0.5 in n 8.541 * [backup-simplify]: Simplify 0.5 into 0.5 8.541 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.541 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.541 * [taylor]: Taking taylor expansion of k in n 8.542 * [backup-simplify]: Simplify k into k 8.542 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.542 * [taylor]: Taking taylor expansion of 1.0 in n 8.542 * [backup-simplify]: Simplify 1.0 into 1.0 8.542 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.542 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.542 * [taylor]: Taking taylor expansion of -2.0 in n 8.542 * [backup-simplify]: Simplify -2.0 into -2.0 8.542 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.542 * [taylor]: Taking taylor expansion of PI in n 8.542 * [backup-simplify]: Simplify PI into PI 8.542 * [taylor]: Taking taylor expansion of n in n 8.542 * [backup-simplify]: Simplify 0 into 0 8.542 * [backup-simplify]: Simplify 1 into 1 8.542 * [backup-simplify]: Simplify (/ PI 1) into PI 8.542 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.543 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.543 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.543 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 8.544 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.545 * [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)))) 8.545 * [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))))) 8.546 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 8.546 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 8.546 * [taylor]: Taking taylor expansion of 0.5 in k 8.546 * [backup-simplify]: Simplify 0.5 into 0.5 8.546 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 8.546 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.546 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.546 * [taylor]: Taking taylor expansion of k in k 8.546 * [backup-simplify]: Simplify 0 into 0 8.546 * [backup-simplify]: Simplify 1 into 1 8.546 * [backup-simplify]: Simplify (/ 1 1) into 1 8.546 * [taylor]: Taking taylor expansion of 1.0 in k 8.546 * [backup-simplify]: Simplify 1.0 into 1.0 8.546 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 8.546 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 8.546 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 8.546 * [taylor]: Taking taylor expansion of -2.0 in k 8.546 * [backup-simplify]: Simplify -2.0 into -2.0 8.546 * [taylor]: Taking taylor expansion of PI in k 8.546 * [backup-simplify]: Simplify PI into PI 8.546 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.547 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.547 * [taylor]: Taking taylor expansion of (log n) in k 8.547 * [taylor]: Taking taylor expansion of n in k 8.547 * [backup-simplify]: Simplify n into n 8.547 * [backup-simplify]: Simplify (log n) into (log n) 8.548 * [backup-simplify]: Simplify (+ 1 0) into 1 8.548 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.548 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 8.549 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 8.550 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 8.550 * [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))))) 8.551 * [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))))) 8.552 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.553 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 8.555 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 8.555 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.556 * [backup-simplify]: Simplify (+ 0 0) into 0 8.556 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 8.558 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.559 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 8.561 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.561 * [taylor]: Taking taylor expansion of 0 in k 8.561 * [backup-simplify]: Simplify 0 into 0 8.561 * [backup-simplify]: Simplify 0 into 0 8.561 * [backup-simplify]: Simplify 0 into 0 8.562 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.564 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.568 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 8.568 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.568 * [backup-simplify]: Simplify (+ 0 0) into 0 8.569 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 8.571 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.572 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 8.575 * [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 8.575 * [taylor]: Taking taylor expansion of 0 in k 8.575 * [backup-simplify]: Simplify 0 into 0 8.575 * [backup-simplify]: Simplify 0 into 0 8.575 * [backup-simplify]: Simplify 0 into 0 8.575 * [backup-simplify]: Simplify 0 into 0 8.576 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.577 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.583 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 8.583 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.584 * [backup-simplify]: Simplify (+ 0 0) into 0 8.584 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 8.585 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.587 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 8.588 * [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 8.588 * [taylor]: Taking taylor expansion of 0 in k 8.588 * [backup-simplify]: Simplify 0 into 0 8.588 * [backup-simplify]: Simplify 0 into 0 8.589 * [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)))))) 8.589 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 2 2) 8.590 * [backup-simplify]: Simplify (pow n (/ (- 1.0 k) 2.0)) into (pow n (* 0.5 (- 1.0 k))) 8.590 * [approximate]: Taking taylor expansion of (pow n (* 0.5 (- 1.0 k))) in (n k) around 0 8.590 * [taylor]: Taking taylor expansion of (pow n (* 0.5 (- 1.0 k))) in k 8.590 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log n))) in k 8.590 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log n)) in k 8.590 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 8.590 * [taylor]: Taking taylor expansion of 0.5 in k 8.590 * [backup-simplify]: Simplify 0.5 into 0.5 8.590 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.590 * [taylor]: Taking taylor expansion of 1.0 in k 8.590 * [backup-simplify]: Simplify 1.0 into 1.0 8.590 * [taylor]: Taking taylor expansion of k in k 8.590 * [backup-simplify]: Simplify 0 into 0 8.590 * [backup-simplify]: Simplify 1 into 1 8.590 * [taylor]: Taking taylor expansion of (log n) in k 8.590 * [taylor]: Taking taylor expansion of n in k 8.590 * [backup-simplify]: Simplify n into n 8.590 * [backup-simplify]: Simplify (log n) into (log n) 8.590 * [backup-simplify]: Simplify (- 0) into 0 8.590 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.591 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 8.591 * [backup-simplify]: Simplify (* 0.5 (log n)) into (* 0.5 (log n)) 8.591 * [backup-simplify]: Simplify (exp (* 0.5 (log n))) into (pow n 0.5) 8.591 * [taylor]: Taking taylor expansion of (pow n (* 0.5 (- 1.0 k))) in n 8.591 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log n))) in n 8.591 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log n)) in n 8.591 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 8.591 * [taylor]: Taking taylor expansion of 0.5 in n 8.591 * [backup-simplify]: Simplify 0.5 into 0.5 8.591 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.591 * [taylor]: Taking taylor expansion of 1.0 in n 8.591 * [backup-simplify]: Simplify 1.0 into 1.0 8.591 * [taylor]: Taking taylor expansion of k in n 8.591 * [backup-simplify]: Simplify k into k 8.591 * [taylor]: Taking taylor expansion of (log n) in n 8.591 * [taylor]: Taking taylor expansion of n in n 8.591 * [backup-simplify]: Simplify 0 into 0 8.591 * [backup-simplify]: Simplify 1 into 1 8.591 * [backup-simplify]: Simplify (log 1) into 0 8.591 * [backup-simplify]: Simplify (- k) into (- k) 8.591 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.591 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 8.592 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 8.592 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (log n)) into (* 0.5 (* (- 1.0 k) (log n))) 8.592 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (log n)))) into (exp (* 0.5 (* (- 1.0 k) (log n)))) 8.592 * [taylor]: Taking taylor expansion of (pow n (* 0.5 (- 1.0 k))) in n 8.592 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log n))) in n 8.592 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log n)) in n 8.592 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 8.592 * [taylor]: Taking taylor expansion of 0.5 in n 8.592 * [backup-simplify]: Simplify 0.5 into 0.5 8.592 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.592 * [taylor]: Taking taylor expansion of 1.0 in n 8.592 * [backup-simplify]: Simplify 1.0 into 1.0 8.592 * [taylor]: Taking taylor expansion of k in n 8.592 * [backup-simplify]: Simplify k into k 8.592 * [taylor]: Taking taylor expansion of (log n) in n 8.592 * [taylor]: Taking taylor expansion of n in n 8.592 * [backup-simplify]: Simplify 0 into 0 8.592 * [backup-simplify]: Simplify 1 into 1 8.592 * [backup-simplify]: Simplify (log 1) into 0 8.592 * [backup-simplify]: Simplify (- k) into (- k) 8.592 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.592 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 8.593 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 8.593 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (log n)) into (* 0.5 (* (- 1.0 k) (log n))) 8.593 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (log n)))) into (exp (* 0.5 (* (- 1.0 k) (log n)))) 8.593 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (log n)))) in k 8.593 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (log n))) in k 8.593 * [taylor]: Taking taylor expansion of 0.5 in k 8.593 * [backup-simplify]: Simplify 0.5 into 0.5 8.593 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (log n)) in k 8.593 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.593 * [taylor]: Taking taylor expansion of 1.0 in k 8.593 * [backup-simplify]: Simplify 1.0 into 1.0 8.593 * [taylor]: Taking taylor expansion of k in k 8.593 * [backup-simplify]: Simplify 0 into 0 8.593 * [backup-simplify]: Simplify 1 into 1 8.593 * [taylor]: Taking taylor expansion of (log n) in k 8.593 * [taylor]: Taking taylor expansion of n in k 8.593 * [backup-simplify]: Simplify n into n 8.593 * [backup-simplify]: Simplify (log n) into (log n) 8.593 * [backup-simplify]: Simplify (- 0) into 0 8.594 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.594 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 8.594 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (log n))) into (* 0.5 (log n)) 8.594 * [backup-simplify]: Simplify (exp (* 0.5 (log n))) into (pow n 0.5) 8.594 * [backup-simplify]: Simplify (pow n 0.5) into (pow n 0.5) 8.595 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 8.595 * [backup-simplify]: Simplify (- 0) into 0 8.595 * [backup-simplify]: Simplify (+ 0 0) into 0 8.596 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 8.596 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 8.596 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (log n))) into 0 8.596 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 8.596 * [taylor]: Taking taylor expansion of 0 in k 8.597 * [backup-simplify]: Simplify 0 into 0 8.597 * [backup-simplify]: Simplify 0 into 0 8.597 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 8.597 * [backup-simplify]: Simplify (- 1) into -1 8.598 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.598 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (log n))) into (- (log n)) 8.598 * [backup-simplify]: Simplify (+ (* 0.5 (- (log n))) (* 0 (* 1.0 (log n)))) into (- (* 0.5 (log n))) 8.598 * [backup-simplify]: Simplify (* (exp (* 0.5 (log n))) (+ (* (/ (pow (- (* 0.5 (log n))) 1) 1)))) into (* -0.5 (* (pow (pow n 1.0) 0.5) (log n))) 8.598 * [backup-simplify]: Simplify (* -0.5 (* (pow (pow n 1.0) 0.5) (log n))) into (* -0.5 (* (pow (pow n 1.0) 0.5) (log n))) 8.600 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 8.600 * [backup-simplify]: Simplify (- 0) into 0 8.600 * [backup-simplify]: Simplify (+ 0 0) into 0 8.601 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 8.601 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 8.601 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0 8.602 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.602 * [taylor]: Taking taylor expansion of 0 in k 8.602 * [backup-simplify]: Simplify 0 into 0 8.602 * [backup-simplify]: Simplify 0 into 0 8.602 * [backup-simplify]: Simplify 0 into 0 8.603 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 8.604 * [backup-simplify]: Simplify (- 0) into 0 8.604 * [backup-simplify]: Simplify (+ 0 0) into 0 8.604 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (log n)))) into 0 8.605 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (log n))) (* 0 (* 1.0 (log n))))) into 0 8.605 * [backup-simplify]: Simplify (* (exp (* 0.5 (log n))) (+ (* (/ (pow (- (* 0.5 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (pow n 1.0) 0.5) (pow (log n) 2))) 8.606 * [backup-simplify]: Simplify (* 0.125 (* (pow (pow n 1.0) 0.5) (pow (log n) 2))) into (* 0.125 (* (pow (pow n 1.0) 0.5) (pow (log n) 2))) 8.606 * [backup-simplify]: Simplify (+ (* (* 0.125 (* (pow (pow n 1.0) 0.5) (pow (log n) 2))) (pow (* k 1) 2)) (+ (* (* -0.5 (* (pow (pow n 1.0) 0.5) (log n))) (* k 1)) (pow n 0.5))) into (- (+ (* 0.125 (* (* (pow k 2) (pow (log n) 2)) (pow (pow n 1.0) 0.5))) (pow n 0.5)) (* 0.5 (* (* k (log n)) (pow (pow n 1.0) 0.5)))) 8.607 * [backup-simplify]: Simplify (pow (/ 1 n) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) 8.607 * [approximate]: Taking taylor expansion of (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 8.607 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) in k 8.607 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n)))) in k 8.607 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n))) in k 8.607 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 8.607 * [taylor]: Taking taylor expansion of 0.5 in k 8.607 * [backup-simplify]: Simplify 0.5 into 0.5 8.607 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.607 * [taylor]: Taking taylor expansion of 1.0 in k 8.607 * [backup-simplify]: Simplify 1.0 into 1.0 8.607 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.607 * [taylor]: Taking taylor expansion of k in k 8.607 * [backup-simplify]: Simplify 0 into 0 8.607 * [backup-simplify]: Simplify 1 into 1 8.607 * [backup-simplify]: Simplify (/ 1 1) into 1 8.607 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k 8.607 * [taylor]: Taking taylor expansion of (/ 1 n) in k 8.607 * [taylor]: Taking taylor expansion of n in k 8.607 * [backup-simplify]: Simplify n into n 8.607 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n) 8.607 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n)) 8.608 * [backup-simplify]: Simplify (- 1) into -1 8.608 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.608 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 8.608 * [backup-simplify]: Simplify (* -0.5 (log (/ 1 n))) into (* -0.5 (log (/ 1 n))) 8.608 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n)))) into (exp (* 0.5 (* (log (/ 1 n)) (- 1.0 (/ 1 k))))) 8.608 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) in n 8.608 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n)))) in n 8.608 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n))) in n 8.608 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 8.608 * [taylor]: Taking taylor expansion of 0.5 in n 8.608 * [backup-simplify]: Simplify 0.5 into 0.5 8.608 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.608 * [taylor]: Taking taylor expansion of 1.0 in n 8.608 * [backup-simplify]: Simplify 1.0 into 1.0 8.608 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.608 * [taylor]: Taking taylor expansion of k in n 8.608 * [backup-simplify]: Simplify k into k 8.608 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.609 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 8.609 * [taylor]: Taking taylor expansion of (/ 1 n) in n 8.609 * [taylor]: Taking taylor expansion of n in n 8.609 * [backup-simplify]: Simplify 0 into 0 8.609 * [backup-simplify]: Simplify 1 into 1 8.609 * [backup-simplify]: Simplify (/ 1 1) into 1 8.609 * [backup-simplify]: Simplify (log 1) into 0 8.609 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.609 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.609 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 8.610 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 8.610 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log n))) into (* -0.5 (* (log n) (- 1.0 (/ 1 k)))) 8.610 * [backup-simplify]: Simplify (exp (* -0.5 (* (log n) (- 1.0 (/ 1 k))))) into (exp (* -0.5 (* (log n) (- 1.0 (/ 1 k))))) 8.610 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) in n 8.610 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n)))) in n 8.610 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n))) in n 8.610 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 8.610 * [taylor]: Taking taylor expansion of 0.5 in n 8.610 * [backup-simplify]: Simplify 0.5 into 0.5 8.610 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.610 * [taylor]: Taking taylor expansion of 1.0 in n 8.610 * [backup-simplify]: Simplify 1.0 into 1.0 8.610 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.610 * [taylor]: Taking taylor expansion of k in n 8.610 * [backup-simplify]: Simplify k into k 8.610 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.610 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 8.610 * [taylor]: Taking taylor expansion of (/ 1 n) in n 8.610 * [taylor]: Taking taylor expansion of n in n 8.610 * [backup-simplify]: Simplify 0 into 0 8.610 * [backup-simplify]: Simplify 1 into 1 8.610 * [backup-simplify]: Simplify (/ 1 1) into 1 8.611 * [backup-simplify]: Simplify (log 1) into 0 8.611 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.611 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.611 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 8.611 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 8.611 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log n))) into (* -0.5 (* (log n) (- 1.0 (/ 1 k)))) 8.611 * [backup-simplify]: Simplify (exp (* -0.5 (* (log n) (- 1.0 (/ 1 k))))) into (exp (* -0.5 (* (log n) (- 1.0 (/ 1 k))))) 8.611 * [taylor]: Taking taylor expansion of (exp (* -0.5 (* (log n) (- 1.0 (/ 1 k))))) in k 8.611 * [taylor]: Taking taylor expansion of (* -0.5 (* (log n) (- 1.0 (/ 1 k)))) in k 8.611 * [taylor]: Taking taylor expansion of -0.5 in k 8.611 * [backup-simplify]: Simplify -0.5 into -0.5 8.611 * [taylor]: Taking taylor expansion of (* (log n) (- 1.0 (/ 1 k))) in k 8.611 * [taylor]: Taking taylor expansion of (log n) in k 8.611 * [taylor]: Taking taylor expansion of n in k 8.611 * [backup-simplify]: Simplify n into n 8.612 * [backup-simplify]: Simplify (log n) into (log n) 8.612 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.612 * [taylor]: Taking taylor expansion of 1.0 in k 8.612 * [backup-simplify]: Simplify 1.0 into 1.0 8.612 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.612 * [taylor]: Taking taylor expansion of k in k 8.612 * [backup-simplify]: Simplify 0 into 0 8.612 * [backup-simplify]: Simplify 1 into 1 8.612 * [backup-simplify]: Simplify (/ 1 1) into 1 8.612 * [backup-simplify]: Simplify (- 1) into -1 8.612 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.612 * [backup-simplify]: Simplify (* (log n) -1) into (* -1 (log n)) 8.612 * [backup-simplify]: Simplify (* -0.5 (* -1 (log n))) into (* 0.5 (log n)) 8.613 * [backup-simplify]: Simplify (exp (* -0.5 (* (log n) (- 1.0 (/ 1 k))))) into (exp (* -0.5 (* (log n) (- 1.0 (/ 1 k))))) 8.613 * [backup-simplify]: Simplify (exp (* -0.5 (* (log n) (- 1.0 (/ 1 k))))) into (exp (* -0.5 (* (log n) (- 1.0 (/ 1 k))))) 8.613 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 8.614 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 8.614 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.614 * [backup-simplify]: Simplify (- 0) into 0 8.615 * [backup-simplify]: Simplify (+ 0 0) into 0 8.615 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 8.615 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 8.615 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 8.616 * [backup-simplify]: Simplify (* (exp (* -0.5 (* (log n) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.616 * [taylor]: Taking taylor expansion of 0 in k 8.616 * [backup-simplify]: Simplify 0 into 0 8.616 * [backup-simplify]: Simplify 0 into 0 8.616 * [backup-simplify]: Simplify 0 into 0 8.616 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.618 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 8.618 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.618 * [backup-simplify]: Simplify (- 0) into 0 8.619 * [backup-simplify]: Simplify (+ 0 0) into 0 8.619 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 8.619 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 8.620 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 8.621 * [backup-simplify]: Simplify (* (exp (* -0.5 (* (log n) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.621 * [taylor]: Taking taylor expansion of 0 in k 8.621 * [backup-simplify]: Simplify 0 into 0 8.621 * [backup-simplify]: Simplify 0 into 0 8.621 * [backup-simplify]: Simplify 0 into 0 8.621 * [backup-simplify]: Simplify 0 into 0 8.621 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.624 * [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 8.624 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.625 * [backup-simplify]: Simplify (- 0) into 0 8.625 * [backup-simplify]: Simplify (+ 0 0) into 0 8.625 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 8.626 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 8.626 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 8.627 * [backup-simplify]: Simplify (* (exp (* -0.5 (* (log n) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 8.627 * [taylor]: Taking taylor expansion of 0 in k 8.627 * [backup-simplify]: Simplify 0 into 0 8.627 * [backup-simplify]: Simplify 0 into 0 8.628 * [backup-simplify]: Simplify (exp (* -0.5 (* (log (/ 1 n)) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* -0.5 (* (- 1.0 k) (log (/ 1 n))))) 8.628 * [backup-simplify]: Simplify (pow (/ 1 (- n)) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) 8.628 * [approximate]: Taking taylor expansion of (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 8.628 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) in k 8.628 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) in k 8.628 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n))) in k 8.628 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 8.628 * [taylor]: Taking taylor expansion of 0.5 in k 8.628 * [backup-simplify]: Simplify 0.5 into 0.5 8.628 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.628 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.628 * [taylor]: Taking taylor expansion of k in k 8.628 * [backup-simplify]: Simplify 0 into 0 8.628 * [backup-simplify]: Simplify 1 into 1 8.628 * [backup-simplify]: Simplify (/ 1 1) into 1 8.628 * [taylor]: Taking taylor expansion of 1.0 in k 8.629 * [backup-simplify]: Simplify 1.0 into 1.0 8.629 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k 8.629 * [taylor]: Taking taylor expansion of (/ -1 n) in k 8.629 * [taylor]: Taking taylor expansion of -1 in k 8.629 * [backup-simplify]: Simplify -1 into -1 8.629 * [taylor]: Taking taylor expansion of n in k 8.629 * [backup-simplify]: Simplify n into n 8.629 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n) 8.629 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n)) 8.629 * [backup-simplify]: Simplify (+ 1 0) into 1 8.629 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 8.629 * [backup-simplify]: Simplify (* 0.5 (log (/ -1 n))) into (* 0.5 (log (/ -1 n))) 8.629 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (/ -1 n))))) 8.629 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) in n 8.629 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) in n 8.630 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n))) in n 8.630 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 8.630 * [taylor]: Taking taylor expansion of 0.5 in n 8.630 * [backup-simplify]: Simplify 0.5 into 0.5 8.630 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.630 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.630 * [taylor]: Taking taylor expansion of k in n 8.630 * [backup-simplify]: Simplify k into k 8.630 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.630 * [taylor]: Taking taylor expansion of 1.0 in n 8.630 * [backup-simplify]: Simplify 1.0 into 1.0 8.630 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 8.630 * [taylor]: Taking taylor expansion of (/ -1 n) in n 8.630 * [taylor]: Taking taylor expansion of -1 in n 8.630 * [backup-simplify]: Simplify -1 into -1 8.630 * [taylor]: Taking taylor expansion of n in n 8.630 * [backup-simplify]: Simplify 0 into 0 8.630 * [backup-simplify]: Simplify 1 into 1 8.630 * [backup-simplify]: Simplify (/ -1 1) into -1 8.630 * [backup-simplify]: Simplify (log -1) into (log -1) 8.630 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.630 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 8.631 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 8.631 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log -1) (log n))) into (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0))) 8.632 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 8.632 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) in n 8.632 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) in n 8.632 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n))) in n 8.632 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 8.632 * [taylor]: Taking taylor expansion of 0.5 in n 8.632 * [backup-simplify]: Simplify 0.5 into 0.5 8.632 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.632 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.632 * [taylor]: Taking taylor expansion of k in n 8.632 * [backup-simplify]: Simplify k into k 8.632 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.632 * [taylor]: Taking taylor expansion of 1.0 in n 8.632 * [backup-simplify]: Simplify 1.0 into 1.0 8.632 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 8.632 * [taylor]: Taking taylor expansion of (/ -1 n) in n 8.632 * [taylor]: Taking taylor expansion of -1 in n 8.632 * [backup-simplify]: Simplify -1 into -1 8.632 * [taylor]: Taking taylor expansion of n in n 8.632 * [backup-simplify]: Simplify 0 into 0 8.632 * [backup-simplify]: Simplify 1 into 1 8.632 * [backup-simplify]: Simplify (/ -1 1) into -1 8.633 * [backup-simplify]: Simplify (log -1) into (log -1) 8.633 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.633 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 8.633 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 8.634 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log -1) (log n))) into (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0))) 8.634 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 8.634 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) in k 8.634 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0))) in k 8.634 * [taylor]: Taking taylor expansion of 0.5 in k 8.634 * [backup-simplify]: Simplify 0.5 into 0.5 8.634 * [taylor]: Taking taylor expansion of (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)) in k 8.634 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k 8.634 * [taylor]: Taking taylor expansion of (log -1) in k 8.634 * [taylor]: Taking taylor expansion of -1 in k 8.634 * [backup-simplify]: Simplify -1 into -1 8.634 * [backup-simplify]: Simplify (log -1) into (log -1) 8.635 * [taylor]: Taking taylor expansion of (log n) in k 8.635 * [taylor]: Taking taylor expansion of n in k 8.635 * [backup-simplify]: Simplify n into n 8.635 * [backup-simplify]: Simplify (log n) into (log n) 8.635 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.635 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.635 * [taylor]: Taking taylor expansion of k in k 8.635 * [backup-simplify]: Simplify 0 into 0 8.635 * [backup-simplify]: Simplify 1 into 1 8.635 * [backup-simplify]: Simplify (/ 1 1) into 1 8.635 * [taylor]: Taking taylor expansion of 1.0 in k 8.635 * [backup-simplify]: Simplify 1.0 into 1.0 8.635 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.635 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n)) 8.636 * [backup-simplify]: Simplify (+ 1 0) into 1 8.636 * [backup-simplify]: Simplify (* (- (log -1) (log n)) 1) into (- (log -1) (log n)) 8.636 * [backup-simplify]: Simplify (* 0.5 (- (log -1) (log n))) into (* 0.5 (- (log -1) (log n))) 8.636 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 8.637 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 8.637 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 8.638 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 8.638 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.639 * [backup-simplify]: Simplify (+ 0 0) into 0 8.639 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 8.639 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 8.645 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log -1) (log n)))) into 0 8.648 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 8.648 * [taylor]: Taking taylor expansion of 0 in k 8.648 * [backup-simplify]: Simplify 0 into 0 8.648 * [backup-simplify]: Simplify 0 into 0 8.648 * [backup-simplify]: Simplify 0 into 0 8.649 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.652 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0 8.652 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.653 * [backup-simplify]: Simplify (+ 0 0) into 0 8.653 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 8.654 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 8.655 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0 8.657 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.657 * [taylor]: Taking taylor expansion of 0 in k 8.657 * [backup-simplify]: Simplify 0 into 0 8.657 * [backup-simplify]: Simplify 0 into 0 8.657 * [backup-simplify]: Simplify 0 into 0 8.657 * [backup-simplify]: Simplify 0 into 0 8.658 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.664 * [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 8.664 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.665 * [backup-simplify]: Simplify (+ 0 0) into 0 8.666 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 8.667 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 8.668 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -1) (log n)))))) into 0 8.670 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 8.671 * [taylor]: Taking taylor expansion of 0 in k 8.671 * [backup-simplify]: Simplify 0 into 0 8.671 * [backup-simplify]: Simplify 0 into 0 8.671 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (- (log -1) (log (/ -1 n)))))) 8.672 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1 2 1) 8.672 * [backup-simplify]: Simplify (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) 8.672 * [approximate]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in (k) around 0 8.672 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in k 8.672 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI)))) in k 8.672 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI))) in k 8.672 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 8.672 * [taylor]: Taking taylor expansion of 0.5 in k 8.672 * [backup-simplify]: Simplify 0.5 into 0.5 8.673 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.673 * [taylor]: Taking taylor expansion of 1.0 in k 8.673 * [backup-simplify]: Simplify 1.0 into 1.0 8.673 * [taylor]: Taking taylor expansion of k in k 8.673 * [backup-simplify]: Simplify 0 into 0 8.673 * [backup-simplify]: Simplify 1 into 1 8.673 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.673 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.673 * [taylor]: Taking taylor expansion of 2.0 in k 8.673 * [backup-simplify]: Simplify 2.0 into 2.0 8.673 * [taylor]: Taking taylor expansion of PI in k 8.673 * [backup-simplify]: Simplify PI into PI 8.673 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.674 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.675 * [backup-simplify]: Simplify (- 0) into 0 8.675 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.676 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 8.677 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 8.680 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 PI)))) into (pow (* 2.0 PI) 0.5) 8.680 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in k 8.680 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI)))) in k 8.680 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI))) in k 8.680 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 8.680 * [taylor]: Taking taylor expansion of 0.5 in k 8.680 * [backup-simplify]: Simplify 0.5 into 0.5 8.680 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.681 * [taylor]: Taking taylor expansion of 1.0 in k 8.681 * [backup-simplify]: Simplify 1.0 into 1.0 8.681 * [taylor]: Taking taylor expansion of k in k 8.681 * [backup-simplify]: Simplify 0 into 0 8.681 * [backup-simplify]: Simplify 1 into 1 8.681 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.681 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.681 * [taylor]: Taking taylor expansion of 2.0 in k 8.681 * [backup-simplify]: Simplify 2.0 into 2.0 8.681 * [taylor]: Taking taylor expansion of PI in k 8.681 * [backup-simplify]: Simplify PI into PI 8.681 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.682 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.683 * [backup-simplify]: Simplify (- 0) into 0 8.683 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.683 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 8.685 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 8.688 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 PI)))) into (pow (* 2.0 PI) 0.5) 8.689 * [backup-simplify]: Simplify (pow (* 2.0 PI) 0.5) into (pow (* 2.0 PI) 0.5) 8.690 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.692 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.692 * [backup-simplify]: Simplify (- 1) into -1 8.692 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.694 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 8.698 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 PI)))) into (- (* 0.5 (log (* 2.0 PI)))) 8.710 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 PI)))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 1) 1)))) into (* -0.5 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) 8.717 * [backup-simplify]: Simplify (* -0.5 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) into (* -0.5 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))) 8.718 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.722 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.722 * [backup-simplify]: Simplify (- 0) into 0 8.723 * [backup-simplify]: Simplify (+ 0 0) into 0 8.724 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 8.725 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 PI))))) into 0 8.741 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 PI)))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) 8.749 * [backup-simplify]: Simplify (* 0.125 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) into (* 0.125 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))) 8.767 * [backup-simplify]: Simplify (+ (* (* 0.125 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))) (pow k 2)) (+ (* (* -0.5 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))) k) (pow (* 2.0 PI) 0.5))) into (- (+ (* 0.125 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))) (pow (* 2.0 PI) 0.5)) (* 0.5 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)))) 8.768 * [backup-simplify]: Simplify (pow (* 2.0 PI) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) 8.768 * [approximate]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in (k) around 0 8.768 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in k 8.768 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) in k 8.768 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI))) in k 8.768 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 8.768 * [taylor]: Taking taylor expansion of 0.5 in k 8.768 * [backup-simplify]: Simplify 0.5 into 0.5 8.768 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.768 * [taylor]: Taking taylor expansion of 1.0 in k 8.768 * [backup-simplify]: Simplify 1.0 into 1.0 8.768 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.768 * [taylor]: Taking taylor expansion of k in k 8.768 * [backup-simplify]: Simplify 0 into 0 8.768 * [backup-simplify]: Simplify 1 into 1 8.769 * [backup-simplify]: Simplify (/ 1 1) into 1 8.769 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.769 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.769 * [taylor]: Taking taylor expansion of 2.0 in k 8.769 * [backup-simplify]: Simplify 2.0 into 2.0 8.769 * [taylor]: Taking taylor expansion of PI in k 8.769 * [backup-simplify]: Simplify PI into PI 8.769 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.770 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.771 * [backup-simplify]: Simplify (- 1) into -1 8.771 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.771 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 8.773 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 PI))) into (* -0.5 (log (* 2.0 PI))) 8.774 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k))))) 8.774 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in k 8.774 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) in k 8.774 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI))) in k 8.774 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 8.775 * [taylor]: Taking taylor expansion of 0.5 in k 8.775 * [backup-simplify]: Simplify 0.5 into 0.5 8.775 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.775 * [taylor]: Taking taylor expansion of 1.0 in k 8.775 * [backup-simplify]: Simplify 1.0 into 1.0 8.775 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.775 * [taylor]: Taking taylor expansion of k in k 8.775 * [backup-simplify]: Simplify 0 into 0 8.775 * [backup-simplify]: Simplify 1 into 1 8.775 * [backup-simplify]: Simplify (/ 1 1) into 1 8.775 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.775 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.775 * [taylor]: Taking taylor expansion of 2.0 in k 8.775 * [backup-simplify]: Simplify 2.0 into 2.0 8.775 * [taylor]: Taking taylor expansion of PI in k 8.775 * [backup-simplify]: Simplify PI into PI 8.776 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.777 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.777 * [backup-simplify]: Simplify (- 1) into -1 8.778 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.778 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 8.780 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 PI))) into (* -0.5 (log (* 2.0 PI))) 8.781 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k))))) 8.783 * [backup-simplify]: Simplify (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 k))))) 8.783 * [backup-simplify]: Simplify 0 into 0 8.783 * [backup-simplify]: Simplify 0 into 0 8.783 * [backup-simplify]: Simplify 0 into 0 8.783 * [backup-simplify]: Simplify 0 into 0 8.783 * [backup-simplify]: Simplify 0 into 0 8.783 * [backup-simplify]: Simplify 0 into 0 8.784 * [backup-simplify]: Simplify (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- 1.0 k) (log (* 2.0 PI))))) 8.785 * [backup-simplify]: Simplify (pow (* 2.0 PI) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) 8.785 * [approximate]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in (k) around 0 8.785 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in k 8.785 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) in k 8.785 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI))) in k 8.785 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 8.785 * [taylor]: Taking taylor expansion of 0.5 in k 8.785 * [backup-simplify]: Simplify 0.5 into 0.5 8.785 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.785 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.785 * [taylor]: Taking taylor expansion of k in k 8.785 * [backup-simplify]: Simplify 0 into 0 8.785 * [backup-simplify]: Simplify 1 into 1 8.786 * [backup-simplify]: Simplify (/ 1 1) into 1 8.786 * [taylor]: Taking taylor expansion of 1.0 in k 8.786 * [backup-simplify]: Simplify 1.0 into 1.0 8.786 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.786 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.786 * [taylor]: Taking taylor expansion of 2.0 in k 8.786 * [backup-simplify]: Simplify 2.0 into 2.0 8.786 * [taylor]: Taking taylor expansion of PI in k 8.786 * [backup-simplify]: Simplify PI into PI 8.786 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.787 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.788 * [backup-simplify]: Simplify (+ 1 0) into 1 8.788 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 8.790 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 8.791 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 8.791 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in k 8.791 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) in k 8.792 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI))) in k 8.792 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 8.792 * [taylor]: Taking taylor expansion of 0.5 in k 8.792 * [backup-simplify]: Simplify 0.5 into 0.5 8.792 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.792 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.792 * [taylor]: Taking taylor expansion of k in k 8.792 * [backup-simplify]: Simplify 0 into 0 8.792 * [backup-simplify]: Simplify 1 into 1 8.792 * [backup-simplify]: Simplify (/ 1 1) into 1 8.792 * [taylor]: Taking taylor expansion of 1.0 in k 8.792 * [backup-simplify]: Simplify 1.0 into 1.0 8.792 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.792 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.792 * [taylor]: Taking taylor expansion of 2.0 in k 8.792 * [backup-simplify]: Simplify 2.0 into 2.0 8.792 * [taylor]: Taking taylor expansion of PI in k 8.792 * [backup-simplify]: Simplify PI into PI 8.793 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.794 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.794 * [backup-simplify]: Simplify (+ 1 0) into 1 8.795 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 8.805 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 8.806 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 8.807 * [backup-simplify]: Simplify (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 8.807 * [backup-simplify]: Simplify 0 into 0 8.808 * [backup-simplify]: Simplify 0 into 0 8.808 * [backup-simplify]: Simplify 0 into 0 8.808 * [backup-simplify]: Simplify 0 into 0 8.808 * [backup-simplify]: Simplify 0 into 0 8.808 * [backup-simplify]: Simplify 0 into 0 8.809 * [backup-simplify]: Simplify (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (log (* 2.0 PI))))) 8.809 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 2 1) 8.810 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 8.810 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 8.810 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.810 * [taylor]: Taking taylor expansion of 2.0 in n 8.810 * [backup-simplify]: Simplify 2.0 into 2.0 8.810 * [taylor]: Taking taylor expansion of (* n PI) in n 8.810 * [taylor]: Taking taylor expansion of n in n 8.810 * [backup-simplify]: Simplify 0 into 0 8.810 * [backup-simplify]: Simplify 1 into 1 8.810 * [taylor]: Taking taylor expansion of PI in n 8.810 * [backup-simplify]: Simplify PI into PI 8.810 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.810 * [taylor]: Taking taylor expansion of 2.0 in n 8.810 * [backup-simplify]: Simplify 2.0 into 2.0 8.810 * [taylor]: Taking taylor expansion of (* n PI) in n 8.810 * [taylor]: Taking taylor expansion of n in n 8.810 * [backup-simplify]: Simplify 0 into 0 8.810 * [backup-simplify]: Simplify 1 into 1 8.810 * [taylor]: Taking taylor expansion of PI in n 8.810 * [backup-simplify]: Simplify PI into PI 8.811 * [backup-simplify]: Simplify (* 0 PI) into 0 8.811 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.811 * [backup-simplify]: Simplify 0 into 0 8.813 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.814 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.815 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.816 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.817 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 8.817 * [backup-simplify]: Simplify 0 into 0 8.818 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 8.819 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 8.819 * [backup-simplify]: Simplify 0 into 0 8.821 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.822 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 8.822 * [backup-simplify]: Simplify 0 into 0 8.824 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.825 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 8.825 * [backup-simplify]: Simplify 0 into 0 8.827 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.829 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 8.829 * [backup-simplify]: Simplify 0 into 0 8.831 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 8.833 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 8.833 * [backup-simplify]: Simplify 0 into 0 8.833 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 8.834 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 8.834 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 8.834 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.834 * [taylor]: Taking taylor expansion of 2.0 in n 8.834 * [backup-simplify]: Simplify 2.0 into 2.0 8.834 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.834 * [taylor]: Taking taylor expansion of PI in n 8.834 * [backup-simplify]: Simplify PI into PI 8.834 * [taylor]: Taking taylor expansion of n in n 8.834 * [backup-simplify]: Simplify 0 into 0 8.834 * [backup-simplify]: Simplify 1 into 1 8.835 * [backup-simplify]: Simplify (/ PI 1) into PI 8.835 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.835 * [taylor]: Taking taylor expansion of 2.0 in n 8.835 * [backup-simplify]: Simplify 2.0 into 2.0 8.835 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.835 * [taylor]: Taking taylor expansion of PI in n 8.835 * [backup-simplify]: Simplify PI into PI 8.835 * [taylor]: Taking taylor expansion of n in n 8.835 * [backup-simplify]: Simplify 0 into 0 8.835 * [backup-simplify]: Simplify 1 into 1 8.836 * [backup-simplify]: Simplify (/ PI 1) into PI 8.836 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.837 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.837 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.838 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.838 * [backup-simplify]: Simplify 0 into 0 8.840 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.841 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.841 * [backup-simplify]: Simplify 0 into 0 8.842 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.843 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.843 * [backup-simplify]: Simplify 0 into 0 8.844 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.845 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.846 * [backup-simplify]: Simplify 0 into 0 8.847 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.848 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.848 * [backup-simplify]: Simplify 0 into 0 8.849 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.851 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.851 * [backup-simplify]: Simplify 0 into 0 8.852 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 8.852 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 8.852 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 8.852 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.852 * [taylor]: Taking taylor expansion of -2.0 in n 8.852 * [backup-simplify]: Simplify -2.0 into -2.0 8.853 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.853 * [taylor]: Taking taylor expansion of PI in n 8.853 * [backup-simplify]: Simplify PI into PI 8.853 * [taylor]: Taking taylor expansion of n in n 8.853 * [backup-simplify]: Simplify 0 into 0 8.853 * [backup-simplify]: Simplify 1 into 1 8.853 * [backup-simplify]: Simplify (/ PI 1) into PI 8.853 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.853 * [taylor]: Taking taylor expansion of -2.0 in n 8.853 * [backup-simplify]: Simplify -2.0 into -2.0 8.853 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.853 * [taylor]: Taking taylor expansion of PI in n 8.853 * [backup-simplify]: Simplify PI into PI 8.853 * [taylor]: Taking taylor expansion of n in n 8.853 * [backup-simplify]: Simplify 0 into 0 8.853 * [backup-simplify]: Simplify 1 into 1 8.854 * [backup-simplify]: Simplify (/ PI 1) into PI 8.854 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.855 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.856 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.857 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 8.857 * [backup-simplify]: Simplify 0 into 0 8.858 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.859 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.859 * [backup-simplify]: Simplify 0 into 0 8.860 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.861 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.861 * [backup-simplify]: Simplify 0 into 0 8.862 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.863 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.864 * [backup-simplify]: Simplify 0 into 0 8.865 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.866 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.866 * [backup-simplify]: Simplify 0 into 0 8.867 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.869 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.869 * [backup-simplify]: Simplify 0 into 0 8.870 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 8.870 * * * [progress]: simplifying candidates 8.873 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (log n) (/ (- 1.0 k) 2.0)) (* (log n) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow n (/ 1.0 2.0)) (pow n (/ k 2.0)) (pow n (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow n (sqrt (/ (- 1.0 k) 2.0))) (pow n (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow n (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow n (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow n (/ (sqrt (- 1.0 k)) 1)) (pow n (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ 1 (sqrt 2.0))) (pow n (/ 1 1)) (pow n (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow n (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow n (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ 1 (sqrt 2.0))) (pow n (/ 1 1)) (pow n 1) (pow n (- 1.0 k)) (pow (* (cbrt n) (cbrt n)) (/ (- 1.0 k) 2.0)) (pow (cbrt n) (/ (- 1.0 k) 2.0)) (pow (sqrt n) (/ (- 1.0 k) 2.0)) (pow (sqrt n) (/ (- 1.0 k) 2.0)) (pow 1 (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow n (/ (- 1.0 k) 2.0))) (exp (pow n (/ (- 1.0 k) 2.0))) (* (cbrt (pow n (/ (- 1.0 k) 2.0))) (cbrt (pow n (/ (- 1.0 k) 2.0)))) (cbrt (pow n (/ (- 1.0 k) 2.0))) (* (* (pow n (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0))) (sqrt (pow n (/ (- 1.0 k) 2.0))) (sqrt (pow n (/ (- 1.0 k) 2.0))) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log 2.0) (log PI)) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 PI)) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 PI)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ 1.0 2.0)) (pow (* 2.0 PI) (/ k 2.0)) (pow (* 2.0 PI) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* 2.0 PI) (sqrt (/ (- 1.0 k) 2.0))) (pow (* 2.0 PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* 2.0 PI) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 PI) (/ (sqrt (- 1.0 k)) 1)) (pow (* 2.0 PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ 1 (sqrt 2.0))) (pow (* 2.0 PI) (/ 1 1)) (pow (* 2.0 PI) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 PI) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* 2.0 PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ 1 (sqrt 2.0))) (pow (* 2.0 PI) (/ 1 1)) (pow (* 2.0 PI) 1) (pow (* 2.0 PI) (- 1.0 k)) (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)) (log (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (exp (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (* (* 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)))))) (- (+ (* 0.125 (* (* (pow k 2) (pow (log n) 2)) (pow (pow n 1.0) 0.5))) (pow n 0.5)) (* 0.5 (* (* k (log n)) (pow (pow n 1.0) 0.5)))) (exp (* -0.5 (* (- 1.0 k) (log (/ 1 n))))) (exp (* 0.5 (* (- 1.0 k) (- (log -1) (log (/ -1 n)))))) (- (+ (* 0.125 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))) (pow (* 2.0 PI) 0.5)) (* 0.5 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)))) (exp (* 0.5 (* (- 1.0 k) (log (* 2.0 PI))))) (exp (* 0.5 (* (- 1.0 k) (log (* 2.0 PI))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 10.190 * * * [progress]: adding candidates to table 11.107 * * [progress]: iteration 4 / 4 11.107 * * * [progress]: picking best candidate 11.163 * * * * [pick]: Picked # 11.163 * * * [progress]: localizing error 11.187 * * * [progress]: generating rewritten candidates 11.187 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 11.226 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 11.287 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 11.323 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 2 1) 11.371 * * * [progress]: generating series expansions 11.371 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 11.372 * [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))) 11.372 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 11.372 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 11.372 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 11.372 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 11.372 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 11.372 * [taylor]: Taking taylor expansion of 0.25 in k 11.372 * [backup-simplify]: Simplify 0.25 into 0.25 11.372 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 11.372 * [taylor]: Taking taylor expansion of 1.0 in k 11.372 * [backup-simplify]: Simplify 1.0 into 1.0 11.372 * [taylor]: Taking taylor expansion of k in k 11.372 * [backup-simplify]: Simplify 0 into 0 11.372 * [backup-simplify]: Simplify 1 into 1 11.372 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 11.372 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 11.372 * [taylor]: Taking taylor expansion of 2.0 in k 11.372 * [backup-simplify]: Simplify 2.0 into 2.0 11.372 * [taylor]: Taking taylor expansion of (* n PI) in k 11.372 * [taylor]: Taking taylor expansion of n in k 11.372 * [backup-simplify]: Simplify n into n 11.372 * [taylor]: Taking taylor expansion of PI in k 11.372 * [backup-simplify]: Simplify PI into PI 11.372 * [backup-simplify]: Simplify (* n PI) into (* n PI) 11.372 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 11.373 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 11.373 * [backup-simplify]: Simplify (- 0) into 0 11.378 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 11.378 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 11.378 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 11.379 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 11.379 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 11.379 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 11.379 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 11.379 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 11.379 * [taylor]: Taking taylor expansion of 0.25 in n 11.379 * [backup-simplify]: Simplify 0.25 into 0.25 11.379 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 11.379 * [taylor]: Taking taylor expansion of 1.0 in n 11.379 * [backup-simplify]: Simplify 1.0 into 1.0 11.379 * [taylor]: Taking taylor expansion of k in n 11.379 * [backup-simplify]: Simplify k into k 11.379 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 11.379 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 11.379 * [taylor]: Taking taylor expansion of 2.0 in n 11.379 * [backup-simplify]: Simplify 2.0 into 2.0 11.379 * [taylor]: Taking taylor expansion of (* n PI) in n 11.379 * [taylor]: Taking taylor expansion of n in n 11.379 * [backup-simplify]: Simplify 0 into 0 11.379 * [backup-simplify]: Simplify 1 into 1 11.379 * [taylor]: Taking taylor expansion of PI in n 11.379 * [backup-simplify]: Simplify PI into PI 11.379 * [backup-simplify]: Simplify (* 0 PI) into 0 11.379 * [backup-simplify]: Simplify (* 2.0 0) into 0 11.381 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.382 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 11.382 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.382 * [backup-simplify]: Simplify (- k) into (- k) 11.382 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 11.382 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 11.383 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.384 * [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)))) 11.385 * [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))))) 11.385 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 11.385 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 11.385 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 11.385 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 11.385 * [taylor]: Taking taylor expansion of 0.25 in n 11.385 * [backup-simplify]: Simplify 0.25 into 0.25 11.385 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 11.385 * [taylor]: Taking taylor expansion of 1.0 in n 11.385 * [backup-simplify]: Simplify 1.0 into 1.0 11.385 * [taylor]: Taking taylor expansion of k in n 11.385 * [backup-simplify]: Simplify k into k 11.385 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 11.385 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 11.385 * [taylor]: Taking taylor expansion of 2.0 in n 11.385 * [backup-simplify]: Simplify 2.0 into 2.0 11.385 * [taylor]: Taking taylor expansion of (* n PI) in n 11.385 * [taylor]: Taking taylor expansion of n in n 11.385 * [backup-simplify]: Simplify 0 into 0 11.385 * [backup-simplify]: Simplify 1 into 1 11.385 * [taylor]: Taking taylor expansion of PI in n 11.385 * [backup-simplify]: Simplify PI into PI 11.385 * [backup-simplify]: Simplify (* 0 PI) into 0 11.385 * [backup-simplify]: Simplify (* 2.0 0) into 0 11.386 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.387 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 11.388 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.388 * [backup-simplify]: Simplify (- k) into (- k) 11.388 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 11.388 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 11.389 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.389 * [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)))) 11.390 * [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))))) 11.390 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 11.390 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 11.390 * [taylor]: Taking taylor expansion of 0.25 in k 11.390 * [backup-simplify]: Simplify 0.25 into 0.25 11.390 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 11.390 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 11.390 * [taylor]: Taking taylor expansion of 1.0 in k 11.390 * [backup-simplify]: Simplify 1.0 into 1.0 11.391 * [taylor]: Taking taylor expansion of k in k 11.391 * [backup-simplify]: Simplify 0 into 0 11.391 * [backup-simplify]: Simplify 1 into 1 11.391 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 11.391 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 11.391 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 11.391 * [taylor]: Taking taylor expansion of 2.0 in k 11.391 * [backup-simplify]: Simplify 2.0 into 2.0 11.391 * [taylor]: Taking taylor expansion of PI in k 11.391 * [backup-simplify]: Simplify PI into PI 11.391 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.392 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.392 * [taylor]: Taking taylor expansion of (log n) in k 11.392 * [taylor]: Taking taylor expansion of n in k 11.392 * [backup-simplify]: Simplify n into n 11.392 * [backup-simplify]: Simplify (log n) into (log n) 11.392 * [backup-simplify]: Simplify (- 0) into 0 11.392 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 11.393 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 11.393 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 11.394 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 11.395 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 11.396 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 11.396 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.397 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 11.398 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 11.398 * [backup-simplify]: Simplify (- 0) into 0 11.398 * [backup-simplify]: Simplify (+ 0 0) into 0 11.399 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 11.400 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.401 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 11.403 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.403 * [taylor]: Taking taylor expansion of 0 in k 11.403 * [backup-simplify]: Simplify 0 into 0 11.403 * [backup-simplify]: Simplify 0 into 0 11.404 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 11.406 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 11.407 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 11.407 * [backup-simplify]: Simplify (+ 0 0) into 0 11.408 * [backup-simplify]: Simplify (- 1) into -1 11.408 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.409 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 11.412 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 11.415 * [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)))))) 11.418 * [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)))))) 11.419 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 11.420 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 11.424 * [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 11.424 * [backup-simplify]: Simplify (- 0) into 0 11.424 * [backup-simplify]: Simplify (+ 0 0) into 0 11.425 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 11.427 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.428 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 11.431 * [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 11.431 * [taylor]: Taking taylor expansion of 0 in k 11.431 * [backup-simplify]: Simplify 0 into 0 11.431 * [backup-simplify]: Simplify 0 into 0 11.431 * [backup-simplify]: Simplify 0 into 0 11.432 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.436 * [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 11.438 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 11.438 * [backup-simplify]: Simplify (+ 0 0) into 0 11.438 * [backup-simplify]: Simplify (- 0) into 0 11.439 * [backup-simplify]: Simplify (+ 0 0) into 0 11.440 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 11.443 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 11.447 * [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))))) 11.453 * [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))))) 11.460 * [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)))))) 11.461 * [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)))) 11.461 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 11.461 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 11.461 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 11.461 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 11.461 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 11.461 * [taylor]: Taking taylor expansion of 0.25 in k 11.461 * [backup-simplify]: Simplify 0.25 into 0.25 11.461 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 11.461 * [taylor]: Taking taylor expansion of 1.0 in k 11.461 * [backup-simplify]: Simplify 1.0 into 1.0 11.461 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.461 * [taylor]: Taking taylor expansion of k in k 11.461 * [backup-simplify]: Simplify 0 into 0 11.461 * [backup-simplify]: Simplify 1 into 1 11.461 * [backup-simplify]: Simplify (/ 1 1) into 1 11.461 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 11.461 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 11.461 * [taylor]: Taking taylor expansion of 2.0 in k 11.461 * [backup-simplify]: Simplify 2.0 into 2.0 11.461 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.461 * [taylor]: Taking taylor expansion of PI in k 11.461 * [backup-simplify]: Simplify PI into PI 11.461 * [taylor]: Taking taylor expansion of n in k 11.461 * [backup-simplify]: Simplify n into n 11.461 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.461 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 11.461 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 11.462 * [backup-simplify]: Simplify (- 1) into -1 11.462 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.462 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 11.462 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 11.462 * [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))))) 11.463 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 11.463 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 11.463 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 11.463 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 11.463 * [taylor]: Taking taylor expansion of 0.25 in n 11.463 * [backup-simplify]: Simplify 0.25 into 0.25 11.463 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 11.463 * [taylor]: Taking taylor expansion of 1.0 in n 11.463 * [backup-simplify]: Simplify 1.0 into 1.0 11.463 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.463 * [taylor]: Taking taylor expansion of k in n 11.463 * [backup-simplify]: Simplify k into k 11.463 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.463 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 11.463 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 11.463 * [taylor]: Taking taylor expansion of 2.0 in n 11.463 * [backup-simplify]: Simplify 2.0 into 2.0 11.463 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.463 * [taylor]: Taking taylor expansion of PI in n 11.463 * [backup-simplify]: Simplify PI into PI 11.463 * [taylor]: Taking taylor expansion of n in n 11.463 * [backup-simplify]: Simplify 0 into 0 11.463 * [backup-simplify]: Simplify 1 into 1 11.463 * [backup-simplify]: Simplify (/ PI 1) into PI 11.464 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.464 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.464 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.464 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 11.464 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 11.465 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.466 * [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)))) 11.467 * [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))))) 11.467 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 11.467 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 11.467 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 11.467 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 11.467 * [taylor]: Taking taylor expansion of 0.25 in n 11.467 * [backup-simplify]: Simplify 0.25 into 0.25 11.467 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 11.467 * [taylor]: Taking taylor expansion of 1.0 in n 11.467 * [backup-simplify]: Simplify 1.0 into 1.0 11.467 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.467 * [taylor]: Taking taylor expansion of k in n 11.467 * [backup-simplify]: Simplify k into k 11.467 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.467 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 11.467 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 11.467 * [taylor]: Taking taylor expansion of 2.0 in n 11.467 * [backup-simplify]: Simplify 2.0 into 2.0 11.467 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.467 * [taylor]: Taking taylor expansion of PI in n 11.467 * [backup-simplify]: Simplify PI into PI 11.467 * [taylor]: Taking taylor expansion of n in n 11.467 * [backup-simplify]: Simplify 0 into 0 11.467 * [backup-simplify]: Simplify 1 into 1 11.468 * [backup-simplify]: Simplify (/ PI 1) into PI 11.468 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.468 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.469 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.469 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 11.469 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 11.470 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.470 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 11.471 * [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))))) 11.471 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 11.471 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 11.471 * [taylor]: Taking taylor expansion of 0.25 in k 11.471 * [backup-simplify]: Simplify 0.25 into 0.25 11.471 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 11.471 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 11.471 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 11.471 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 11.471 * [taylor]: Taking taylor expansion of 2.0 in k 11.471 * [backup-simplify]: Simplify 2.0 into 2.0 11.471 * [taylor]: Taking taylor expansion of PI in k 11.471 * [backup-simplify]: Simplify PI into PI 11.472 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.472 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.472 * [taylor]: Taking taylor expansion of (log n) in k 11.472 * [taylor]: Taking taylor expansion of n in k 11.472 * [backup-simplify]: Simplify n into n 11.472 * [backup-simplify]: Simplify (log n) into (log n) 11.472 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 11.472 * [taylor]: Taking taylor expansion of 1.0 in k 11.472 * [backup-simplify]: Simplify 1.0 into 1.0 11.472 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.472 * [taylor]: Taking taylor expansion of k in k 11.472 * [backup-simplify]: Simplify 0 into 0 11.472 * [backup-simplify]: Simplify 1 into 1 11.473 * [backup-simplify]: Simplify (/ 1 1) into 1 11.473 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 11.473 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 11.474 * [backup-simplify]: Simplify (- 1) into -1 11.474 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.475 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 11.475 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 11.476 * [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))))) 11.477 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 11.477 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.478 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 11.479 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 11.479 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.479 * [backup-simplify]: Simplify (- 0) into 0 11.479 * [backup-simplify]: Simplify (+ 0 0) into 0 11.480 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 11.481 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.481 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 11.483 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.483 * [taylor]: Taking taylor expansion of 0 in k 11.483 * [backup-simplify]: Simplify 0 into 0 11.483 * [backup-simplify]: Simplify 0 into 0 11.483 * [backup-simplify]: Simplify 0 into 0 11.483 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.484 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.486 * [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 11.486 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.486 * [backup-simplify]: Simplify (- 0) into 0 11.486 * [backup-simplify]: Simplify (+ 0 0) into 0 11.487 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 11.488 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.498 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 11.501 * [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 11.501 * [taylor]: Taking taylor expansion of 0 in k 11.501 * [backup-simplify]: Simplify 0 into 0 11.501 * [backup-simplify]: Simplify 0 into 0 11.501 * [backup-simplify]: Simplify 0 into 0 11.501 * [backup-simplify]: Simplify 0 into 0 11.502 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.503 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.509 * [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 11.510 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.510 * [backup-simplify]: Simplify (- 0) into 0 11.511 * [backup-simplify]: Simplify (+ 0 0) into 0 11.512 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 11.513 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.515 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 11.518 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 11.518 * [taylor]: Taking taylor expansion of 0 in k 11.518 * [backup-simplify]: Simplify 0 into 0 11.518 * [backup-simplify]: Simplify 0 into 0 11.519 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 11.520 * [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))) 11.520 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 11.520 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 11.520 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 11.520 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 11.520 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 11.520 * [taylor]: Taking taylor expansion of 0.25 in k 11.520 * [backup-simplify]: Simplify 0.25 into 0.25 11.520 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 11.520 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.520 * [taylor]: Taking taylor expansion of k in k 11.520 * [backup-simplify]: Simplify 0 into 0 11.520 * [backup-simplify]: Simplify 1 into 1 11.521 * [backup-simplify]: Simplify (/ 1 1) into 1 11.521 * [taylor]: Taking taylor expansion of 1.0 in k 11.521 * [backup-simplify]: Simplify 1.0 into 1.0 11.521 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 11.521 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 11.521 * [taylor]: Taking taylor expansion of -2.0 in k 11.521 * [backup-simplify]: Simplify -2.0 into -2.0 11.521 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.521 * [taylor]: Taking taylor expansion of PI in k 11.521 * [backup-simplify]: Simplify PI into PI 11.521 * [taylor]: Taking taylor expansion of n in k 11.521 * [backup-simplify]: Simplify n into n 11.521 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.521 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 11.521 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 11.522 * [backup-simplify]: Simplify (+ 1 0) into 1 11.522 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 11.522 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 11.523 * [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)))))) 11.523 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 11.523 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 11.523 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 11.523 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 11.523 * [taylor]: Taking taylor expansion of 0.25 in n 11.523 * [backup-simplify]: Simplify 0.25 into 0.25 11.523 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 11.523 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.523 * [taylor]: Taking taylor expansion of k in n 11.523 * [backup-simplify]: Simplify k into k 11.523 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.523 * [taylor]: Taking taylor expansion of 1.0 in n 11.523 * [backup-simplify]: Simplify 1.0 into 1.0 11.523 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 11.523 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 11.523 * [taylor]: Taking taylor expansion of -2.0 in n 11.523 * [backup-simplify]: Simplify -2.0 into -2.0 11.523 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.523 * [taylor]: Taking taylor expansion of PI in n 11.523 * [backup-simplify]: Simplify PI into PI 11.523 * [taylor]: Taking taylor expansion of n in n 11.523 * [backup-simplify]: Simplify 0 into 0 11.523 * [backup-simplify]: Simplify 1 into 1 11.524 * [backup-simplify]: Simplify (/ PI 1) into PI 11.525 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.526 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 11.526 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 11.526 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 11.527 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.528 * [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)))) 11.530 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 11.530 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 11.530 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 11.530 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 11.530 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 11.530 * [taylor]: Taking taylor expansion of 0.25 in n 11.530 * [backup-simplify]: Simplify 0.25 into 0.25 11.530 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 11.530 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.530 * [taylor]: Taking taylor expansion of k in n 11.530 * [backup-simplify]: Simplify k into k 11.530 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.530 * [taylor]: Taking taylor expansion of 1.0 in n 11.530 * [backup-simplify]: Simplify 1.0 into 1.0 11.530 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 11.530 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 11.530 * [taylor]: Taking taylor expansion of -2.0 in n 11.530 * [backup-simplify]: Simplify -2.0 into -2.0 11.530 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.530 * [taylor]: Taking taylor expansion of PI in n 11.530 * [backup-simplify]: Simplify PI into PI 11.530 * [taylor]: Taking taylor expansion of n in n 11.530 * [backup-simplify]: Simplify 0 into 0 11.530 * [backup-simplify]: Simplify 1 into 1 11.531 * [backup-simplify]: Simplify (/ PI 1) into PI 11.532 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.533 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 11.533 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 11.533 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 11.534 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.536 * [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)))) 11.537 * [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))))) 11.537 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 11.537 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 11.537 * [taylor]: Taking taylor expansion of 0.25 in k 11.537 * [backup-simplify]: Simplify 0.25 into 0.25 11.538 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 11.538 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 11.538 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.538 * [taylor]: Taking taylor expansion of k in k 11.538 * [backup-simplify]: Simplify 0 into 0 11.538 * [backup-simplify]: Simplify 1 into 1 11.538 * [backup-simplify]: Simplify (/ 1 1) into 1 11.538 * [taylor]: Taking taylor expansion of 1.0 in k 11.538 * [backup-simplify]: Simplify 1.0 into 1.0 11.538 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 11.538 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 11.538 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 11.538 * [taylor]: Taking taylor expansion of -2.0 in k 11.538 * [backup-simplify]: Simplify -2.0 into -2.0 11.538 * [taylor]: Taking taylor expansion of PI in k 11.538 * [backup-simplify]: Simplify PI into PI 11.539 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.540 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 11.540 * [taylor]: Taking taylor expansion of (log n) in k 11.540 * [taylor]: Taking taylor expansion of n in k 11.540 * [backup-simplify]: Simplify n into n 11.540 * [backup-simplify]: Simplify (log n) into (log n) 11.540 * [backup-simplify]: Simplify (+ 1 0) into 1 11.541 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 11.541 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 11.542 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 11.543 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 11.543 * [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))))) 11.544 * [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))))) 11.545 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.545 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 11.546 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 11.546 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.547 * [backup-simplify]: Simplify (+ 0 0) into 0 11.547 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 11.548 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.548 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 11.550 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.550 * [taylor]: Taking taylor expansion of 0 in k 11.550 * [backup-simplify]: Simplify 0 into 0 11.550 * [backup-simplify]: Simplify 0 into 0 11.550 * [backup-simplify]: Simplify 0 into 0 11.550 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.551 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.553 * [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 11.553 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.553 * [backup-simplify]: Simplify (+ 0 0) into 0 11.554 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 11.555 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.556 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 11.557 * [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 11.557 * [taylor]: Taking taylor expansion of 0 in k 11.557 * [backup-simplify]: Simplify 0 into 0 11.557 * [backup-simplify]: Simplify 0 into 0 11.557 * [backup-simplify]: Simplify 0 into 0 11.557 * [backup-simplify]: Simplify 0 into 0 11.558 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.558 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.562 * [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 11.562 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.562 * [backup-simplify]: Simplify (+ 0 0) into 0 11.563 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 11.564 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.565 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 11.567 * [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 11.567 * [taylor]: Taking taylor expansion of 0 in k 11.567 * [backup-simplify]: Simplify 0 into 0 11.567 * [backup-simplify]: Simplify 0 into 0 11.568 * [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)))))) 11.568 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 11.568 * [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))) 11.568 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 11.568 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 11.568 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 11.568 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 11.568 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 11.568 * [taylor]: Taking taylor expansion of 0.25 in k 11.568 * [backup-simplify]: Simplify 0.25 into 0.25 11.568 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 11.568 * [taylor]: Taking taylor expansion of 1.0 in k 11.568 * [backup-simplify]: Simplify 1.0 into 1.0 11.568 * [taylor]: Taking taylor expansion of k in k 11.568 * [backup-simplify]: Simplify 0 into 0 11.568 * [backup-simplify]: Simplify 1 into 1 11.568 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 11.568 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 11.568 * [taylor]: Taking taylor expansion of 2.0 in k 11.568 * [backup-simplify]: Simplify 2.0 into 2.0 11.568 * [taylor]: Taking taylor expansion of (* n PI) in k 11.569 * [taylor]: Taking taylor expansion of n in k 11.569 * [backup-simplify]: Simplify n into n 11.569 * [taylor]: Taking taylor expansion of PI in k 11.569 * [backup-simplify]: Simplify PI into PI 11.569 * [backup-simplify]: Simplify (* n PI) into (* n PI) 11.569 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 11.569 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 11.569 * [backup-simplify]: Simplify (- 0) into 0 11.569 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 11.569 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 11.570 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 11.570 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 11.570 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 11.570 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 11.570 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 11.570 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 11.570 * [taylor]: Taking taylor expansion of 0.25 in n 11.570 * [backup-simplify]: Simplify 0.25 into 0.25 11.570 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 11.570 * [taylor]: Taking taylor expansion of 1.0 in n 11.570 * [backup-simplify]: Simplify 1.0 into 1.0 11.570 * [taylor]: Taking taylor expansion of k in n 11.570 * [backup-simplify]: Simplify k into k 11.570 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 11.570 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 11.570 * [taylor]: Taking taylor expansion of 2.0 in n 11.570 * [backup-simplify]: Simplify 2.0 into 2.0 11.570 * [taylor]: Taking taylor expansion of (* n PI) in n 11.570 * [taylor]: Taking taylor expansion of n in n 11.570 * [backup-simplify]: Simplify 0 into 0 11.570 * [backup-simplify]: Simplify 1 into 1 11.570 * [taylor]: Taking taylor expansion of PI in n 11.570 * [backup-simplify]: Simplify PI into PI 11.570 * [backup-simplify]: Simplify (* 0 PI) into 0 11.571 * [backup-simplify]: Simplify (* 2.0 0) into 0 11.572 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.573 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 11.574 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.574 * [backup-simplify]: Simplify (- k) into (- k) 11.574 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 11.574 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 11.576 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.577 * [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)))) 11.578 * [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))))) 11.578 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 11.578 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 11.578 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 11.579 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 11.579 * [taylor]: Taking taylor expansion of 0.25 in n 11.579 * [backup-simplify]: Simplify 0.25 into 0.25 11.579 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 11.579 * [taylor]: Taking taylor expansion of 1.0 in n 11.579 * [backup-simplify]: Simplify 1.0 into 1.0 11.579 * [taylor]: Taking taylor expansion of k in n 11.579 * [backup-simplify]: Simplify k into k 11.579 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 11.579 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 11.579 * [taylor]: Taking taylor expansion of 2.0 in n 11.579 * [backup-simplify]: Simplify 2.0 into 2.0 11.579 * [taylor]: Taking taylor expansion of (* n PI) in n 11.579 * [taylor]: Taking taylor expansion of n in n 11.579 * [backup-simplify]: Simplify 0 into 0 11.579 * [backup-simplify]: Simplify 1 into 1 11.579 * [taylor]: Taking taylor expansion of PI in n 11.579 * [backup-simplify]: Simplify PI into PI 11.580 * [backup-simplify]: Simplify (* 0 PI) into 0 11.580 * [backup-simplify]: Simplify (* 2.0 0) into 0 11.582 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.583 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 11.584 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.585 * [backup-simplify]: Simplify (- k) into (- k) 11.585 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 11.585 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 11.586 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.587 * [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)))) 11.588 * [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))))) 11.588 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 11.588 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 11.588 * [taylor]: Taking taylor expansion of 0.25 in k 11.588 * [backup-simplify]: Simplify 0.25 into 0.25 11.588 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 11.588 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 11.588 * [taylor]: Taking taylor expansion of 1.0 in k 11.588 * [backup-simplify]: Simplify 1.0 into 1.0 11.588 * [taylor]: Taking taylor expansion of k in k 11.588 * [backup-simplify]: Simplify 0 into 0 11.588 * [backup-simplify]: Simplify 1 into 1 11.588 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 11.588 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 11.588 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 11.588 * [taylor]: Taking taylor expansion of 2.0 in k 11.588 * [backup-simplify]: Simplify 2.0 into 2.0 11.588 * [taylor]: Taking taylor expansion of PI in k 11.588 * [backup-simplify]: Simplify PI into PI 11.589 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.589 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.589 * [taylor]: Taking taylor expansion of (log n) in k 11.589 * [taylor]: Taking taylor expansion of n in k 11.589 * [backup-simplify]: Simplify n into n 11.589 * [backup-simplify]: Simplify (log n) into (log n) 11.590 * [backup-simplify]: Simplify (- 0) into 0 11.590 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 11.591 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 11.591 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 11.592 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 11.593 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 11.593 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 11.594 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.595 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 11.596 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 11.596 * [backup-simplify]: Simplify (- 0) into 0 11.596 * [backup-simplify]: Simplify (+ 0 0) into 0 11.596 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 11.597 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.598 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 11.599 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.599 * [taylor]: Taking taylor expansion of 0 in k 11.599 * [backup-simplify]: Simplify 0 into 0 11.599 * [backup-simplify]: Simplify 0 into 0 11.600 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 11.601 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 11.601 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 11.601 * [backup-simplify]: Simplify (+ 0 0) into 0 11.602 * [backup-simplify]: Simplify (- 1) into -1 11.602 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.603 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 11.604 * [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)))) 11.606 * [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)))))) 11.608 * [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)))))) 11.609 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 11.615 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 11.617 * [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 11.617 * [backup-simplify]: Simplify (- 0) into 0 11.618 * [backup-simplify]: Simplify (+ 0 0) into 0 11.618 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 11.619 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.621 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 11.623 * [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 11.623 * [taylor]: Taking taylor expansion of 0 in k 11.623 * [backup-simplify]: Simplify 0 into 0 11.623 * [backup-simplify]: Simplify 0 into 0 11.623 * [backup-simplify]: Simplify 0 into 0 11.624 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.628 * [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 11.630 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 11.630 * [backup-simplify]: Simplify (+ 0 0) into 0 11.631 * [backup-simplify]: Simplify (- 0) into 0 11.631 * [backup-simplify]: Simplify (+ 0 0) into 0 11.633 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 11.636 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 11.640 * [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))))) 11.645 * [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))))) 11.654 * [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)))))) 11.655 * [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)))) 11.655 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 11.655 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 11.655 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 11.655 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 11.655 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 11.655 * [taylor]: Taking taylor expansion of 0.25 in k 11.655 * [backup-simplify]: Simplify 0.25 into 0.25 11.655 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 11.655 * [taylor]: Taking taylor expansion of 1.0 in k 11.655 * [backup-simplify]: Simplify 1.0 into 1.0 11.655 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.655 * [taylor]: Taking taylor expansion of k in k 11.655 * [backup-simplify]: Simplify 0 into 0 11.655 * [backup-simplify]: Simplify 1 into 1 11.655 * [backup-simplify]: Simplify (/ 1 1) into 1 11.655 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 11.655 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 11.655 * [taylor]: Taking taylor expansion of 2.0 in k 11.655 * [backup-simplify]: Simplify 2.0 into 2.0 11.655 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.655 * [taylor]: Taking taylor expansion of PI in k 11.656 * [backup-simplify]: Simplify PI into PI 11.656 * [taylor]: Taking taylor expansion of n in k 11.656 * [backup-simplify]: Simplify n into n 11.656 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.656 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 11.656 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 11.656 * [backup-simplify]: Simplify (- 1) into -1 11.656 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.656 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 11.657 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 11.657 * [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))))) 11.657 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 11.657 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 11.657 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 11.657 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 11.657 * [taylor]: Taking taylor expansion of 0.25 in n 11.657 * [backup-simplify]: Simplify 0.25 into 0.25 11.657 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 11.657 * [taylor]: Taking taylor expansion of 1.0 in n 11.657 * [backup-simplify]: Simplify 1.0 into 1.0 11.657 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.657 * [taylor]: Taking taylor expansion of k in n 11.657 * [backup-simplify]: Simplify k into k 11.657 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.657 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 11.657 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 11.657 * [taylor]: Taking taylor expansion of 2.0 in n 11.657 * [backup-simplify]: Simplify 2.0 into 2.0 11.657 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.657 * [taylor]: Taking taylor expansion of PI in n 11.657 * [backup-simplify]: Simplify PI into PI 11.657 * [taylor]: Taking taylor expansion of n in n 11.657 * [backup-simplify]: Simplify 0 into 0 11.657 * [backup-simplify]: Simplify 1 into 1 11.657 * [backup-simplify]: Simplify (/ PI 1) into PI 11.658 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.658 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.658 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.659 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 11.659 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 11.660 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.660 * [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)))) 11.661 * [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))))) 11.661 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 11.661 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 11.661 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 11.661 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 11.661 * [taylor]: Taking taylor expansion of 0.25 in n 11.661 * [backup-simplify]: Simplify 0.25 into 0.25 11.661 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 11.661 * [taylor]: Taking taylor expansion of 1.0 in n 11.661 * [backup-simplify]: Simplify 1.0 into 1.0 11.661 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.661 * [taylor]: Taking taylor expansion of k in n 11.661 * [backup-simplify]: Simplify k into k 11.661 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.661 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 11.661 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 11.661 * [taylor]: Taking taylor expansion of 2.0 in n 11.661 * [backup-simplify]: Simplify 2.0 into 2.0 11.661 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.661 * [taylor]: Taking taylor expansion of PI in n 11.661 * [backup-simplify]: Simplify PI into PI 11.661 * [taylor]: Taking taylor expansion of n in n 11.661 * [backup-simplify]: Simplify 0 into 0 11.661 * [backup-simplify]: Simplify 1 into 1 11.662 * [backup-simplify]: Simplify (/ PI 1) into PI 11.662 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.663 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.663 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.663 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 11.663 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 11.664 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.665 * [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)))) 11.665 * [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))))) 11.665 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 11.665 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 11.665 * [taylor]: Taking taylor expansion of 0.25 in k 11.665 * [backup-simplify]: Simplify 0.25 into 0.25 11.666 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 11.666 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 11.666 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 11.666 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 11.666 * [taylor]: Taking taylor expansion of 2.0 in k 11.666 * [backup-simplify]: Simplify 2.0 into 2.0 11.666 * [taylor]: Taking taylor expansion of PI in k 11.666 * [backup-simplify]: Simplify PI into PI 11.666 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.667 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.667 * [taylor]: Taking taylor expansion of (log n) in k 11.667 * [taylor]: Taking taylor expansion of n in k 11.667 * [backup-simplify]: Simplify n into n 11.667 * [backup-simplify]: Simplify (log n) into (log n) 11.667 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 11.667 * [taylor]: Taking taylor expansion of 1.0 in k 11.667 * [backup-simplify]: Simplify 1.0 into 1.0 11.667 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.667 * [taylor]: Taking taylor expansion of k in k 11.667 * [backup-simplify]: Simplify 0 into 0 11.667 * [backup-simplify]: Simplify 1 into 1 11.667 * [backup-simplify]: Simplify (/ 1 1) into 1 11.667 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 11.668 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 11.668 * [backup-simplify]: Simplify (- 1) into -1 11.668 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.669 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 11.670 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 11.670 * [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))))) 11.671 * [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))))) 11.672 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.672 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 11.673 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 11.673 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.673 * [backup-simplify]: Simplify (- 0) into 0 11.674 * [backup-simplify]: Simplify (+ 0 0) into 0 11.674 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 11.675 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.676 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 11.677 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.677 * [taylor]: Taking taylor expansion of 0 in k 11.677 * [backup-simplify]: Simplify 0 into 0 11.677 * [backup-simplify]: Simplify 0 into 0 11.677 * [backup-simplify]: Simplify 0 into 0 11.678 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.678 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.680 * [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 11.681 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.681 * [backup-simplify]: Simplify (- 0) into 0 11.681 * [backup-simplify]: Simplify (+ 0 0) into 0 11.682 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 11.683 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.684 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 11.685 * [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 11.685 * [taylor]: Taking taylor expansion of 0 in k 11.685 * [backup-simplify]: Simplify 0 into 0 11.685 * [backup-simplify]: Simplify 0 into 0 11.686 * [backup-simplify]: Simplify 0 into 0 11.686 * [backup-simplify]: Simplify 0 into 0 11.686 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.687 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.690 * [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 11.690 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.691 * [backup-simplify]: Simplify (- 0) into 0 11.691 * [backup-simplify]: Simplify (+ 0 0) into 0 11.692 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 11.692 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.694 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 11.695 * [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 11.695 * [taylor]: Taking taylor expansion of 0 in k 11.695 * [backup-simplify]: Simplify 0 into 0 11.695 * [backup-simplify]: Simplify 0 into 0 11.696 * [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)))) 11.697 * [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))) 11.697 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 11.697 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 11.697 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 11.697 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 11.697 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 11.697 * [taylor]: Taking taylor expansion of 0.25 in k 11.697 * [backup-simplify]: Simplify 0.25 into 0.25 11.697 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 11.697 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.697 * [taylor]: Taking taylor expansion of k in k 11.697 * [backup-simplify]: Simplify 0 into 0 11.697 * [backup-simplify]: Simplify 1 into 1 11.697 * [backup-simplify]: Simplify (/ 1 1) into 1 11.697 * [taylor]: Taking taylor expansion of 1.0 in k 11.697 * [backup-simplify]: Simplify 1.0 into 1.0 11.697 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 11.697 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 11.697 * [taylor]: Taking taylor expansion of -2.0 in k 11.697 * [backup-simplify]: Simplify -2.0 into -2.0 11.697 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.697 * [taylor]: Taking taylor expansion of PI in k 11.697 * [backup-simplify]: Simplify PI into PI 11.697 * [taylor]: Taking taylor expansion of n in k 11.697 * [backup-simplify]: Simplify n into n 11.697 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.697 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 11.697 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 11.698 * [backup-simplify]: Simplify (+ 1 0) into 1 11.698 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 11.698 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 11.698 * [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)))))) 11.698 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 11.698 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 11.698 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 11.698 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 11.698 * [taylor]: Taking taylor expansion of 0.25 in n 11.698 * [backup-simplify]: Simplify 0.25 into 0.25 11.698 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 11.698 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.698 * [taylor]: Taking taylor expansion of k in n 11.698 * [backup-simplify]: Simplify k into k 11.698 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.698 * [taylor]: Taking taylor expansion of 1.0 in n 11.698 * [backup-simplify]: Simplify 1.0 into 1.0 11.698 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 11.699 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 11.699 * [taylor]: Taking taylor expansion of -2.0 in n 11.699 * [backup-simplify]: Simplify -2.0 into -2.0 11.699 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.699 * [taylor]: Taking taylor expansion of PI in n 11.699 * [backup-simplify]: Simplify PI into PI 11.699 * [taylor]: Taking taylor expansion of n in n 11.699 * [backup-simplify]: Simplify 0 into 0 11.699 * [backup-simplify]: Simplify 1 into 1 11.699 * [backup-simplify]: Simplify (/ PI 1) into PI 11.699 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.700 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 11.700 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 11.700 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 11.701 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.702 * [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)))) 11.702 * [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))))) 11.703 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 11.703 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 11.703 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 11.703 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 11.703 * [taylor]: Taking taylor expansion of 0.25 in n 11.703 * [backup-simplify]: Simplify 0.25 into 0.25 11.703 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 11.703 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.703 * [taylor]: Taking taylor expansion of k in n 11.703 * [backup-simplify]: Simplify k into k 11.703 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.703 * [taylor]: Taking taylor expansion of 1.0 in n 11.703 * [backup-simplify]: Simplify 1.0 into 1.0 11.703 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 11.703 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 11.703 * [taylor]: Taking taylor expansion of -2.0 in n 11.703 * [backup-simplify]: Simplify -2.0 into -2.0 11.703 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.703 * [taylor]: Taking taylor expansion of PI in n 11.703 * [backup-simplify]: Simplify PI into PI 11.703 * [taylor]: Taking taylor expansion of n in n 11.703 * [backup-simplify]: Simplify 0 into 0 11.703 * [backup-simplify]: Simplify 1 into 1 11.703 * [backup-simplify]: Simplify (/ PI 1) into PI 11.704 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.704 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 11.704 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 11.704 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 11.705 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.706 * [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)))) 11.707 * [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))))) 11.707 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 11.707 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 11.707 * [taylor]: Taking taylor expansion of 0.25 in k 11.707 * [backup-simplify]: Simplify 0.25 into 0.25 11.707 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 11.707 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 11.707 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.707 * [taylor]: Taking taylor expansion of k in k 11.707 * [backup-simplify]: Simplify 0 into 0 11.707 * [backup-simplify]: Simplify 1 into 1 11.707 * [backup-simplify]: Simplify (/ 1 1) into 1 11.707 * [taylor]: Taking taylor expansion of 1.0 in k 11.707 * [backup-simplify]: Simplify 1.0 into 1.0 11.707 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 11.707 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 11.707 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 11.707 * [taylor]: Taking taylor expansion of -2.0 in k 11.707 * [backup-simplify]: Simplify -2.0 into -2.0 11.708 * [taylor]: Taking taylor expansion of PI in k 11.708 * [backup-simplify]: Simplify PI into PI 11.708 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.709 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 11.709 * [taylor]: Taking taylor expansion of (log n) in k 11.709 * [taylor]: Taking taylor expansion of n in k 11.709 * [backup-simplify]: Simplify n into n 11.709 * [backup-simplify]: Simplify (log n) into (log n) 11.710 * [backup-simplify]: Simplify (+ 1 0) into 1 11.710 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 11.711 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 11.712 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 11.713 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 11.715 * [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))))) 11.716 * [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))))) 11.717 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.718 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 11.719 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 11.719 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.720 * [backup-simplify]: Simplify (+ 0 0) into 0 11.720 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 11.721 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.722 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 11.729 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.729 * [taylor]: Taking taylor expansion of 0 in k 11.729 * [backup-simplify]: Simplify 0 into 0 11.729 * [backup-simplify]: Simplify 0 into 0 11.729 * [backup-simplify]: Simplify 0 into 0 11.730 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.731 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.733 * [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 11.733 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.733 * [backup-simplify]: Simplify (+ 0 0) into 0 11.734 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 11.735 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.736 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 11.737 * [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 11.737 * [taylor]: Taking taylor expansion of 0 in k 11.737 * [backup-simplify]: Simplify 0 into 0 11.737 * [backup-simplify]: Simplify 0 into 0 11.737 * [backup-simplify]: Simplify 0 into 0 11.737 * [backup-simplify]: Simplify 0 into 0 11.738 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.739 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.742 * [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 11.742 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.742 * [backup-simplify]: Simplify (+ 0 0) into 0 11.743 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 11.744 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.745 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 11.747 * [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 11.747 * [taylor]: Taking taylor expansion of 0 in k 11.747 * [backup-simplify]: Simplify 0 into 0 11.747 * [backup-simplify]: Simplify 0 into 0 11.748 * [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)))))) 11.748 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 11.748 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 11.748 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 11.748 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 11.748 * [taylor]: Taking taylor expansion of 2.0 in n 11.748 * [backup-simplify]: Simplify 2.0 into 2.0 11.748 * [taylor]: Taking taylor expansion of (* n PI) in n 11.748 * [taylor]: Taking taylor expansion of n in n 11.748 * [backup-simplify]: Simplify 0 into 0 11.748 * [backup-simplify]: Simplify 1 into 1 11.748 * [taylor]: Taking taylor expansion of PI in n 11.748 * [backup-simplify]: Simplify PI into PI 11.748 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 11.748 * [taylor]: Taking taylor expansion of 2.0 in n 11.748 * [backup-simplify]: Simplify 2.0 into 2.0 11.748 * [taylor]: Taking taylor expansion of (* n PI) in n 11.748 * [taylor]: Taking taylor expansion of n in n 11.748 * [backup-simplify]: Simplify 0 into 0 11.748 * [backup-simplify]: Simplify 1 into 1 11.748 * [taylor]: Taking taylor expansion of PI in n 11.748 * [backup-simplify]: Simplify PI into PI 11.749 * [backup-simplify]: Simplify (* 0 PI) into 0 11.749 * [backup-simplify]: Simplify (* 2.0 0) into 0 11.749 * [backup-simplify]: Simplify 0 into 0 11.750 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.751 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 11.751 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.752 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.752 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 11.752 * [backup-simplify]: Simplify 0 into 0 11.753 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 11.754 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 11.754 * [backup-simplify]: Simplify 0 into 0 11.755 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.755 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 11.755 * [backup-simplify]: Simplify 0 into 0 11.756 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.757 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 11.757 * [backup-simplify]: Simplify 0 into 0 11.758 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.759 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 11.759 * [backup-simplify]: Simplify 0 into 0 11.760 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 11.761 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 11.761 * [backup-simplify]: Simplify 0 into 0 11.761 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 11.762 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 11.762 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 11.762 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 11.762 * [taylor]: Taking taylor expansion of 2.0 in n 11.762 * [backup-simplify]: Simplify 2.0 into 2.0 11.762 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.762 * [taylor]: Taking taylor expansion of PI in n 11.762 * [backup-simplify]: Simplify PI into PI 11.762 * [taylor]: Taking taylor expansion of n in n 11.762 * [backup-simplify]: Simplify 0 into 0 11.762 * [backup-simplify]: Simplify 1 into 1 11.762 * [backup-simplify]: Simplify (/ PI 1) into PI 11.762 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 11.762 * [taylor]: Taking taylor expansion of 2.0 in n 11.762 * [backup-simplify]: Simplify 2.0 into 2.0 11.762 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.762 * [taylor]: Taking taylor expansion of PI in n 11.762 * [backup-simplify]: Simplify PI into PI 11.762 * [taylor]: Taking taylor expansion of n in n 11.762 * [backup-simplify]: Simplify 0 into 0 11.762 * [backup-simplify]: Simplify 1 into 1 11.763 * [backup-simplify]: Simplify (/ PI 1) into PI 11.763 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.763 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.764 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.764 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 11.764 * [backup-simplify]: Simplify 0 into 0 11.765 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.766 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.766 * [backup-simplify]: Simplify 0 into 0 11.766 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.767 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.767 * [backup-simplify]: Simplify 0 into 0 11.768 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.768 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.768 * [backup-simplify]: Simplify 0 into 0 11.769 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.770 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.770 * [backup-simplify]: Simplify 0 into 0 11.770 * [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 11.771 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.771 * [backup-simplify]: Simplify 0 into 0 11.772 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 11.772 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 11.772 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 11.772 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 11.772 * [taylor]: Taking taylor expansion of -2.0 in n 11.772 * [backup-simplify]: Simplify -2.0 into -2.0 11.772 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.772 * [taylor]: Taking taylor expansion of PI in n 11.772 * [backup-simplify]: Simplify PI into PI 11.772 * [taylor]: Taking taylor expansion of n in n 11.772 * [backup-simplify]: Simplify 0 into 0 11.772 * [backup-simplify]: Simplify 1 into 1 11.773 * [backup-simplify]: Simplify (/ PI 1) into PI 11.773 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 11.773 * [taylor]: Taking taylor expansion of -2.0 in n 11.773 * [backup-simplify]: Simplify -2.0 into -2.0 11.773 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.773 * [taylor]: Taking taylor expansion of PI in n 11.773 * [backup-simplify]: Simplify PI into PI 11.773 * [taylor]: Taking taylor expansion of n in n 11.773 * [backup-simplify]: Simplify 0 into 0 11.773 * [backup-simplify]: Simplify 1 into 1 11.773 * [backup-simplify]: Simplify (/ PI 1) into PI 11.774 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.774 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.774 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.775 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 11.775 * [backup-simplify]: Simplify 0 into 0 11.775 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.776 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.776 * [backup-simplify]: Simplify 0 into 0 11.777 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.777 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.777 * [backup-simplify]: Simplify 0 into 0 11.778 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.779 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.779 * [backup-simplify]: Simplify 0 into 0 11.779 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.780 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.780 * [backup-simplify]: Simplify 0 into 0 11.781 * [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 11.782 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.782 * [backup-simplify]: Simplify 0 into 0 11.782 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 11.783 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 2 1) 11.783 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 11.783 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 11.783 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 11.783 * [taylor]: Taking taylor expansion of 2.0 in n 11.783 * [backup-simplify]: Simplify 2.0 into 2.0 11.783 * [taylor]: Taking taylor expansion of (* n PI) in n 11.783 * [taylor]: Taking taylor expansion of n in n 11.783 * [backup-simplify]: Simplify 0 into 0 11.783 * [backup-simplify]: Simplify 1 into 1 11.783 * [taylor]: Taking taylor expansion of PI in n 11.783 * [backup-simplify]: Simplify PI into PI 11.783 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 11.783 * [taylor]: Taking taylor expansion of 2.0 in n 11.783 * [backup-simplify]: Simplify 2.0 into 2.0 11.783 * [taylor]: Taking taylor expansion of (* n PI) in n 11.783 * [taylor]: Taking taylor expansion of n in n 11.783 * [backup-simplify]: Simplify 0 into 0 11.783 * [backup-simplify]: Simplify 1 into 1 11.783 * [taylor]: Taking taylor expansion of PI in n 11.783 * [backup-simplify]: Simplify PI into PI 11.784 * [backup-simplify]: Simplify (* 0 PI) into 0 11.784 * [backup-simplify]: Simplify (* 2.0 0) into 0 11.784 * [backup-simplify]: Simplify 0 into 0 11.785 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.786 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 11.786 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.787 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.787 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 11.787 * [backup-simplify]: Simplify 0 into 0 11.789 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 11.790 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 11.790 * [backup-simplify]: Simplify 0 into 0 11.792 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.793 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 11.793 * [backup-simplify]: Simplify 0 into 0 11.795 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.796 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 11.796 * [backup-simplify]: Simplify 0 into 0 11.798 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.800 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 11.800 * [backup-simplify]: Simplify 0 into 0 11.802 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 11.804 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 11.804 * [backup-simplify]: Simplify 0 into 0 11.805 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 11.805 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 11.805 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 11.805 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 11.805 * [taylor]: Taking taylor expansion of 2.0 in n 11.805 * [backup-simplify]: Simplify 2.0 into 2.0 11.805 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.805 * [taylor]: Taking taylor expansion of PI in n 11.805 * [backup-simplify]: Simplify PI into PI 11.805 * [taylor]: Taking taylor expansion of n in n 11.805 * [backup-simplify]: Simplify 0 into 0 11.806 * [backup-simplify]: Simplify 1 into 1 11.806 * [backup-simplify]: Simplify (/ PI 1) into PI 11.806 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 11.806 * [taylor]: Taking taylor expansion of 2.0 in n 11.806 * [backup-simplify]: Simplify 2.0 into 2.0 11.806 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.806 * [taylor]: Taking taylor expansion of PI in n 11.806 * [backup-simplify]: Simplify PI into PI 11.806 * [taylor]: Taking taylor expansion of n in n 11.806 * [backup-simplify]: Simplify 0 into 0 11.806 * [backup-simplify]: Simplify 1 into 1 11.807 * [backup-simplify]: Simplify (/ PI 1) into PI 11.807 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.808 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.809 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.810 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 11.810 * [backup-simplify]: Simplify 0 into 0 11.811 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.812 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.812 * [backup-simplify]: Simplify 0 into 0 11.813 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.814 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.814 * [backup-simplify]: Simplify 0 into 0 11.815 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.816 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.816 * [backup-simplify]: Simplify 0 into 0 11.818 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.819 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.819 * [backup-simplify]: Simplify 0 into 0 11.820 * [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 11.822 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.822 * [backup-simplify]: Simplify 0 into 0 11.823 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 11.823 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 11.824 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 11.824 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 11.824 * [taylor]: Taking taylor expansion of -2.0 in n 11.824 * [backup-simplify]: Simplify -2.0 into -2.0 11.824 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.824 * [taylor]: Taking taylor expansion of PI in n 11.824 * [backup-simplify]: Simplify PI into PI 11.824 * [taylor]: Taking taylor expansion of n in n 11.824 * [backup-simplify]: Simplify 0 into 0 11.824 * [backup-simplify]: Simplify 1 into 1 11.824 * [backup-simplify]: Simplify (/ PI 1) into PI 11.824 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 11.824 * [taylor]: Taking taylor expansion of -2.0 in n 11.824 * [backup-simplify]: Simplify -2.0 into -2.0 11.824 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.824 * [taylor]: Taking taylor expansion of PI in n 11.824 * [backup-simplify]: Simplify PI into PI 11.825 * [taylor]: Taking taylor expansion of n in n 11.825 * [backup-simplify]: Simplify 0 into 0 11.825 * [backup-simplify]: Simplify 1 into 1 11.825 * [backup-simplify]: Simplify (/ PI 1) into PI 11.826 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.826 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.827 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.828 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 11.828 * [backup-simplify]: Simplify 0 into 0 11.829 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.830 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.830 * [backup-simplify]: Simplify 0 into 0 11.831 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.832 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.832 * [backup-simplify]: Simplify 0 into 0 11.834 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.835 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.835 * [backup-simplify]: Simplify 0 into 0 11.836 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.838 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.838 * [backup-simplify]: Simplify 0 into 0 11.848 * [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 11.849 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.849 * [backup-simplify]: Simplify 0 into 0 11.850 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 11.850 * * * [progress]: simplifying candidates 11.853 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 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2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (* (+ (+ (log 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 (* (* 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(* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (* (* 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) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 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)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 12.995 * * * [progress]: adding candidates to table 14.021 * [progress]: [Phase 3 of 3] Extracting. 14.021 * * [regime]: Finding splitpoints for: (# # # # # # # # #) 14.029 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 14.029 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # # # #) 14.115 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # #) 14.149 * * * * [regimes]: Trying to branch on n from (# # # # # # # # #) 14.222 * * * * [regimes]: Trying to branch on k from (# # # # # # # # #) 14.290 * * * [regime]: Found split indices: #