66.073 * [progress]: [Phase 1 of 3] Setting up. 0.002 * * * [progress]: [1/2] Preparing points 0.255 * * * [progress]: [2/2] Setting up program. 0.258 * [progress]: [Phase 2 of 3] Improving. 0.258 * * * * [progress]: [ 1 / 1 ] simplifiying candidate # 0.258 * [simplify]: Simplifying: (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 0.259 * * [simplify]: iteration 1: (13 enodes) 0.262 * * [simplify]: iteration 2: (29 enodes) 0.267 * * [simplify]: iteration 3: (60 enodes) 0.287 * * [simplify]: iteration 4: (123 enodes) 0.352 * * [simplify]: iteration 5: (322 enodes) 0.569 * * [simplify]: iteration 6: (821 enodes) 1.406 * * [simplify]: Extracting #0: cost 1 inf + 0 1.406 * * [simplify]: Extracting #1: cost 58 inf + 0 1.408 * * [simplify]: Extracting #2: cost 184 inf + 1 1.410 * * [simplify]: Extracting #3: cost 251 inf + 46 1.413 * * [simplify]: Extracting #4: cost 228 inf + 1879 1.417 * * [simplify]: Extracting #5: cost 157 inf + 21169 1.439 * * [simplify]: Extracting #6: cost 45 inf + 113683 1.470 * * [simplify]: Extracting #7: cost 0 inf + 157567 1.522 * * [simplify]: Extracting #8: cost 0 inf + 157407 1.555 * [simplify]: Simplified to: (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1.561 * * [progress]: iteration 1 / 4 1.562 * * * [progress]: picking best candidate 1.567 * * * * [pick]: Picked # 1.567 * * * [progress]: localizing error 1.596 * * * [progress]: generating rewritten candidates 1.596 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1) 1.619 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1) 1.633 * * * * [progress]: [ 3 / 3 ] rewriting at (2) 1.674 * * * [progress]: generating series expansions 1.674 * * * * [progress]: [ 1 / 3 ] generating series at (2 1) 1.674 * [backup-simplify]: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1.674 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1.674 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1.674 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1.674 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1.674 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1.674 * [taylor]: Taking taylor expansion of 1/2 in k 1.674 * [backup-simplify]: Simplify 1/2 into 1/2 1.674 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 1.674 * [taylor]: Taking taylor expansion of 1/2 in k 1.674 * [backup-simplify]: Simplify 1/2 into 1/2 1.674 * [taylor]: Taking taylor expansion of k in k 1.674 * [backup-simplify]: Simplify 0 into 0 1.674 * [backup-simplify]: Simplify 1 into 1 1.674 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 1.675 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 1.675 * [taylor]: Taking taylor expansion of 2 in k 1.675 * [backup-simplify]: Simplify 2 into 2 1.675 * [taylor]: Taking taylor expansion of (* n PI) in k 1.675 * [taylor]: Taking taylor expansion of n in k 1.675 * [backup-simplify]: Simplify n into n 1.675 * [taylor]: Taking taylor expansion of PI in k 1.675 * [backup-simplify]: Simplify PI into PI 1.675 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.675 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1.675 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1.676 * [backup-simplify]: Simplify (* 1/2 0) into 0 1.676 * [backup-simplify]: Simplify (- 0) into 0 1.676 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 1.677 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1.677 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1.677 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1.677 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1.677 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1.677 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1.677 * [taylor]: Taking taylor expansion of 1/2 in n 1.677 * [backup-simplify]: Simplify 1/2 into 1/2 1.677 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 1.677 * [taylor]: Taking taylor expansion of 1/2 in n 1.677 * [backup-simplify]: Simplify 1/2 into 1/2 1.677 * [taylor]: Taking taylor expansion of k in n 1.677 * [backup-simplify]: Simplify k into k 1.677 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.677 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.677 * [taylor]: Taking taylor expansion of 2 in n 1.677 * [backup-simplify]: Simplify 2 into 2 1.677 * [taylor]: Taking taylor expansion of (* n PI) in n 1.677 * [taylor]: Taking taylor expansion of n in n 1.677 * [backup-simplify]: Simplify 0 into 0 1.677 * [backup-simplify]: Simplify 1 into 1 1.677 * [taylor]: Taking taylor expansion of PI in n 1.677 * [backup-simplify]: Simplify PI into PI 1.678 * [backup-simplify]: Simplify (* 0 PI) into 0 1.678 * [backup-simplify]: Simplify (* 2 0) into 0 1.680 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.682 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1.683 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.683 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 1.683 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1.683 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1.685 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.686 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1.687 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1.687 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1.687 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1.687 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1.687 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1.687 * [taylor]: Taking taylor expansion of 1/2 in n 1.687 * [backup-simplify]: Simplify 1/2 into 1/2 1.687 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 1.687 * [taylor]: Taking taylor expansion of 1/2 in n 1.687 * [backup-simplify]: Simplify 1/2 into 1/2 1.687 * [taylor]: Taking taylor expansion of k in n 1.687 * [backup-simplify]: Simplify k into k 1.687 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.687 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.687 * [taylor]: Taking taylor expansion of 2 in n 1.687 * [backup-simplify]: Simplify 2 into 2 1.687 * [taylor]: Taking taylor expansion of (* n PI) in n 1.687 * [taylor]: Taking taylor expansion of n in n 1.687 * [backup-simplify]: Simplify 0 into 0 1.687 * [backup-simplify]: Simplify 1 into 1 1.687 * [taylor]: Taking taylor expansion of PI in n 1.688 * [backup-simplify]: Simplify PI into PI 1.688 * [backup-simplify]: Simplify (* 0 PI) into 0 1.688 * [backup-simplify]: Simplify (* 2 0) into 0 1.690 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.692 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1.693 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.693 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 1.693 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1.693 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1.694 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.696 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1.697 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1.697 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1.697 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1.697 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1.697 * [taylor]: Taking taylor expansion of 1/2 in k 1.697 * [backup-simplify]: Simplify 1/2 into 1/2 1.697 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 1.697 * [taylor]: Taking taylor expansion of 1/2 in k 1.697 * [backup-simplify]: Simplify 1/2 into 1/2 1.697 * [taylor]: Taking taylor expansion of k in k 1.697 * [backup-simplify]: Simplify 0 into 0 1.697 * [backup-simplify]: Simplify 1 into 1 1.697 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1.697 * [taylor]: Taking taylor expansion of (log n) in k 1.697 * [taylor]: Taking taylor expansion of n in k 1.697 * [backup-simplify]: Simplify n into n 1.697 * [backup-simplify]: Simplify (log n) into (log n) 1.697 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 1.697 * [taylor]: Taking taylor expansion of (* 2 PI) in k 1.697 * [taylor]: Taking taylor expansion of 2 in k 1.697 * [backup-simplify]: Simplify 2 into 2 1.697 * [taylor]: Taking taylor expansion of PI in k 1.697 * [backup-simplify]: Simplify PI into PI 1.698 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 1.699 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.699 * [backup-simplify]: Simplify (* 1/2 0) into 0 1.700 * [backup-simplify]: Simplify (- 0) into 0 1.700 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 1.701 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.702 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1.704 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1.705 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1.706 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.707 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1.709 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1.710 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1.710 * [backup-simplify]: Simplify (- 0) into 0 1.711 * [backup-simplify]: Simplify (+ 0 0) into 0 1.712 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.713 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1.715 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.715 * [taylor]: Taking taylor expansion of 0 in k 1.715 * [backup-simplify]: Simplify 0 into 0 1.715 * [backup-simplify]: Simplify 0 into 0 1.716 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.717 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 1.719 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1.719 * [backup-simplify]: Simplify (+ 0 0) into 0 1.720 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1.721 * [backup-simplify]: Simplify (- 1/2) into -1/2 1.721 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 1.722 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1.725 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1.737 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1.738 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.739 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.743 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1.743 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1.744 * [backup-simplify]: Simplify (- 0) into 0 1.744 * [backup-simplify]: Simplify (+ 0 0) into 0 1.745 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.747 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1.749 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.749 * [taylor]: Taking taylor expansion of 0 in k 1.749 * [backup-simplify]: Simplify 0 into 0 1.749 * [backup-simplify]: Simplify 0 into 0 1.749 * [backup-simplify]: Simplify 0 into 0 1.751 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.752 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1.755 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1.755 * [backup-simplify]: Simplify (+ 0 0) into 0 1.756 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1.757 * [backup-simplify]: Simplify (- 0) into 0 1.757 * [backup-simplify]: Simplify (+ 0 0) into 0 1.759 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1.762 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1.767 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1.774 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 1.774 * [backup-simplify]: Simplify (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1.774 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1.774 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1.774 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1.774 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1.774 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1.774 * [taylor]: Taking taylor expansion of 1/2 in k 1.774 * [backup-simplify]: Simplify 1/2 into 1/2 1.774 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1.774 * [taylor]: Taking taylor expansion of 1/2 in k 1.774 * [backup-simplify]: Simplify 1/2 into 1/2 1.774 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.774 * [taylor]: Taking taylor expansion of k in k 1.774 * [backup-simplify]: Simplify 0 into 0 1.774 * [backup-simplify]: Simplify 1 into 1 1.775 * [backup-simplify]: Simplify (/ 1 1) into 1 1.775 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1.775 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 1.775 * [taylor]: Taking taylor expansion of 2 in k 1.775 * [backup-simplify]: Simplify 2 into 2 1.775 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.775 * [taylor]: Taking taylor expansion of PI in k 1.775 * [backup-simplify]: Simplify PI into PI 1.775 * [taylor]: Taking taylor expansion of n in k 1.775 * [backup-simplify]: Simplify n into n 1.775 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.775 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1.775 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1.775 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 1.775 * [backup-simplify]: Simplify (- 1/2) into -1/2 1.776 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 1.776 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1.776 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1.776 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1.776 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1.776 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1.776 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1.776 * [taylor]: Taking taylor expansion of 1/2 in n 1.776 * [backup-simplify]: Simplify 1/2 into 1/2 1.776 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1.776 * [taylor]: Taking taylor expansion of 1/2 in n 1.776 * [backup-simplify]: Simplify 1/2 into 1/2 1.776 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.776 * [taylor]: Taking taylor expansion of k in n 1.776 * [backup-simplify]: Simplify k into k 1.776 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.776 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1.776 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.776 * [taylor]: Taking taylor expansion of 2 in n 1.776 * [backup-simplify]: Simplify 2 into 2 1.776 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.776 * [taylor]: Taking taylor expansion of PI in n 1.776 * [backup-simplify]: Simplify PI into PI 1.776 * [taylor]: Taking taylor expansion of n in n 1.776 * [backup-simplify]: Simplify 0 into 0 1.776 * [backup-simplify]: Simplify 1 into 1 1.777 * [backup-simplify]: Simplify (/ PI 1) into PI 1.777 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 1.778 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.778 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1.778 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1.778 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1.779 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1.779 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1.780 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1.780 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1.780 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1.780 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1.780 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1.780 * [taylor]: Taking taylor expansion of 1/2 in n 1.780 * [backup-simplify]: Simplify 1/2 into 1/2 1.780 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1.780 * [taylor]: Taking taylor expansion of 1/2 in n 1.780 * [backup-simplify]: Simplify 1/2 into 1/2 1.780 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.780 * [taylor]: Taking taylor expansion of k in n 1.780 * [backup-simplify]: Simplify k into k 1.780 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.780 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1.780 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.780 * [taylor]: Taking taylor expansion of 2 in n 1.780 * [backup-simplify]: Simplify 2 into 2 1.780 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.780 * [taylor]: Taking taylor expansion of PI in n 1.780 * [backup-simplify]: Simplify PI into PI 1.780 * [taylor]: Taking taylor expansion of n in n 1.780 * [backup-simplify]: Simplify 0 into 0 1.780 * [backup-simplify]: Simplify 1 into 1 1.781 * [backup-simplify]: Simplify (/ PI 1) into PI 1.781 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 1.782 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.782 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1.782 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1.782 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1.783 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1.784 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1.784 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1.785 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1.785 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1.785 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1.785 * [taylor]: Taking taylor expansion of 1/2 in k 1.785 * [backup-simplify]: Simplify 1/2 into 1/2 1.785 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1.785 * [taylor]: Taking taylor expansion of 1/2 in k 1.785 * [backup-simplify]: Simplify 1/2 into 1/2 1.785 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.785 * [taylor]: Taking taylor expansion of k in k 1.785 * [backup-simplify]: Simplify 0 into 0 1.785 * [backup-simplify]: Simplify 1 into 1 1.785 * [backup-simplify]: Simplify (/ 1 1) into 1 1.785 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1.785 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 1.785 * [taylor]: Taking taylor expansion of (* 2 PI) in k 1.785 * [taylor]: Taking taylor expansion of 2 in k 1.785 * [backup-simplify]: Simplify 2 into 2 1.785 * [taylor]: Taking taylor expansion of PI in k 1.785 * [backup-simplify]: Simplify PI into PI 1.785 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 1.786 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.786 * [taylor]: Taking taylor expansion of (log n) in k 1.786 * [taylor]: Taking taylor expansion of n in k 1.786 * [backup-simplify]: Simplify n into n 1.786 * [backup-simplify]: Simplify (log n) into (log n) 1.786 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 1.787 * [backup-simplify]: Simplify (- 1/2) into -1/2 1.787 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 1.787 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.788 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1.788 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1.789 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1.790 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1.790 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.791 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 1.792 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1.792 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.792 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1.792 * [backup-simplify]: Simplify (- 0) into 0 1.793 * [backup-simplify]: Simplify (+ 0 0) into 0 1.794 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1.794 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1.795 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1.795 * [taylor]: Taking taylor expansion of 0 in k 1.796 * [backup-simplify]: Simplify 0 into 0 1.796 * [backup-simplify]: Simplify 0 into 0 1.796 * [backup-simplify]: Simplify 0 into 0 1.796 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.797 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1.799 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1.799 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.799 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1.800 * [backup-simplify]: Simplify (- 0) into 0 1.800 * [backup-simplify]: Simplify (+ 0 0) into 0 1.801 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1.802 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1.804 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.805 * [taylor]: Taking taylor expansion of 0 in k 1.805 * [backup-simplify]: Simplify 0 into 0 1.805 * [backup-simplify]: Simplify 0 into 0 1.805 * [backup-simplify]: Simplify 0 into 0 1.805 * [backup-simplify]: Simplify 0 into 0 1.806 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.808 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.813 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1.814 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.815 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1.815 * [backup-simplify]: Simplify (- 0) into 0 1.816 * [backup-simplify]: Simplify (+ 0 0) into 0 1.818 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1.820 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1.823 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1.823 * [taylor]: Taking taylor expansion of 0 in k 1.823 * [backup-simplify]: Simplify 0 into 0 1.823 * [backup-simplify]: Simplify 0 into 0 1.824 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1.824 * [backup-simplify]: Simplify (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 1.824 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1.824 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1.825 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1.825 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1.825 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1.825 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1.825 * [taylor]: Taking taylor expansion of 1/2 in k 1.825 * [backup-simplify]: Simplify 1/2 into 1/2 1.825 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.825 * [taylor]: Taking taylor expansion of k in k 1.825 * [backup-simplify]: Simplify 0 into 0 1.825 * [backup-simplify]: Simplify 1 into 1 1.825 * [backup-simplify]: Simplify (/ 1 1) into 1 1.825 * [taylor]: Taking taylor expansion of 1/2 in k 1.825 * [backup-simplify]: Simplify 1/2 into 1/2 1.825 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1.825 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 1.825 * [taylor]: Taking taylor expansion of -2 in k 1.825 * [backup-simplify]: Simplify -2 into -2 1.825 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.825 * [taylor]: Taking taylor expansion of PI in k 1.825 * [backup-simplify]: Simplify PI into PI 1.826 * [taylor]: Taking taylor expansion of n in k 1.826 * [backup-simplify]: Simplify n into n 1.826 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.826 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1.826 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1.826 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 1.827 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 1.827 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1.827 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 1.827 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1.827 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1.827 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1.827 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1.827 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1.827 * [taylor]: Taking taylor expansion of 1/2 in n 1.828 * [backup-simplify]: Simplify 1/2 into 1/2 1.828 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.828 * [taylor]: Taking taylor expansion of k in n 1.828 * [backup-simplify]: Simplify k into k 1.828 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.828 * [taylor]: Taking taylor expansion of 1/2 in n 1.828 * [backup-simplify]: Simplify 1/2 into 1/2 1.828 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1.828 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 1.828 * [taylor]: Taking taylor expansion of -2 in n 1.828 * [backup-simplify]: Simplify -2 into -2 1.828 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.828 * [taylor]: Taking taylor expansion of PI in n 1.828 * [backup-simplify]: Simplify PI into PI 1.828 * [taylor]: Taking taylor expansion of n in n 1.828 * [backup-simplify]: Simplify 0 into 0 1.828 * [backup-simplify]: Simplify 1 into 1 1.829 * [backup-simplify]: Simplify (/ PI 1) into PI 1.829 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 1.830 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1.830 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1.830 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1.832 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1.833 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1.834 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1.834 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1.834 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1.834 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1.834 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1.834 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1.834 * [taylor]: Taking taylor expansion of 1/2 in n 1.834 * [backup-simplify]: Simplify 1/2 into 1/2 1.834 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.834 * [taylor]: Taking taylor expansion of k in n 1.834 * [backup-simplify]: Simplify k into k 1.834 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.834 * [taylor]: Taking taylor expansion of 1/2 in n 1.834 * [backup-simplify]: Simplify 1/2 into 1/2 1.834 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1.834 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 1.834 * [taylor]: Taking taylor expansion of -2 in n 1.834 * [backup-simplify]: Simplify -2 into -2 1.834 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.834 * [taylor]: Taking taylor expansion of PI in n 1.834 * [backup-simplify]: Simplify PI into PI 1.834 * [taylor]: Taking taylor expansion of n in n 1.834 * [backup-simplify]: Simplify 0 into 0 1.834 * [backup-simplify]: Simplify 1 into 1 1.834 * [backup-simplify]: Simplify (/ PI 1) into PI 1.835 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 1.835 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1.835 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1.835 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1.836 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1.837 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1.838 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1.838 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1.838 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1.838 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1.838 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1.838 * [taylor]: Taking taylor expansion of 1/2 in k 1.838 * [backup-simplify]: Simplify 1/2 into 1/2 1.838 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.838 * [taylor]: Taking taylor expansion of k in k 1.838 * [backup-simplify]: Simplify 0 into 0 1.838 * [backup-simplify]: Simplify 1 into 1 1.838 * [backup-simplify]: Simplify (/ 1 1) into 1 1.838 * [taylor]: Taking taylor expansion of 1/2 in k 1.838 * [backup-simplify]: Simplify 1/2 into 1/2 1.838 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1.838 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 1.838 * [taylor]: Taking taylor expansion of (* -2 PI) in k 1.838 * [taylor]: Taking taylor expansion of -2 in k 1.838 * [backup-simplify]: Simplify -2 into -2 1.838 * [taylor]: Taking taylor expansion of PI in k 1.838 * [backup-simplify]: Simplify PI into PI 1.839 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 1.839 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1.839 * [taylor]: Taking taylor expansion of (log n) in k 1.839 * [taylor]: Taking taylor expansion of n in k 1.839 * [backup-simplify]: Simplify n into n 1.840 * [backup-simplify]: Simplify (log n) into (log n) 1.840 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 1.840 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 1.840 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.841 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1.841 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1.842 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1.843 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1.843 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.844 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 1.845 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1.845 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.845 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1.845 * [backup-simplify]: Simplify (+ 0 0) into 0 1.849 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1.849 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1.851 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1.851 * [taylor]: Taking taylor expansion of 0 in k 1.851 * [backup-simplify]: Simplify 0 into 0 1.851 * [backup-simplify]: Simplify 0 into 0 1.851 * [backup-simplify]: Simplify 0 into 0 1.851 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.852 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1.854 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 1.854 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.855 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1.855 * [backup-simplify]: Simplify (+ 0 0) into 0 1.856 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1.857 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1.858 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.858 * [taylor]: Taking taylor expansion of 0 in k 1.858 * [backup-simplify]: Simplify 0 into 0 1.858 * [backup-simplify]: Simplify 0 into 0 1.858 * [backup-simplify]: Simplify 0 into 0 1.858 * [backup-simplify]: Simplify 0 into 0 1.859 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.860 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.864 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 1.865 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.866 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1.866 * [backup-simplify]: Simplify (+ 0 0) into 0 1.868 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1.870 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1.873 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1.873 * [taylor]: Taking taylor expansion of 0 in k 1.873 * [backup-simplify]: Simplify 0 into 0 1.873 * [backup-simplify]: Simplify 0 into 0 1.874 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1.874 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1) 1.875 * [backup-simplify]: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1.875 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1.875 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.875 * [taylor]: Taking taylor expansion of 2 in n 1.875 * [backup-simplify]: Simplify 2 into 2 1.875 * [taylor]: Taking taylor expansion of (* n PI) in n 1.875 * [taylor]: Taking taylor expansion of n in n 1.875 * [backup-simplify]: Simplify 0 into 0 1.875 * [backup-simplify]: Simplify 1 into 1 1.875 * [taylor]: Taking taylor expansion of PI in n 1.875 * [backup-simplify]: Simplify PI into PI 1.875 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.875 * [taylor]: Taking taylor expansion of 2 in n 1.875 * [backup-simplify]: Simplify 2 into 2 1.875 * [taylor]: Taking taylor expansion of (* n PI) in n 1.875 * [taylor]: Taking taylor expansion of n in n 1.875 * [backup-simplify]: Simplify 0 into 0 1.875 * [backup-simplify]: Simplify 1 into 1 1.875 * [taylor]: Taking taylor expansion of PI in n 1.875 * [backup-simplify]: Simplify PI into PI 1.876 * [backup-simplify]: Simplify (* 0 PI) into 0 1.876 * [backup-simplify]: Simplify (* 2 0) into 0 1.876 * [backup-simplify]: Simplify 0 into 0 1.877 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.878 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1.879 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 1.879 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.880 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1.880 * [backup-simplify]: Simplify 0 into 0 1.881 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.881 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.881 * [backup-simplify]: Simplify 0 into 0 1.882 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.883 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1.883 * [backup-simplify]: Simplify 0 into 0 1.884 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.885 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1.885 * [backup-simplify]: Simplify 0 into 0 1.886 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.887 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1.887 * [backup-simplify]: Simplify 0 into 0 1.888 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1.889 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1.889 * [backup-simplify]: Simplify 0 into 0 1.889 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1.889 * [backup-simplify]: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1.890 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1.890 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.890 * [taylor]: Taking taylor expansion of 2 in n 1.890 * [backup-simplify]: Simplify 2 into 2 1.890 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.890 * [taylor]: Taking taylor expansion of PI in n 1.890 * [backup-simplify]: Simplify PI into PI 1.890 * [taylor]: Taking taylor expansion of n in n 1.890 * [backup-simplify]: Simplify 0 into 0 1.890 * [backup-simplify]: Simplify 1 into 1 1.890 * [backup-simplify]: Simplify (/ PI 1) into PI 1.890 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.890 * [taylor]: Taking taylor expansion of 2 in n 1.890 * [backup-simplify]: Simplify 2 into 2 1.890 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.890 * [taylor]: Taking taylor expansion of PI in n 1.890 * [backup-simplify]: Simplify PI into PI 1.890 * [taylor]: Taking taylor expansion of n in n 1.890 * [backup-simplify]: Simplify 0 into 0 1.890 * [backup-simplify]: Simplify 1 into 1 1.890 * [backup-simplify]: Simplify (/ PI 1) into PI 1.891 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 1.891 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 1.892 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.892 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 1.892 * [backup-simplify]: Simplify 0 into 0 1.893 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.893 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1.893 * [backup-simplify]: Simplify 0 into 0 1.894 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.895 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.895 * [backup-simplify]: Simplify 0 into 0 1.895 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.896 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.896 * [backup-simplify]: Simplify 0 into 0 1.897 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.898 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.898 * [backup-simplify]: Simplify 0 into 0 1.899 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.899 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.900 * [backup-simplify]: Simplify 0 into 0 1.900 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1.900 * [backup-simplify]: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1.900 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1.900 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 1.900 * [taylor]: Taking taylor expansion of -2 in n 1.900 * [backup-simplify]: Simplify -2 into -2 1.900 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.900 * [taylor]: Taking taylor expansion of PI in n 1.900 * [backup-simplify]: Simplify PI into PI 1.900 * [taylor]: Taking taylor expansion of n in n 1.900 * [backup-simplify]: Simplify 0 into 0 1.900 * [backup-simplify]: Simplify 1 into 1 1.900 * [backup-simplify]: Simplify (/ PI 1) into PI 1.900 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 1.900 * [taylor]: Taking taylor expansion of -2 in n 1.900 * [backup-simplify]: Simplify -2 into -2 1.901 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.901 * [taylor]: Taking taylor expansion of PI in n 1.901 * [backup-simplify]: Simplify PI into PI 1.901 * [taylor]: Taking taylor expansion of n in n 1.901 * [backup-simplify]: Simplify 0 into 0 1.901 * [backup-simplify]: Simplify 1 into 1 1.901 * [backup-simplify]: Simplify (/ PI 1) into PI 1.901 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 1.902 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 1.902 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.903 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 1.903 * [backup-simplify]: Simplify 0 into 0 1.903 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.904 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1.904 * [backup-simplify]: Simplify 0 into 0 1.904 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.905 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.905 * [backup-simplify]: Simplify 0 into 0 1.906 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.907 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.907 * [backup-simplify]: Simplify 0 into 0 1.907 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.908 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.908 * [backup-simplify]: Simplify 0 into 0 1.909 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.910 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.911 * [backup-simplify]: Simplify 0 into 0 1.911 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1.911 * * * * [progress]: [ 3 / 3 ] generating series at (2) 1.912 * [backup-simplify]: Simplify (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 1.912 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 1.912 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1.912 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.912 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.912 * [taylor]: Taking taylor expansion of k in k 1.912 * [backup-simplify]: Simplify 0 into 0 1.912 * [backup-simplify]: Simplify 1 into 1 1.912 * [backup-simplify]: Simplify (/ 1 1) into 1 1.913 * [backup-simplify]: Simplify (sqrt 0) into 0 1.914 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.914 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1.914 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1.914 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1.914 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1.914 * [taylor]: Taking taylor expansion of 1/2 in k 1.914 * [backup-simplify]: Simplify 1/2 into 1/2 1.914 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 1.914 * [taylor]: Taking taylor expansion of 1/2 in k 1.914 * [backup-simplify]: Simplify 1/2 into 1/2 1.914 * [taylor]: Taking taylor expansion of k in k 1.914 * [backup-simplify]: Simplify 0 into 0 1.914 * [backup-simplify]: Simplify 1 into 1 1.914 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 1.914 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 1.915 * [taylor]: Taking taylor expansion of 2 in k 1.915 * [backup-simplify]: Simplify 2 into 2 1.915 * [taylor]: Taking taylor expansion of (* n PI) in k 1.915 * [taylor]: Taking taylor expansion of n in k 1.915 * [backup-simplify]: Simplify n into n 1.915 * [taylor]: Taking taylor expansion of PI in k 1.915 * [backup-simplify]: Simplify PI into PI 1.915 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.915 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1.915 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1.915 * [backup-simplify]: Simplify (* 1/2 0) into 0 1.916 * [backup-simplify]: Simplify (- 0) into 0 1.916 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 1.916 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1.916 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1.917 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1.917 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 1.917 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.917 * [taylor]: Taking taylor expansion of k in n 1.917 * [backup-simplify]: Simplify k into k 1.917 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.917 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1.917 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.917 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1.917 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1.917 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1.917 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1.917 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1.917 * [taylor]: Taking taylor expansion of 1/2 in n 1.917 * [backup-simplify]: Simplify 1/2 into 1/2 1.917 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 1.917 * [taylor]: Taking taylor expansion of 1/2 in n 1.917 * [backup-simplify]: Simplify 1/2 into 1/2 1.917 * [taylor]: Taking taylor expansion of k in n 1.917 * [backup-simplify]: Simplify k into k 1.917 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.917 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.917 * [taylor]: Taking taylor expansion of 2 in n 1.917 * [backup-simplify]: Simplify 2 into 2 1.917 * [taylor]: Taking taylor expansion of (* n PI) in n 1.918 * [taylor]: Taking taylor expansion of n in n 1.918 * [backup-simplify]: Simplify 0 into 0 1.918 * [backup-simplify]: Simplify 1 into 1 1.918 * [taylor]: Taking taylor expansion of PI in n 1.918 * [backup-simplify]: Simplify PI into PI 1.918 * [backup-simplify]: Simplify (* 0 PI) into 0 1.919 * [backup-simplify]: Simplify (* 2 0) into 0 1.920 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.922 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1.923 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.923 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 1.923 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1.923 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1.925 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.926 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1.927 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1.927 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1.927 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 1.927 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.927 * [taylor]: Taking taylor expansion of k in n 1.927 * [backup-simplify]: Simplify k into k 1.927 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.927 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1.928 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.928 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1.928 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1.928 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1.928 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1.928 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1.928 * [taylor]: Taking taylor expansion of 1/2 in n 1.928 * [backup-simplify]: Simplify 1/2 into 1/2 1.928 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 1.928 * [taylor]: Taking taylor expansion of 1/2 in n 1.928 * [backup-simplify]: Simplify 1/2 into 1/2 1.928 * [taylor]: Taking taylor expansion of k in n 1.928 * [backup-simplify]: Simplify k into k 1.928 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.928 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.928 * [taylor]: Taking taylor expansion of 2 in n 1.928 * [backup-simplify]: Simplify 2 into 2 1.928 * [taylor]: Taking taylor expansion of (* n PI) in n 1.928 * [taylor]: Taking taylor expansion of n in n 1.928 * [backup-simplify]: Simplify 0 into 0 1.928 * [backup-simplify]: Simplify 1 into 1 1.928 * [taylor]: Taking taylor expansion of PI in n 1.928 * [backup-simplify]: Simplify PI into PI 1.929 * [backup-simplify]: Simplify (* 0 PI) into 0 1.929 * [backup-simplify]: Simplify (* 2 0) into 0 1.931 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.933 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1.934 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.934 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 1.934 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1.934 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1.935 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.937 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1.938 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1.939 * [backup-simplify]: Simplify (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) 1.939 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 1.939 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1.939 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1.939 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1.939 * [taylor]: Taking taylor expansion of 1/2 in k 1.940 * [backup-simplify]: Simplify 1/2 into 1/2 1.940 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 1.940 * [taylor]: Taking taylor expansion of 1/2 in k 1.940 * [backup-simplify]: Simplify 1/2 into 1/2 1.940 * [taylor]: Taking taylor expansion of k in k 1.940 * [backup-simplify]: Simplify 0 into 0 1.940 * [backup-simplify]: Simplify 1 into 1 1.940 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1.940 * [taylor]: Taking taylor expansion of (log n) in k 1.940 * [taylor]: Taking taylor expansion of n in k 1.940 * [backup-simplify]: Simplify n into n 1.940 * [backup-simplify]: Simplify (log n) into (log n) 1.940 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 1.940 * [taylor]: Taking taylor expansion of (* 2 PI) in k 1.940 * [taylor]: Taking taylor expansion of 2 in k 1.940 * [backup-simplify]: Simplify 2 into 2 1.940 * [taylor]: Taking taylor expansion of PI in k 1.940 * [backup-simplify]: Simplify PI into PI 1.941 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 1.942 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1.942 * [backup-simplify]: Simplify (* 1/2 0) into 0 1.942 * [backup-simplify]: Simplify (- 0) into 0 1.943 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 1.944 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.945 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1.946 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1.946 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.946 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.946 * [taylor]: Taking taylor expansion of k in k 1.946 * [backup-simplify]: Simplify 0 into 0 1.946 * [backup-simplify]: Simplify 1 into 1 1.947 * [backup-simplify]: Simplify (/ 1 1) into 1 1.947 * [backup-simplify]: Simplify (sqrt 0) into 0 1.949 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.950 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 1.950 * [backup-simplify]: Simplify 0 into 0 1.951 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.952 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1.954 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1.954 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1.955 * [backup-simplify]: Simplify (- 0) into 0 1.955 * [backup-simplify]: Simplify (+ 0 0) into 0 1.957 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.958 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1.960 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.961 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 1.962 * [taylor]: Taking taylor expansion of 0 in k 1.962 * [backup-simplify]: Simplify 0 into 0 1.962 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.963 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 1.968 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1.969 * [backup-simplify]: Simplify (+ 0 0) into 0 1.970 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1.970 * [backup-simplify]: Simplify (- 1/2) into -1/2 1.971 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 1.972 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1.976 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1.980 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1.981 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1.982 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.983 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.984 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1.985 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1.985 * [backup-simplify]: Simplify (- 0) into 0 1.985 * [backup-simplify]: Simplify (+ 0 0) into 0 1.986 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1.987 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1.989 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.989 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.989 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1.990 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 1.990 * [taylor]: Taking taylor expansion of 0 in k 1.990 * [backup-simplify]: Simplify 0 into 0 1.990 * [backup-simplify]: Simplify 0 into 0 1.991 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1.993 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.994 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.994 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1.996 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1.996 * [backup-simplify]: Simplify (+ 0 0) into 0 1.997 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1.997 * [backup-simplify]: Simplify (- 0) into 0 1.997 * [backup-simplify]: Simplify (+ 0 0) into 0 1.998 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.001 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 2.006 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) 2.009 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) 2.010 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.011 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.014 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 2.015 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 2.015 * [backup-simplify]: Simplify (- 0) into 0 2.015 * [backup-simplify]: Simplify (+ 0 0) into 0 2.016 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.017 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 2.019 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.019 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.019 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 2.021 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0 2.021 * [taylor]: Taking taylor expansion of 0 in k 2.021 * [backup-simplify]: Simplify 0 into 0 2.021 * [backup-simplify]: Simplify 0 into 0 2.021 * [backup-simplify]: Simplify 0 into 0 2.021 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.024 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.026 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 2.026 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.029 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 2.030 * [backup-simplify]: Simplify (+ 0 0) into 0 2.030 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 2.031 * [backup-simplify]: Simplify (- 0) into 0 2.031 * [backup-simplify]: Simplify (+ 0 0) into 0 2.032 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 2.036 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 2.047 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) 2.057 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) 2.081 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))) 2.081 * [backup-simplify]: Simplify (/ (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 2.081 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 2.081 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 2.081 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.081 * [taylor]: Taking taylor expansion of k in k 2.081 * [backup-simplify]: Simplify 0 into 0 2.081 * [backup-simplify]: Simplify 1 into 1 2.082 * [backup-simplify]: Simplify (sqrt 0) into 0 2.082 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.082 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 2.082 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 2.083 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 2.083 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.083 * [taylor]: Taking taylor expansion of 1/2 in k 2.083 * [backup-simplify]: Simplify 1/2 into 1/2 2.083 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.083 * [taylor]: Taking taylor expansion of 1/2 in k 2.083 * [backup-simplify]: Simplify 1/2 into 1/2 2.083 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.083 * [taylor]: Taking taylor expansion of k in k 2.083 * [backup-simplify]: Simplify 0 into 0 2.083 * [backup-simplify]: Simplify 1 into 1 2.083 * [backup-simplify]: Simplify (/ 1 1) into 1 2.083 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 2.083 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 2.083 * [taylor]: Taking taylor expansion of 2 in k 2.083 * [backup-simplify]: Simplify 2 into 2 2.083 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.083 * [taylor]: Taking taylor expansion of PI in k 2.083 * [backup-simplify]: Simplify PI into PI 2.083 * [taylor]: Taking taylor expansion of n in k 2.083 * [backup-simplify]: Simplify n into n 2.083 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.083 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 2.083 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 2.083 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.084 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.084 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.084 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 2.084 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 2.084 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 2.084 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.084 * [taylor]: Taking taylor expansion of k in n 2.084 * [backup-simplify]: Simplify k into k 2.084 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.084 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.084 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.084 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.084 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.084 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.084 * [taylor]: Taking taylor expansion of 1/2 in n 2.084 * [backup-simplify]: Simplify 1/2 into 1/2 2.084 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.084 * [taylor]: Taking taylor expansion of 1/2 in n 2.084 * [backup-simplify]: Simplify 1/2 into 1/2 2.084 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.084 * [taylor]: Taking taylor expansion of k in n 2.084 * [backup-simplify]: Simplify k into k 2.085 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.085 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.085 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.085 * [taylor]: Taking taylor expansion of 2 in n 2.085 * [backup-simplify]: Simplify 2 into 2 2.085 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.085 * [taylor]: Taking taylor expansion of PI in n 2.085 * [backup-simplify]: Simplify PI into PI 2.085 * [taylor]: Taking taylor expansion of n in n 2.085 * [backup-simplify]: Simplify 0 into 0 2.085 * [backup-simplify]: Simplify 1 into 1 2.085 * [backup-simplify]: Simplify (/ PI 1) into PI 2.085 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.086 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.086 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.086 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.086 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.087 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.088 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 2.088 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 2.088 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 2.088 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.088 * [taylor]: Taking taylor expansion of k in n 2.088 * [backup-simplify]: Simplify k into k 2.089 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.089 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.089 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.089 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.089 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.089 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.089 * [taylor]: Taking taylor expansion of 1/2 in n 2.089 * [backup-simplify]: Simplify 1/2 into 1/2 2.089 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.089 * [taylor]: Taking taylor expansion of 1/2 in n 2.089 * [backup-simplify]: Simplify 1/2 into 1/2 2.089 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.089 * [taylor]: Taking taylor expansion of k in n 2.089 * [backup-simplify]: Simplify k into k 2.089 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.089 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.089 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.089 * [taylor]: Taking taylor expansion of 2 in n 2.089 * [backup-simplify]: Simplify 2 into 2 2.089 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.089 * [taylor]: Taking taylor expansion of PI in n 2.089 * [backup-simplify]: Simplify PI into PI 2.089 * [taylor]: Taking taylor expansion of n in n 2.089 * [backup-simplify]: Simplify 0 into 0 2.089 * [backup-simplify]: Simplify 1 into 1 2.089 * [backup-simplify]: Simplify (/ PI 1) into PI 2.090 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.090 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.090 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.090 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.090 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.091 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.092 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 2.093 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 2.094 * [backup-simplify]: Simplify (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) 2.094 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 2.094 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 2.094 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 2.094 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.094 * [taylor]: Taking taylor expansion of 1/2 in k 2.094 * [backup-simplify]: Simplify 1/2 into 1/2 2.094 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.094 * [taylor]: Taking taylor expansion of 1/2 in k 2.094 * [backup-simplify]: Simplify 1/2 into 1/2 2.094 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.094 * [taylor]: Taking taylor expansion of k in k 2.094 * [backup-simplify]: Simplify 0 into 0 2.094 * [backup-simplify]: Simplify 1 into 1 2.094 * [backup-simplify]: Simplify (/ 1 1) into 1 2.094 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 2.094 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.094 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.094 * [taylor]: Taking taylor expansion of 2 in k 2.094 * [backup-simplify]: Simplify 2 into 2 2.094 * [taylor]: Taking taylor expansion of PI in k 2.094 * [backup-simplify]: Simplify PI into PI 2.094 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.095 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.095 * [taylor]: Taking taylor expansion of (log n) in k 2.095 * [taylor]: Taking taylor expansion of n in k 2.095 * [backup-simplify]: Simplify n into n 2.095 * [backup-simplify]: Simplify (log n) into (log n) 2.095 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.096 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.096 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.096 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.097 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 2.097 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 2.098 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 2.098 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.098 * [taylor]: Taking taylor expansion of k in k 2.098 * [backup-simplify]: Simplify 0 into 0 2.098 * [backup-simplify]: Simplify 1 into 1 2.098 * [backup-simplify]: Simplify (sqrt 0) into 0 2.099 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.100 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 2.100 * [backup-simplify]: Simplify 0 into 0 2.100 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.101 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.102 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.102 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.102 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.103 * [backup-simplify]: Simplify (- 0) into 0 2.103 * [backup-simplify]: Simplify (+ 0 0) into 0 2.104 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.104 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 2.105 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.106 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 2.106 * [taylor]: Taking taylor expansion of 0 in k 2.106 * [backup-simplify]: Simplify 0 into 0 2.106 * [backup-simplify]: Simplify 0 into 0 2.107 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 2.108 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 2.109 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.110 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.111 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 2.111 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.112 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.112 * [backup-simplify]: Simplify (- 0) into 0 2.112 * [backup-simplify]: Simplify (+ 0 0) into 0 2.114 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.115 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 2.118 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.119 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 2.120 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 2.120 * [taylor]: Taking taylor expansion of 0 in k 2.120 * [backup-simplify]: Simplify 0 into 0 2.120 * [backup-simplify]: Simplify 0 into 0 2.120 * [backup-simplify]: Simplify 0 into 0 2.123 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.125 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 2.127 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 2.128 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.129 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.135 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 2.135 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.137 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 2.137 * [backup-simplify]: Simplify (- 0) into 0 2.138 * [backup-simplify]: Simplify (+ 0 0) into 0 2.139 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.141 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 2.145 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.145 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 2.148 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 2.148 * [taylor]: Taking taylor expansion of 0 in k 2.148 * [backup-simplify]: Simplify 0 into 0 2.148 * [backup-simplify]: Simplify 0 into 0 2.148 * [backup-simplify]: Simplify 0 into 0 2.148 * [backup-simplify]: Simplify 0 into 0 2.152 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.154 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 2.156 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 2.160 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 2.160 * [backup-simplify]: Simplify (/ (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 2.161 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 2.161 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 2.161 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 2.161 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 2.161 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 2.161 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.161 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.161 * [taylor]: Taking taylor expansion of 1/2 in k 2.161 * [backup-simplify]: Simplify 1/2 into 1/2 2.161 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.161 * [taylor]: Taking taylor expansion of k in k 2.161 * [backup-simplify]: Simplify 0 into 0 2.161 * [backup-simplify]: Simplify 1 into 1 2.161 * [backup-simplify]: Simplify (/ 1 1) into 1 2.161 * [taylor]: Taking taylor expansion of 1/2 in k 2.161 * [backup-simplify]: Simplify 1/2 into 1/2 2.162 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 2.162 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 2.162 * [taylor]: Taking taylor expansion of -2 in k 2.162 * [backup-simplify]: Simplify -2 into -2 2.162 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.162 * [taylor]: Taking taylor expansion of PI in k 2.162 * [backup-simplify]: Simplify PI into PI 2.162 * [taylor]: Taking taylor expansion of n in k 2.162 * [backup-simplify]: Simplify n into n 2.162 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.162 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 2.162 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 2.162 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.163 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.163 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 2.163 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 2.163 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.163 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.163 * [taylor]: Taking taylor expansion of -1 in k 2.163 * [backup-simplify]: Simplify -1 into -1 2.163 * [taylor]: Taking taylor expansion of k in k 2.163 * [backup-simplify]: Simplify 0 into 0 2.163 * [backup-simplify]: Simplify 1 into 1 2.164 * [backup-simplify]: Simplify (/ -1 1) into -1 2.164 * [backup-simplify]: Simplify (sqrt 0) into 0 2.166 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.166 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 2.166 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 2.166 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.166 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.166 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.166 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.166 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.166 * [taylor]: Taking taylor expansion of 1/2 in n 2.166 * [backup-simplify]: Simplify 1/2 into 1/2 2.166 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.166 * [taylor]: Taking taylor expansion of k in n 2.166 * [backup-simplify]: Simplify k into k 2.166 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.166 * [taylor]: Taking taylor expansion of 1/2 in n 2.166 * [backup-simplify]: Simplify 1/2 into 1/2 2.166 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.166 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.167 * [taylor]: Taking taylor expansion of -2 in n 2.167 * [backup-simplify]: Simplify -2 into -2 2.167 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.167 * [taylor]: Taking taylor expansion of PI in n 2.167 * [backup-simplify]: Simplify PI into PI 2.167 * [taylor]: Taking taylor expansion of n in n 2.167 * [backup-simplify]: Simplify 0 into 0 2.167 * [backup-simplify]: Simplify 1 into 1 2.167 * [backup-simplify]: Simplify (/ PI 1) into PI 2.168 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.169 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.169 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.169 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.171 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.172 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 2.173 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 2.173 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.173 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.173 * [taylor]: Taking taylor expansion of -1 in n 2.173 * [backup-simplify]: Simplify -1 into -1 2.173 * [taylor]: Taking taylor expansion of k in n 2.173 * [backup-simplify]: Simplify k into k 2.173 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.173 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.174 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.174 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.175 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 2.175 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 2.175 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.175 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.175 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.175 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.175 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.175 * [taylor]: Taking taylor expansion of 1/2 in n 2.175 * [backup-simplify]: Simplify 1/2 into 1/2 2.175 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.175 * [taylor]: Taking taylor expansion of k in n 2.176 * [backup-simplify]: Simplify k into k 2.176 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.176 * [taylor]: Taking taylor expansion of 1/2 in n 2.176 * [backup-simplify]: Simplify 1/2 into 1/2 2.176 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.176 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.176 * [taylor]: Taking taylor expansion of -2 in n 2.176 * [backup-simplify]: Simplify -2 into -2 2.176 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.176 * [taylor]: Taking taylor expansion of PI in n 2.176 * [backup-simplify]: Simplify PI into PI 2.176 * [taylor]: Taking taylor expansion of n in n 2.176 * [backup-simplify]: Simplify 0 into 0 2.176 * [backup-simplify]: Simplify 1 into 1 2.176 * [backup-simplify]: Simplify (/ PI 1) into PI 2.177 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.178 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.178 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.178 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.180 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.181 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 2.182 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 2.182 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.182 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.182 * [taylor]: Taking taylor expansion of -1 in n 2.182 * [backup-simplify]: Simplify -1 into -1 2.182 * [taylor]: Taking taylor expansion of k in n 2.183 * [backup-simplify]: Simplify k into k 2.183 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.183 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.183 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.183 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.184 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 2.184 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 2.184 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 2.184 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 2.184 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.185 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.185 * [taylor]: Taking taylor expansion of 1/2 in k 2.185 * [backup-simplify]: Simplify 1/2 into 1/2 2.185 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.185 * [taylor]: Taking taylor expansion of k in k 2.185 * [backup-simplify]: Simplify 0 into 0 2.185 * [backup-simplify]: Simplify 1 into 1 2.188 * [backup-simplify]: Simplify (/ 1 1) into 1 2.189 * [taylor]: Taking taylor expansion of 1/2 in k 2.189 * [backup-simplify]: Simplify 1/2 into 1/2 2.189 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 2.189 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 2.189 * [taylor]: Taking taylor expansion of (* -2 PI) in k 2.189 * [taylor]: Taking taylor expansion of -2 in k 2.189 * [backup-simplify]: Simplify -2 into -2 2.189 * [taylor]: Taking taylor expansion of PI in k 2.189 * [backup-simplify]: Simplify PI into PI 2.190 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.191 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.191 * [taylor]: Taking taylor expansion of (log n) in k 2.191 * [taylor]: Taking taylor expansion of n in k 2.191 * [backup-simplify]: Simplify n into n 2.191 * [backup-simplify]: Simplify (log n) into (log n) 2.192 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.192 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.192 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.193 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 2.195 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 2.196 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 2.196 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.196 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.196 * [taylor]: Taking taylor expansion of -1 in k 2.196 * [backup-simplify]: Simplify -1 into -1 2.196 * [taylor]: Taking taylor expansion of k in k 2.196 * [backup-simplify]: Simplify 0 into 0 2.196 * [backup-simplify]: Simplify 1 into 1 2.197 * [backup-simplify]: Simplify (/ -1 1) into -1 2.197 * [backup-simplify]: Simplify (sqrt 0) into 0 2.198 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.200 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 2.201 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 2.202 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.203 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.205 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 2.205 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.206 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.206 * [backup-simplify]: Simplify (+ 0 0) into 0 2.208 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.209 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 2.211 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.213 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 2.213 * [taylor]: Taking taylor expansion of 0 in k 2.213 * [backup-simplify]: Simplify 0 into 0 2.213 * [backup-simplify]: Simplify 0 into 0 2.214 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.217 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.219 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 2.220 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 2.222 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.223 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.226 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 2.227 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.228 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.228 * [backup-simplify]: Simplify (+ 0 0) into 0 2.229 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.231 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 2.233 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.233 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.234 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 2.235 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 2.235 * [taylor]: Taking taylor expansion of 0 in k 2.235 * [backup-simplify]: Simplify 0 into 0 2.235 * [backup-simplify]: Simplify 0 into 0 2.235 * [backup-simplify]: Simplify 0 into 0 2.235 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.238 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.240 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 2.241 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 2.244 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 2.244 * * * [progress]: simplifying candidates 2.244 * * * * [progress]: [ 1 / 442 ] simplifiying candidate # 2.244 * * * * [progress]: [ 2 / 442 ] simplifiying candidate # 2.244 * * * * [progress]: [ 3 / 442 ] simplifiying candidate # 2.244 * * * * [progress]: [ 4 / 442 ] simplifiying candidate # 2.244 * * * * [progress]: [ 5 / 442 ] simplifiying candidate # 2.244 * * * * [progress]: [ 6 / 442 ] simplifiying candidate # 2.244 * * * * [progress]: [ 7 / 442 ] simplifiying candidate # 2.244 * * * * [progress]: [ 8 / 442 ] simplifiying candidate # 2.244 * * * * [progress]: [ 9 / 442 ] simplifiying candidate # 2.244 * * * * [progress]: [ 10 / 442 ] simplifiying candidate # 2.244 * * * * [progress]: [ 11 / 442 ] simplifiying candidate # 2.244 * * * * [progress]: [ 12 / 442 ] simplifiying candidate # 2.244 * * * * [progress]: [ 13 / 442 ] simplifiying candidate # 2.244 * * * * [progress]: [ 14 / 442 ] simplifiying candidate # 2.244 * * * * 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(cbrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (pow (* PI (* n 2)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* PI (* n 2)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (pow (* PI (* n 2)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow (* PI (* n 2)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* PI (* n 2)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (pow (* PI (* n 2)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (pow (* PI (* n 2)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (pow (* PI (* n 2)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 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1 n))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 2.287 * * [simplify]: iteration 1: (695 enodes) 2.640 * * [simplify]: iteration 2: (1514 enodes) 3.819 * * [simplify]: Extracting #0: cost 209 inf + 0 3.821 * * [simplify]: Extracting #1: cost 781 inf + 1 3.828 * * [simplify]: Extracting #2: cost 1210 inf + 2911 3.846 * * [simplify]: Extracting #3: cost 1363 inf + 37527 3.867 * * [simplify]: Extracting #4: cost 1060 inf + 148290 3.927 * * [simplify]: Extracting #5: cost 603 inf + 339750 4.052 * * [simplify]: Extracting #6: cost 281 inf + 529112 4.172 * * [simplify]: Extracting #7: cost 48 inf + 685517 4.336 * * [simplify]: Extracting #8: cost 1 inf + 720252 4.513 * * [simplify]: Extracting #9: cost 0 inf + 719138 4.709 * * [simplify]: Extracting #10: cost 0 inf + 718928 4.915 * [simplify]: Simplified to: (expm1 (pow (* (* 2 n) PI) (- 1/2 (* 1/2 k)))) (log1p (pow (* (* 2 n) PI) (- 1/2 (* 1/2 k)))) (* (log (* (* 2 n) PI)) (- 1/2 (* 1/2 k))) (* (log (* (* 2 n) PI)) (- 1/2 (* 1/2 k))) (* (log (* (* 2 n) PI)) (- 1/2 (* 1/2 k))) (* (log (* (* 2 n) PI)) (- 1/2 (* 1/2 k))) (- 1/2 (* 1/2 k)) (- 1/2 (* 1/2 k)) (- 1/2 (* 1/2 k)) (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (* 1/2 k)) (pow (* (* 2 n) PI) (* (cbrt (- 1/2 (* 1/2 k))) (cbrt (- 1/2 (* 1/2 k))))) (pow (* (* 2 n) PI) (sqrt (- 1/2 (* 1/2 k)))) (* (* 2 n) PI) (pow (* (* 2 n) PI) (+ (sqrt 1/2) (sqrt (* 1/2 k)))) (pow (* (* 2 n) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (* (* 2 n) PI) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* -1/2 k))) (pow (* (* 2 n) PI) (fma -1/2 k (* 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2)) (/ (sqrt k) (cbrt 2))) (cbrt 2))) (/ (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (cbrt 2))) (cbrt 2))))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (/ (sqrt k) (sqrt 2)) (+ (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (+ (- (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2))) (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2))))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma (/ k (sqrt 2)) (/ -1 (sqrt 2)) (/ (/ k (sqrt 2)) (sqrt 2))))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))) (+ (- (/ (cbrt k) (cbrt 2))) (/ (cbrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (/ (cbrt k) (sqrt 2)) (+ (- (/ (* (cbrt k) (cbrt k)) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (* (cbrt k) (cbrt k)) (+ (- (/ (cbrt k) 2)) (/ (cbrt k) 2))))) (/ (sqrt k) (pow (* (* 2 n) PI) (+ (- (/ (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (cbrt 2))) (cbrt 2))) (/ (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (cbrt 2))) (cbrt 2))))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (/ (sqrt k) (sqrt 2)) (+ (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (+ (- (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2))) (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2))))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma (/ k (sqrt 2)) (/ -1 (sqrt 2)) (/ (/ k (sqrt 2)) (sqrt 2))))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (* -1/2 k))) (/ (sqrt k) (pow (* (* 2 n) PI) (* -1/2 k))) (/ (sqrt k) (pow (* 2 n) (- 1/2 (* 1/2 k)))) (/ (sqrt k) (cbrt (pow (* (* 2 n) PI) (- 1/2 (* 1/2 k))))) (/ (sqrt k) (sqrt (pow (* (* 2 n) PI) (- 1/2 (* 1/2 k))))) (/ (sqrt k) (pow (* (* 2 n) PI) (- 1/2 (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (- 1/4 (/ k 4)))) (* (pow (* (* 2 n) PI) (* 1/2 k)) (sqrt k)) (fma (* 1/4 (log (* PI 2))) (* (* (exp (* (log (* (* 2 n) PI)) 1/2)) (log n)) (* k k)) (- (fma (* (* (* k (log n)) (* k (log n))) (exp (* (log (* (* 2 n) PI)) 1/2))) 1/8 (fma 1/8 (* (* (exp (* (log (* (* 2 n) PI)) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* k k)) (exp (* (log (* (* 2 n) PI)) 1/2)))) (* (* k (+ (* (exp (* (log (* (* 2 n) PI)) 1/2)) (log n)) (* (exp (* (log (* (* 2 n) PI)) 1/2)) (log (* PI 2))))) 1/2))) (exp (* (log (* (* 2 n) PI)) (- 1/2 (* 1/2 k)))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n))))) (* (* 2 n) PI) (* (* 2 n) PI) (* (* 2 n) PI) (+ (* (* (exp (* (log (* (* 2 n) PI)) 1/2)) (* (* (* k k) (log n)) (log (* PI 2)))) (- +nan.0)) (- (* (* (exp (* (log (* (* 2 n) PI)) 1/2)) (log (* PI 2))) (* (* k k) +nan.0)) (fma (* (exp (* (log (* (* 2 n) PI)) 1/2)) +nan.0) (* (* k (log n)) (* k (log n))) (+ (* (* (exp (* (log (* (* 2 n) PI)) 1/2)) k) (- +nan.0)) (+ (- (* (exp (* (log (* (* 2 n) PI)) 1/2)) +nan.0) (* (* (log (* PI 2)) (log (* PI 2))) (* (* (exp (* (log (* (* 2 n) PI)) 1/2)) +nan.0) (* k k)))) (fma (* (exp (* (log (* (* 2 n) PI)) 1/2)) +nan.0) (* (* k k) (log n)) (- (- (* (* (exp (* (log (* (* 2 n) PI)) 1/2)) +nan.0) (* k k)) (* +nan.0 (- (* (log (* PI 2)) (* (exp (* (log (* (* 2 n) PI)) 1/2)) k)) (* (* (exp (* (log (* (* 2 n) PI)) 1/2)) k) (log n)))))))))))) (- (- (* +nan.0 (/ (exp (* (log (* (* 2 n) PI)) (- 1/2 (* 1/2 k)))) (* (* k k) k))) (* +nan.0 (- (/ (exp (* (log (* (* 2 n) PI)) (- 1/2 (* 1/2 k)))) k) (/ (exp (* (log (* (* 2 n) PI)) (- 1/2 (* 1/2 k)))) (* k k)))))) (+ (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n))))) k))) (* +nan.0 (- (/ (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n))))) k) k) (exp (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n)))))))) 5.062 * * * [progress]: adding candidates to table 11.825 * * [progress]: iteration 2 / 4 11.825 * * * [progress]: picking best candidate 11.877 * * * * [pick]: Picked # 11.877 * * * [progress]: localizing error 11.909 * * * [progress]: generating rewritten candidates 11.909 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 11.944 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 11.954 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 11.979 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 12.040 * * * [progress]: generating series expansions 12.040 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 12.041 * [backup-simplify]: Simplify (pow (* (* 2 PI) n) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) 12.041 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0 12.041 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 12.041 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 12.041 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 12.041 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k 12.041 * [taylor]: Taking taylor expansion of 1/2 in k 12.041 * [backup-simplify]: Simplify 1/2 into 1/2 12.041 * [taylor]: Taking taylor expansion of (- 1 k) in k 12.041 * [taylor]: Taking taylor expansion of 1 in k 12.041 * [backup-simplify]: Simplify 1 into 1 12.041 * [taylor]: Taking taylor expansion of k in k 12.041 * [backup-simplify]: Simplify 0 into 0 12.041 * [backup-simplify]: Simplify 1 into 1 12.042 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 12.042 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 12.042 * [taylor]: Taking taylor expansion of 2 in k 12.042 * [backup-simplify]: Simplify 2 into 2 12.042 * [taylor]: Taking taylor expansion of (* n PI) in k 12.042 * [taylor]: Taking taylor expansion of n in k 12.042 * [backup-simplify]: Simplify n into n 12.042 * [taylor]: Taking taylor expansion of PI in k 12.042 * [backup-simplify]: Simplify PI into PI 12.042 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.042 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 12.042 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 12.042 * [backup-simplify]: Simplify (- 0) into 0 12.043 * [backup-simplify]: Simplify (+ 1 0) into 1 12.043 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.043 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 12.044 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 12.044 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 12.044 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 12.044 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 12.044 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n 12.044 * [taylor]: Taking taylor expansion of 1/2 in n 12.044 * [backup-simplify]: Simplify 1/2 into 1/2 12.044 * [taylor]: Taking taylor expansion of (- 1 k) in n 12.044 * [taylor]: Taking taylor expansion of 1 in n 12.044 * [backup-simplify]: Simplify 1 into 1 12.044 * [taylor]: Taking taylor expansion of k in n 12.044 * [backup-simplify]: Simplify k into k 12.044 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 12.044 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 12.044 * [taylor]: Taking taylor expansion of 2 in n 12.044 * [backup-simplify]: Simplify 2 into 2 12.044 * [taylor]: Taking taylor expansion of (* n PI) in n 12.044 * [taylor]: Taking taylor expansion of n in n 12.044 * [backup-simplify]: Simplify 0 into 0 12.044 * [backup-simplify]: Simplify 1 into 1 12.044 * [taylor]: Taking taylor expansion of PI in n 12.044 * [backup-simplify]: Simplify PI into PI 12.045 * [backup-simplify]: Simplify (* 0 PI) into 0 12.045 * [backup-simplify]: Simplify (* 2 0) into 0 12.047 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.048 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 12.049 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.049 * [backup-simplify]: Simplify (- k) into (- k) 12.050 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k) 12.050 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 12.051 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.052 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 12.053 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 12.053 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 12.053 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 12.053 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 12.054 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n 12.054 * [taylor]: Taking taylor expansion of 1/2 in n 12.054 * [backup-simplify]: Simplify 1/2 into 1/2 12.054 * [taylor]: Taking taylor expansion of (- 1 k) in n 12.054 * [taylor]: Taking taylor expansion of 1 in n 12.054 * [backup-simplify]: Simplify 1 into 1 12.054 * [taylor]: Taking taylor expansion of k in n 12.054 * [backup-simplify]: Simplify k into k 12.054 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 12.054 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 12.054 * [taylor]: Taking taylor expansion of 2 in n 12.054 * [backup-simplify]: Simplify 2 into 2 12.054 * [taylor]: Taking taylor expansion of (* n PI) in n 12.054 * [taylor]: Taking taylor expansion of n in n 12.054 * [backup-simplify]: Simplify 0 into 0 12.054 * [backup-simplify]: Simplify 1 into 1 12.054 * [taylor]: Taking taylor expansion of PI in n 12.054 * [backup-simplify]: Simplify PI into PI 12.054 * [backup-simplify]: Simplify (* 0 PI) into 0 12.055 * [backup-simplify]: Simplify (* 2 0) into 0 12.056 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.058 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 12.059 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.059 * [backup-simplify]: Simplify (- k) into (- k) 12.059 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k) 12.059 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 12.061 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.062 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 12.063 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 12.063 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k 12.063 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k 12.063 * [taylor]: Taking taylor expansion of 1/2 in k 12.063 * [backup-simplify]: Simplify 1/2 into 1/2 12.063 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k 12.063 * [taylor]: Taking taylor expansion of (- 1 k) in k 12.063 * [taylor]: Taking taylor expansion of 1 in k 12.063 * [backup-simplify]: Simplify 1 into 1 12.063 * [taylor]: Taking taylor expansion of k in k 12.063 * [backup-simplify]: Simplify 0 into 0 12.063 * [backup-simplify]: Simplify 1 into 1 12.064 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 12.064 * [taylor]: Taking taylor expansion of (log n) in k 12.064 * [taylor]: Taking taylor expansion of n in k 12.064 * [backup-simplify]: Simplify n into n 12.064 * [backup-simplify]: Simplify (log n) into (log n) 12.064 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 12.064 * [taylor]: Taking taylor expansion of (* 2 PI) in k 12.064 * [taylor]: Taking taylor expansion of 2 in k 12.064 * [backup-simplify]: Simplify 2 into 2 12.064 * [taylor]: Taking taylor expansion of PI in k 12.064 * [backup-simplify]: Simplify PI into PI 12.064 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.065 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.066 * [backup-simplify]: Simplify (- 0) into 0 12.066 * [backup-simplify]: Simplify (+ 1 0) into 1 12.067 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.068 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI))) 12.069 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 12.071 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 12.072 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 12.073 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.074 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 12.075 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 12.076 * [backup-simplify]: Simplify (- 0) into 0 12.076 * [backup-simplify]: Simplify (+ 0 0) into 0 12.077 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0 12.078 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.079 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 12.081 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.081 * [taylor]: Taking taylor expansion of 0 in k 12.081 * [backup-simplify]: Simplify 0 into 0 12.081 * [backup-simplify]: Simplify 0 into 0 12.082 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 12.083 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 12.084 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 12.085 * [backup-simplify]: Simplify (+ 0 0) into 0 12.085 * [backup-simplify]: Simplify (- 1) into -1 12.086 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.087 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n))) 12.089 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 12.093 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 12.095 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 12.097 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.098 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 12.101 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 12.102 * [backup-simplify]: Simplify (- 0) into 0 12.102 * [backup-simplify]: Simplify (+ 0 0) into 0 12.103 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0 12.104 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.106 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 12.108 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.108 * [taylor]: Taking taylor expansion of 0 in k 12.108 * [backup-simplify]: Simplify 0 into 0 12.108 * [backup-simplify]: Simplify 0 into 0 12.108 * [backup-simplify]: Simplify 0 into 0 12.110 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 12.111 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 12.114 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 12.114 * [backup-simplify]: Simplify (+ 0 0) into 0 12.115 * [backup-simplify]: Simplify (- 0) into 0 12.115 * [backup-simplify]: Simplify (+ 0 0) into 0 12.117 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 12.120 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 12.123 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 12.129 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 12.138 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 12.139 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) 12.139 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0 12.139 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 12.139 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 12.139 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 12.139 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 12.139 * [taylor]: Taking taylor expansion of 1/2 in k 12.139 * [backup-simplify]: Simplify 1/2 into 1/2 12.139 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 12.139 * [taylor]: Taking taylor expansion of 1 in k 12.139 * [backup-simplify]: Simplify 1 into 1 12.139 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.139 * [taylor]: Taking taylor expansion of k in k 12.140 * [backup-simplify]: Simplify 0 into 0 12.140 * [backup-simplify]: Simplify 1 into 1 12.140 * [backup-simplify]: Simplify (/ 1 1) into 1 12.140 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 12.140 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 12.140 * [taylor]: Taking taylor expansion of 2 in k 12.140 * [backup-simplify]: Simplify 2 into 2 12.140 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.140 * [taylor]: Taking taylor expansion of PI in k 12.140 * [backup-simplify]: Simplify PI into PI 12.140 * [taylor]: Taking taylor expansion of n in k 12.140 * [backup-simplify]: Simplify n into n 12.140 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.140 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 12.140 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 12.141 * [backup-simplify]: Simplify (- 1) into -1 12.141 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.142 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2 12.142 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 12.142 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 12.142 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 12.142 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 12.142 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 12.142 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 12.142 * [taylor]: Taking taylor expansion of 1/2 in n 12.142 * [backup-simplify]: Simplify 1/2 into 1/2 12.142 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 12.142 * [taylor]: Taking taylor expansion of 1 in n 12.142 * [backup-simplify]: Simplify 1 into 1 12.142 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.142 * [taylor]: Taking taylor expansion of k in n 12.143 * [backup-simplify]: Simplify k into k 12.143 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.143 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 12.143 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 12.143 * [taylor]: Taking taylor expansion of 2 in n 12.143 * [backup-simplify]: Simplify 2 into 2 12.143 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.143 * [taylor]: Taking taylor expansion of PI in n 12.143 * [backup-simplify]: Simplify PI into PI 12.143 * [taylor]: Taking taylor expansion of n in n 12.143 * [backup-simplify]: Simplify 0 into 0 12.143 * [backup-simplify]: Simplify 1 into 1 12.143 * [backup-simplify]: Simplify (/ PI 1) into PI 12.144 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.145 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.145 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.145 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 12.145 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 12.147 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.148 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 12.149 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 12.149 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 12.149 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 12.149 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 12.149 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 12.149 * [taylor]: Taking taylor expansion of 1/2 in n 12.149 * [backup-simplify]: Simplify 1/2 into 1/2 12.149 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 12.149 * [taylor]: Taking taylor expansion of 1 in n 12.149 * [backup-simplify]: Simplify 1 into 1 12.149 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.149 * [taylor]: Taking taylor expansion of k in n 12.149 * [backup-simplify]: Simplify k into k 12.149 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.149 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 12.149 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 12.149 * [taylor]: Taking taylor expansion of 2 in n 12.149 * [backup-simplify]: Simplify 2 into 2 12.149 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.149 * [taylor]: Taking taylor expansion of PI in n 12.149 * [backup-simplify]: Simplify PI into PI 12.149 * [taylor]: Taking taylor expansion of n in n 12.149 * [backup-simplify]: Simplify 0 into 0 12.149 * [backup-simplify]: Simplify 1 into 1 12.150 * [backup-simplify]: Simplify (/ PI 1) into PI 12.150 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.151 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.152 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.152 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 12.152 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 12.153 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.154 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 12.155 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 12.156 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k 12.156 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k 12.156 * [taylor]: Taking taylor expansion of 1/2 in k 12.156 * [backup-simplify]: Simplify 1/2 into 1/2 12.156 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k 12.156 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 12.156 * [taylor]: Taking taylor expansion of 1 in k 12.156 * [backup-simplify]: Simplify 1 into 1 12.156 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.156 * [taylor]: Taking taylor expansion of k in k 12.156 * [backup-simplify]: Simplify 0 into 0 12.156 * [backup-simplify]: Simplify 1 into 1 12.156 * [backup-simplify]: Simplify (/ 1 1) into 1 12.156 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 12.156 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 12.156 * [taylor]: Taking taylor expansion of (* 2 PI) in k 12.156 * [taylor]: Taking taylor expansion of 2 in k 12.156 * [backup-simplify]: Simplify 2 into 2 12.156 * [taylor]: Taking taylor expansion of PI in k 12.156 * [backup-simplify]: Simplify PI into PI 12.157 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.158 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.158 * [taylor]: Taking taylor expansion of (log n) in k 12.158 * [taylor]: Taking taylor expansion of n in k 12.158 * [backup-simplify]: Simplify n into n 12.158 * [backup-simplify]: Simplify (log n) into (log n) 12.158 * [backup-simplify]: Simplify (- 1) into -1 12.159 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.159 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.160 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 12.161 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) 12.162 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) 12.163 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 12.164 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 12.173 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.174 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 12.176 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 12.176 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.176 * [backup-simplify]: Simplify (- 0) into 0 12.177 * [backup-simplify]: Simplify (+ 0 0) into 0 12.177 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0 12.179 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.181 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 12.183 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.183 * [taylor]: Taking taylor expansion of 0 in k 12.183 * [backup-simplify]: Simplify 0 into 0 12.183 * [backup-simplify]: Simplify 0 into 0 12.183 * [backup-simplify]: Simplify 0 into 0 12.184 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.185 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 12.189 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 12.189 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.189 * [backup-simplify]: Simplify (- 0) into 0 12.190 * [backup-simplify]: Simplify (+ 0 0) into 0 12.191 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0 12.193 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.195 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 12.197 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.197 * [taylor]: Taking taylor expansion of 0 in k 12.197 * [backup-simplify]: Simplify 0 into 0 12.197 * [backup-simplify]: Simplify 0 into 0 12.197 * [backup-simplify]: Simplify 0 into 0 12.197 * [backup-simplify]: Simplify 0 into 0 12.199 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.200 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.206 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 12.207 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.207 * [backup-simplify]: Simplify (- 0) into 0 12.208 * [backup-simplify]: Simplify (+ 0 0) into 0 12.209 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0 12.210 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.212 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 12.215 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 12.215 * [taylor]: Taking taylor expansion of 0 in k 12.215 * [backup-simplify]: Simplify 0 into 0 12.215 * [backup-simplify]: Simplify 0 into 0 12.216 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) 12.217 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) 12.217 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0 12.217 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 12.217 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 12.217 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 12.217 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 12.217 * [taylor]: Taking taylor expansion of 1/2 in k 12.217 * [backup-simplify]: Simplify 1/2 into 1/2 12.217 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 12.217 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.217 * [taylor]: Taking taylor expansion of k in k 12.217 * [backup-simplify]: Simplify 0 into 0 12.217 * [backup-simplify]: Simplify 1 into 1 12.218 * [backup-simplify]: Simplify (/ 1 1) into 1 12.218 * [taylor]: Taking taylor expansion of 1 in k 12.218 * [backup-simplify]: Simplify 1 into 1 12.218 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 12.218 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 12.218 * [taylor]: Taking taylor expansion of -2 in k 12.218 * [backup-simplify]: Simplify -2 into -2 12.218 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.218 * [taylor]: Taking taylor expansion of PI in k 12.218 * [backup-simplify]: Simplify PI into PI 12.218 * [taylor]: Taking taylor expansion of n in k 12.218 * [backup-simplify]: Simplify n into n 12.218 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.218 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 12.218 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 12.219 * [backup-simplify]: Simplify (+ 1 0) into 1 12.219 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.219 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 12.219 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 12.220 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 12.220 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 12.220 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 12.220 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 12.220 * [taylor]: Taking taylor expansion of 1/2 in n 12.220 * [backup-simplify]: Simplify 1/2 into 1/2 12.220 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 12.220 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.220 * [taylor]: Taking taylor expansion of k in n 12.220 * [backup-simplify]: Simplify k into k 12.220 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.220 * [taylor]: Taking taylor expansion of 1 in n 12.220 * [backup-simplify]: Simplify 1 into 1 12.220 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 12.220 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.220 * [taylor]: Taking taylor expansion of -2 in n 12.220 * [backup-simplify]: Simplify -2 into -2 12.220 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.220 * [taylor]: Taking taylor expansion of PI in n 12.220 * [backup-simplify]: Simplify PI into PI 12.220 * [taylor]: Taking taylor expansion of n in n 12.220 * [backup-simplify]: Simplify 0 into 0 12.220 * [backup-simplify]: Simplify 1 into 1 12.221 * [backup-simplify]: Simplify (/ PI 1) into PI 12.221 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.222 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.222 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 12.222 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 12.223 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.223 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 12.224 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 12.224 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 12.224 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 12.224 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 12.224 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 12.224 * [taylor]: Taking taylor expansion of 1/2 in n 12.224 * [backup-simplify]: Simplify 1/2 into 1/2 12.224 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 12.224 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.224 * [taylor]: Taking taylor expansion of k in n 12.224 * [backup-simplify]: Simplify k into k 12.224 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.224 * [taylor]: Taking taylor expansion of 1 in n 12.224 * [backup-simplify]: Simplify 1 into 1 12.224 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 12.224 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.224 * [taylor]: Taking taylor expansion of -2 in n 12.224 * [backup-simplify]: Simplify -2 into -2 12.224 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.224 * [taylor]: Taking taylor expansion of PI in n 12.224 * [backup-simplify]: Simplify PI into PI 12.224 * [taylor]: Taking taylor expansion of n in n 12.225 * [backup-simplify]: Simplify 0 into 0 12.225 * [backup-simplify]: Simplify 1 into 1 12.225 * [backup-simplify]: Simplify (/ PI 1) into PI 12.225 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.226 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.226 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 12.226 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 12.227 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.227 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 12.228 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 12.228 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k 12.228 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k 12.228 * [taylor]: Taking taylor expansion of 1/2 in k 12.228 * [backup-simplify]: Simplify 1/2 into 1/2 12.228 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k 12.228 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 12.228 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.228 * [taylor]: Taking taylor expansion of k in k 12.228 * [backup-simplify]: Simplify 0 into 0 12.228 * [backup-simplify]: Simplify 1 into 1 12.229 * [backup-simplify]: Simplify (/ 1 1) into 1 12.229 * [taylor]: Taking taylor expansion of 1 in k 12.229 * [backup-simplify]: Simplify 1 into 1 12.229 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 12.229 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 12.229 * [taylor]: Taking taylor expansion of (* -2 PI) in k 12.229 * [taylor]: Taking taylor expansion of -2 in k 12.229 * [backup-simplify]: Simplify -2 into -2 12.229 * [taylor]: Taking taylor expansion of PI in k 12.229 * [backup-simplify]: Simplify PI into PI 12.229 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.230 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.230 * [taylor]: Taking taylor expansion of (log n) in k 12.230 * [taylor]: Taking taylor expansion of n in k 12.230 * [backup-simplify]: Simplify n into n 12.230 * [backup-simplify]: Simplify (log n) into (log n) 12.230 * [backup-simplify]: Simplify (+ 1 0) into 1 12.230 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.231 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 12.231 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) 12.232 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 12.233 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 12.234 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 12.234 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.235 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 12.236 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 12.236 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.236 * [backup-simplify]: Simplify (+ 0 0) into 0 12.236 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0 12.237 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.238 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 12.239 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.239 * [taylor]: Taking taylor expansion of 0 in k 12.239 * [backup-simplify]: Simplify 0 into 0 12.239 * [backup-simplify]: Simplify 0 into 0 12.239 * [backup-simplify]: Simplify 0 into 0 12.240 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.241 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 12.242 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 12.243 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.243 * [backup-simplify]: Simplify (+ 0 0) into 0 12.243 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0 12.244 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.245 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 12.247 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.247 * [taylor]: Taking taylor expansion of 0 in k 12.247 * [backup-simplify]: Simplify 0 into 0 12.247 * [backup-simplify]: Simplify 0 into 0 12.247 * [backup-simplify]: Simplify 0 into 0 12.247 * [backup-simplify]: Simplify 0 into 0 12.247 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.248 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.254 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 12.254 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.255 * [backup-simplify]: Simplify (+ 0 0) into 0 12.256 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0 12.257 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.259 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 12.262 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 12.262 * [taylor]: Taking taylor expansion of 0 in k 12.262 * [backup-simplify]: Simplify 0 into 0 12.262 * [backup-simplify]: Simplify 0 into 0 12.263 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) 12.263 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 12.263 * [backup-simplify]: Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k)) 12.263 * [approximate]: Taking taylor expansion of (sqrt (/ 1 k)) in (k) around 0 12.263 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 12.263 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.263 * [taylor]: Taking taylor expansion of k in k 12.263 * [backup-simplify]: Simplify 0 into 0 12.263 * [backup-simplify]: Simplify 1 into 1 12.264 * [backup-simplify]: Simplify (/ 1 1) into 1 12.264 * [backup-simplify]: Simplify (sqrt 0) into 0 12.265 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.266 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 12.266 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.266 * [taylor]: Taking taylor expansion of k in k 12.266 * [backup-simplify]: Simplify 0 into 0 12.266 * [backup-simplify]: Simplify 1 into 1 12.266 * [backup-simplify]: Simplify (/ 1 1) into 1 12.266 * [backup-simplify]: Simplify (sqrt 0) into 0 12.268 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.268 * [backup-simplify]: Simplify 0 into 0 12.268 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.268 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 12.271 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.271 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.272 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.276 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.276 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.276 * [backup-simplify]: Simplify (+ (* +nan.0 (pow k 2)) (+ (* +nan.0 k) +nan.0)) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 12.276 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k) 12.276 * [approximate]: Taking taylor expansion of (sqrt k) in (k) around 0 12.276 * [taylor]: Taking taylor expansion of (sqrt k) in k 12.276 * [taylor]: Taking taylor expansion of k in k 12.276 * [backup-simplify]: Simplify 0 into 0 12.276 * [backup-simplify]: Simplify 1 into 1 12.277 * [backup-simplify]: Simplify (sqrt 0) into 0 12.278 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.278 * [taylor]: Taking taylor expansion of (sqrt k) in k 12.278 * [taylor]: Taking taylor expansion of k in k 12.278 * [backup-simplify]: Simplify 0 into 0 12.278 * [backup-simplify]: Simplify 1 into 1 12.279 * [backup-simplify]: Simplify (sqrt 0) into 0 12.280 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.280 * [backup-simplify]: Simplify 0 into 0 12.280 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.283 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.283 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.287 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.287 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.287 * [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)))))))) 12.287 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 (- k)))) into (/ 1 (sqrt (/ -1 k))) 12.287 * [approximate]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in (k) around 0 12.287 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 12.287 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.287 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.287 * [taylor]: Taking taylor expansion of -1 in k 12.287 * [backup-simplify]: Simplify -1 into -1 12.287 * [taylor]: Taking taylor expansion of k in k 12.287 * [backup-simplify]: Simplify 0 into 0 12.287 * [backup-simplify]: Simplify 1 into 1 12.288 * [backup-simplify]: Simplify (/ -1 1) into -1 12.288 * [backup-simplify]: Simplify (sqrt 0) into 0 12.290 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.290 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 12.290 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 12.290 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.290 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.290 * [taylor]: Taking taylor expansion of -1 in k 12.290 * [backup-simplify]: Simplify -1 into -1 12.290 * [taylor]: Taking taylor expansion of k in k 12.290 * [backup-simplify]: Simplify 0 into 0 12.290 * [backup-simplify]: Simplify 1 into 1 12.291 * [backup-simplify]: Simplify (/ -1 1) into -1 12.291 * [backup-simplify]: Simplify (sqrt 0) into 0 12.293 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.293 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 12.293 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.294 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 12.304 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.306 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 12.307 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.308 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.312 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.316 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 12.316 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.317 * [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))))) 12.318 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 12.318 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 12.318 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 12.318 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 12.318 * [taylor]: Taking taylor expansion of 2 in n 12.318 * [backup-simplify]: Simplify 2 into 2 12.318 * [taylor]: Taking taylor expansion of (* n PI) in n 12.319 * [taylor]: Taking taylor expansion of n in n 12.319 * [backup-simplify]: Simplify 0 into 0 12.319 * [backup-simplify]: Simplify 1 into 1 12.319 * [taylor]: Taking taylor expansion of PI in n 12.319 * [backup-simplify]: Simplify PI into PI 12.319 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 12.319 * [taylor]: Taking taylor expansion of 2 in n 12.319 * [backup-simplify]: Simplify 2 into 2 12.319 * [taylor]: Taking taylor expansion of (* n PI) in n 12.319 * [taylor]: Taking taylor expansion of n in n 12.319 * [backup-simplify]: Simplify 0 into 0 12.319 * [backup-simplify]: Simplify 1 into 1 12.319 * [taylor]: Taking taylor expansion of PI in n 12.319 * [backup-simplify]: Simplify PI into PI 12.320 * [backup-simplify]: Simplify (* 0 PI) into 0 12.320 * [backup-simplify]: Simplify (* 2 0) into 0 12.320 * [backup-simplify]: Simplify 0 into 0 12.322 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.323 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 12.323 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.325 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.326 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 12.326 * [backup-simplify]: Simplify 0 into 0 12.327 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.328 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 12.328 * [backup-simplify]: Simplify 0 into 0 12.329 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 12.331 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 12.331 * [backup-simplify]: Simplify 0 into 0 12.332 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 12.334 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 12.334 * [backup-simplify]: Simplify 0 into 0 12.335 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 12.337 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 12.337 * [backup-simplify]: Simplify 0 into 0 12.339 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 12.341 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 12.341 * [backup-simplify]: Simplify 0 into 0 12.341 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 12.342 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n)) 12.342 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 12.342 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 12.342 * [taylor]: Taking taylor expansion of 2 in n 12.342 * [backup-simplify]: Simplify 2 into 2 12.342 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.342 * [taylor]: Taking taylor expansion of PI in n 12.342 * [backup-simplify]: Simplify PI into PI 12.342 * [taylor]: Taking taylor expansion of n in n 12.342 * [backup-simplify]: Simplify 0 into 0 12.342 * [backup-simplify]: Simplify 1 into 1 12.343 * [backup-simplify]: Simplify (/ PI 1) into PI 12.343 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 12.343 * [taylor]: Taking taylor expansion of 2 in n 12.343 * [backup-simplify]: Simplify 2 into 2 12.343 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.343 * [taylor]: Taking taylor expansion of PI in n 12.343 * [backup-simplify]: Simplify PI into PI 12.343 * [taylor]: Taking taylor expansion of n in n 12.343 * [backup-simplify]: Simplify 0 into 0 12.343 * [backup-simplify]: Simplify 1 into 1 12.343 * [backup-simplify]: Simplify (/ PI 1) into PI 12.344 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.344 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.345 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.346 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 12.346 * [backup-simplify]: Simplify 0 into 0 12.347 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.348 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 12.348 * [backup-simplify]: Simplify 0 into 0 12.349 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.351 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.351 * [backup-simplify]: Simplify 0 into 0 12.352 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.354 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 12.354 * [backup-simplify]: Simplify 0 into 0 12.355 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.357 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 12.357 * [backup-simplify]: Simplify 0 into 0 12.358 * [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 12.360 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 12.360 * [backup-simplify]: Simplify 0 into 0 12.361 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 12.361 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (- n))) into (* -2 (/ PI n)) 12.361 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 12.361 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.361 * [taylor]: Taking taylor expansion of -2 in n 12.361 * [backup-simplify]: Simplify -2 into -2 12.361 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.361 * [taylor]: Taking taylor expansion of PI in n 12.361 * [backup-simplify]: Simplify PI into PI 12.361 * [taylor]: Taking taylor expansion of n in n 12.361 * [backup-simplify]: Simplify 0 into 0 12.362 * [backup-simplify]: Simplify 1 into 1 12.362 * [backup-simplify]: Simplify (/ PI 1) into PI 12.362 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.362 * [taylor]: Taking taylor expansion of -2 in n 12.362 * [backup-simplify]: Simplify -2 into -2 12.362 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.362 * [taylor]: Taking taylor expansion of PI in n 12.362 * [backup-simplify]: Simplify PI into PI 12.362 * [taylor]: Taking taylor expansion of n in n 12.362 * [backup-simplify]: Simplify 0 into 0 12.362 * [backup-simplify]: Simplify 1 into 1 12.363 * [backup-simplify]: Simplify (/ PI 1) into PI 12.363 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.364 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.365 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.366 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 12.366 * [backup-simplify]: Simplify 0 into 0 12.367 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.368 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 12.368 * [backup-simplify]: Simplify 0 into 0 12.369 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.371 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.371 * [backup-simplify]: Simplify 0 into 0 12.372 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.374 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 12.374 * [backup-simplify]: Simplify 0 into 0 12.375 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.377 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 12.377 * [backup-simplify]: Simplify 0 into 0 12.379 * [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 12.381 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 12.381 * [backup-simplify]: Simplify 0 into 0 12.382 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 12.382 * * * * [progress]: [ 4 / 4 ] generating series at (2) 12.382 * [backup-simplify]: Simplify (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) 12.383 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k n) around 0 12.383 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n 12.383 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 12.383 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 12.383 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 12.383 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n 12.383 * [taylor]: Taking taylor expansion of 1/2 in n 12.383 * [backup-simplify]: Simplify 1/2 into 1/2 12.383 * [taylor]: Taking taylor expansion of (- 1 k) in n 12.383 * [taylor]: Taking taylor expansion of 1 in n 12.383 * [backup-simplify]: Simplify 1 into 1 12.383 * [taylor]: Taking taylor expansion of k in n 12.383 * [backup-simplify]: Simplify k into k 12.383 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 12.383 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 12.383 * [taylor]: Taking taylor expansion of 2 in n 12.383 * [backup-simplify]: Simplify 2 into 2 12.383 * [taylor]: Taking taylor expansion of (* n PI) in n 12.383 * [taylor]: Taking taylor expansion of n in n 12.383 * [backup-simplify]: Simplify 0 into 0 12.383 * [backup-simplify]: Simplify 1 into 1 12.383 * [taylor]: Taking taylor expansion of PI in n 12.383 * [backup-simplify]: Simplify PI into PI 12.384 * [backup-simplify]: Simplify (* 0 PI) into 0 12.384 * [backup-simplify]: Simplify (* 2 0) into 0 12.386 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.388 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 12.389 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.389 * [backup-simplify]: Simplify (- k) into (- k) 12.389 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k) 12.389 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k)) 12.390 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.392 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 12.393 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 12.393 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 12.393 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.393 * [taylor]: Taking taylor expansion of k in n 12.393 * [backup-simplify]: Simplify k into k 12.393 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.393 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 12.393 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.393 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 12.393 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k 12.393 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 12.393 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 12.393 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 12.393 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k 12.393 * [taylor]: Taking taylor expansion of 1/2 in k 12.394 * [backup-simplify]: Simplify 1/2 into 1/2 12.394 * [taylor]: Taking taylor expansion of (- 1 k) in k 12.394 * [taylor]: Taking taylor expansion of 1 in k 12.394 * [backup-simplify]: Simplify 1 into 1 12.394 * [taylor]: Taking taylor expansion of k in k 12.394 * [backup-simplify]: Simplify 0 into 0 12.394 * [backup-simplify]: Simplify 1 into 1 12.394 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 12.394 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 12.394 * [taylor]: Taking taylor expansion of 2 in k 12.394 * [backup-simplify]: Simplify 2 into 2 12.394 * [taylor]: Taking taylor expansion of (* n PI) in k 12.394 * [taylor]: Taking taylor expansion of n in k 12.394 * [backup-simplify]: Simplify n into n 12.394 * [taylor]: Taking taylor expansion of PI in k 12.394 * [backup-simplify]: Simplify PI into PI 12.394 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.394 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 12.394 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 12.395 * [backup-simplify]: Simplify (- 0) into 0 12.395 * [backup-simplify]: Simplify (+ 1 0) into 1 12.396 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.396 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 12.396 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 12.396 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 12.396 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.396 * [taylor]: Taking taylor expansion of k in k 12.396 * [backup-simplify]: Simplify 0 into 0 12.396 * [backup-simplify]: Simplify 1 into 1 12.396 * [backup-simplify]: Simplify (/ 1 1) into 1 12.397 * [backup-simplify]: Simplify (sqrt 0) into 0 12.398 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.398 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k 12.398 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 12.398 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 12.398 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 12.398 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k 12.398 * [taylor]: Taking taylor expansion of 1/2 in k 12.398 * [backup-simplify]: Simplify 1/2 into 1/2 12.399 * [taylor]: Taking taylor expansion of (- 1 k) in k 12.399 * [taylor]: Taking taylor expansion of 1 in k 12.399 * [backup-simplify]: Simplify 1 into 1 12.399 * [taylor]: Taking taylor expansion of k in k 12.399 * [backup-simplify]: Simplify 0 into 0 12.399 * [backup-simplify]: Simplify 1 into 1 12.399 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 12.399 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 12.399 * [taylor]: Taking taylor expansion of 2 in k 12.399 * [backup-simplify]: Simplify 2 into 2 12.399 * [taylor]: Taking taylor expansion of (* n PI) in k 12.399 * [taylor]: Taking taylor expansion of n in k 12.399 * [backup-simplify]: Simplify n into n 12.399 * [taylor]: Taking taylor expansion of PI in k 12.399 * [backup-simplify]: Simplify PI into PI 12.399 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.399 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 12.399 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 12.400 * [backup-simplify]: Simplify (- 0) into 0 12.400 * [backup-simplify]: Simplify (+ 1 0) into 1 12.400 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.401 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 12.401 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 12.401 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 12.401 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.401 * [taylor]: Taking taylor expansion of k in k 12.401 * [backup-simplify]: Simplify 0 into 0 12.401 * [backup-simplify]: Simplify 1 into 1 12.401 * [backup-simplify]: Simplify (/ 1 1) into 1 12.402 * [backup-simplify]: Simplify (sqrt 0) into 0 12.403 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.403 * [backup-simplify]: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0 12.403 * [taylor]: Taking taylor expansion of 0 in n 12.404 * [backup-simplify]: Simplify 0 into 0 12.404 * [backup-simplify]: Simplify 0 into 0 12.404 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 12.405 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 12.406 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 12.406 * [backup-simplify]: Simplify (- 1) into -1 12.406 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.407 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2 12.408 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 12.408 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 12.409 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 12.409 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 12.409 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 12.409 * [taylor]: Taking taylor expansion of +nan.0 in n 12.409 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.409 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 12.409 * [taylor]: Taking taylor expansion of (sqrt 2) in n 12.409 * [taylor]: Taking taylor expansion of 2 in n 12.409 * [backup-simplify]: Simplify 2 into 2 12.409 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 12.410 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 12.410 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 12.410 * [taylor]: Taking taylor expansion of (* n PI) in n 12.410 * [taylor]: Taking taylor expansion of n in n 12.410 * [backup-simplify]: Simplify 0 into 0 12.410 * [backup-simplify]: Simplify 1 into 1 12.410 * [taylor]: Taking taylor expansion of PI in n 12.410 * [backup-simplify]: Simplify PI into PI 12.411 * [backup-simplify]: Simplify (* 0 PI) into 0 12.412 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.413 * [backup-simplify]: Simplify (sqrt 0) into 0 12.414 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 12.415 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 12.415 * [backup-simplify]: Simplify (* +nan.0 0) into 0 12.416 * [backup-simplify]: Simplify (- 0) into 0 12.416 * [backup-simplify]: Simplify 0 into 0 12.416 * [backup-simplify]: Simplify 0 into 0 12.417 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 12.420 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.420 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 12.421 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 12.423 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0 12.424 * [backup-simplify]: Simplify (- 0) into 0 12.424 * [backup-simplify]: Simplify (+ 0 0) into 0 12.425 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0 12.426 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 12.427 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 12.428 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) 12.428 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 12.428 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 12.428 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 12.428 * [taylor]: Taking taylor expansion of +nan.0 in n 12.428 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.428 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 12.428 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 12.428 * [taylor]: Taking taylor expansion of (sqrt 2) in n 12.428 * [taylor]: Taking taylor expansion of 2 in n 12.428 * [backup-simplify]: Simplify 2 into 2 12.429 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 12.429 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 12.429 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 12.429 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 12.430 * [taylor]: Taking taylor expansion of 2 in n 12.430 * [backup-simplify]: Simplify 2 into 2 12.430 * [taylor]: Taking taylor expansion of (* n PI) in n 12.430 * [taylor]: Taking taylor expansion of n in n 12.430 * [backup-simplify]: Simplify 0 into 0 12.430 * [backup-simplify]: Simplify 1 into 1 12.430 * [taylor]: Taking taylor expansion of PI in n 12.430 * [backup-simplify]: Simplify PI into PI 12.430 * [backup-simplify]: Simplify (* 0 PI) into 0 12.431 * [backup-simplify]: Simplify (* 2 0) into 0 12.432 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.434 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 12.435 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.435 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 12.435 * [taylor]: Taking taylor expansion of (* n PI) in n 12.435 * [taylor]: Taking taylor expansion of n in n 12.435 * [backup-simplify]: Simplify 0 into 0 12.435 * [backup-simplify]: Simplify 1 into 1 12.435 * [taylor]: Taking taylor expansion of PI in n 12.435 * [backup-simplify]: Simplify PI into PI 12.436 * [backup-simplify]: Simplify (* 0 PI) into 0 12.438 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.438 * [backup-simplify]: Simplify (sqrt 0) into 0 12.440 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 12.440 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 12.440 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 12.440 * [taylor]: Taking taylor expansion of +nan.0 in n 12.440 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.440 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 12.440 * [taylor]: Taking taylor expansion of (sqrt 2) in n 12.440 * [taylor]: Taking taylor expansion of 2 in n 12.440 * [backup-simplify]: Simplify 2 into 2 12.441 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 12.441 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 12.441 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 12.441 * [taylor]: Taking taylor expansion of (* n PI) in n 12.441 * [taylor]: Taking taylor expansion of n in n 12.441 * [backup-simplify]: Simplify 0 into 0 12.441 * [backup-simplify]: Simplify 1 into 1 12.441 * [taylor]: Taking taylor expansion of PI in n 12.441 * [backup-simplify]: Simplify PI into PI 12.442 * [backup-simplify]: Simplify (* 0 PI) into 0 12.444 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.444 * [backup-simplify]: Simplify (sqrt 0) into 0 12.446 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 12.447 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.449 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 12.450 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 12.451 * [backup-simplify]: Simplify (* +nan.0 0) into 0 12.451 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 12.459 * [backup-simplify]: Simplify (* +nan.0 0) into 0 12.460 * [backup-simplify]: Simplify (- 0) into 0 12.460 * [backup-simplify]: Simplify (+ 0 0) into 0 12.460 * [backup-simplify]: Simplify (- 0) into 0 12.461 * [backup-simplify]: Simplify 0 into 0 12.464 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 12.470 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 12.474 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 12.477 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 12.477 * [backup-simplify]: Simplify 0 into 0 12.478 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.483 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.484 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.485 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 12.488 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 (* n PI)) 1)))) 6) into 0 12.489 * [backup-simplify]: Simplify (- 0) into 0 12.489 * [backup-simplify]: Simplify (+ 0 0) into 0 12.490 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0 12.492 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 12.493 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 12.494 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (+ (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) +nan.0) (* (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) 12.495 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) in n 12.495 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))))) in n 12.495 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 12.495 * [taylor]: Taking taylor expansion of +nan.0 in n 12.495 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.495 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 12.495 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 12.495 * [taylor]: Taking taylor expansion of (sqrt 2) in n 12.495 * [taylor]: Taking taylor expansion of 2 in n 12.495 * [backup-simplify]: Simplify 2 into 2 12.495 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 12.496 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 12.496 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 12.496 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 12.496 * [taylor]: Taking taylor expansion of 2 in n 12.496 * [backup-simplify]: Simplify 2 into 2 12.496 * [taylor]: Taking taylor expansion of (* n PI) in n 12.496 * [taylor]: Taking taylor expansion of n in n 12.496 * [backup-simplify]: Simplify 0 into 0 12.496 * [backup-simplify]: Simplify 1 into 1 12.496 * [taylor]: Taking taylor expansion of PI in n 12.496 * [backup-simplify]: Simplify PI into PI 12.497 * [backup-simplify]: Simplify (* 0 PI) into 0 12.497 * [backup-simplify]: Simplify (* 2 0) into 0 12.499 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.500 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 12.501 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.501 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 12.501 * [taylor]: Taking taylor expansion of (* n PI) in n 12.501 * [taylor]: Taking taylor expansion of n in n 12.501 * [backup-simplify]: Simplify 0 into 0 12.501 * [backup-simplify]: Simplify 1 into 1 12.501 * [taylor]: Taking taylor expansion of PI in n 12.501 * [backup-simplify]: Simplify PI into PI 12.502 * [backup-simplify]: Simplify (* 0 PI) into 0 12.503 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.504 * [backup-simplify]: Simplify (sqrt 0) into 0 12.505 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 12.505 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))) in n 12.505 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))) in n 12.505 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 12.505 * [taylor]: Taking taylor expansion of +nan.0 in n 12.505 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.505 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 12.505 * [taylor]: Taking taylor expansion of (sqrt 2) in n 12.505 * [taylor]: Taking taylor expansion of 2 in n 12.505 * [backup-simplify]: Simplify 2 into 2 12.506 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 12.506 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 12.506 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 12.507 * [taylor]: Taking taylor expansion of (* n PI) in n 12.507 * [taylor]: Taking taylor expansion of n in n 12.507 * [backup-simplify]: Simplify 0 into 0 12.507 * [backup-simplify]: Simplify 1 into 1 12.507 * [taylor]: Taking taylor expansion of PI in n 12.507 * [backup-simplify]: Simplify PI into PI 12.507 * [backup-simplify]: Simplify (* 0 PI) into 0 12.509 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.509 * [backup-simplify]: Simplify (sqrt 0) into 0 12.510 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 12.510 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n 12.510 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 12.510 * [taylor]: Taking taylor expansion of +nan.0 in n 12.510 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.510 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 12.510 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 12.510 * [taylor]: Taking taylor expansion of (sqrt 2) in n 12.510 * [taylor]: Taking taylor expansion of 2 in n 12.510 * [backup-simplify]: Simplify 2 into 2 12.511 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 12.511 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 12.511 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 12.511 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 12.511 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 12.511 * [taylor]: Taking taylor expansion of 2 in n 12.511 * [backup-simplify]: Simplify 2 into 2 12.512 * [taylor]: Taking taylor expansion of (* n PI) in n 12.512 * [taylor]: Taking taylor expansion of n in n 12.512 * [backup-simplify]: Simplify 0 into 0 12.512 * [backup-simplify]: Simplify 1 into 1 12.512 * [taylor]: Taking taylor expansion of PI in n 12.512 * [backup-simplify]: Simplify PI into PI 12.512 * [backup-simplify]: Simplify (* 0 PI) into 0 12.512 * [backup-simplify]: Simplify (* 2 0) into 0 12.514 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.516 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 12.517 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.518 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.518 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 12.518 * [taylor]: Taking taylor expansion of (* n PI) in n 12.518 * [taylor]: Taking taylor expansion of n in n 12.518 * [backup-simplify]: Simplify 0 into 0 12.518 * [backup-simplify]: Simplify 1 into 1 12.518 * [taylor]: Taking taylor expansion of PI in n 12.518 * [backup-simplify]: Simplify PI into PI 12.519 * [backup-simplify]: Simplify (* 0 PI) into 0 12.520 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.521 * [backup-simplify]: Simplify (sqrt 0) into 0 12.522 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 12.523 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.523 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 12.524 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 12.525 * [backup-simplify]: Simplify (* +nan.0 0) into 0 12.525 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 12.525 * [backup-simplify]: Simplify (* +nan.0 0) into 0 12.526 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.527 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.528 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 12.529 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 12.530 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 12.530 * [backup-simplify]: Simplify (* +nan.0 0) into 0 12.531 * [backup-simplify]: Simplify (- 0) into 0 12.531 * [backup-simplify]: Simplify (+ 0 0) into 0 12.531 * [backup-simplify]: Simplify (- 0) into 0 12.531 * [backup-simplify]: Simplify (+ 0 0) into 0 12.531 * [backup-simplify]: Simplify (- 0) into 0 12.531 * [backup-simplify]: Simplify 0 into 0 12.532 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.533 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 12.534 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 12.535 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.536 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 12.538 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 12.542 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 12.544 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 12.547 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 12.550 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 12.555 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))))) 12.560 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 12.564 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 12.565 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.573 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 12.574 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 12.577 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 12.582 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 12.584 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 12.587 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 12.595 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) 12.596 * [backup-simplify]: Simplify (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) 12.596 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k n) around 0 12.596 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n 12.596 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 12.596 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 12.596 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 12.596 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 12.596 * [taylor]: Taking taylor expansion of 1/2 in n 12.596 * [backup-simplify]: Simplify 1/2 into 1/2 12.596 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 12.596 * [taylor]: Taking taylor expansion of 1 in n 12.596 * [backup-simplify]: Simplify 1 into 1 12.596 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.596 * [taylor]: Taking taylor expansion of k in n 12.596 * [backup-simplify]: Simplify k into k 12.596 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.596 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 12.596 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 12.596 * [taylor]: Taking taylor expansion of 2 in n 12.596 * [backup-simplify]: Simplify 2 into 2 12.596 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.596 * [taylor]: Taking taylor expansion of PI in n 12.596 * [backup-simplify]: Simplify PI into PI 12.596 * [taylor]: Taking taylor expansion of n in n 12.596 * [backup-simplify]: Simplify 0 into 0 12.596 * [backup-simplify]: Simplify 1 into 1 12.596 * [backup-simplify]: Simplify (/ PI 1) into PI 12.597 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.597 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.598 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.598 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 12.598 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k))) 12.599 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.599 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 12.600 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 12.600 * [taylor]: Taking taylor expansion of (sqrt k) in n 12.600 * [taylor]: Taking taylor expansion of k in n 12.600 * [backup-simplify]: Simplify k into k 12.600 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 12.600 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 12.600 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k 12.600 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 12.600 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 12.600 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 12.600 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 12.600 * [taylor]: Taking taylor expansion of 1/2 in k 12.600 * [backup-simplify]: Simplify 1/2 into 1/2 12.600 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 12.600 * [taylor]: Taking taylor expansion of 1 in k 12.600 * [backup-simplify]: Simplify 1 into 1 12.600 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.600 * [taylor]: Taking taylor expansion of k in k 12.600 * [backup-simplify]: Simplify 0 into 0 12.600 * [backup-simplify]: Simplify 1 into 1 12.601 * [backup-simplify]: Simplify (/ 1 1) into 1 12.601 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 12.601 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 12.601 * [taylor]: Taking taylor expansion of 2 in k 12.601 * [backup-simplify]: Simplify 2 into 2 12.601 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.601 * [taylor]: Taking taylor expansion of PI in k 12.601 * [backup-simplify]: Simplify PI into PI 12.601 * [taylor]: Taking taylor expansion of n in k 12.601 * [backup-simplify]: Simplify n into n 12.601 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.601 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 12.601 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 12.601 * [backup-simplify]: Simplify (- 1) into -1 12.602 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.602 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2 12.602 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 12.603 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 12.603 * [taylor]: Taking taylor expansion of (sqrt k) in k 12.603 * [taylor]: Taking taylor expansion of k in k 12.603 * [backup-simplify]: Simplify 0 into 0 12.603 * [backup-simplify]: Simplify 1 into 1 12.603 * [backup-simplify]: Simplify (sqrt 0) into 0 12.604 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.605 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k 12.605 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 12.605 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 12.605 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 12.605 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 12.605 * [taylor]: Taking taylor expansion of 1/2 in k 12.605 * [backup-simplify]: Simplify 1/2 into 1/2 12.605 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 12.605 * [taylor]: Taking taylor expansion of 1 in k 12.605 * [backup-simplify]: Simplify 1 into 1 12.605 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.605 * [taylor]: Taking taylor expansion of k in k 12.605 * [backup-simplify]: Simplify 0 into 0 12.605 * [backup-simplify]: Simplify 1 into 1 12.605 * [backup-simplify]: Simplify (/ 1 1) into 1 12.605 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 12.605 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 12.605 * [taylor]: Taking taylor expansion of 2 in k 12.605 * [backup-simplify]: Simplify 2 into 2 12.605 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.605 * [taylor]: Taking taylor expansion of PI in k 12.605 * [backup-simplify]: Simplify PI into PI 12.605 * [taylor]: Taking taylor expansion of n in k 12.605 * [backup-simplify]: Simplify n into n 12.606 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.606 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 12.606 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 12.606 * [backup-simplify]: Simplify (- 1) into -1 12.607 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.608 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2 12.608 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 12.608 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 12.608 * [taylor]: Taking taylor expansion of (sqrt k) in k 12.608 * [taylor]: Taking taylor expansion of k in k 12.608 * [backup-simplify]: Simplify 0 into 0 12.608 * [backup-simplify]: Simplify 1 into 1 12.609 * [backup-simplify]: Simplify (sqrt 0) into 0 12.610 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.611 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 0) into 0 12.611 * [taylor]: Taking taylor expansion of 0 in n 12.611 * [backup-simplify]: Simplify 0 into 0 12.611 * [backup-simplify]: Simplify 0 into 0 12.611 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 12.611 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 12.611 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 12.611 * [taylor]: Taking taylor expansion of +nan.0 in n 12.611 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.611 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 12.611 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 12.611 * [taylor]: Taking taylor expansion of 1/2 in n 12.611 * [backup-simplify]: Simplify 1/2 into 1/2 12.611 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 12.612 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 12.612 * [taylor]: Taking taylor expansion of 1 in n 12.612 * [backup-simplify]: Simplify 1 into 1 12.612 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.612 * [taylor]: Taking taylor expansion of k in n 12.612 * [backup-simplify]: Simplify k into k 12.612 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.612 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 12.612 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 12.612 * [taylor]: Taking taylor expansion of 2 in n 12.612 * [backup-simplify]: Simplify 2 into 2 12.612 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.612 * [taylor]: Taking taylor expansion of PI in n 12.612 * [backup-simplify]: Simplify PI into PI 12.612 * [taylor]: Taking taylor expansion of n in n 12.612 * [backup-simplify]: Simplify 0 into 0 12.612 * [backup-simplify]: Simplify 1 into 1 12.612 * [backup-simplify]: Simplify (/ PI 1) into PI 12.613 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.614 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.614 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.614 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 12.615 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.617 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 12.618 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 12.619 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 12.620 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 12.621 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 12.623 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 12.623 * [backup-simplify]: Simplify 0 into 0 12.626 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.627 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 12.627 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 12.627 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 12.627 * [taylor]: Taking taylor expansion of +nan.0 in n 12.627 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.627 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 12.627 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 12.627 * [taylor]: Taking taylor expansion of 1/2 in n 12.627 * [backup-simplify]: Simplify 1/2 into 1/2 12.627 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 12.627 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 12.627 * [taylor]: Taking taylor expansion of 1 in n 12.627 * [backup-simplify]: Simplify 1 into 1 12.627 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.627 * [taylor]: Taking taylor expansion of k in n 12.627 * [backup-simplify]: Simplify k into k 12.627 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.627 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 12.627 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 12.627 * [taylor]: Taking taylor expansion of 2 in n 12.627 * [backup-simplify]: Simplify 2 into 2 12.627 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.627 * [taylor]: Taking taylor expansion of PI in n 12.627 * [backup-simplify]: Simplify PI into PI 12.628 * [taylor]: Taking taylor expansion of n in n 12.628 * [backup-simplify]: Simplify 0 into 0 12.628 * [backup-simplify]: Simplify 1 into 1 12.628 * [backup-simplify]: Simplify (/ PI 1) into PI 12.629 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.630 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.630 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.630 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 12.631 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.632 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 12.633 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 12.635 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 12.636 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 12.637 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 12.638 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 12.639 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.640 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 12.642 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 12.642 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.642 * [backup-simplify]: Simplify (- 0) into 0 12.643 * [backup-simplify]: Simplify (+ 0 0) into 0 12.644 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.645 * [backup-simplify]: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 12.647 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0 12.649 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.650 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0 12.651 * [backup-simplify]: Simplify (- 0) into 0 12.651 * [backup-simplify]: Simplify 0 into 0 12.651 * [backup-simplify]: Simplify 0 into 0 12.655 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.656 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) 12.656 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n 12.656 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n 12.656 * [taylor]: Taking taylor expansion of +nan.0 in n 12.656 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.656 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n 12.656 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n 12.656 * [taylor]: Taking taylor expansion of 1/2 in n 12.656 * [backup-simplify]: Simplify 1/2 into 1/2 12.656 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n 12.656 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 12.656 * [taylor]: Taking taylor expansion of 1 in n 12.656 * [backup-simplify]: Simplify 1 into 1 12.656 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.656 * [taylor]: Taking taylor expansion of k in n 12.656 * [backup-simplify]: Simplify k into k 12.656 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.656 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 12.656 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 12.656 * [taylor]: Taking taylor expansion of 2 in n 12.657 * [backup-simplify]: Simplify 2 into 2 12.657 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.657 * [taylor]: Taking taylor expansion of PI in n 12.657 * [backup-simplify]: Simplify PI into PI 12.657 * [taylor]: Taking taylor expansion of n in n 12.657 * [backup-simplify]: Simplify 0 into 0 12.657 * [backup-simplify]: Simplify 1 into 1 12.657 * [backup-simplify]: Simplify (/ PI 1) into PI 12.658 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.659 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.659 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.659 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) 12.660 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.661 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) 12.663 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) 12.664 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 12.665 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 12.666 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 12.667 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 12.671 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))) 12.672 * [backup-simplify]: Simplify (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) 12.672 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (k n) around 0 12.672 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n 12.672 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 12.672 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 12.673 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 12.673 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 12.673 * [taylor]: Taking taylor expansion of 1/2 in n 12.673 * [backup-simplify]: Simplify 1/2 into 1/2 12.673 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 12.673 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.673 * [taylor]: Taking taylor expansion of k in n 12.673 * [backup-simplify]: Simplify k into k 12.673 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.673 * [taylor]: Taking taylor expansion of 1 in n 12.673 * [backup-simplify]: Simplify 1 into 1 12.673 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 12.673 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.673 * [taylor]: Taking taylor expansion of -2 in n 12.673 * [backup-simplify]: Simplify -2 into -2 12.673 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.673 * [taylor]: Taking taylor expansion of PI in n 12.673 * [backup-simplify]: Simplify PI into PI 12.673 * [taylor]: Taking taylor expansion of n in n 12.673 * [backup-simplify]: Simplify 0 into 0 12.673 * [backup-simplify]: Simplify 1 into 1 12.673 * [backup-simplify]: Simplify (/ PI 1) into PI 12.674 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.675 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.675 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 12.675 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1)) 12.677 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.678 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 12.679 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 12.679 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 12.679 * [taylor]: Taking taylor expansion of (/ -1 k) in n 12.679 * [taylor]: Taking taylor expansion of -1 in n 12.679 * [backup-simplify]: Simplify -1 into -1 12.679 * [taylor]: Taking taylor expansion of k in n 12.679 * [backup-simplify]: Simplify k into k 12.679 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 12.679 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 12.679 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 12.679 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 12.681 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) 12.681 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k 12.681 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 12.681 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 12.681 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 12.681 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 12.681 * [taylor]: Taking taylor expansion of 1/2 in k 12.681 * [backup-simplify]: Simplify 1/2 into 1/2 12.681 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 12.681 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.681 * [taylor]: Taking taylor expansion of k in k 12.681 * [backup-simplify]: Simplify 0 into 0 12.681 * [backup-simplify]: Simplify 1 into 1 12.682 * [backup-simplify]: Simplify (/ 1 1) into 1 12.682 * [taylor]: Taking taylor expansion of 1 in k 12.682 * [backup-simplify]: Simplify 1 into 1 12.682 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 12.682 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 12.682 * [taylor]: Taking taylor expansion of -2 in k 12.682 * [backup-simplify]: Simplify -2 into -2 12.682 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.682 * [taylor]: Taking taylor expansion of PI in k 12.682 * [backup-simplify]: Simplify PI into PI 12.682 * [taylor]: Taking taylor expansion of n in k 12.682 * [backup-simplify]: Simplify n into n 12.682 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.682 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 12.682 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 12.683 * [backup-simplify]: Simplify (+ 1 0) into 1 12.683 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.683 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 12.683 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 12.683 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.683 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.683 * [taylor]: Taking taylor expansion of -1 in k 12.683 * [backup-simplify]: Simplify -1 into -1 12.684 * [taylor]: Taking taylor expansion of k in k 12.684 * [backup-simplify]: Simplify 0 into 0 12.684 * [backup-simplify]: Simplify 1 into 1 12.684 * [backup-simplify]: Simplify (/ -1 1) into -1 12.684 * [backup-simplify]: Simplify (sqrt 0) into 0 12.686 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.686 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) 12.686 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k 12.686 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 12.686 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 12.686 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 12.686 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 12.686 * [taylor]: Taking taylor expansion of 1/2 in k 12.686 * [backup-simplify]: Simplify 1/2 into 1/2 12.686 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 12.686 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.686 * [taylor]: Taking taylor expansion of k in k 12.686 * [backup-simplify]: Simplify 0 into 0 12.686 * [backup-simplify]: Simplify 1 into 1 12.687 * [backup-simplify]: Simplify (/ 1 1) into 1 12.687 * [taylor]: Taking taylor expansion of 1 in k 12.687 * [backup-simplify]: Simplify 1 into 1 12.687 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 12.687 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 12.687 * [taylor]: Taking taylor expansion of -2 in k 12.687 * [backup-simplify]: Simplify -2 into -2 12.687 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.687 * [taylor]: Taking taylor expansion of PI in k 12.687 * [backup-simplify]: Simplify PI into PI 12.687 * [taylor]: Taking taylor expansion of n in k 12.687 * [backup-simplify]: Simplify n into n 12.687 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.687 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 12.687 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 12.688 * [backup-simplify]: Simplify (+ 1 0) into 1 12.688 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.688 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 12.688 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) 12.689 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.689 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.689 * [taylor]: Taking taylor expansion of -1 in k 12.689 * [backup-simplify]: Simplify -1 into -1 12.689 * [taylor]: Taking taylor expansion of k in k 12.689 * [backup-simplify]: Simplify 0 into 0 12.689 * [backup-simplify]: Simplify 1 into 1 12.689 * [backup-simplify]: Simplify (/ -1 1) into -1 12.689 * [backup-simplify]: Simplify (sqrt 0) into 0 12.691 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.691 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) 12.691 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 12.691 * [taylor]: Taking taylor expansion of +nan.0 in n 12.691 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.691 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 12.691 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 12.691 * [taylor]: Taking taylor expansion of 1/2 in n 12.691 * [backup-simplify]: Simplify 1/2 into 1/2 12.691 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 12.691 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 12.691 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.691 * [taylor]: Taking taylor expansion of -2 in n 12.691 * [backup-simplify]: Simplify -2 into -2 12.691 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.691 * [taylor]: Taking taylor expansion of PI in n 12.692 * [backup-simplify]: Simplify PI into PI 12.692 * [taylor]: Taking taylor expansion of n in n 12.692 * [backup-simplify]: Simplify 0 into 0 12.692 * [backup-simplify]: Simplify 1 into 1 12.692 * [backup-simplify]: Simplify (/ PI 1) into PI 12.693 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.700 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.700 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 12.700 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.700 * [taylor]: Taking taylor expansion of k in n 12.700 * [backup-simplify]: Simplify k into k 12.700 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.700 * [taylor]: Taking taylor expansion of 1 in n 12.701 * [backup-simplify]: Simplify 1 into 1 12.702 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.702 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 12.704 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 12.705 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 12.705 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 12.706 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 12.707 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 12.707 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 12.709 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.710 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) 12.710 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 12.710 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 12.710 * [taylor]: Taking taylor expansion of +nan.0 in n 12.710 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.710 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 12.710 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 12.710 * [taylor]: Taking taylor expansion of 1/2 in n 12.710 * [backup-simplify]: Simplify 1/2 into 1/2 12.710 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 12.710 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 12.710 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.710 * [taylor]: Taking taylor expansion of -2 in n 12.710 * [backup-simplify]: Simplify -2 into -2 12.710 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.710 * [taylor]: Taking taylor expansion of PI in n 12.710 * [backup-simplify]: Simplify PI into PI 12.710 * [taylor]: Taking taylor expansion of n in n 12.710 * [backup-simplify]: Simplify 0 into 0 12.710 * [backup-simplify]: Simplify 1 into 1 12.711 * [backup-simplify]: Simplify (/ PI 1) into PI 12.711 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.711 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.711 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 12.712 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.712 * [taylor]: Taking taylor expansion of k in n 12.712 * [backup-simplify]: Simplify k into k 12.712 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.712 * [taylor]: Taking taylor expansion of 1 in n 12.712 * [backup-simplify]: Simplify 1 into 1 12.712 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.713 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 12.713 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 12.714 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 12.715 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 12.715 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 12.716 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 12.717 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 12.718 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.718 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.718 * [backup-simplify]: Simplify (+ 0 0) into 0 12.719 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.719 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 12.720 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 12.721 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0 12.722 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0 12.723 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.724 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0 12.725 * [backup-simplify]: Simplify 0 into 0 12.725 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.728 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.729 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) 12.729 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n 12.729 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n 12.729 * [taylor]: Taking taylor expansion of +nan.0 in n 12.729 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.729 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n 12.729 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n 12.729 * [taylor]: Taking taylor expansion of 1/2 in n 12.729 * [backup-simplify]: Simplify 1/2 into 1/2 12.729 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n 12.729 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 12.729 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.729 * [taylor]: Taking taylor expansion of -2 in n 12.729 * [backup-simplify]: Simplify -2 into -2 12.729 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.729 * [taylor]: Taking taylor expansion of PI in n 12.729 * [backup-simplify]: Simplify PI into PI 12.729 * [taylor]: Taking taylor expansion of n in n 12.729 * [backup-simplify]: Simplify 0 into 0 12.729 * [backup-simplify]: Simplify 1 into 1 12.730 * [backup-simplify]: Simplify (/ PI 1) into PI 12.730 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.731 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.731 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 12.731 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.731 * [taylor]: Taking taylor expansion of k in n 12.731 * [backup-simplify]: Simplify k into k 12.731 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.731 * [taylor]: Taking taylor expansion of 1 in n 12.731 * [backup-simplify]: Simplify 1 into 1 12.732 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.732 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) 12.732 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) 12.733 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) 12.735 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 12.736 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 12.736 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 12.737 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) 12.740 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 12.740 * * * [progress]: simplifying candidates 12.740 * * * * [progress]: [ 1 / 192 ] simplifiying candidate # 12.740 * * * * [progress]: [ 2 / 192 ] simplifiying candidate # 12.740 * * * * [progress]: [ 3 / 192 ] simplifiying candidate # 12.740 * * * * [progress]: [ 4 / 192 ] simplifiying candidate # 12.740 * * * * [progress]: [ 5 / 192 ] simplifiying candidate # 12.740 * * * * [progress]: [ 6 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simplifiying candidate # 12.747 * * * * [progress]: [ 174 / 192 ] simplifiying candidate # 12.748 * * * * [progress]: [ 175 / 192 ] simplifiying candidate # 12.748 * * * * [progress]: [ 176 / 192 ] simplifiying candidate # 12.748 * * * * [progress]: [ 177 / 192 ] simplifiying candidate # 12.748 * * * * [progress]: [ 178 / 192 ] simplifiying candidate # 12.748 * * * * [progress]: [ 179 / 192 ] simplifiying candidate # 12.748 * * * * [progress]: [ 180 / 192 ] simplifiying candidate # 12.748 * * * * [progress]: [ 181 / 192 ] simplifiying candidate # 12.748 * * * * [progress]: [ 182 / 192 ] simplifiying candidate # 12.748 * * * * [progress]: [ 183 / 192 ] simplifiying candidate # 12.748 * * * * [progress]: [ 184 / 192 ] simplifiying candidate # 12.748 * * * * [progress]: [ 185 / 192 ] simplifiying candidate # 12.748 * * * * [progress]: [ 186 / 192 ] simplifiying candidate # 12.748 * * * * [progress]: [ 187 / 192 ] simplifiying candidate # 12.748 * * * * [progress]: [ 188 / 192 ] simplifiying candidate # 12.748 * * * * [progress]: [ 189 / 192 ] simplifiying candidate # 12.748 * * * * [progress]: [ 190 / 192 ] simplifiying candidate # 12.748 * * * * [progress]: [ 191 / 192 ] simplifiying candidate # 12.748 * * * * [progress]: [ 192 / 192 ] simplifiying candidate # 12.750 * [simplify]: Simplifying: (expm1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (log1p (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) (* 1 (/ (- 1 k) 2)) (* 1 (/ (- 1 k) 2)) (* 1 (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)) (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) 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#0: cost 98 inf + 0 13.808 * * [simplify]: Extracting #1: cost 438 inf + 3 13.814 * * [simplify]: Extracting #2: cost 789 inf + 7203 13.832 * * [simplify]: Extracting #3: cost 721 inf + 63398 13.880 * * [simplify]: Extracting #4: cost 377 inf + 200444 13.941 * * [simplify]: Extracting #5: cost 122 inf + 301873 13.994 * * [simplify]: Extracting #6: cost 49 inf + 335032 14.047 * * [simplify]: Extracting #7: cost 27 inf + 341278 14.102 * * [simplify]: Extracting #8: cost 3 inf + 355071 14.177 * * [simplify]: Extracting #9: cost 0 inf + 355374 14.250 * * [simplify]: Extracting #10: cost 0 inf + 354904 14.336 * * [simplify]: Extracting #11: cost 0 inf + 354814 14.448 * [simplify]: Simplified to: (expm1 (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (log1p (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (/ (* (log (* 2 (* n PI))) (- 1 k)) 2) (/ (* (log (* 2 (* n PI))) (- 1 k)) 2) (/ (* (log (* 2 (* n PI))) (- 1 k)) 2) (/ (* (log (* 2 (* n PI))) (- 1 k)) 2) (/ (- 1 k) 2) (/ (- 1 k) 2) (/ (- 1 k) 2) (sqrt (* 2 (* n 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PI))) (- 1 k)) 2) (log (sqrt k))) (- (/ (* (log (* 2 (* n PI))) (- 1 k)) 2) (log (sqrt k))) (- (/ (* (log (* 2 (* n PI))) (- 1 k)) 2) (log (sqrt k))) (- (/ (* (log (* 2 (* n PI))) (- 1 k)) 2) (log (sqrt k))) (- (/ (* (log (* 2 (* n PI))) (- 1 k)) 2) (log (sqrt k))) (- (/ (* (log (* 2 (* n PI))) (- 1 k)) 2) (log (sqrt k))) (- (/ (* (log (* 2 (* n PI))) (- 1 k)) 2) (log (sqrt k))) (- (/ (* (log (* 2 (* n PI))) (- 1 k)) 2) (log (sqrt k))) (- (/ (* (log (* 2 (* n PI))) (- 1 k)) 2) (log (sqrt k))) (- (/ (* (log (* 2 (* n PI))) (- 1 k)) 2) (log (sqrt k))) (exp (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (/ (/ (pow (pow (* 2 (* n PI)) (/ (- 1 k) 2)) 3) k) (sqrt k)) (* (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)) (* (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))) (* (cbrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (* (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)) (* (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (* 2 (* n PI))) (* (pow (* 2 (* n PI)) (/ k 2)) (sqrt k)) (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) (* (pow (* 2 (* n PI)) (/ (- 1 k) 4)) (sqrt (/ 1 (sqrt k)))) (* (pow (* 2 (* n PI)) (/ (- 1 k) 4)) (sqrt (/ 1 (sqrt k)))) (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 4)) (sqrt (sqrt k))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (/ (* (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) (sqrt k)) (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt k)) (/ 1 (sqrt k)) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 4)) (sqrt k)) (* (cbrt (/ 1 (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (* (sqrt (/ 1 (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (cbrt (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (cbrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (cbrt (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (cbrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (cbrt (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (cbrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (sqrt (* 2 (* n PI))) (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (- (fma (* (log (* PI 2)) 1/4) (* (log n) (* (* k k) (exp (* 1/2 (log (* 2 (* n PI))))))) (fma (* 1/8 (exp (* 1/2 (log (* 2 (* n PI)))))) (* (* k (log n)) (* k (log n))) (fma (* (* (* (* k k) (exp (* 1/2 (log (* 2 (* n PI)))))) (log (* PI 2))) (log (* PI 2))) 1/8 (exp (* 1/2 (log (* 2 (* n PI)))))))) (* (* k (+ (* (exp (* 1/2 (log (* 2 (* n PI))))) (log n)) (* (exp (* 1/2 (log (* 2 (* n PI))))) (log (* PI 2))))) 1/2)) (exp (* (* (log (* 2 (* n PI))) (- 1 k)) 1/2)) (exp (* 1/2 (* (- 1 k) (- (log (* PI -2)) (log (/ -1 n)))))) (- (- (* (* k k) +nan.0) (- +nan.0 (* k +nan.0)))) (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) (/ +nan.0 (* k (* k k))))) (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) +nan.0)) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (- (- (* +nan.0 (* (* n PI) (* k (sqrt 2)))) (fma (* (sqrt 2) +nan.0) (* n PI) (- (- (* (log (* PI 2)) (* +nan.0 (* (* n PI) (* k (sqrt 2))))) (* (* (sqrt 2) +nan.0) (- (* (* n PI) (* (log n) k)) (* (* n PI) (* n PI))))))))) (- (+ (- (* (/ (exp (* (* (log (* 2 (* n PI))) (- 1 k)) 1/2)) k) +nan.0) (/ (* (/ (exp (* (* (log (* 2 (* n PI))) (- 1 k)) 1/2)) k) +nan.0) k)) (* (/ +nan.0 k) (/ (exp (* (* (log (* 2 (* n PI))) (- 1 k)) 1/2)) (* k k))))) (- (fma (/ (exp (* 1/2 (* (- 1 k) (- (log (* PI -2)) (log (/ -1 n)))))) k) +nan.0 (- (* +nan.0 (- (/ (/ (exp (* 1/2 (* (- 1 k) (- (log (* PI -2)) (log (/ -1 n)))))) k) k) (exp (* 1/2 (* (- 1 k) (- (log (* PI -2)) (log (/ -1 n))))))))))) 14.472 * * * [progress]: adding candidates to table 16.595 * * [progress]: iteration 3 / 4 16.595 * * * [progress]: picking best candidate 16.621 * * * * [pick]: Picked # 16.621 * * * [progress]: localizing error 16.657 * * * [progress]: generating rewritten candidates 16.657 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 16.674 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1) 16.698 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2) 16.721 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 16.839 * * * [progress]: generating series expansions 16.839 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 16.839 * [backup-simplify]: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 16.839 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 16.839 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 16.839 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 16.839 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 16.839 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 16.839 * [taylor]: Taking taylor expansion of 1/2 in k 16.839 * [backup-simplify]: Simplify 1/2 into 1/2 16.839 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 16.839 * [taylor]: Taking taylor expansion of 1/2 in k 16.839 * [backup-simplify]: Simplify 1/2 into 1/2 16.839 * [taylor]: Taking taylor expansion of k in k 16.839 * [backup-simplify]: Simplify 0 into 0 16.839 * [backup-simplify]: Simplify 1 into 1 16.839 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 16.839 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 16.839 * [taylor]: Taking taylor expansion of 2 in k 16.839 * [backup-simplify]: Simplify 2 into 2 16.839 * [taylor]: Taking taylor expansion of (* n PI) in k 16.839 * [taylor]: Taking taylor expansion of n in k 16.839 * [backup-simplify]: Simplify n into n 16.839 * [taylor]: Taking taylor expansion of PI in k 16.839 * [backup-simplify]: Simplify PI into PI 16.839 * [backup-simplify]: Simplify (* n PI) into (* n PI) 16.839 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 16.839 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 16.840 * [backup-simplify]: Simplify (* 1/2 0) into 0 16.840 * [backup-simplify]: Simplify (- 0) into 0 16.840 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 16.841 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 16.841 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 16.841 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 16.841 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 16.841 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 16.841 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 16.841 * [taylor]: Taking taylor expansion of 1/2 in n 16.841 * [backup-simplify]: Simplify 1/2 into 1/2 16.841 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 16.841 * [taylor]: Taking taylor expansion of 1/2 in n 16.841 * [backup-simplify]: Simplify 1/2 into 1/2 16.841 * [taylor]: Taking taylor expansion of k in n 16.841 * [backup-simplify]: Simplify k into k 16.841 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 16.841 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 16.841 * [taylor]: Taking taylor expansion of 2 in n 16.841 * [backup-simplify]: Simplify 2 into 2 16.841 * [taylor]: Taking taylor expansion of (* n PI) in n 16.841 * [taylor]: Taking taylor expansion of n in n 16.841 * [backup-simplify]: Simplify 0 into 0 16.841 * [backup-simplify]: Simplify 1 into 1 16.841 * [taylor]: Taking taylor expansion of PI in n 16.841 * [backup-simplify]: Simplify PI into PI 16.841 * [backup-simplify]: Simplify (* 0 PI) into 0 16.842 * [backup-simplify]: Simplify (* 2 0) into 0 16.843 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.844 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 16.844 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 16.844 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 16.844 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 16.844 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 16.845 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 16.846 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 16.847 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 16.847 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 16.847 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 16.847 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 16.847 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 16.847 * [taylor]: Taking taylor expansion of 1/2 in n 16.847 * [backup-simplify]: Simplify 1/2 into 1/2 16.847 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 16.847 * [taylor]: Taking taylor expansion of 1/2 in n 16.847 * [backup-simplify]: Simplify 1/2 into 1/2 16.847 * [taylor]: Taking taylor expansion of k in n 16.847 * [backup-simplify]: Simplify k into k 16.847 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 16.847 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 16.847 * [taylor]: Taking taylor expansion of 2 in n 16.847 * [backup-simplify]: Simplify 2 into 2 16.847 * [taylor]: Taking taylor expansion of (* n PI) in n 16.847 * [taylor]: Taking taylor expansion of n in n 16.847 * [backup-simplify]: Simplify 0 into 0 16.847 * [backup-simplify]: Simplify 1 into 1 16.847 * [taylor]: Taking taylor expansion of PI in n 16.847 * [backup-simplify]: Simplify PI into PI 16.847 * [backup-simplify]: Simplify (* 0 PI) into 0 16.848 * [backup-simplify]: Simplify (* 2 0) into 0 16.849 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.849 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 16.850 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 16.850 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 16.850 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 16.850 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 16.851 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 16.852 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 16.853 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 16.853 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 16.853 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 16.853 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 16.853 * [taylor]: Taking taylor expansion of 1/2 in k 16.853 * [backup-simplify]: Simplify 1/2 into 1/2 16.853 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 16.853 * [taylor]: Taking taylor expansion of 1/2 in k 16.853 * [backup-simplify]: Simplify 1/2 into 1/2 16.853 * [taylor]: Taking taylor expansion of k in k 16.853 * [backup-simplify]: Simplify 0 into 0 16.853 * [backup-simplify]: Simplify 1 into 1 16.853 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 16.853 * [taylor]: Taking taylor expansion of (log n) in k 16.853 * [taylor]: Taking taylor expansion of n in k 16.853 * [backup-simplify]: Simplify n into n 16.853 * [backup-simplify]: Simplify (log n) into (log n) 16.853 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 16.853 * [taylor]: Taking taylor expansion of (* 2 PI) in k 16.853 * [taylor]: Taking taylor expansion of 2 in k 16.853 * [backup-simplify]: Simplify 2 into 2 16.853 * [taylor]: Taking taylor expansion of PI in k 16.853 * [backup-simplify]: Simplify PI into PI 16.853 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 16.854 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 16.854 * [backup-simplify]: Simplify (* 1/2 0) into 0 16.855 * [backup-simplify]: Simplify (- 0) into 0 16.855 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 16.855 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 16.856 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 16.857 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 16.858 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 16.859 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 16.860 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 16.862 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 16.863 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 16.863 * [backup-simplify]: Simplify (- 0) into 0 16.864 * [backup-simplify]: Simplify (+ 0 0) into 0 16.865 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 16.866 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 16.868 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 16.868 * [taylor]: Taking taylor expansion of 0 in k 16.868 * [backup-simplify]: Simplify 0 into 0 16.868 * [backup-simplify]: Simplify 0 into 0 16.869 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 16.870 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 16.872 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 16.873 * [backup-simplify]: Simplify (+ 0 0) into 0 16.874 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 16.874 * [backup-simplify]: Simplify (- 1/2) into -1/2 16.874 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 16.876 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 17.258 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 17.260 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 17.261 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 17.261 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 17.263 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 17.264 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 17.264 * [backup-simplify]: Simplify (- 0) into 0 17.264 * [backup-simplify]: Simplify (+ 0 0) into 0 17.265 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 17.266 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 17.269 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.270 * [taylor]: Taking taylor expansion of 0 in k 17.270 * [backup-simplify]: Simplify 0 into 0 17.270 * [backup-simplify]: Simplify 0 into 0 17.270 * [backup-simplify]: Simplify 0 into 0 17.271 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 17.271 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 17.273 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 17.273 * [backup-simplify]: Simplify (+ 0 0) into 0 17.274 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 17.274 * [backup-simplify]: Simplify (- 0) into 0 17.274 * [backup-simplify]: Simplify (+ 0 0) into 0 17.276 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 17.278 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 17.281 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 17.287 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 17.287 * [backup-simplify]: Simplify (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 17.287 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 17.287 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 17.287 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 17.287 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 17.287 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 17.287 * [taylor]: Taking taylor expansion of 1/2 in k 17.287 * [backup-simplify]: Simplify 1/2 into 1/2 17.287 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 17.287 * [taylor]: Taking taylor expansion of 1/2 in k 17.287 * [backup-simplify]: Simplify 1/2 into 1/2 17.287 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.287 * [taylor]: Taking taylor expansion of k in k 17.287 * [backup-simplify]: Simplify 0 into 0 17.287 * [backup-simplify]: Simplify 1 into 1 17.287 * [backup-simplify]: Simplify (/ 1 1) into 1 17.287 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 17.287 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 17.287 * [taylor]: Taking taylor expansion of 2 in k 17.287 * [backup-simplify]: Simplify 2 into 2 17.287 * [taylor]: Taking taylor expansion of (/ PI n) in k 17.287 * [taylor]: Taking taylor expansion of PI in k 17.288 * [backup-simplify]: Simplify PI into PI 17.288 * [taylor]: Taking taylor expansion of n in k 17.288 * [backup-simplify]: Simplify n into n 17.288 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 17.288 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 17.288 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 17.288 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 17.288 * [backup-simplify]: Simplify (- 1/2) into -1/2 17.288 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 17.289 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 17.289 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 17.289 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 17.289 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 17.289 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 17.289 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 17.289 * [taylor]: Taking taylor expansion of 1/2 in n 17.289 * [backup-simplify]: Simplify 1/2 into 1/2 17.289 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 17.289 * [taylor]: Taking taylor expansion of 1/2 in n 17.289 * [backup-simplify]: Simplify 1/2 into 1/2 17.289 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.289 * [taylor]: Taking taylor expansion of k in n 17.289 * [backup-simplify]: Simplify k into k 17.289 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.289 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 17.289 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 17.289 * [taylor]: Taking taylor expansion of 2 in n 17.289 * [backup-simplify]: Simplify 2 into 2 17.289 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.289 * [taylor]: Taking taylor expansion of PI in n 17.289 * [backup-simplify]: Simplify PI into PI 17.289 * [taylor]: Taking taylor expansion of n in n 17.289 * [backup-simplify]: Simplify 0 into 0 17.289 * [backup-simplify]: Simplify 1 into 1 17.289 * [backup-simplify]: Simplify (/ PI 1) into PI 17.290 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 17.290 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 17.290 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 17.290 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 17.291 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 17.291 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 17.292 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 17.293 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 17.293 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 17.293 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 17.293 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 17.293 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 17.293 * [taylor]: Taking taylor expansion of 1/2 in n 17.293 * [backup-simplify]: Simplify 1/2 into 1/2 17.293 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 17.293 * [taylor]: Taking taylor expansion of 1/2 in n 17.293 * [backup-simplify]: Simplify 1/2 into 1/2 17.293 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.293 * [taylor]: Taking taylor expansion of k in n 17.293 * [backup-simplify]: Simplify k into k 17.293 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.293 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 17.293 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 17.293 * [taylor]: Taking taylor expansion of 2 in n 17.293 * [backup-simplify]: Simplify 2 into 2 17.293 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.293 * [taylor]: Taking taylor expansion of PI in n 17.293 * [backup-simplify]: Simplify PI into PI 17.293 * [taylor]: Taking taylor expansion of n in n 17.293 * [backup-simplify]: Simplify 0 into 0 17.293 * [backup-simplify]: Simplify 1 into 1 17.294 * [backup-simplify]: Simplify (/ PI 1) into PI 17.294 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 17.296 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 17.296 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 17.296 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 17.296 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 17.297 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 17.299 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 17.300 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 17.300 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 17.300 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 17.300 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 17.300 * [taylor]: Taking taylor expansion of 1/2 in k 17.300 * [backup-simplify]: Simplify 1/2 into 1/2 17.300 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 17.300 * [taylor]: Taking taylor expansion of 1/2 in k 17.300 * [backup-simplify]: Simplify 1/2 into 1/2 17.300 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.300 * [taylor]: Taking taylor expansion of k in k 17.300 * [backup-simplify]: Simplify 0 into 0 17.300 * [backup-simplify]: Simplify 1 into 1 17.301 * [backup-simplify]: Simplify (/ 1 1) into 1 17.301 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 17.301 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 17.301 * [taylor]: Taking taylor expansion of (* 2 PI) in k 17.301 * [taylor]: Taking taylor expansion of 2 in k 17.301 * [backup-simplify]: Simplify 2 into 2 17.301 * [taylor]: Taking taylor expansion of PI in k 17.301 * [backup-simplify]: Simplify PI into PI 17.301 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 17.302 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 17.302 * [taylor]: Taking taylor expansion of (log n) in k 17.302 * [taylor]: Taking taylor expansion of n in k 17.302 * [backup-simplify]: Simplify n into n 17.302 * [backup-simplify]: Simplify (log n) into (log n) 17.303 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 17.303 * [backup-simplify]: Simplify (- 1/2) into -1/2 17.304 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 17.304 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 17.305 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 17.306 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 17.307 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 17.309 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 17.310 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.310 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 17.312 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 17.312 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 17.313 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 17.313 * [backup-simplify]: Simplify (- 0) into 0 17.314 * [backup-simplify]: Simplify (+ 0 0) into 0 17.315 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 17.316 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 17.318 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 17.318 * [taylor]: Taking taylor expansion of 0 in k 17.319 * [backup-simplify]: Simplify 0 into 0 17.319 * [backup-simplify]: Simplify 0 into 0 17.319 * [backup-simplify]: Simplify 0 into 0 17.320 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.321 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 17.324 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 17.324 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.325 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 17.326 * [backup-simplify]: Simplify (- 0) into 0 17.326 * [backup-simplify]: Simplify (+ 0 0) into 0 17.327 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 17.329 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 17.331 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.331 * [taylor]: Taking taylor expansion of 0 in k 17.332 * [backup-simplify]: Simplify 0 into 0 17.332 * [backup-simplify]: Simplify 0 into 0 17.332 * [backup-simplify]: Simplify 0 into 0 17.332 * [backup-simplify]: Simplify 0 into 0 17.333 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.334 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 17.339 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 17.339 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.340 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 17.340 * [backup-simplify]: Simplify (- 0) into 0 17.340 * [backup-simplify]: Simplify (+ 0 0) into 0 17.341 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 17.342 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 17.344 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.344 * [taylor]: Taking taylor expansion of 0 in k 17.344 * [backup-simplify]: Simplify 0 into 0 17.344 * [backup-simplify]: Simplify 0 into 0 17.344 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 17.345 * [backup-simplify]: Simplify (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 17.345 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 17.345 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 17.345 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 17.345 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 17.345 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 17.345 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 17.345 * [taylor]: Taking taylor expansion of 1/2 in k 17.345 * [backup-simplify]: Simplify 1/2 into 1/2 17.345 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.345 * [taylor]: Taking taylor expansion of k in k 17.345 * [backup-simplify]: Simplify 0 into 0 17.345 * [backup-simplify]: Simplify 1 into 1 17.345 * [backup-simplify]: Simplify (/ 1 1) into 1 17.345 * [taylor]: Taking taylor expansion of 1/2 in k 17.345 * [backup-simplify]: Simplify 1/2 into 1/2 17.345 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 17.345 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 17.345 * [taylor]: Taking taylor expansion of -2 in k 17.345 * [backup-simplify]: Simplify -2 into -2 17.345 * [taylor]: Taking taylor expansion of (/ PI n) in k 17.345 * [taylor]: Taking taylor expansion of PI in k 17.345 * [backup-simplify]: Simplify PI into PI 17.345 * [taylor]: Taking taylor expansion of n in k 17.345 * [backup-simplify]: Simplify n into n 17.345 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 17.345 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 17.345 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 17.346 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 17.346 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 17.346 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 17.346 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 17.346 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 17.346 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 17.346 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 17.346 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 17.346 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 17.346 * [taylor]: Taking taylor expansion of 1/2 in n 17.346 * [backup-simplify]: Simplify 1/2 into 1/2 17.346 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.346 * [taylor]: Taking taylor expansion of k in n 17.346 * [backup-simplify]: Simplify k into k 17.346 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.346 * [taylor]: Taking taylor expansion of 1/2 in n 17.346 * [backup-simplify]: Simplify 1/2 into 1/2 17.346 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 17.346 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 17.346 * [taylor]: Taking taylor expansion of -2 in n 17.346 * [backup-simplify]: Simplify -2 into -2 17.346 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.347 * [taylor]: Taking taylor expansion of PI in n 17.347 * [backup-simplify]: Simplify PI into PI 17.347 * [taylor]: Taking taylor expansion of n in n 17.347 * [backup-simplify]: Simplify 0 into 0 17.347 * [backup-simplify]: Simplify 1 into 1 17.347 * [backup-simplify]: Simplify (/ PI 1) into PI 17.347 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 17.348 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 17.348 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 17.348 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 17.349 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 17.350 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 17.351 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 17.351 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 17.351 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 17.351 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 17.351 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 17.351 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 17.351 * [taylor]: Taking taylor expansion of 1/2 in n 17.351 * [backup-simplify]: Simplify 1/2 into 1/2 17.351 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.351 * [taylor]: Taking taylor expansion of k in n 17.351 * [backup-simplify]: Simplify k into k 17.351 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.351 * [taylor]: Taking taylor expansion of 1/2 in n 17.351 * [backup-simplify]: Simplify 1/2 into 1/2 17.351 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 17.351 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 17.351 * [taylor]: Taking taylor expansion of -2 in n 17.351 * [backup-simplify]: Simplify -2 into -2 17.351 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.351 * [taylor]: Taking taylor expansion of PI in n 17.351 * [backup-simplify]: Simplify PI into PI 17.351 * [taylor]: Taking taylor expansion of n in n 17.351 * [backup-simplify]: Simplify 0 into 0 17.351 * [backup-simplify]: Simplify 1 into 1 17.351 * [backup-simplify]: Simplify (/ PI 1) into PI 17.352 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 17.352 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 17.352 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 17.352 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 17.353 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 17.354 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 17.355 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 17.355 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 17.355 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 17.355 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 17.355 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 17.355 * [taylor]: Taking taylor expansion of 1/2 in k 17.355 * [backup-simplify]: Simplify 1/2 into 1/2 17.355 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.355 * [taylor]: Taking taylor expansion of k in k 17.355 * [backup-simplify]: Simplify 0 into 0 17.355 * [backup-simplify]: Simplify 1 into 1 17.355 * [backup-simplify]: Simplify (/ 1 1) into 1 17.355 * [taylor]: Taking taylor expansion of 1/2 in k 17.355 * [backup-simplify]: Simplify 1/2 into 1/2 17.355 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 17.355 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 17.355 * [taylor]: Taking taylor expansion of (* -2 PI) in k 17.355 * [taylor]: Taking taylor expansion of -2 in k 17.355 * [backup-simplify]: Simplify -2 into -2 17.356 * [taylor]: Taking taylor expansion of PI in k 17.356 * [backup-simplify]: Simplify PI into PI 17.356 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 17.356 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 17.356 * [taylor]: Taking taylor expansion of (log n) in k 17.357 * [taylor]: Taking taylor expansion of n in k 17.357 * [backup-simplify]: Simplify n into n 17.357 * [backup-simplify]: Simplify (log n) into (log n) 17.357 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 17.357 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 17.357 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 17.358 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 17.358 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 17.359 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 17.360 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 17.361 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.361 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 17.366 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 17.366 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 17.367 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 17.367 * [backup-simplify]: Simplify (+ 0 0) into 0 17.368 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 17.369 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 17.370 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 17.370 * [taylor]: Taking taylor expansion of 0 in k 17.370 * [backup-simplify]: Simplify 0 into 0 17.370 * [backup-simplify]: Simplify 0 into 0 17.370 * [backup-simplify]: Simplify 0 into 0 17.371 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.371 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 17.373 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 17.373 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.374 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 17.374 * [backup-simplify]: Simplify (+ 0 0) into 0 17.375 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 17.376 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 17.377 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.377 * [taylor]: Taking taylor expansion of 0 in k 17.377 * [backup-simplify]: Simplify 0 into 0 17.377 * [backup-simplify]: Simplify 0 into 0 17.377 * [backup-simplify]: Simplify 0 into 0 17.377 * [backup-simplify]: Simplify 0 into 0 17.378 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.379 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 17.382 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 17.382 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.383 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 17.383 * [backup-simplify]: Simplify (+ 0 0) into 0 17.384 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 17.385 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 17.387 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.387 * [taylor]: Taking taylor expansion of 0 in k 17.387 * [backup-simplify]: Simplify 0 into 0 17.387 * [backup-simplify]: Simplify 0 into 0 17.388 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 17.388 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1) 17.388 * [backup-simplify]: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 17.388 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 17.388 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 17.388 * [taylor]: Taking taylor expansion of 2 in n 17.388 * [backup-simplify]: Simplify 2 into 2 17.388 * [taylor]: Taking taylor expansion of (* n PI) in n 17.388 * [taylor]: Taking taylor expansion of n in n 17.388 * [backup-simplify]: Simplify 0 into 0 17.388 * [backup-simplify]: Simplify 1 into 1 17.388 * [taylor]: Taking taylor expansion of PI in n 17.388 * [backup-simplify]: Simplify PI into PI 17.388 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 17.388 * [taylor]: Taking taylor expansion of 2 in n 17.388 * [backup-simplify]: Simplify 2 into 2 17.388 * [taylor]: Taking taylor expansion of (* n PI) in n 17.388 * [taylor]: Taking taylor expansion of n in n 17.388 * [backup-simplify]: Simplify 0 into 0 17.388 * [backup-simplify]: Simplify 1 into 1 17.388 * [taylor]: Taking taylor expansion of PI in n 17.388 * [backup-simplify]: Simplify PI into PI 17.389 * [backup-simplify]: Simplify (* 0 PI) into 0 17.389 * [backup-simplify]: Simplify (* 2 0) into 0 17.389 * [backup-simplify]: Simplify 0 into 0 17.390 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.391 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 17.391 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 17.392 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 17.392 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 17.392 * [backup-simplify]: Simplify 0 into 0 17.393 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 17.394 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 17.394 * [backup-simplify]: Simplify 0 into 0 17.395 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 17.395 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 17.395 * [backup-simplify]: Simplify 0 into 0 17.396 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 17.397 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 17.397 * [backup-simplify]: Simplify 0 into 0 17.398 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 17.399 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 17.399 * [backup-simplify]: Simplify 0 into 0 17.400 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 17.401 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 17.401 * [backup-simplify]: Simplify 0 into 0 17.402 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 17.402 * [backup-simplify]: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 17.402 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 17.402 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 17.402 * [taylor]: Taking taylor expansion of 2 in n 17.402 * [backup-simplify]: Simplify 2 into 2 17.402 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.402 * [taylor]: Taking taylor expansion of PI in n 17.402 * [backup-simplify]: Simplify PI into PI 17.402 * [taylor]: Taking taylor expansion of n in n 17.402 * [backup-simplify]: Simplify 0 into 0 17.402 * [backup-simplify]: Simplify 1 into 1 17.402 * [backup-simplify]: Simplify (/ PI 1) into PI 17.402 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 17.402 * [taylor]: Taking taylor expansion of 2 in n 17.402 * [backup-simplify]: Simplify 2 into 2 17.402 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.402 * [taylor]: Taking taylor expansion of PI in n 17.402 * [backup-simplify]: Simplify PI into PI 17.402 * [taylor]: Taking taylor expansion of n in n 17.402 * [backup-simplify]: Simplify 0 into 0 17.402 * [backup-simplify]: Simplify 1 into 1 17.403 * [backup-simplify]: Simplify (/ PI 1) into PI 17.403 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 17.403 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 17.404 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.404 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 17.404 * [backup-simplify]: Simplify 0 into 0 17.405 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.406 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 17.406 * [backup-simplify]: Simplify 0 into 0 17.406 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.407 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 17.407 * [backup-simplify]: Simplify 0 into 0 17.408 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.408 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 17.408 * [backup-simplify]: Simplify 0 into 0 17.409 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.410 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 17.410 * [backup-simplify]: Simplify 0 into 0 17.411 * [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 17.412 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 17.412 * [backup-simplify]: Simplify 0 into 0 17.412 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 17.412 * [backup-simplify]: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 17.412 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 17.412 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 17.412 * [taylor]: Taking taylor expansion of -2 in n 17.412 * [backup-simplify]: Simplify -2 into -2 17.412 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.412 * [taylor]: Taking taylor expansion of PI in n 17.412 * [backup-simplify]: Simplify PI into PI 17.412 * [taylor]: Taking taylor expansion of n in n 17.412 * [backup-simplify]: Simplify 0 into 0 17.412 * [backup-simplify]: Simplify 1 into 1 17.413 * [backup-simplify]: Simplify (/ PI 1) into PI 17.413 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 17.413 * [taylor]: Taking taylor expansion of -2 in n 17.413 * [backup-simplify]: Simplify -2 into -2 17.413 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.413 * [taylor]: Taking taylor expansion of PI in n 17.413 * [backup-simplify]: Simplify PI into PI 17.413 * [taylor]: Taking taylor expansion of n in n 17.413 * [backup-simplify]: Simplify 0 into 0 17.413 * [backup-simplify]: Simplify 1 into 1 17.413 * [backup-simplify]: Simplify (/ PI 1) into PI 17.413 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 17.414 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 17.414 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.415 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 17.415 * [backup-simplify]: Simplify 0 into 0 17.415 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.416 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 17.416 * [backup-simplify]: Simplify 0 into 0 17.416 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.417 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 17.417 * [backup-simplify]: Simplify 0 into 0 17.419 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.420 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 17.420 * [backup-simplify]: Simplify 0 into 0 17.421 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.422 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 17.422 * [backup-simplify]: Simplify 0 into 0 17.423 * [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 17.424 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 17.424 * [backup-simplify]: Simplify 0 into 0 17.424 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 17.424 * * * * [progress]: [ 3 / 4 ] generating series at (2 2) 17.424 * [backup-simplify]: Simplify (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) into (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) 17.424 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in (k n) around 0 17.424 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in n 17.424 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 17.424 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 17.424 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 17.424 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 17.424 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 17.425 * [taylor]: Taking taylor expansion of 1/2 in n 17.425 * [backup-simplify]: Simplify 1/2 into 1/2 17.425 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 17.425 * [taylor]: Taking taylor expansion of 1/2 in n 17.425 * [backup-simplify]: Simplify 1/2 into 1/2 17.425 * [taylor]: Taking taylor expansion of k in n 17.425 * [backup-simplify]: Simplify k into k 17.425 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 17.425 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 17.425 * [taylor]: Taking taylor expansion of 2 in n 17.425 * [backup-simplify]: Simplify 2 into 2 17.425 * [taylor]: Taking taylor expansion of (* n PI) in n 17.425 * [taylor]: Taking taylor expansion of n in n 17.425 * [backup-simplify]: Simplify 0 into 0 17.425 * [backup-simplify]: Simplify 1 into 1 17.425 * [taylor]: Taking taylor expansion of PI in n 17.425 * [backup-simplify]: Simplify PI into PI 17.425 * [backup-simplify]: Simplify (* 0 PI) into 0 17.425 * [backup-simplify]: Simplify (* 2 0) into 0 17.426 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.427 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 17.428 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 17.428 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 17.428 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 17.428 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 17.429 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 17.430 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 17.430 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 17.431 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 17.431 * [taylor]: Taking taylor expansion of (sqrt k) in n 17.431 * [taylor]: Taking taylor expansion of k in n 17.431 * [backup-simplify]: Simplify k into k 17.431 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 17.431 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 17.431 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 17.431 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 17.431 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 17.431 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 17.431 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 17.431 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 17.431 * [taylor]: Taking taylor expansion of 1/2 in k 17.431 * [backup-simplify]: Simplify 1/2 into 1/2 17.431 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 17.431 * [taylor]: Taking taylor expansion of 1/2 in k 17.431 * [backup-simplify]: Simplify 1/2 into 1/2 17.431 * [taylor]: Taking taylor expansion of k in k 17.431 * [backup-simplify]: Simplify 0 into 0 17.431 * [backup-simplify]: Simplify 1 into 1 17.431 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 17.431 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 17.431 * [taylor]: Taking taylor expansion of 2 in k 17.431 * [backup-simplify]: Simplify 2 into 2 17.431 * [taylor]: Taking taylor expansion of (* n PI) in k 17.431 * [taylor]: Taking taylor expansion of n in k 17.431 * [backup-simplify]: Simplify n into n 17.431 * [taylor]: Taking taylor expansion of PI in k 17.431 * [backup-simplify]: Simplify PI into PI 17.431 * [backup-simplify]: Simplify (* n PI) into (* n PI) 17.432 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 17.432 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 17.432 * [backup-simplify]: Simplify (* 1/2 0) into 0 17.432 * [backup-simplify]: Simplify (- 0) into 0 17.432 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 17.432 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 17.432 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 17.433 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 17.433 * [taylor]: Taking taylor expansion of (sqrt k) in k 17.433 * [taylor]: Taking taylor expansion of k in k 17.433 * [backup-simplify]: Simplify 0 into 0 17.433 * [backup-simplify]: Simplify 1 into 1 17.433 * [backup-simplify]: Simplify (sqrt 0) into 0 17.434 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 17.434 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 17.434 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 17.434 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 17.434 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 17.434 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 17.434 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 17.434 * [taylor]: Taking taylor expansion of 1/2 in k 17.434 * [backup-simplify]: Simplify 1/2 into 1/2 17.434 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 17.434 * [taylor]: Taking taylor expansion of 1/2 in k 17.434 * [backup-simplify]: Simplify 1/2 into 1/2 17.434 * [taylor]: Taking taylor expansion of k in k 17.434 * [backup-simplify]: Simplify 0 into 0 17.434 * [backup-simplify]: Simplify 1 into 1 17.434 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 17.434 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 17.434 * [taylor]: Taking taylor expansion of 2 in k 17.434 * [backup-simplify]: Simplify 2 into 2 17.434 * [taylor]: Taking taylor expansion of (* n PI) in k 17.434 * [taylor]: Taking taylor expansion of n in k 17.434 * [backup-simplify]: Simplify n into n 17.434 * [taylor]: Taking taylor expansion of PI in k 17.434 * [backup-simplify]: Simplify PI into PI 17.434 * [backup-simplify]: Simplify (* n PI) into (* n PI) 17.434 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 17.434 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 17.435 * [backup-simplify]: Simplify (* 1/2 0) into 0 17.435 * [backup-simplify]: Simplify (- 0) into 0 17.435 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 17.435 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 17.435 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 17.435 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 17.435 * [taylor]: Taking taylor expansion of (sqrt k) in k 17.435 * [taylor]: Taking taylor expansion of k in k 17.435 * [backup-simplify]: Simplify 0 into 0 17.435 * [backup-simplify]: Simplify 1 into 1 17.436 * [backup-simplify]: Simplify (sqrt 0) into 0 17.436 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 17.436 * [backup-simplify]: Simplify (* (sqrt (/ 1 (* PI (* n 2)))) 0) into 0 17.437 * [taylor]: Taking taylor expansion of 0 in n 17.437 * [backup-simplify]: Simplify 0 into 0 17.437 * [backup-simplify]: Simplify 0 into 0 17.437 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 17.437 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 17.438 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 17.438 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 17.438 * [backup-simplify]: Simplify (- 1/2) into -1/2 17.439 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 17.439 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 17.439 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 17.440 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 17.441 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) 17.441 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 17.441 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 17.441 * [taylor]: Taking taylor expansion of +nan.0 in n 17.441 * [backup-simplify]: Simplify +nan.0 into +nan.0 17.441 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 17.441 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 17.441 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 17.441 * [taylor]: Taking taylor expansion of (* n PI) in n 17.441 * [taylor]: Taking taylor expansion of n in n 17.441 * [backup-simplify]: Simplify 0 into 0 17.441 * [backup-simplify]: Simplify 1 into 1 17.441 * [taylor]: Taking taylor expansion of PI in n 17.441 * [backup-simplify]: Simplify PI into PI 17.441 * [backup-simplify]: Simplify (* 0 PI) into 0 17.442 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.442 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 17.443 * [backup-simplify]: Simplify (sqrt 0) into 0 17.444 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 17.444 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 17.444 * [taylor]: Taking taylor expansion of 1/2 in n 17.444 * [backup-simplify]: Simplify 1/2 into 1/2 17.444 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 17.445 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 17.446 * [backup-simplify]: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 17.447 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0 17.450 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 17.452 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 17.457 * [backup-simplify]: Simplify (- (* +nan.0 (/ (sqrt 1/2) PI))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 17.458 * [backup-simplify]: Simplify 0 into 0 17.461 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 17.461 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 17.462 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 17.464 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0 17.465 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 17.465 * [backup-simplify]: Simplify (- 0) into 0 17.465 * [backup-simplify]: Simplify (+ 0 0) into 0 17.466 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 17.467 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 17.471 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) (pow (* 2 (* n PI)) 1/2))) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 17.477 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (+ (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) +nan.0) (* (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) 17.477 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) in n 17.477 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))) in n 17.477 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) in n 17.477 * [taylor]: Taking taylor expansion of +nan.0 in n 17.477 * [backup-simplify]: Simplify +nan.0 into +nan.0 17.477 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))) in n 17.477 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) in n 17.477 * [taylor]: Taking taylor expansion of (sqrt 2) in n 17.477 * [taylor]: Taking taylor expansion of 2 in n 17.478 * [backup-simplify]: Simplify 2 into 2 17.478 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 17.479 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 17.479 * [taylor]: Taking taylor expansion of (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2)) in n 17.479 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 17.479 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 17.479 * [taylor]: Taking taylor expansion of 2 in n 17.479 * [backup-simplify]: Simplify 2 into 2 17.479 * [taylor]: Taking taylor expansion of (* n PI) in n 17.479 * [taylor]: Taking taylor expansion of n in n 17.479 * [backup-simplify]: Simplify 0 into 0 17.479 * [backup-simplify]: Simplify 1 into 1 17.479 * [taylor]: Taking taylor expansion of PI in n 17.479 * [backup-simplify]: Simplify PI into PI 17.479 * [backup-simplify]: Simplify (* 0 PI) into 0 17.480 * [backup-simplify]: Simplify (* 2 0) into 0 17.481 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.483 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 17.484 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 17.484 * [taylor]: Taking taylor expansion of (pow (sqrt 1/2) 2) in n 17.484 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 17.484 * [taylor]: Taking taylor expansion of 1/2 in n 17.484 * [backup-simplify]: Simplify 1/2 into 1/2 17.484 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 17.485 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 17.485 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 17.485 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 17.485 * [taylor]: Taking taylor expansion of (* n PI) in n 17.485 * [taylor]: Taking taylor expansion of n in n 17.485 * [backup-simplify]: Simplify 0 into 0 17.485 * [backup-simplify]: Simplify 1 into 1 17.485 * [taylor]: Taking taylor expansion of PI in n 17.485 * [backup-simplify]: Simplify PI into PI 17.486 * [backup-simplify]: Simplify (* 0 PI) into 0 17.487 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.488 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 17.488 * [backup-simplify]: Simplify (sqrt 0) into 0 17.490 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 17.490 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 17.491 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 17.491 * [taylor]: Taking taylor expansion of +nan.0 in n 17.491 * [backup-simplify]: Simplify +nan.0 into +nan.0 17.491 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 17.491 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 17.491 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 17.491 * [taylor]: Taking taylor expansion of (* n PI) in n 17.491 * [taylor]: Taking taylor expansion of n in n 17.491 * [backup-simplify]: Simplify 0 into 0 17.491 * [backup-simplify]: Simplify 1 into 1 17.491 * [taylor]: Taking taylor expansion of PI in n 17.491 * [backup-simplify]: Simplify PI into PI 17.491 * [backup-simplify]: Simplify (* 0 PI) into 0 17.493 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.493 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 17.494 * [backup-simplify]: Simplify (sqrt 0) into 0 17.496 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 17.496 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 17.496 * [taylor]: Taking taylor expansion of 1/2 in n 17.496 * [backup-simplify]: Simplify 1/2 into 1/2 17.496 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 17.497 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 17.499 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 17.500 * [backup-simplify]: Simplify (* (sqrt 1/2) (sqrt 1/2)) into (pow (sqrt 1/2) 2) 17.502 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (pow (sqrt 1/2) 2)) into (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))) 17.504 * [backup-simplify]: Simplify (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) into (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 17.506 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 17.506 * [backup-simplify]: Simplify (+ (* (sqrt 1/2) 0) (* 0 (sqrt 1/2))) into 0 17.508 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 17.509 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 17.510 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 17.512 * [backup-simplify]: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (* 0 (pow (sqrt 1/2) 2))) into 0 17.515 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))))) into 0 17.518 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) (/ +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 17.521 * [backup-simplify]: Simplify (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 0) into 0 17.533 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 17.536 * [backup-simplify]: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 17.537 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0 17.542 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 17.546 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 17.560 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 17.581 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 17.602 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 17.602 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1/2))) into 0 17.603 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 17.604 * [backup-simplify]: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)))) into 0 17.606 * [backup-simplify]: Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2)) 17.610 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* (/ +nan.0 PI) 0) (* (/ +nan.0 (pow PI 2)) (sqrt 1/2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 17.615 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 17.618 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 17.621 * [backup-simplify]: Simplify (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 17.636 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) (* n k)) (+ (* (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (/ (sqrt 1/2) PI))) (* 1 k)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) 17.636 * [backup-simplify]: Simplify (/ (sqrt (/ 1 k)) (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2)))) into (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) 17.636 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in (k n) around 0 17.636 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in n 17.636 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 17.636 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 17.636 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 17.636 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 17.636 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 17.636 * [taylor]: Taking taylor expansion of 1/2 in n 17.636 * [backup-simplify]: Simplify 1/2 into 1/2 17.636 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 17.636 * [taylor]: Taking taylor expansion of 1/2 in n 17.636 * [backup-simplify]: Simplify 1/2 into 1/2 17.636 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.636 * [taylor]: Taking taylor expansion of k in n 17.636 * [backup-simplify]: Simplify k into k 17.636 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.636 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 17.636 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 17.636 * [taylor]: Taking taylor expansion of 2 in n 17.636 * [backup-simplify]: Simplify 2 into 2 17.636 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.636 * [taylor]: Taking taylor expansion of PI in n 17.637 * [backup-simplify]: Simplify PI into PI 17.637 * [taylor]: Taking taylor expansion of n in n 17.637 * [backup-simplify]: Simplify 0 into 0 17.637 * [backup-simplify]: Simplify 1 into 1 17.637 * [backup-simplify]: Simplify (/ PI 1) into PI 17.637 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 17.638 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 17.638 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 17.638 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 17.638 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 17.639 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 17.640 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 17.641 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 17.641 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 17.642 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 17.642 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.642 * [taylor]: Taking taylor expansion of k in n 17.642 * [backup-simplify]: Simplify k into k 17.642 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.642 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 17.642 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 17.642 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 17.642 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 17.642 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 17.642 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 17.642 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 17.642 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 17.642 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 17.642 * [taylor]: Taking taylor expansion of 1/2 in k 17.642 * [backup-simplify]: Simplify 1/2 into 1/2 17.642 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 17.642 * [taylor]: Taking taylor expansion of 1/2 in k 17.642 * [backup-simplify]: Simplify 1/2 into 1/2 17.642 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.642 * [taylor]: Taking taylor expansion of k in k 17.642 * [backup-simplify]: Simplify 0 into 0 17.642 * [backup-simplify]: Simplify 1 into 1 17.642 * [backup-simplify]: Simplify (/ 1 1) into 1 17.642 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 17.642 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 17.642 * [taylor]: Taking taylor expansion of 2 in k 17.642 * [backup-simplify]: Simplify 2 into 2 17.642 * [taylor]: Taking taylor expansion of (/ PI n) in k 17.642 * [taylor]: Taking taylor expansion of PI in k 17.642 * [backup-simplify]: Simplify PI into PI 17.642 * [taylor]: Taking taylor expansion of n in k 17.642 * [backup-simplify]: Simplify n into n 17.642 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 17.643 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 17.643 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 17.643 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 17.643 * [backup-simplify]: Simplify (- 1/2) into -1/2 17.643 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 17.643 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 17.644 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 17.644 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 17.644 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 17.644 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.644 * [taylor]: Taking taylor expansion of k in k 17.644 * [backup-simplify]: Simplify 0 into 0 17.644 * [backup-simplify]: Simplify 1 into 1 17.644 * [backup-simplify]: Simplify (/ 1 1) into 1 17.644 * [backup-simplify]: Simplify (sqrt 0) into 0 17.645 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 17.645 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 17.645 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 17.645 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 17.645 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 17.645 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 17.645 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 17.645 * [taylor]: Taking taylor expansion of 1/2 in k 17.645 * [backup-simplify]: Simplify 1/2 into 1/2 17.645 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 17.645 * [taylor]: Taking taylor expansion of 1/2 in k 17.645 * [backup-simplify]: Simplify 1/2 into 1/2 17.645 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.645 * [taylor]: Taking taylor expansion of k in k 17.645 * [backup-simplify]: Simplify 0 into 0 17.645 * [backup-simplify]: Simplify 1 into 1 17.646 * [backup-simplify]: Simplify (/ 1 1) into 1 17.646 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 17.646 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 17.646 * [taylor]: Taking taylor expansion of 2 in k 17.646 * [backup-simplify]: Simplify 2 into 2 17.646 * [taylor]: Taking taylor expansion of (/ PI n) in k 17.646 * [taylor]: Taking taylor expansion of PI in k 17.646 * [backup-simplify]: Simplify PI into PI 17.646 * [taylor]: Taking taylor expansion of n in k 17.646 * [backup-simplify]: Simplify n into n 17.646 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 17.646 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 17.646 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 17.646 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 17.646 * [backup-simplify]: Simplify (- 1/2) into -1/2 17.647 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 17.647 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 17.647 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 17.647 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 17.647 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 17.647 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.647 * [taylor]: Taking taylor expansion of k in k 17.647 * [backup-simplify]: Simplify 0 into 0 17.647 * [backup-simplify]: Simplify 1 into 1 17.647 * [backup-simplify]: Simplify (/ 1 1) into 1 17.647 * [backup-simplify]: Simplify (sqrt 0) into 0 17.648 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 17.649 * [backup-simplify]: Simplify (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 17.649 * [taylor]: Taking taylor expansion of 0 in n 17.649 * [backup-simplify]: Simplify 0 into 0 17.649 * [backup-simplify]: Simplify 0 into 0 17.649 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 17.649 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 17.649 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 17.649 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 17.649 * [taylor]: Taking taylor expansion of +nan.0 in n 17.649 * [backup-simplify]: Simplify +nan.0 into +nan.0 17.649 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 17.649 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 17.649 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 17.649 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 17.649 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 17.649 * [taylor]: Taking taylor expansion of 1/2 in n 17.649 * [backup-simplify]: Simplify 1/2 into 1/2 17.649 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 17.649 * [taylor]: Taking taylor expansion of 1/2 in n 17.649 * [backup-simplify]: Simplify 1/2 into 1/2 17.649 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.649 * [taylor]: Taking taylor expansion of k in n 17.649 * [backup-simplify]: Simplify k into k 17.649 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.649 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 17.650 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 17.650 * [taylor]: Taking taylor expansion of 2 in n 17.650 * [backup-simplify]: Simplify 2 into 2 17.650 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.650 * [taylor]: Taking taylor expansion of PI in n 17.650 * [backup-simplify]: Simplify PI into PI 17.650 * [taylor]: Taking taylor expansion of n in n 17.650 * [backup-simplify]: Simplify 0 into 0 17.650 * [backup-simplify]: Simplify 1 into 1 17.650 * [backup-simplify]: Simplify (/ PI 1) into PI 17.650 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 17.651 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 17.651 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 17.651 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 17.651 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 17.652 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 17.653 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 17.653 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 17.654 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 17.655 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 17.656 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 17.656 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 17.656 * [backup-simplify]: Simplify 0 into 0 17.657 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 17.659 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 17.659 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 17.659 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 17.659 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 17.659 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 17.659 * [taylor]: Taking taylor expansion of +nan.0 in n 17.659 * [backup-simplify]: Simplify +nan.0 into +nan.0 17.659 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 17.659 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 17.659 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 17.659 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 17.660 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 17.660 * [taylor]: Taking taylor expansion of 1/2 in n 17.660 * [backup-simplify]: Simplify 1/2 into 1/2 17.660 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 17.660 * [taylor]: Taking taylor expansion of 1/2 in n 17.660 * [backup-simplify]: Simplify 1/2 into 1/2 17.660 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.660 * [taylor]: Taking taylor expansion of k in n 17.660 * [backup-simplify]: Simplify k into k 17.660 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.660 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 17.660 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 17.660 * [taylor]: Taking taylor expansion of 2 in n 17.660 * [backup-simplify]: Simplify 2 into 2 17.660 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.660 * [taylor]: Taking taylor expansion of PI in n 17.660 * [backup-simplify]: Simplify PI into PI 17.660 * [taylor]: Taking taylor expansion of n in n 17.660 * [backup-simplify]: Simplify 0 into 0 17.660 * [backup-simplify]: Simplify 1 into 1 17.660 * [backup-simplify]: Simplify (/ PI 1) into PI 17.660 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 17.661 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 17.661 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 17.661 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 17.661 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 17.662 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 17.663 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 17.664 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 17.664 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 17.665 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 17.666 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 17.666 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 17.667 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.668 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 17.669 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 17.669 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 17.669 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 17.669 * [backup-simplify]: Simplify (- 0) into 0 17.670 * [backup-simplify]: Simplify (+ 0 0) into 0 17.670 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 17.671 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 17.672 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 17.674 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 17.675 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 17.675 * [backup-simplify]: Simplify (- 0) into 0 17.675 * [backup-simplify]: Simplify 0 into 0 17.675 * [backup-simplify]: Simplify 0 into 0 17.676 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.678 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 17.678 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 17.679 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 17.679 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 17.679 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 17.679 * [taylor]: Taking taylor expansion of +nan.0 in n 17.679 * [backup-simplify]: Simplify +nan.0 into +nan.0 17.679 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 17.679 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 17.679 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 17.679 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 17.679 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 17.679 * [taylor]: Taking taylor expansion of 1/2 in n 17.679 * [backup-simplify]: Simplify 1/2 into 1/2 17.679 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 17.679 * [taylor]: Taking taylor expansion of 1/2 in n 17.679 * [backup-simplify]: Simplify 1/2 into 1/2 17.679 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.679 * [taylor]: Taking taylor expansion of k in n 17.679 * [backup-simplify]: Simplify k into k 17.679 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.679 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 17.679 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 17.679 * [taylor]: Taking taylor expansion of 2 in n 17.679 * [backup-simplify]: Simplify 2 into 2 17.679 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.679 * [taylor]: Taking taylor expansion of PI in n 17.679 * [backup-simplify]: Simplify PI into PI 17.679 * [taylor]: Taking taylor expansion of n in n 17.679 * [backup-simplify]: Simplify 0 into 0 17.679 * [backup-simplify]: Simplify 1 into 1 17.680 * [backup-simplify]: Simplify (/ PI 1) into PI 17.680 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 17.681 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 17.681 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 17.681 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 17.681 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 17.682 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 17.682 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 17.686 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 17.687 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 17.688 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 17.688 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 17.689 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 17.691 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) 17.692 * [backup-simplify]: Simplify (/ (sqrt (/ 1 (- k))) (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2)))) into (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 17.692 * [approximate]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (k n) around 0 17.692 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 17.692 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 17.692 * [taylor]: Taking taylor expansion of (/ -1 k) in n 17.692 * [taylor]: Taking taylor expansion of -1 in n 17.692 * [backup-simplify]: Simplify -1 into -1 17.692 * [taylor]: Taking taylor expansion of k in n 17.692 * [backup-simplify]: Simplify k into k 17.692 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 17.692 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 17.692 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 17.692 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 17.692 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 17.692 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 17.692 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 17.692 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 17.692 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 17.692 * [taylor]: Taking taylor expansion of 1/2 in n 17.692 * [backup-simplify]: Simplify 1/2 into 1/2 17.692 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.692 * [taylor]: Taking taylor expansion of k in n 17.692 * [backup-simplify]: Simplify k into k 17.692 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.692 * [taylor]: Taking taylor expansion of 1/2 in n 17.692 * [backup-simplify]: Simplify 1/2 into 1/2 17.692 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 17.692 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 17.692 * [taylor]: Taking taylor expansion of -2 in n 17.692 * [backup-simplify]: Simplify -2 into -2 17.692 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.692 * [taylor]: Taking taylor expansion of PI in n 17.692 * [backup-simplify]: Simplify PI into PI 17.692 * [taylor]: Taking taylor expansion of n in n 17.692 * [backup-simplify]: Simplify 0 into 0 17.692 * [backup-simplify]: Simplify 1 into 1 17.693 * [backup-simplify]: Simplify (/ PI 1) into PI 17.693 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 17.694 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 17.694 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 17.694 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 17.695 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 17.695 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 17.696 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 17.697 * [backup-simplify]: Simplify (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 17.697 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 17.697 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 17.697 * [taylor]: Taking taylor expansion of (/ -1 k) in k 17.697 * [taylor]: Taking taylor expansion of -1 in k 17.697 * [backup-simplify]: Simplify -1 into -1 17.697 * [taylor]: Taking taylor expansion of k in k 17.697 * [backup-simplify]: Simplify 0 into 0 17.697 * [backup-simplify]: Simplify 1 into 1 17.697 * [backup-simplify]: Simplify (/ -1 1) into -1 17.698 * [backup-simplify]: Simplify (sqrt 0) into 0 17.698 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 17.698 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 17.698 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 17.698 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 17.698 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 17.698 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 17.698 * [taylor]: Taking taylor expansion of 1/2 in k 17.698 * [backup-simplify]: Simplify 1/2 into 1/2 17.698 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.698 * [taylor]: Taking taylor expansion of k in k 17.699 * [backup-simplify]: Simplify 0 into 0 17.699 * [backup-simplify]: Simplify 1 into 1 17.699 * [backup-simplify]: Simplify (/ 1 1) into 1 17.699 * [taylor]: Taking taylor expansion of 1/2 in k 17.699 * [backup-simplify]: Simplify 1/2 into 1/2 17.699 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 17.699 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 17.699 * [taylor]: Taking taylor expansion of -2 in k 17.699 * [backup-simplify]: Simplify -2 into -2 17.699 * [taylor]: Taking taylor expansion of (/ PI n) in k 17.699 * [taylor]: Taking taylor expansion of PI in k 17.699 * [backup-simplify]: Simplify PI into PI 17.699 * [taylor]: Taking taylor expansion of n in k 17.699 * [backup-simplify]: Simplify n into n 17.699 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 17.699 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 17.699 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 17.699 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 17.700 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 17.700 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 17.700 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 17.700 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 17.700 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 17.700 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 17.700 * [taylor]: Taking taylor expansion of (/ -1 k) in k 17.700 * [taylor]: Taking taylor expansion of -1 in k 17.700 * [backup-simplify]: Simplify -1 into -1 17.700 * [taylor]: Taking taylor expansion of k in k 17.700 * [backup-simplify]: Simplify 0 into 0 17.700 * [backup-simplify]: Simplify 1 into 1 17.701 * [backup-simplify]: Simplify (/ -1 1) into -1 17.701 * [backup-simplify]: Simplify (sqrt 0) into 0 17.702 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 17.702 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 17.702 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 17.702 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 17.702 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 17.702 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 17.702 * [taylor]: Taking taylor expansion of 1/2 in k 17.702 * [backup-simplify]: Simplify 1/2 into 1/2 17.702 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.702 * [taylor]: Taking taylor expansion of k in k 17.702 * [backup-simplify]: Simplify 0 into 0 17.702 * [backup-simplify]: Simplify 1 into 1 17.702 * [backup-simplify]: Simplify (/ 1 1) into 1 17.702 * [taylor]: Taking taylor expansion of 1/2 in k 17.702 * [backup-simplify]: Simplify 1/2 into 1/2 17.702 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 17.702 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 17.702 * [taylor]: Taking taylor expansion of -2 in k 17.702 * [backup-simplify]: Simplify -2 into -2 17.702 * [taylor]: Taking taylor expansion of (/ PI n) in k 17.702 * [taylor]: Taking taylor expansion of PI in k 17.702 * [backup-simplify]: Simplify PI into PI 17.702 * [taylor]: Taking taylor expansion of n in k 17.702 * [backup-simplify]: Simplify n into n 17.702 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 17.702 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 17.702 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 17.703 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 17.703 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 17.703 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 17.703 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 17.703 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 17.703 * [taylor]: Taking taylor expansion of (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 17.703 * [taylor]: Taking taylor expansion of +nan.0 in n 17.703 * [backup-simplify]: Simplify +nan.0 into +nan.0 17.703 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 17.703 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 17.703 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 17.703 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 17.704 * [taylor]: Taking taylor expansion of -2 in n 17.704 * [backup-simplify]: Simplify -2 into -2 17.704 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.704 * [taylor]: Taking taylor expansion of PI in n 17.704 * [backup-simplify]: Simplify PI into PI 17.704 * [taylor]: Taking taylor expansion of n in n 17.704 * [backup-simplify]: Simplify 0 into 0 17.704 * [backup-simplify]: Simplify 1 into 1 17.704 * [backup-simplify]: Simplify (/ PI 1) into PI 17.704 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 17.705 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 17.705 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 17.705 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 17.705 * [taylor]: Taking taylor expansion of 1/2 in n 17.705 * [backup-simplify]: Simplify 1/2 into 1/2 17.705 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.705 * [taylor]: Taking taylor expansion of k in n 17.705 * [backup-simplify]: Simplify k into k 17.705 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.705 * [taylor]: Taking taylor expansion of 1/2 in n 17.705 * [backup-simplify]: Simplify 1/2 into 1/2 17.707 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 17.707 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 17.707 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 17.708 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 17.709 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 17.710 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 17.712 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 17.713 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 17.716 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 17.716 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 17.716 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 17.716 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 17.716 * [taylor]: Taking taylor expansion of +nan.0 in n 17.716 * [backup-simplify]: Simplify +nan.0 into +nan.0 17.717 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 17.717 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 17.717 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 17.717 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 17.717 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 17.717 * [taylor]: Taking taylor expansion of -2 in n 17.717 * [backup-simplify]: Simplify -2 into -2 17.717 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.717 * [taylor]: Taking taylor expansion of PI in n 17.717 * [backup-simplify]: Simplify PI into PI 17.717 * [taylor]: Taking taylor expansion of n in n 17.717 * [backup-simplify]: Simplify 0 into 0 17.717 * [backup-simplify]: Simplify 1 into 1 17.717 * [backup-simplify]: Simplify (/ PI 1) into PI 17.718 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 17.719 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 17.719 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 17.719 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 17.719 * [taylor]: Taking taylor expansion of 1/2 in n 17.719 * [backup-simplify]: Simplify 1/2 into 1/2 17.719 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.719 * [taylor]: Taking taylor expansion of k in n 17.719 * [backup-simplify]: Simplify k into k 17.719 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.719 * [taylor]: Taking taylor expansion of 1/2 in n 17.719 * [backup-simplify]: Simplify 1/2 into 1/2 17.721 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 17.721 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 17.721 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 17.722 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 17.723 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 17.724 * [backup-simplify]: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 17.726 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 17.727 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 17.728 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 17.730 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 17.730 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 17.730 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 17.731 * [backup-simplify]: Simplify (+ 0 0) into 0 17.732 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.732 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 17.734 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 17.735 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 17.737 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 17.741 * [backup-simplify]: Simplify (- (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 17.741 * [backup-simplify]: Simplify 0 into 0 17.742 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.746 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 17.747 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (* (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 17.747 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 17.747 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 17.748 * [taylor]: Taking taylor expansion of +nan.0 in n 17.748 * [backup-simplify]: Simplify +nan.0 into +nan.0 17.748 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 17.748 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 17.748 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 17.748 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 17.748 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 17.748 * [taylor]: Taking taylor expansion of -2 in n 17.748 * [backup-simplify]: Simplify -2 into -2 17.748 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.748 * [taylor]: Taking taylor expansion of PI in n 17.748 * [backup-simplify]: Simplify PI into PI 17.748 * [taylor]: Taking taylor expansion of n in n 17.748 * [backup-simplify]: Simplify 0 into 0 17.748 * [backup-simplify]: Simplify 1 into 1 17.748 * [backup-simplify]: Simplify (/ PI 1) into PI 17.749 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 17.750 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 17.750 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 17.750 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 17.750 * [taylor]: Taking taylor expansion of 1/2 in n 17.750 * [backup-simplify]: Simplify 1/2 into 1/2 17.750 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.750 * [taylor]: Taking taylor expansion of k in n 17.750 * [backup-simplify]: Simplify k into k 17.750 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.750 * [taylor]: Taking taylor expansion of 1/2 in n 17.750 * [backup-simplify]: Simplify 1/2 into 1/2 17.752 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 17.752 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 17.752 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 17.754 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 17.755 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 17.756 * [backup-simplify]: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 17.758 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 17.759 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 17.760 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 17.764 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 17.765 * * * * [progress]: [ 4 / 4 ] generating series at (2) 17.765 * [backup-simplify]: Simplify (/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 17.765 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (k n) around 0 17.765 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 17.765 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 17.765 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.765 * [taylor]: Taking taylor expansion of k in n 17.765 * [backup-simplify]: Simplify k into k 17.765 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.765 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 17.765 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 17.765 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 17.765 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 17.765 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 17.765 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 17.765 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 17.765 * [taylor]: Taking taylor expansion of 1/2 in n 17.765 * [backup-simplify]: Simplify 1/2 into 1/2 17.765 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 17.765 * [taylor]: Taking taylor expansion of 1/2 in n 17.765 * [backup-simplify]: Simplify 1/2 into 1/2 17.765 * [taylor]: Taking taylor expansion of k in n 17.765 * [backup-simplify]: Simplify k into k 17.765 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 17.765 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 17.765 * [taylor]: Taking taylor expansion of 2 in n 17.765 * [backup-simplify]: Simplify 2 into 2 17.765 * [taylor]: Taking taylor expansion of (* n PI) in n 17.766 * [taylor]: Taking taylor expansion of n in n 17.766 * [backup-simplify]: Simplify 0 into 0 17.766 * [backup-simplify]: Simplify 1 into 1 17.766 * [taylor]: Taking taylor expansion of PI in n 17.766 * [backup-simplify]: Simplify PI into PI 17.766 * [backup-simplify]: Simplify (* 0 PI) into 0 17.766 * [backup-simplify]: Simplify (* 2 0) into 0 17.767 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.768 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 17.769 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 17.769 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 17.769 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 17.769 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 17.770 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 17.770 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 17.771 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 17.771 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 17.771 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 17.771 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.771 * [taylor]: Taking taylor expansion of k in k 17.771 * [backup-simplify]: Simplify 0 into 0 17.771 * [backup-simplify]: Simplify 1 into 1 17.771 * [backup-simplify]: Simplify (/ 1 1) into 1 17.772 * [backup-simplify]: Simplify (sqrt 0) into 0 17.773 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 17.773 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 17.773 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 17.773 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 17.773 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 17.773 * [taylor]: Taking taylor expansion of 1/2 in k 17.773 * [backup-simplify]: Simplify 1/2 into 1/2 17.773 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 17.773 * [taylor]: Taking taylor expansion of 1/2 in k 17.773 * [backup-simplify]: Simplify 1/2 into 1/2 17.773 * [taylor]: Taking taylor expansion of k in k 17.773 * [backup-simplify]: Simplify 0 into 0 17.773 * [backup-simplify]: Simplify 1 into 1 17.773 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 17.773 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 17.773 * [taylor]: Taking taylor expansion of 2 in k 17.773 * [backup-simplify]: Simplify 2 into 2 17.773 * [taylor]: Taking taylor expansion of (* n PI) in k 17.773 * [taylor]: Taking taylor expansion of n in k 17.773 * [backup-simplify]: Simplify n into n 17.773 * [taylor]: Taking taylor expansion of PI in k 17.773 * [backup-simplify]: Simplify PI into PI 17.773 * [backup-simplify]: Simplify (* n PI) into (* n PI) 17.773 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 17.773 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 17.773 * [backup-simplify]: Simplify (* 1/2 0) into 0 17.774 * [backup-simplify]: Simplify (- 0) into 0 17.774 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 17.774 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 17.774 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 17.774 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 17.774 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 17.774 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.774 * [taylor]: Taking taylor expansion of k in k 17.774 * [backup-simplify]: Simplify 0 into 0 17.774 * [backup-simplify]: Simplify 1 into 1 17.774 * [backup-simplify]: Simplify (/ 1 1) into 1 17.775 * [backup-simplify]: Simplify (sqrt 0) into 0 17.775 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 17.775 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 17.775 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 17.775 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 17.775 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 17.775 * [taylor]: Taking taylor expansion of 1/2 in k 17.776 * [backup-simplify]: Simplify 1/2 into 1/2 17.776 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 17.776 * [taylor]: Taking taylor expansion of 1/2 in k 17.776 * [backup-simplify]: Simplify 1/2 into 1/2 17.776 * [taylor]: Taking taylor expansion of k in k 17.776 * [backup-simplify]: Simplify 0 into 0 17.776 * [backup-simplify]: Simplify 1 into 1 17.776 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 17.776 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 17.776 * [taylor]: Taking taylor expansion of 2 in k 17.776 * [backup-simplify]: Simplify 2 into 2 17.776 * [taylor]: Taking taylor expansion of (* n PI) in k 17.776 * [taylor]: Taking taylor expansion of n in k 17.776 * [backup-simplify]: Simplify n into n 17.776 * [taylor]: Taking taylor expansion of PI in k 17.776 * [backup-simplify]: Simplify PI into PI 17.776 * [backup-simplify]: Simplify (* n PI) into (* n PI) 17.776 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 17.776 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 17.776 * [backup-simplify]: Simplify (* 1/2 0) into 0 17.776 * [backup-simplify]: Simplify (- 0) into 0 17.777 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 17.777 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 17.777 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 17.777 * [backup-simplify]: Simplify (* 0 (pow (* 2 (* n PI)) 1/2)) into 0 17.777 * [taylor]: Taking taylor expansion of 0 in n 17.777 * [backup-simplify]: Simplify 0 into 0 17.777 * [backup-simplify]: Simplify 0 into 0 17.777 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 17.778 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 17.778 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 17.779 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 17.779 * [backup-simplify]: Simplify (- 1/2) into -1/2 17.779 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 17.779 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 17.780 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 17.780 * [backup-simplify]: Simplify (+ (* 0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 17.780 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 17.780 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 17.780 * [taylor]: Taking taylor expansion of +nan.0 in n 17.780 * [backup-simplify]: Simplify +nan.0 into +nan.0 17.780 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 17.780 * [taylor]: Taking taylor expansion of (sqrt 2) in n 17.780 * [taylor]: Taking taylor expansion of 2 in n 17.780 * [backup-simplify]: Simplify 2 into 2 17.780 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 17.781 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 17.781 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 17.781 * [taylor]: Taking taylor expansion of (* n PI) in n 17.781 * [taylor]: Taking taylor expansion of n in n 17.781 * [backup-simplify]: Simplify 0 into 0 17.781 * [backup-simplify]: Simplify 1 into 1 17.781 * [taylor]: Taking taylor expansion of PI in n 17.781 * [backup-simplify]: Simplify PI into PI 17.781 * [backup-simplify]: Simplify (* 0 PI) into 0 17.782 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.782 * [backup-simplify]: Simplify (sqrt 0) into 0 17.783 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 17.783 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 17.784 * [backup-simplify]: Simplify (* +nan.0 0) into 0 17.784 * [backup-simplify]: Simplify (- 0) into 0 17.784 * [backup-simplify]: Simplify 0 into 0 17.784 * [backup-simplify]: Simplify 0 into 0 17.785 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 17.785 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 17.786 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0 17.787 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 17.787 * [backup-simplify]: Simplify (- 0) into 0 17.787 * [backup-simplify]: Simplify (+ 0 0) into 0 17.788 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 17.788 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 17.789 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 17.791 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 17.791 * [backup-simplify]: Simplify (+ (* 0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) 17.791 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 17.791 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 17.791 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 17.791 * [taylor]: Taking taylor expansion of +nan.0 in n 17.791 * [backup-simplify]: Simplify +nan.0 into +nan.0 17.791 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 17.791 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 17.791 * [taylor]: Taking taylor expansion of (sqrt 2) in n 17.791 * [taylor]: Taking taylor expansion of 2 in n 17.791 * [backup-simplify]: Simplify 2 into 2 17.792 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 17.792 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 17.792 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 17.792 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 17.792 * [taylor]: Taking taylor expansion of 2 in n 17.792 * [backup-simplify]: Simplify 2 into 2 17.792 * [taylor]: Taking taylor expansion of (* n PI) in n 17.792 * [taylor]: Taking taylor expansion of n in n 17.792 * [backup-simplify]: Simplify 0 into 0 17.792 * [backup-simplify]: Simplify 1 into 1 17.792 * [taylor]: Taking taylor expansion of PI in n 17.792 * [backup-simplify]: Simplify PI into PI 17.792 * [backup-simplify]: Simplify (* 0 PI) into 0 17.793 * [backup-simplify]: Simplify (* 2 0) into 0 17.794 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.795 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 17.795 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 17.795 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 17.795 * [taylor]: Taking taylor expansion of (* n PI) in n 17.795 * [taylor]: Taking taylor expansion of n in n 17.795 * [backup-simplify]: Simplify 0 into 0 17.795 * [backup-simplify]: Simplify 1 into 1 17.795 * [taylor]: Taking taylor expansion of PI in n 17.795 * [backup-simplify]: Simplify PI into PI 17.796 * [backup-simplify]: Simplify (* 0 PI) into 0 17.799 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.800 * [backup-simplify]: Simplify (sqrt 0) into 0 17.801 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 17.801 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 17.801 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 17.801 * [taylor]: Taking taylor expansion of +nan.0 in n 17.801 * [backup-simplify]: Simplify +nan.0 into +nan.0 17.801 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 17.801 * [taylor]: Taking taylor expansion of (sqrt 2) in n 17.801 * [taylor]: Taking taylor expansion of 2 in n 17.801 * [backup-simplify]: Simplify 2 into 2 17.801 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 17.801 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 17.802 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 17.802 * [taylor]: Taking taylor expansion of (* n PI) in n 17.802 * [taylor]: Taking taylor expansion of n in n 17.802 * [backup-simplify]: Simplify 0 into 0 17.802 * [backup-simplify]: Simplify 1 into 1 17.802 * [taylor]: Taking taylor expansion of PI in n 17.802 * [backup-simplify]: Simplify PI into PI 17.802 * [backup-simplify]: Simplify (* 0 PI) into 0 17.803 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.803 * [backup-simplify]: Simplify (sqrt 0) into 0 17.804 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 17.805 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 17.806 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 17.807 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 17.807 * [backup-simplify]: Simplify (* +nan.0 0) into 0 17.807 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 17.807 * [backup-simplify]: Simplify (* +nan.0 0) into 0 17.808 * [backup-simplify]: Simplify (- 0) into 0 17.808 * [backup-simplify]: Simplify (+ 0 0) into 0 17.808 * [backup-simplify]: Simplify (- 0) into 0 17.808 * [backup-simplify]: Simplify 0 into 0 17.810 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 17.813 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 17.817 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 17.820 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 17.820 * [backup-simplify]: Simplify 0 into 0 17.821 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 17.822 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 17.825 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 (* n PI)) 1)))) 6) into 0 17.826 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 17.826 * [backup-simplify]: Simplify (- 0) into 0 17.826 * [backup-simplify]: Simplify (+ 0 0) into 0 17.827 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 17.828 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 17.829 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.831 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 17.832 * [backup-simplify]: Simplify (+ (* 0 (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3)))) (+ (* +nan.0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) 17.832 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) in n 17.832 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))) in n 17.832 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 17.832 * [taylor]: Taking taylor expansion of +nan.0 in n 17.832 * [backup-simplify]: Simplify +nan.0 into +nan.0 17.832 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 17.832 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 17.832 * [taylor]: Taking taylor expansion of (sqrt 2) in n 17.832 * [taylor]: Taking taylor expansion of 2 in n 17.832 * [backup-simplify]: Simplify 2 into 2 17.832 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 17.833 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 17.833 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 17.833 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 17.833 * [taylor]: Taking taylor expansion of 2 in n 17.833 * [backup-simplify]: Simplify 2 into 2 17.833 * [taylor]: Taking taylor expansion of (* n PI) in n 17.833 * [taylor]: Taking taylor expansion of n in n 17.833 * [backup-simplify]: Simplify 0 into 0 17.833 * [backup-simplify]: Simplify 1 into 1 17.833 * [taylor]: Taking taylor expansion of PI in n 17.833 * [backup-simplify]: Simplify PI into PI 17.833 * [backup-simplify]: Simplify (* 0 PI) into 0 17.833 * [backup-simplify]: Simplify (* 2 0) into 0 17.834 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.835 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 17.836 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 17.836 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 17.836 * [taylor]: Taking taylor expansion of (* n PI) in n 17.836 * [taylor]: Taking taylor expansion of n in n 17.836 * [backup-simplify]: Simplify 0 into 0 17.836 * [backup-simplify]: Simplify 1 into 1 17.836 * [taylor]: Taking taylor expansion of PI in n 17.836 * [backup-simplify]: Simplify PI into PI 17.836 * [backup-simplify]: Simplify (* 0 PI) into 0 17.837 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.837 * [backup-simplify]: Simplify (sqrt 0) into 0 17.838 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 17.838 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 17.838 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 17.838 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 17.838 * [taylor]: Taking taylor expansion of +nan.0 in n 17.838 * [backup-simplify]: Simplify +nan.0 into +nan.0 17.838 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 17.838 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 17.838 * [taylor]: Taking taylor expansion of (sqrt 2) in n 17.838 * [taylor]: Taking taylor expansion of 2 in n 17.838 * [backup-simplify]: Simplify 2 into 2 17.839 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 17.839 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 17.839 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 17.839 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 17.839 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 17.839 * [taylor]: Taking taylor expansion of 2 in n 17.839 * [backup-simplify]: Simplify 2 into 2 17.839 * [taylor]: Taking taylor expansion of (* n PI) in n 17.839 * [taylor]: Taking taylor expansion of n in n 17.839 * [backup-simplify]: Simplify 0 into 0 17.839 * [backup-simplify]: Simplify 1 into 1 17.839 * [taylor]: Taking taylor expansion of PI in n 17.839 * [backup-simplify]: Simplify PI into PI 17.840 * [backup-simplify]: Simplify (* 0 PI) into 0 17.840 * [backup-simplify]: Simplify (* 2 0) into 0 17.841 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.842 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 17.842 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 17.843 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 17.843 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 17.843 * [taylor]: Taking taylor expansion of (* n PI) in n 17.843 * [taylor]: Taking taylor expansion of n in n 17.843 * [backup-simplify]: Simplify 0 into 0 17.843 * [backup-simplify]: Simplify 1 into 1 17.843 * [taylor]: Taking taylor expansion of PI in n 17.843 * [backup-simplify]: Simplify PI into PI 17.844 * [backup-simplify]: Simplify (* 0 PI) into 0 17.845 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.845 * [backup-simplify]: Simplify (sqrt 0) into 0 17.846 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 17.846 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 17.846 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 17.846 * [taylor]: Taking taylor expansion of +nan.0 in n 17.846 * [backup-simplify]: Simplify +nan.0 into +nan.0 17.846 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 17.846 * [taylor]: Taking taylor expansion of (sqrt 2) in n 17.846 * [taylor]: Taking taylor expansion of 2 in n 17.846 * [backup-simplify]: Simplify 2 into 2 17.846 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 17.846 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 17.846 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 17.846 * [taylor]: Taking taylor expansion of (* n PI) in n 17.846 * [taylor]: Taking taylor expansion of n in n 17.846 * [backup-simplify]: Simplify 0 into 0 17.846 * [backup-simplify]: Simplify 1 into 1 17.846 * [taylor]: Taking taylor expansion of PI in n 17.846 * [backup-simplify]: Simplify PI into PI 17.847 * [backup-simplify]: Simplify (* 0 PI) into 0 17.848 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.848 * [backup-simplify]: Simplify (sqrt 0) into 0 17.849 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 17.850 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 17.850 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 17.851 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 17.852 * [backup-simplify]: Simplify (* +nan.0 0) into 0 17.853 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 17.854 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 17.856 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 17.857 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 17.859 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 17.859 * [backup-simplify]: Simplify (* +nan.0 0) into 0 17.860 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 17.860 * [backup-simplify]: Simplify (* +nan.0 0) into 0 17.861 * [backup-simplify]: Simplify (- 0) into 0 17.862 * [backup-simplify]: Simplify (+ 0 0) into 0 17.862 * [backup-simplify]: Simplify (- 0) into 0 17.862 * [backup-simplify]: Simplify (+ 0 0) into 0 17.863 * [backup-simplify]: Simplify (- 0) into 0 17.863 * [backup-simplify]: Simplify 0 into 0 17.864 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 17.865 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 17.867 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 17.868 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 17.870 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 17.872 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 17.879 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 17.882 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 17.888 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 17.892 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 17.899 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))))) 17.904 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 17.911 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 17.912 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 17.915 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 17.915 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 17.918 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 17.923 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 17.926 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 17.928 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 17.939 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) 17.940 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (/ 1 k)) (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 17.940 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (k n) around 0 17.940 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 17.940 * [taylor]: Taking taylor expansion of (sqrt k) in n 17.940 * [taylor]: Taking taylor expansion of k in n 17.940 * [backup-simplify]: Simplify k into k 17.940 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 17.940 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 17.940 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 17.940 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 17.940 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 17.940 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 17.940 * [taylor]: Taking taylor expansion of 1/2 in n 17.940 * [backup-simplify]: Simplify 1/2 into 1/2 17.940 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 17.940 * [taylor]: Taking taylor expansion of 1/2 in n 17.940 * [backup-simplify]: Simplify 1/2 into 1/2 17.940 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.940 * [taylor]: Taking taylor expansion of k in n 17.940 * [backup-simplify]: Simplify k into k 17.940 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.941 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 17.941 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 17.941 * [taylor]: Taking taylor expansion of 2 in n 17.941 * [backup-simplify]: Simplify 2 into 2 17.941 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.941 * [taylor]: Taking taylor expansion of PI in n 17.941 * [backup-simplify]: Simplify PI into PI 17.941 * [taylor]: Taking taylor expansion of n in n 17.941 * [backup-simplify]: Simplify 0 into 0 17.941 * [backup-simplify]: Simplify 1 into 1 17.941 * [backup-simplify]: Simplify (/ PI 1) into PI 17.942 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 17.942 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 17.942 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 17.942 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 17.942 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 17.943 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 17.944 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 17.945 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 17.945 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 17.945 * [taylor]: Taking taylor expansion of (sqrt k) in k 17.945 * [taylor]: Taking taylor expansion of k in k 17.945 * [backup-simplify]: Simplify 0 into 0 17.945 * [backup-simplify]: Simplify 1 into 1 17.945 * [backup-simplify]: Simplify (sqrt 0) into 0 17.946 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 17.946 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 17.946 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 17.946 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 17.946 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 17.946 * [taylor]: Taking taylor expansion of 1/2 in k 17.946 * [backup-simplify]: Simplify 1/2 into 1/2 17.946 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 17.946 * [taylor]: Taking taylor expansion of 1/2 in k 17.946 * [backup-simplify]: Simplify 1/2 into 1/2 17.946 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.946 * [taylor]: Taking taylor expansion of k in k 17.946 * [backup-simplify]: Simplify 0 into 0 17.946 * [backup-simplify]: Simplify 1 into 1 17.946 * [backup-simplify]: Simplify (/ 1 1) into 1 17.946 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 17.946 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 17.946 * [taylor]: Taking taylor expansion of 2 in k 17.946 * [backup-simplify]: Simplify 2 into 2 17.946 * [taylor]: Taking taylor expansion of (/ PI n) in k 17.946 * [taylor]: Taking taylor expansion of PI in k 17.946 * [backup-simplify]: Simplify PI into PI 17.946 * [taylor]: Taking taylor expansion of n in k 17.946 * [backup-simplify]: Simplify n into n 17.946 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 17.947 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 17.947 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 17.947 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 17.947 * [backup-simplify]: Simplify (- 1/2) into -1/2 17.947 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 17.947 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 17.948 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 17.948 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 17.948 * [taylor]: Taking taylor expansion of (sqrt k) in k 17.948 * [taylor]: Taking taylor expansion of k in k 17.948 * [backup-simplify]: Simplify 0 into 0 17.948 * [backup-simplify]: Simplify 1 into 1 17.948 * [backup-simplify]: Simplify (sqrt 0) into 0 17.949 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 17.949 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 17.949 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 17.949 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 17.949 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 17.949 * [taylor]: Taking taylor expansion of 1/2 in k 17.949 * [backup-simplify]: Simplify 1/2 into 1/2 17.949 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 17.949 * [taylor]: Taking taylor expansion of 1/2 in k 17.949 * [backup-simplify]: Simplify 1/2 into 1/2 17.949 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.949 * [taylor]: Taking taylor expansion of k in k 17.949 * [backup-simplify]: Simplify 0 into 0 17.949 * [backup-simplify]: Simplify 1 into 1 17.949 * [backup-simplify]: Simplify (/ 1 1) into 1 17.949 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 17.949 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 17.949 * [taylor]: Taking taylor expansion of 2 in k 17.950 * [backup-simplify]: Simplify 2 into 2 17.950 * [taylor]: Taking taylor expansion of (/ PI n) in k 17.950 * [taylor]: Taking taylor expansion of PI in k 17.950 * [backup-simplify]: Simplify PI into PI 17.950 * [taylor]: Taking taylor expansion of n in k 17.950 * [backup-simplify]: Simplify n into n 17.950 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 17.950 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 17.950 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 17.950 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 17.950 * [backup-simplify]: Simplify (- 1/2) into -1/2 17.951 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 17.951 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 17.951 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 17.951 * [backup-simplify]: Simplify (* 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into 0 17.951 * [taylor]: Taking taylor expansion of 0 in n 17.951 * [backup-simplify]: Simplify 0 into 0 17.951 * [backup-simplify]: Simplify 0 into 0 17.951 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 17.951 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 17.951 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 17.951 * [taylor]: Taking taylor expansion of +nan.0 in n 17.951 * [backup-simplify]: Simplify +nan.0 into +nan.0 17.951 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 17.951 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 17.951 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 17.951 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 17.951 * [taylor]: Taking taylor expansion of 1/2 in n 17.952 * [backup-simplify]: Simplify 1/2 into 1/2 17.952 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 17.952 * [taylor]: Taking taylor expansion of 1/2 in n 17.952 * [backup-simplify]: Simplify 1/2 into 1/2 17.952 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.952 * [taylor]: Taking taylor expansion of k in n 17.952 * [backup-simplify]: Simplify k into k 17.952 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.952 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 17.952 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 17.952 * [taylor]: Taking taylor expansion of 2 in n 17.952 * [backup-simplify]: Simplify 2 into 2 17.952 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.952 * [taylor]: Taking taylor expansion of PI in n 17.952 * [backup-simplify]: Simplify PI into PI 17.952 * [taylor]: Taking taylor expansion of n in n 17.952 * [backup-simplify]: Simplify 0 into 0 17.952 * [backup-simplify]: Simplify 1 into 1 17.952 * [backup-simplify]: Simplify (/ PI 1) into PI 17.953 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 17.953 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 17.953 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 17.953 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 17.954 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 17.955 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 17.955 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 17.956 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 17.957 * [backup-simplify]: Simplify (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 17.958 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 17.958 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 17.958 * [backup-simplify]: Simplify 0 into 0 17.960 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 17.961 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 17.961 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 17.961 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 17.961 * [taylor]: Taking taylor expansion of +nan.0 in n 17.961 * [backup-simplify]: Simplify +nan.0 into +nan.0 17.961 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 17.961 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 17.961 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 17.961 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 17.961 * [taylor]: Taking taylor expansion of 1/2 in n 17.961 * [backup-simplify]: Simplify 1/2 into 1/2 17.961 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 17.961 * [taylor]: Taking taylor expansion of 1/2 in n 17.961 * [backup-simplify]: Simplify 1/2 into 1/2 17.961 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.961 * [taylor]: Taking taylor expansion of k in n 17.961 * [backup-simplify]: Simplify k into k 17.961 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.961 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 17.961 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 17.961 * [taylor]: Taking taylor expansion of 2 in n 17.961 * [backup-simplify]: Simplify 2 into 2 17.961 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.961 * [taylor]: Taking taylor expansion of PI in n 17.961 * [backup-simplify]: Simplify PI into PI 17.961 * [taylor]: Taking taylor expansion of n in n 17.961 * [backup-simplify]: Simplify 0 into 0 17.961 * [backup-simplify]: Simplify 1 into 1 17.962 * [backup-simplify]: Simplify (/ PI 1) into PI 17.962 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 17.963 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 17.963 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 17.963 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 17.963 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 17.964 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 17.964 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 17.965 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 17.966 * [backup-simplify]: Simplify (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 17.967 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 17.967 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 17.968 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.969 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 17.970 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 17.970 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 17.970 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 17.970 * [backup-simplify]: Simplify (- 0) into 0 17.970 * [backup-simplify]: Simplify (+ 0 0) into 0 17.971 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 17.972 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 17.973 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 17.974 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 17.975 * [backup-simplify]: Simplify (- 0) into 0 17.975 * [backup-simplify]: Simplify 0 into 0 17.975 * [backup-simplify]: Simplify 0 into 0 17.977 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 17.978 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 17.978 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 17.978 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 17.978 * [taylor]: Taking taylor expansion of +nan.0 in n 17.978 * [backup-simplify]: Simplify +nan.0 into +nan.0 17.978 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 17.978 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 17.978 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 17.978 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 17.978 * [taylor]: Taking taylor expansion of 1/2 in n 17.978 * [backup-simplify]: Simplify 1/2 into 1/2 17.978 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 17.978 * [taylor]: Taking taylor expansion of 1/2 in n 17.978 * [backup-simplify]: Simplify 1/2 into 1/2 17.978 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.978 * [taylor]: Taking taylor expansion of k in n 17.978 * [backup-simplify]: Simplify k into k 17.978 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.978 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 17.978 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 17.978 * [taylor]: Taking taylor expansion of 2 in n 17.978 * [backup-simplify]: Simplify 2 into 2 17.978 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.978 * [taylor]: Taking taylor expansion of PI in n 17.978 * [backup-simplify]: Simplify PI into PI 17.978 * [taylor]: Taking taylor expansion of n in n 17.978 * [backup-simplify]: Simplify 0 into 0 17.978 * [backup-simplify]: Simplify 1 into 1 17.979 * [backup-simplify]: Simplify (/ PI 1) into PI 17.979 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 17.980 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 17.980 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 17.980 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 17.980 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 17.981 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 17.982 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 17.983 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 17.985 * [backup-simplify]: Simplify (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 17.986 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 17.987 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 17.991 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 17.992 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (/ 1 (- k))) (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 17.992 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (k n) around 0 17.992 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 17.992 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 17.992 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 17.992 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 17.992 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 17.992 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 17.992 * [taylor]: Taking taylor expansion of 1/2 in n 17.992 * [backup-simplify]: Simplify 1/2 into 1/2 17.992 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.992 * [taylor]: Taking taylor expansion of k in n 17.992 * [backup-simplify]: Simplify k into k 17.992 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.992 * [taylor]: Taking taylor expansion of 1/2 in n 17.992 * [backup-simplify]: Simplify 1/2 into 1/2 17.992 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 17.992 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 17.992 * [taylor]: Taking taylor expansion of -2 in n 17.992 * [backup-simplify]: Simplify -2 into -2 17.993 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.993 * [taylor]: Taking taylor expansion of PI in n 17.993 * [backup-simplify]: Simplify PI into PI 17.993 * [taylor]: Taking taylor expansion of n in n 17.993 * [backup-simplify]: Simplify 0 into 0 17.993 * [backup-simplify]: Simplify 1 into 1 17.993 * [backup-simplify]: Simplify (/ PI 1) into PI 17.994 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 17.995 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 17.995 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 17.995 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 17.996 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 17.997 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 17.999 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 17.999 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 17.999 * [taylor]: Taking taylor expansion of (/ -1 k) in n 17.999 * [taylor]: Taking taylor expansion of -1 in n 17.999 * [backup-simplify]: Simplify -1 into -1 17.999 * [taylor]: Taking taylor expansion of k in n 17.999 * [backup-simplify]: Simplify k into k 17.999 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 17.999 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 17.999 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 17.999 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 18.000 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 18.001 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 18.001 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 18.001 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 18.001 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 18.001 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 18.001 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 18.001 * [taylor]: Taking taylor expansion of 1/2 in k 18.001 * [backup-simplify]: Simplify 1/2 into 1/2 18.001 * [taylor]: Taking taylor expansion of (/ 1 k) in k 18.001 * [taylor]: Taking taylor expansion of k in k 18.001 * [backup-simplify]: Simplify 0 into 0 18.001 * [backup-simplify]: Simplify 1 into 1 18.001 * [backup-simplify]: Simplify (/ 1 1) into 1 18.001 * [taylor]: Taking taylor expansion of 1/2 in k 18.001 * [backup-simplify]: Simplify 1/2 into 1/2 18.001 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 18.001 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 18.001 * [taylor]: Taking taylor expansion of -2 in k 18.001 * [backup-simplify]: Simplify -2 into -2 18.001 * [taylor]: Taking taylor expansion of (/ PI n) in k 18.001 * [taylor]: Taking taylor expansion of PI in k 18.001 * [backup-simplify]: Simplify PI into PI 18.002 * [taylor]: Taking taylor expansion of n in k 18.002 * [backup-simplify]: Simplify n into n 18.002 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 18.002 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 18.002 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 18.002 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 18.003 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 18.003 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 18.003 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 18.003 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 18.003 * [taylor]: Taking taylor expansion of (/ -1 k) in k 18.003 * [taylor]: Taking taylor expansion of -1 in k 18.003 * [backup-simplify]: Simplify -1 into -1 18.003 * [taylor]: Taking taylor expansion of k in k 18.003 * [backup-simplify]: Simplify 0 into 0 18.003 * [backup-simplify]: Simplify 1 into 1 18.004 * [backup-simplify]: Simplify (/ -1 1) into -1 18.004 * [backup-simplify]: Simplify (sqrt 0) into 0 18.009 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 18.009 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 18.010 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 18.010 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 18.010 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 18.010 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 18.010 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 18.010 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 18.010 * [taylor]: Taking taylor expansion of 1/2 in k 18.010 * [backup-simplify]: Simplify 1/2 into 1/2 18.010 * [taylor]: Taking taylor expansion of (/ 1 k) in k 18.010 * [taylor]: Taking taylor expansion of k in k 18.010 * [backup-simplify]: Simplify 0 into 0 18.010 * [backup-simplify]: Simplify 1 into 1 18.010 * [backup-simplify]: Simplify (/ 1 1) into 1 18.010 * [taylor]: Taking taylor expansion of 1/2 in k 18.010 * [backup-simplify]: Simplify 1/2 into 1/2 18.010 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 18.010 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 18.010 * [taylor]: Taking taylor expansion of -2 in k 18.010 * [backup-simplify]: Simplify -2 into -2 18.010 * [taylor]: Taking taylor expansion of (/ PI n) in k 18.010 * [taylor]: Taking taylor expansion of PI in k 18.010 * [backup-simplify]: Simplify PI into PI 18.011 * [taylor]: Taking taylor expansion of n in k 18.011 * [backup-simplify]: Simplify n into n 18.011 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 18.011 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 18.011 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 18.011 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 18.012 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 18.012 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 18.012 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 18.012 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 18.012 * [taylor]: Taking taylor expansion of (/ -1 k) in k 18.012 * [taylor]: Taking taylor expansion of -1 in k 18.012 * [backup-simplify]: Simplify -1 into -1 18.013 * [taylor]: Taking taylor expansion of k in k 18.013 * [backup-simplify]: Simplify 0 into 0 18.013 * [backup-simplify]: Simplify 1 into 1 18.013 * [backup-simplify]: Simplify (/ -1 1) into -1 18.014 * [backup-simplify]: Simplify (sqrt 0) into 0 18.015 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 18.015 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 18.015 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 18.015 * [taylor]: Taking taylor expansion of +nan.0 in n 18.015 * [backup-simplify]: Simplify +nan.0 into +nan.0 18.016 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 18.016 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 18.016 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 18.016 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 18.016 * [taylor]: Taking taylor expansion of -2 in n 18.016 * [backup-simplify]: Simplify -2 into -2 18.016 * [taylor]: Taking taylor expansion of (/ PI n) in n 18.016 * [taylor]: Taking taylor expansion of PI in n 18.016 * [backup-simplify]: Simplify PI into PI 18.016 * [taylor]: Taking taylor expansion of n in n 18.016 * [backup-simplify]: Simplify 0 into 0 18.016 * [backup-simplify]: Simplify 1 into 1 18.016 * [backup-simplify]: Simplify (/ PI 1) into PI 18.017 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 18.018 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 18.018 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 18.018 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 18.018 * [taylor]: Taking taylor expansion of 1/2 in n 18.018 * [backup-simplify]: Simplify 1/2 into 1/2 18.018 * [taylor]: Taking taylor expansion of (/ 1 k) in n 18.018 * [taylor]: Taking taylor expansion of k in n 18.018 * [backup-simplify]: Simplify k into k 18.018 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 18.018 * [taylor]: Taking taylor expansion of 1/2 in n 18.018 * [backup-simplify]: Simplify 1/2 into 1/2 18.020 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 18.020 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 18.020 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 18.021 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 18.022 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 18.023 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 18.025 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 18.026 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 18.028 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 18.029 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 18.030 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 18.030 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 18.030 * [taylor]: Taking taylor expansion of +nan.0 in n 18.030 * [backup-simplify]: Simplify +nan.0 into +nan.0 18.030 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 18.030 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 18.030 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 18.030 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 18.030 * [taylor]: Taking taylor expansion of -2 in n 18.030 * [backup-simplify]: Simplify -2 into -2 18.030 * [taylor]: Taking taylor expansion of (/ PI n) in n 18.030 * [taylor]: Taking taylor expansion of PI in n 18.030 * [backup-simplify]: Simplify PI into PI 18.030 * [taylor]: Taking taylor expansion of n in n 18.030 * [backup-simplify]: Simplify 0 into 0 18.030 * [backup-simplify]: Simplify 1 into 1 18.030 * [backup-simplify]: Simplify (/ PI 1) into PI 18.031 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 18.032 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 18.032 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 18.032 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 18.032 * [taylor]: Taking taylor expansion of 1/2 in n 18.032 * [backup-simplify]: Simplify 1/2 into 1/2 18.032 * [taylor]: Taking taylor expansion of (/ 1 k) in n 18.032 * [taylor]: Taking taylor expansion of k in n 18.032 * [backup-simplify]: Simplify k into k 18.032 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 18.032 * [taylor]: Taking taylor expansion of 1/2 in n 18.032 * [backup-simplify]: Simplify 1/2 into 1/2 18.034 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 18.034 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 18.034 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 18.035 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 18.036 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 18.038 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 18.039 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 18.040 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 18.042 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 18.042 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 18.042 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 18.043 * [backup-simplify]: Simplify (+ 0 0) into 0 18.044 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 18.044 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 18.046 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 18.046 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 18.047 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 18.048 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into 0 18.049 * [backup-simplify]: Simplify 0 into 0 18.049 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 18.051 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 18.052 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 18.052 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 18.052 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 18.052 * [taylor]: Taking taylor expansion of +nan.0 in n 18.052 * [backup-simplify]: Simplify +nan.0 into +nan.0 18.053 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 18.053 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 18.053 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 18.053 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 18.053 * [taylor]: Taking taylor expansion of -2 in n 18.053 * [backup-simplify]: Simplify -2 into -2 18.053 * [taylor]: Taking taylor expansion of (/ PI n) in n 18.053 * [taylor]: Taking taylor expansion of PI in n 18.053 * [backup-simplify]: Simplify PI into PI 18.053 * [taylor]: Taking taylor expansion of n in n 18.053 * [backup-simplify]: Simplify 0 into 0 18.053 * [backup-simplify]: Simplify 1 into 1 18.053 * [backup-simplify]: Simplify (/ PI 1) into PI 18.053 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 18.054 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 18.054 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 18.054 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 18.054 * [taylor]: Taking taylor expansion of 1/2 in n 18.054 * [backup-simplify]: Simplify 1/2 into 1/2 18.054 * [taylor]: Taking taylor expansion of (/ 1 k) in n 18.054 * [taylor]: Taking taylor expansion of k in n 18.054 * [backup-simplify]: Simplify k into k 18.054 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 18.054 * [taylor]: Taking taylor expansion of 1/2 in n 18.054 * [backup-simplify]: Simplify 1/2 into 1/2 18.055 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 18.055 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 18.055 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 18.056 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 18.057 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 18.057 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 18.058 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 18.059 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 18.061 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 18.061 * * * [progress]: simplifying candidates 18.061 * * * * [progress]: [ 1 / 1607 ] simplifiying candidate # 18.062 * * * * [progress]: [ 2 / 1607 ] simplifiying candidate # 18.062 * * * * [progress]: [ 3 / 1607 ] simplifiying candidate # 18.062 * * * * [progress]: [ 4 / 1607 ] simplifiying candidate # 18.062 * * * * [progress]: [ 5 / 1607 ] simplifiying candidate # 18.062 * * * * [progress]: [ 6 / 1607 ] simplifiying candidate # 18.062 * * * * [progress]: [ 7 / 1607 ] simplifiying candidate # 18.062 * * * * [progress]: [ 8 / 1607 ] simplifiying candidate # 18.062 * * * * [progress]: [ 9 / 1607 ] simplifiying candidate # 18.062 * * * * [progress]: [ 10 / 1607 ] simplifiying candidate # 18.062 * * * * [progress]: [ 11 / 1607 ] simplifiying candidate # 18.062 * * * * [progress]: [ 12 / 1607 ] simplifiying candidate # 18.062 * * * * [progress]: [ 13 / 1607 ] simplifiying candidate # 18.062 * * * * [progress]: [ 14 / 1607 ] simplifiying candidate # 18.062 * * * * [progress]: [ 15 / 1607 ] simplifiying candidate # 18.062 * * * * [progress]: [ 16 / 1607 ] simplifiying candidate # 18.062 * * * * [progress]: [ 17 / 1607 ] simplifiying candidate # 18.062 * * * * [progress]: [ 18 / 1607 ] simplifiying candidate # 18.062 * * * * [progress]: [ 19 / 1607 ] simplifiying candidate # 18.062 * * * * [progress]: [ 20 / 1607 ] simplifiying candidate # 18.062 * * * * [progress]: [ 21 / 1607 ] simplifiying candidate # 18.062 * * * * [progress]: [ 22 / 1607 ] simplifiying candidate # 18.063 * * * * [progress]: [ 23 / 1607 ] simplifiying candidate # 18.063 * * * * [progress]: [ 24 / 1607 ] simplifiying candidate # 18.063 * * * * [progress]: [ 25 / 1607 ] simplifiying candidate # 18.063 * * * * [progress]: [ 26 / 1607 ] simplifiying candidate # 18.063 * * * * [progress]: [ 27 / 1607 ] 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(cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (pow (* PI (* n 2)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* PI (* n 2)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (pow (* PI (* n 2)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow (* PI (* n 2)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) 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(log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 18.393 * * [simplify]: iteration 1: (1727 enodes) 122.717 * * [simplify]: Extracting #0: cost 583 inf + 0 122.725 * * [simplify]: Extracting #1: cost 1638 inf + 2 122.734 * * [simplify]: Extracting #2: cost 1704 inf + 4403 122.742 * * [simplify]: Extracting #3: cost 1715 inf + 17327 122.769 * * [simplify]: Extracting #4: cost 1123 inf + 160579 122.838 * * [simplify]: Extracting #5: cost 747 inf + 326303 122.963 * * [simplify]: Extracting #6: cost 466 inf + 509741 123.079 * * [simplify]: Extracting #7: cost 181 inf + 710410 123.254 * * [simplify]: Extracting #8: cost 59 inf + 792821 123.420 * * [simplify]: Extracting #9: cost 19 inf + 820725 123.594 * * [simplify]: Extracting #10: cost 10 inf + 824641 123.752 * * [simplify]: Extracting #11: cost 4 inf + 829577 123.912 * * [simplify]: Extracting #12: cost 1 inf + 832875 124.099 * * [simplify]: Extracting #13: cost 0 inf + 834201 124.275 * * [simplify]: Extracting #14: cost 0 inf + 834186 124.533 * [simplify]: Simplified to: (expm1 (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (log1p (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (- 1/2 (/ k 2)) (- 1/2 (/ k 2)) (- 1/2 (/ k 2)) (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)) (pow (* (* 2 n) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* (* 2 n) PI) (sqrt (- 1/2 (/ k 2)))) (* (* 2 n) PI) (pow (* (* 2 n) PI) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* (* 2 n) PI) 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(/ (sqrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) (/ 1 (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (- 1/4 (/ (/ k 2) 2)))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (/ k 2)))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (/ (cbrt k) (cbrt 2)) (- (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (/ (cbrt k) (sqrt 2)) (- (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (/ (* (cbrt k) (* (cbrt k) (cbrt k))) 2)))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (/ (sqrt k) (cbrt 2)) (- (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)))))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (/ (* (sqrt k) (sqrt k)) 2)))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (/ (* (/ k (cbrt 2)) 1) (* (cbrt 2) (cbrt 2)))))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (/ k (sqrt 2)) (- (/ 1 (sqrt 2)))))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (/ k 2)))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (/ k 2)))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* -1/2 k))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (/ k 2)))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (cbrt k) (cbrt 2)) (- (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (cbrt k) (sqrt 2)) (- (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (/ (* (cbrt k) (* (cbrt k) (cbrt k))) 2)))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (sqrt k) (cbrt 2)) (- (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)))))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (/ (* (sqrt k) (sqrt k)) 2)))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (/ (* (/ k (cbrt 2)) 1) (* (cbrt 2) (cbrt 2)))))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ k (sqrt 2)) (- (/ 1 (sqrt 2)))))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (/ k 2)))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (/ k 2)))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* -1/2 k))) (pow (* (* 2 n) PI) (+ 1/2 (* (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* (* 2 n) PI) (+ 1/2 (- (/ k 2)))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (cbrt k) (cbrt 2)) (- (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (cbrt k) (sqrt 2)) (- (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* (* 2 n) PI) (+ 1/2 (- (/ (* (cbrt k) (* (cbrt k) (cbrt k))) 2)))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (sqrt k) (cbrt 2)) (- (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)))))) (pow (* (* 2 n) PI) (+ 1/2 (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* (* 2 n) PI) (+ 1/2 (- (/ (* (sqrt k) (sqrt k)) 2)))) (pow (* (* 2 n) PI) (+ 1/2 (- (/ (* (/ k (cbrt 2)) 1) (* (cbrt 2) (cbrt 2)))))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ k (sqrt 2)) (- (/ 1 (sqrt 2)))))) (pow (* (* 2 n) PI) (+ 1/2 (- (/ k 2)))) (pow (* (* 2 n) PI) (+ 1/2 (- (/ k 2)))) (pow (* (* 2 n) PI) (- 1/2 (* k 1/2))) (sqrt (* (* 2 n) PI)) (sqrt (* (* 2 n) PI)) (pow PI (- 1/2 (/ k 2))) (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) 1 (pow (* (* 2 n) PI) (- 1/4 (/ (/ k 2) 2))) 1 (/ 1 (sqrt k)) (* (/ 1 (sqrt k)) (sqrt (* (* 2 n) PI))) (/ (sqrt k) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ 1 (sqrt k)) (- (fma 1/4 (* (* (exp (* (+ (log (* PI 2)) (log n)) 1/2)) (* (* k k) (log n))) (log (* PI 2))) (fma 1/8 (* (* (* k k) (* (log n) (log n))) (exp (* (+ (log (* PI 2)) (log n)) 1/2))) (+ (exp (* (+ (log (* PI 2)) (log n)) 1/2)) (* (* (* (log (* PI 2)) (log (* PI 2))) (* (* k k) (exp (* (+ (log (* PI 2)) (log n)) 1/2)))) 1/8)))) (* 1/2 (+ (* (* (log n) k) (exp (* (+ (log (* PI 2)) (log n)) 1/2))) (* (* (log (* PI 2)) (exp (* (+ (log (* PI 2)) (log n)) 1/2))) k)))) (exp (* (- 1/2 (* k 1/2)) (- (log (* PI 2)) (- (log n))))) (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n))))) (* (* 2 n) PI) (* (* 2 n) PI) (* (* 2 n) PI) (- (- (/ (* +nan.0 (* (* (* k k) (* (log (* PI 2)) (* (sqrt 1/2) (sqrt 1/2)))) (sqrt 2))) PI) (- (* +nan.0 (/ (sqrt 1/2) (/ PI (* k k)))) (- (/ (* +nan.0 (* (* n (sqrt 1/2)) k)) (* PI PI)) (- (* +nan.0 (/ (log n) (/ PI (* (sqrt 2) (* (* k k) (* (sqrt 1/2) (sqrt 1/2))))))) (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))) (- (- (* (/ (exp (- (* (- 1/2 (* k 1/2)) (- (log (* PI 2)) (- (log n)))))) k) +nan.0) (- (* +nan.0 (/ (exp (- (* (- 1/2 (* k 1/2)) (- (log (* PI 2)) (- (log n)))))) (* k k))) (* +nan.0 (exp (- (* (- 1/2 (* k 1/2)) (- (log (* PI 2)) (- (log n)))))))))) (- (- (* +nan.0 (/ (exp (- (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n)))))) (* k k))) (- (* (/ (exp (- (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n)))))) k) +nan.0) (* (exp (- (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n)))))) +nan.0)))) (- (- (* (* (sqrt 2) (* (* PI n) k)) +nan.0) (- (* (* (sqrt 2) (* PI n)) +nan.0) (- (* +nan.0 (* (* (sqrt 2) (* (* PI n) k)) (log (* PI 2)))) (- (* (* +nan.0 (sqrt 2)) (* (* PI n) (* (log n) k))) (* (* +nan.0 (sqrt 2)) (* (* n n) (* PI PI)))))))) (- (- (/ (* +nan.0 (exp (* (- 1/2 (* k 1/2)) (- (log (* PI 2)) (- (log n)))))) (* (* k k) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* k 1/2)) (- (log (* PI 2)) (- (log n))))) k)) (* +nan.0 (/ (exp (* (- 1/2 (* k 1/2)) (- (log (* PI 2)) (- (log n))))) (* k k)))))) (- (- (/ (* +nan.0 (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n)))))) k) (- (/ (* +nan.0 (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n)))))) (* k k)) (* +nan.0 (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n))))))))) 125.051 * * * [progress]: adding candidates to table 153.407 * * [progress]: iteration 4 / 4 153.407 * * * [progress]: picking best candidate 153.432 * * * * [pick]: Picked # 153.432 * * * [progress]: localizing error 153.481 * * * [progress]: generating rewritten candidates 153.481 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1) 153.487 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2) 153.496 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 153.505 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2) 153.570 * * * [progress]: generating series expansions 153.570 * * * * [progress]: [ 1 / 4 ] generating series at (2 1) 153.570 * [backup-simplify]: Simplify (pow PI (- 1/2 (/ k 2))) into (pow PI (- 1/2 (* 1/2 k))) 153.570 * [approximate]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in (k) around 0 153.570 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 153.570 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 153.570 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 153.570 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 153.570 * [taylor]: Taking taylor expansion of 1/2 in k 153.570 * [backup-simplify]: Simplify 1/2 into 1/2 153.570 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 153.570 * [taylor]: Taking taylor expansion of 1/2 in k 153.570 * [backup-simplify]: Simplify 1/2 into 1/2 153.570 * [taylor]: Taking taylor expansion of k in k 153.570 * [backup-simplify]: Simplify 0 into 0 153.570 * [backup-simplify]: Simplify 1 into 1 153.570 * [taylor]: Taking taylor expansion of (log PI) in k 153.570 * [taylor]: Taking taylor expansion of PI in k 153.570 * [backup-simplify]: Simplify PI into PI 153.571 * [backup-simplify]: Simplify (log PI) into (log PI) 153.572 * [backup-simplify]: Simplify (* 1/2 0) into 0 153.572 * [backup-simplify]: Simplify (- 0) into 0 153.573 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 153.574 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 153.575 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 153.575 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 153.576 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 153.576 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 153.576 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 153.576 * [taylor]: Taking taylor expansion of 1/2 in k 153.576 * [backup-simplify]: Simplify 1/2 into 1/2 153.576 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 153.576 * [taylor]: Taking taylor expansion of 1/2 in k 153.576 * [backup-simplify]: Simplify 1/2 into 1/2 153.576 * [taylor]: Taking taylor expansion of k in k 153.576 * [backup-simplify]: Simplify 0 into 0 153.576 * [backup-simplify]: Simplify 1 into 1 153.576 * [taylor]: Taking taylor expansion of (log PI) in k 153.576 * [taylor]: Taking taylor expansion of PI in k 153.576 * [backup-simplify]: Simplify PI into PI 153.576 * [backup-simplify]: Simplify (log PI) into (log PI) 153.577 * [backup-simplify]: Simplify (* 1/2 0) into 0 153.577 * [backup-simplify]: Simplify (- 0) into 0 153.578 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 153.578 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 153.579 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 153.580 * [backup-simplify]: Simplify (pow PI 1/2) into (pow PI 1/2) 153.581 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 153.581 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 153.581 * [backup-simplify]: Simplify (- 1/2) into -1/2 153.582 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 153.583 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 153.589 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 153.590 * [backup-simplify]: Simplify (* -1/2 (* (log PI) (sqrt PI))) into (* -1/2 (* (log PI) (sqrt PI))) 153.592 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 153.593 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 153.593 * [backup-simplify]: Simplify (- 0) into 0 153.593 * [backup-simplify]: Simplify (+ 0 0) into 0 153.594 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 153.601 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 153.603 * [backup-simplify]: Simplify (* 1/8 (* (pow (log PI) 2) (sqrt PI))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 153.606 * [backup-simplify]: Simplify (+ (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (log PI) (sqrt PI))) k) (pow PI 1/2))) into (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) 153.607 * [backup-simplify]: Simplify (pow PI (- 1/2 (/ (/ 1 k) 2))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 153.607 * [approximate]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in (k) around 0 153.607 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 153.607 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 153.607 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 153.607 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 153.607 * [taylor]: Taking taylor expansion of 1/2 in k 153.607 * [backup-simplify]: Simplify 1/2 into 1/2 153.607 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 153.607 * [taylor]: Taking taylor expansion of 1/2 in k 153.607 * [backup-simplify]: Simplify 1/2 into 1/2 153.607 * [taylor]: Taking taylor expansion of (/ 1 k) in k 153.607 * [taylor]: Taking taylor expansion of k in k 153.607 * [backup-simplify]: Simplify 0 into 0 153.607 * [backup-simplify]: Simplify 1 into 1 153.607 * [backup-simplify]: Simplify (/ 1 1) into 1 153.607 * [taylor]: Taking taylor expansion of (log PI) in k 153.607 * [taylor]: Taking taylor expansion of PI in k 153.607 * [backup-simplify]: Simplify PI into PI 153.607 * [backup-simplify]: Simplify (log PI) into (log PI) 153.608 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 153.608 * [backup-simplify]: Simplify (- 1/2) into -1/2 153.608 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 153.609 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 153.609 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 153.609 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 153.609 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 153.609 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 153.609 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 153.609 * [taylor]: Taking taylor expansion of 1/2 in k 153.609 * [backup-simplify]: Simplify 1/2 into 1/2 153.609 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 153.609 * [taylor]: Taking taylor expansion of 1/2 in k 153.609 * [backup-simplify]: Simplify 1/2 into 1/2 153.609 * [taylor]: Taking taylor expansion of (/ 1 k) in k 153.609 * [taylor]: Taking taylor expansion of k in k 153.609 * [backup-simplify]: Simplify 0 into 0 153.609 * [backup-simplify]: Simplify 1 into 1 153.610 * [backup-simplify]: Simplify (/ 1 1) into 1 153.610 * [taylor]: Taking taylor expansion of (log PI) in k 153.610 * [taylor]: Taking taylor expansion of PI in k 153.610 * [backup-simplify]: Simplify PI into PI 153.610 * [backup-simplify]: Simplify (log PI) into (log PI) 153.610 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 153.610 * [backup-simplify]: Simplify (- 1/2) into -1/2 153.611 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 153.611 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 153.612 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 153.612 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 k)))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 153.612 * [backup-simplify]: Simplify 0 into 0 153.612 * [backup-simplify]: Simplify 0 into 0 153.612 * [backup-simplify]: Simplify 0 into 0 153.612 * [backup-simplify]: Simplify 0 into 0 153.612 * [backup-simplify]: Simplify 0 into 0 153.612 * [backup-simplify]: Simplify 0 into 0 153.612 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) into (pow PI (- 1/2 (* 1/2 k))) 153.612 * [backup-simplify]: Simplify (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 153.612 * [approximate]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in (k) around 0 153.612 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 153.612 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 153.612 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 153.612 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 153.612 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 153.612 * [taylor]: Taking taylor expansion of 1/2 in k 153.612 * [backup-simplify]: Simplify 1/2 into 1/2 153.612 * [taylor]: Taking taylor expansion of (/ 1 k) in k 153.612 * [taylor]: Taking taylor expansion of k in k 153.612 * [backup-simplify]: Simplify 0 into 0 153.612 * [backup-simplify]: Simplify 1 into 1 153.612 * [backup-simplify]: Simplify (/ 1 1) into 1 153.612 * [taylor]: Taking taylor expansion of 1/2 in k 153.613 * [backup-simplify]: Simplify 1/2 into 1/2 153.613 * [taylor]: Taking taylor expansion of (log PI) in k 153.613 * [taylor]: Taking taylor expansion of PI in k 153.613 * [backup-simplify]: Simplify PI into PI 153.613 * [backup-simplify]: Simplify (log PI) into (log PI) 153.613 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 153.613 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 153.614 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 153.614 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 153.614 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 153.614 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 153.614 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 153.614 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 153.614 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 153.614 * [taylor]: Taking taylor expansion of 1/2 in k 153.614 * [backup-simplify]: Simplify 1/2 into 1/2 153.614 * [taylor]: Taking taylor expansion of (/ 1 k) in k 153.614 * [taylor]: Taking taylor expansion of k in k 153.614 * [backup-simplify]: Simplify 0 into 0 153.614 * [backup-simplify]: Simplify 1 into 1 153.615 * [backup-simplify]: Simplify (/ 1 1) into 1 153.615 * [taylor]: Taking taylor expansion of 1/2 in k 153.615 * [backup-simplify]: Simplify 1/2 into 1/2 153.615 * [taylor]: Taking taylor expansion of (log PI) in k 153.615 * [taylor]: Taking taylor expansion of PI in k 153.615 * [backup-simplify]: Simplify PI into PI 153.615 * [backup-simplify]: Simplify (log PI) into (log PI) 153.615 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 153.616 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 153.616 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 153.617 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 153.617 * [backup-simplify]: Simplify (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 153.617 * [backup-simplify]: Simplify 0 into 0 153.617 * [backup-simplify]: Simplify 0 into 0 153.617 * [backup-simplify]: Simplify 0 into 0 153.617 * [backup-simplify]: Simplify 0 into 0 153.617 * [backup-simplify]: Simplify 0 into 0 153.617 * [backup-simplify]: Simplify 0 into 0 153.617 * [backup-simplify]: Simplify (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) into (pow PI (- 1/2 (* 1/2 k))) 153.617 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2) 153.617 * [backup-simplify]: Simplify (pow (* 2 n) (- 1/2 (/ k 2))) into (pow (* 2 n) (- 1/2 (* 1/2 k))) 153.617 * [approximate]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in (n k) around 0 153.617 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 153.617 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 153.617 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 153.617 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 153.617 * [taylor]: Taking taylor expansion of 1/2 in k 153.617 * [backup-simplify]: Simplify 1/2 into 1/2 153.617 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 153.617 * [taylor]: Taking taylor expansion of 1/2 in k 153.617 * [backup-simplify]: Simplify 1/2 into 1/2 153.617 * [taylor]: Taking taylor expansion of k in k 153.618 * [backup-simplify]: Simplify 0 into 0 153.618 * [backup-simplify]: Simplify 1 into 1 153.618 * [taylor]: Taking taylor expansion of (log (* 2 n)) in k 153.618 * [taylor]: Taking taylor expansion of (* 2 n) in k 153.618 * [taylor]: Taking taylor expansion of 2 in k 153.618 * [backup-simplify]: Simplify 2 into 2 153.618 * [taylor]: Taking taylor expansion of n in k 153.618 * [backup-simplify]: Simplify n into n 153.618 * [backup-simplify]: Simplify (* 2 n) into (* 2 n) 153.618 * [backup-simplify]: Simplify (log (* 2 n)) into (log (* 2 n)) 153.618 * [backup-simplify]: Simplify (* 1/2 0) into 0 153.619 * [backup-simplify]: Simplify (- 0) into 0 153.619 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 153.619 * [backup-simplify]: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 153.619 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 153.619 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 153.619 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 153.619 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 153.619 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 153.619 * [taylor]: Taking taylor expansion of 1/2 in n 153.619 * [backup-simplify]: Simplify 1/2 into 1/2 153.619 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 153.619 * [taylor]: Taking taylor expansion of 1/2 in n 153.619 * [backup-simplify]: Simplify 1/2 into 1/2 153.619 * [taylor]: Taking taylor expansion of k in n 153.619 * [backup-simplify]: Simplify k into k 153.620 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 153.620 * [taylor]: Taking taylor expansion of (* 2 n) in n 153.620 * [taylor]: Taking taylor expansion of 2 in n 153.620 * [backup-simplify]: Simplify 2 into 2 153.620 * [taylor]: Taking taylor expansion of n in n 153.620 * [backup-simplify]: Simplify 0 into 0 153.620 * [backup-simplify]: Simplify 1 into 1 153.620 * [backup-simplify]: Simplify (* 2 0) into 0 153.621 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 153.621 * [backup-simplify]: Simplify (log 2) into (log 2) 153.621 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 153.621 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 153.621 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 153.622 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 153.623 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 153.623 * [backup-simplify]: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 153.623 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 153.623 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 153.623 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 153.623 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 153.623 * [taylor]: Taking taylor expansion of 1/2 in n 153.623 * [backup-simplify]: Simplify 1/2 into 1/2 153.623 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 153.623 * [taylor]: Taking taylor expansion of 1/2 in n 153.623 * [backup-simplify]: Simplify 1/2 into 1/2 153.623 * [taylor]: Taking taylor expansion of k in n 153.623 * [backup-simplify]: Simplify k into k 153.623 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 153.623 * [taylor]: Taking taylor expansion of (* 2 n) in n 153.623 * [taylor]: Taking taylor expansion of 2 in n 153.623 * [backup-simplify]: Simplify 2 into 2 153.623 * [taylor]: Taking taylor expansion of n in n 153.624 * [backup-simplify]: Simplify 0 into 0 153.624 * [backup-simplify]: Simplify 1 into 1 153.624 * [backup-simplify]: Simplify (* 2 0) into 0 153.625 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 153.625 * [backup-simplify]: Simplify (log 2) into (log 2) 153.625 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 153.625 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 153.625 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 153.626 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 153.626 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 153.627 * [backup-simplify]: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 153.627 * [taylor]: Taking taylor expansion of (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) in k 153.627 * [taylor]: Taking taylor expansion of (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) in k 153.627 * [taylor]: Taking taylor expansion of (+ (log 2) (log n)) in k 153.627 * [taylor]: Taking taylor expansion of (log 2) in k 153.627 * [taylor]: Taking taylor expansion of 2 in k 153.627 * [backup-simplify]: Simplify 2 into 2 153.628 * [backup-simplify]: Simplify (log 2) into (log 2) 153.628 * [taylor]: Taking taylor expansion of (log n) in k 153.628 * [taylor]: Taking taylor expansion of n in k 153.628 * [backup-simplify]: Simplify n into n 153.628 * [backup-simplify]: Simplify (log n) into (log n) 153.628 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 153.628 * [taylor]: Taking taylor expansion of 1/2 in k 153.628 * [backup-simplify]: Simplify 1/2 into 1/2 153.628 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 153.628 * [taylor]: Taking taylor expansion of 1/2 in k 153.628 * [backup-simplify]: Simplify 1/2 into 1/2 153.628 * [taylor]: Taking taylor expansion of k in k 153.628 * [backup-simplify]: Simplify 0 into 0 153.628 * [backup-simplify]: Simplify 1 into 1 153.628 * [backup-simplify]: Simplify (+ (log 2) (log n)) into (+ (log 2) (log n)) 153.629 * [backup-simplify]: Simplify (* 1/2 0) into 0 153.629 * [backup-simplify]: Simplify (- 0) into 0 153.629 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 153.630 * [backup-simplify]: Simplify (* (+ (log 2) (log n)) 1/2) into (* 1/2 (+ (log 2) (log n))) 153.630 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 153.631 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 153.632 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0 153.633 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 153.634 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 153.634 * [backup-simplify]: Simplify (- 0) into 0 153.634 * [backup-simplify]: Simplify (+ 0 0) into 0 153.635 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 153.636 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log 2) (log n)))) into 0 153.637 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 153.637 * [taylor]: Taking taylor expansion of 0 in k 153.637 * [backup-simplify]: Simplify 0 into 0 153.637 * [backup-simplify]: Simplify 0 into 0 153.638 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 153.638 * [backup-simplify]: Simplify (- 1/2) into -1/2 153.638 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 153.640 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 153.641 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 153.641 * [backup-simplify]: Simplify (+ 0 0) into 0 153.642 * [backup-simplify]: Simplify (+ (* (+ (log 2) (log n)) -1/2) (* 0 1/2)) into (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 153.643 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 153.645 * [backup-simplify]: Simplify (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 153.646 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 153.649 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 153.650 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 153.650 * [backup-simplify]: Simplify (- 0) into 0 153.651 * [backup-simplify]: Simplify (+ 0 0) into 0 153.651 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 153.652 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0 153.654 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 153.654 * [taylor]: Taking taylor expansion of 0 in k 153.654 * [backup-simplify]: Simplify 0 into 0 153.654 * [backup-simplify]: Simplify 0 into 0 153.654 * [backup-simplify]: Simplify 0 into 0 153.655 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 153.656 * [backup-simplify]: Simplify (- 0) into 0 153.656 * [backup-simplify]: Simplify (+ 0 0) into 0 153.659 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 153.661 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 153.661 * [backup-simplify]: Simplify (+ 0 0) into 0 153.662 * [backup-simplify]: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 -1/2) (* 0 1/2))) into 0 153.664 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 153.667 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 153.673 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log 2) (log n)))))) into (- (+ (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (+ (* 1/4 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (* 1/8 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k))) (* 1/2 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k))))) 153.673 * [backup-simplify]: Simplify (pow (* 2 (/ 1 n)) (- 1/2 (/ (/ 1 k) 2))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 153.673 * [approximate]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 153.673 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 153.673 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 153.673 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 153.673 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 153.674 * [taylor]: Taking taylor expansion of 1/2 in k 153.674 * [backup-simplify]: Simplify 1/2 into 1/2 153.674 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 153.674 * [taylor]: Taking taylor expansion of 1/2 in k 153.674 * [backup-simplify]: Simplify 1/2 into 1/2 153.674 * [taylor]: Taking taylor expansion of (/ 1 k) in k 153.674 * [taylor]: Taking taylor expansion of k in k 153.674 * [backup-simplify]: Simplify 0 into 0 153.674 * [backup-simplify]: Simplify 1 into 1 153.674 * [backup-simplify]: Simplify (/ 1 1) into 1 153.674 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in k 153.674 * [taylor]: Taking taylor expansion of (/ 2 n) in k 153.674 * [taylor]: Taking taylor expansion of 2 in k 153.674 * [backup-simplify]: Simplify 2 into 2 153.674 * [taylor]: Taking taylor expansion of n in k 153.674 * [backup-simplify]: Simplify n into n 153.674 * [backup-simplify]: Simplify (/ 2 n) into (/ 2 n) 153.674 * [backup-simplify]: Simplify (log (/ 2 n)) into (log (/ 2 n)) 153.675 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 153.675 * [backup-simplify]: Simplify (- 1/2) into -1/2 153.676 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 153.676 * [backup-simplify]: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 153.676 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 153.676 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 153.676 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 153.676 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 153.676 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 153.676 * [taylor]: Taking taylor expansion of 1/2 in n 153.676 * [backup-simplify]: Simplify 1/2 into 1/2 153.676 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 153.676 * [taylor]: Taking taylor expansion of 1/2 in n 153.676 * [backup-simplify]: Simplify 1/2 into 1/2 153.676 * [taylor]: Taking taylor expansion of (/ 1 k) in n 153.676 * [taylor]: Taking taylor expansion of k in n 153.676 * [backup-simplify]: Simplify k into k 153.676 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 153.676 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 153.676 * [taylor]: Taking taylor expansion of (/ 2 n) in n 153.676 * [taylor]: Taking taylor expansion of 2 in n 153.676 * [backup-simplify]: Simplify 2 into 2 153.676 * [taylor]: Taking taylor expansion of n in n 153.676 * [backup-simplify]: Simplify 0 into 0 153.676 * [backup-simplify]: Simplify 1 into 1 153.677 * [backup-simplify]: Simplify (/ 2 1) into 2 153.677 * [backup-simplify]: Simplify (log 2) into (log 2) 153.677 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 153.677 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 153.677 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 153.678 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 153.679 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 153.679 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 153.679 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 153.679 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 153.679 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 153.679 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 153.679 * [taylor]: Taking taylor expansion of 1/2 in n 153.679 * [backup-simplify]: Simplify 1/2 into 1/2 153.679 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 153.679 * [taylor]: Taking taylor expansion of 1/2 in n 153.679 * [backup-simplify]: Simplify 1/2 into 1/2 153.679 * [taylor]: Taking taylor expansion of (/ 1 k) in n 153.680 * [taylor]: Taking taylor expansion of k in n 153.680 * [backup-simplify]: Simplify k into k 153.680 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 153.680 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 153.680 * [taylor]: Taking taylor expansion of (/ 2 n) in n 153.680 * [taylor]: Taking taylor expansion of 2 in n 153.680 * [backup-simplify]: Simplify 2 into 2 153.680 * [taylor]: Taking taylor expansion of n in n 153.680 * [backup-simplify]: Simplify 0 into 0 153.680 * [backup-simplify]: Simplify 1 into 1 153.680 * [backup-simplify]: Simplify (/ 2 1) into 2 153.681 * [backup-simplify]: Simplify (log 2) into (log 2) 153.681 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 153.681 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 153.681 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 153.682 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 153.682 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 153.683 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 153.683 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) in k 153.683 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) in k 153.683 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 153.683 * [taylor]: Taking taylor expansion of 1/2 in k 153.683 * [backup-simplify]: Simplify 1/2 into 1/2 153.683 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 153.683 * [taylor]: Taking taylor expansion of 1/2 in k 153.683 * [backup-simplify]: Simplify 1/2 into 1/2 153.683 * [taylor]: Taking taylor expansion of (/ 1 k) in k 153.683 * [taylor]: Taking taylor expansion of k in k 153.683 * [backup-simplify]: Simplify 0 into 0 153.683 * [backup-simplify]: Simplify 1 into 1 153.683 * [backup-simplify]: Simplify (/ 1 1) into 1 153.684 * [taylor]: Taking taylor expansion of (- (log 2) (log n)) in k 153.684 * [taylor]: Taking taylor expansion of (log 2) in k 153.684 * [taylor]: Taking taylor expansion of 2 in k 153.684 * [backup-simplify]: Simplify 2 into 2 153.684 * [backup-simplify]: Simplify (log 2) into (log 2) 153.684 * [taylor]: Taking taylor expansion of (log n) in k 153.684 * [taylor]: Taking taylor expansion of n in k 153.684 * [backup-simplify]: Simplify n into n 153.684 * [backup-simplify]: Simplify (log n) into (log n) 153.685 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 153.685 * [backup-simplify]: Simplify (- 1/2) into -1/2 153.685 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 153.686 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 153.694 * [backup-simplify]: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) 153.694 * [backup-simplify]: Simplify (* -1/2 (- (log 2) (log n))) into (* -1/2 (- (log 2) (log n))) 153.695 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 153.695 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 153.696 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0 153.698 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 153.698 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 153.698 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 153.699 * [backup-simplify]: Simplify (- 0) into 0 153.699 * [backup-simplify]: Simplify (+ 0 0) into 0 153.700 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 153.700 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 153.701 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 153.702 * [taylor]: Taking taylor expansion of 0 in k 153.702 * [backup-simplify]: Simplify 0 into 0 153.702 * [backup-simplify]: Simplify 0 into 0 153.702 * [backup-simplify]: Simplify 0 into 0 153.703 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 153.705 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 153.706 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 153.706 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 153.707 * [backup-simplify]: Simplify (- 0) into 0 153.707 * [backup-simplify]: Simplify (+ 0 0) into 0 153.708 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 153.709 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 153.710 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 153.710 * [taylor]: Taking taylor expansion of 0 in k 153.710 * [backup-simplify]: Simplify 0 into 0 153.710 * [backup-simplify]: Simplify 0 into 0 153.711 * [backup-simplify]: Simplify 0 into 0 153.711 * [backup-simplify]: Simplify 0 into 0 153.712 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 153.717 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 153.717 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 153.718 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 153.719 * [backup-simplify]: Simplify (- 0) into 0 153.719 * [backup-simplify]: Simplify (+ 0 0) into 0 153.720 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 153.721 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 153.723 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 153.723 * [taylor]: Taking taylor expansion of 0 in k 153.723 * [backup-simplify]: Simplify 0 into 0 153.723 * [backup-simplify]: Simplify 0 into 0 153.724 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))) into (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) 153.724 * [backup-simplify]: Simplify (pow (* 2 (/ 1 (- n))) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 153.724 * [approximate]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 153.724 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 153.724 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 153.724 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 153.724 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 153.724 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 153.724 * [taylor]: Taking taylor expansion of 1/2 in k 153.724 * [backup-simplify]: Simplify 1/2 into 1/2 153.724 * [taylor]: Taking taylor expansion of (/ 1 k) in k 153.724 * [taylor]: Taking taylor expansion of k in k 153.724 * [backup-simplify]: Simplify 0 into 0 153.724 * [backup-simplify]: Simplify 1 into 1 153.724 * [backup-simplify]: Simplify (/ 1 1) into 1 153.724 * [taylor]: Taking taylor expansion of 1/2 in k 153.724 * [backup-simplify]: Simplify 1/2 into 1/2 153.725 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in k 153.725 * [taylor]: Taking taylor expansion of (/ -2 n) in k 153.725 * [taylor]: Taking taylor expansion of -2 in k 153.725 * [backup-simplify]: Simplify -2 into -2 153.725 * [taylor]: Taking taylor expansion of n in k 153.725 * [backup-simplify]: Simplify n into n 153.725 * [backup-simplify]: Simplify (/ -2 n) into (/ -2 n) 153.725 * [backup-simplify]: Simplify (log (/ -2 n)) into (log (/ -2 n)) 153.725 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 153.726 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 153.726 * [backup-simplify]: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 153.726 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 153.726 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 153.726 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 153.726 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 153.726 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 153.726 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 153.726 * [taylor]: Taking taylor expansion of 1/2 in n 153.726 * [backup-simplify]: Simplify 1/2 into 1/2 153.726 * [taylor]: Taking taylor expansion of (/ 1 k) in n 153.726 * [taylor]: Taking taylor expansion of k in n 153.726 * [backup-simplify]: Simplify k into k 153.726 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 153.726 * [taylor]: Taking taylor expansion of 1/2 in n 153.726 * [backup-simplify]: Simplify 1/2 into 1/2 153.726 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 153.726 * [taylor]: Taking taylor expansion of (/ -2 n) in n 153.726 * [taylor]: Taking taylor expansion of -2 in n 153.726 * [backup-simplify]: Simplify -2 into -2 153.726 * [taylor]: Taking taylor expansion of n in n 153.726 * [backup-simplify]: Simplify 0 into 0 153.726 * [backup-simplify]: Simplify 1 into 1 153.727 * [backup-simplify]: Simplify (/ -2 1) into -2 153.727 * [backup-simplify]: Simplify (log -2) into (log -2) 153.727 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 153.727 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 153.728 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 153.729 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 153.729 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 153.729 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 153.729 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 153.729 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 153.729 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 153.729 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 153.729 * [taylor]: Taking taylor expansion of 1/2 in n 153.729 * [backup-simplify]: Simplify 1/2 into 1/2 153.729 * [taylor]: Taking taylor expansion of (/ 1 k) in n 153.729 * [taylor]: Taking taylor expansion of k in n 153.729 * [backup-simplify]: Simplify k into k 153.729 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 153.729 * [taylor]: Taking taylor expansion of 1/2 in n 153.729 * [backup-simplify]: Simplify 1/2 into 1/2 153.729 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 153.729 * [taylor]: Taking taylor expansion of (/ -2 n) in n 153.729 * [taylor]: Taking taylor expansion of -2 in n 153.730 * [backup-simplify]: Simplify -2 into -2 153.730 * [taylor]: Taking taylor expansion of n in n 153.730 * [backup-simplify]: Simplify 0 into 0 153.730 * [backup-simplify]: Simplify 1 into 1 153.730 * [backup-simplify]: Simplify (/ -2 1) into -2 153.730 * [backup-simplify]: Simplify (log -2) into (log -2) 153.730 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 153.731 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 153.731 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 153.732 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 153.732 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 153.732 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) in k 153.732 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) in k 153.732 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 153.732 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 153.732 * [taylor]: Taking taylor expansion of 1/2 in k 153.733 * [backup-simplify]: Simplify 1/2 into 1/2 153.733 * [taylor]: Taking taylor expansion of (/ 1 k) in k 153.733 * [taylor]: Taking taylor expansion of k in k 153.733 * [backup-simplify]: Simplify 0 into 0 153.733 * [backup-simplify]: Simplify 1 into 1 153.733 * [backup-simplify]: Simplify (/ 1 1) into 1 153.733 * [taylor]: Taking taylor expansion of 1/2 in k 153.733 * [backup-simplify]: Simplify 1/2 into 1/2 153.733 * [taylor]: Taking taylor expansion of (- (log -2) (log n)) in k 153.733 * [taylor]: Taking taylor expansion of (log -2) in k 153.733 * [taylor]: Taking taylor expansion of -2 in k 153.733 * [backup-simplify]: Simplify -2 into -2 153.733 * [backup-simplify]: Simplify (log -2) into (log -2) 153.734 * [taylor]: Taking taylor expansion of (log n) in k 153.734 * [taylor]: Taking taylor expansion of n in k 153.734 * [backup-simplify]: Simplify n into n 153.734 * [backup-simplify]: Simplify (log n) into (log n) 153.734 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 153.734 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 153.734 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 153.735 * [backup-simplify]: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) 153.735 * [backup-simplify]: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) 153.736 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 153.736 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 153.737 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0 153.739 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 153.739 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 153.739 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 153.740 * [backup-simplify]: Simplify (+ 0 0) into 0 153.740 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 153.741 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -2) (log n)))) into 0 153.742 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 153.742 * [taylor]: Taking taylor expansion of 0 in k 153.742 * [backup-simplify]: Simplify 0 into 0 153.742 * [backup-simplify]: Simplify 0 into 0 153.742 * [backup-simplify]: Simplify 0 into 0 153.743 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 153.746 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 153.747 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 153.748 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 153.748 * [backup-simplify]: Simplify (+ 0 0) into 0 153.749 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 153.750 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 153.752 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 153.752 * [taylor]: Taking taylor expansion of 0 in k 153.753 * [backup-simplify]: Simplify 0 into 0 153.753 * [backup-simplify]: Simplify 0 into 0 153.753 * [backup-simplify]: Simplify 0 into 0 153.753 * [backup-simplify]: Simplify 0 into 0 153.754 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 153.760 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -2 1)))) 6) into 0 153.760 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 153.761 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 153.762 * [backup-simplify]: Simplify (+ 0 0) into 0 153.762 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 153.764 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -2) (log n)))))) into 0 153.766 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 153.766 * [taylor]: Taking taylor expansion of 0 in k 153.766 * [backup-simplify]: Simplify 0 into 0 153.766 * [backup-simplify]: Simplify 0 into 0 153.767 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) 153.767 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 153.767 * [backup-simplify]: Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k)) 153.767 * [approximate]: Taking taylor expansion of (sqrt (/ 1 k)) in (k) around 0 153.767 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 153.767 * [taylor]: Taking taylor expansion of (/ 1 k) in k 153.767 * [taylor]: Taking taylor expansion of k in k 153.767 * [backup-simplify]: Simplify 0 into 0 153.767 * [backup-simplify]: Simplify 1 into 1 153.768 * [backup-simplify]: Simplify (/ 1 1) into 1 153.768 * [backup-simplify]: Simplify (sqrt 0) into 0 153.770 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 153.770 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 153.770 * [taylor]: Taking taylor expansion of (/ 1 k) in k 153.770 * [taylor]: Taking taylor expansion of k in k 153.770 * [backup-simplify]: Simplify 0 into 0 153.770 * [backup-simplify]: Simplify 1 into 1 153.770 * [backup-simplify]: Simplify (/ 1 1) into 1 153.771 * [backup-simplify]: Simplify (sqrt 0) into 0 153.772 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 153.772 * [backup-simplify]: Simplify 0 into 0 153.772 * [backup-simplify]: Simplify +nan.0 into +nan.0 153.773 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 153.775 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 153.775 * [backup-simplify]: Simplify +nan.0 into +nan.0 153.775 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 153.778 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 153.778 * [backup-simplify]: Simplify +nan.0 into +nan.0 153.778 * [backup-simplify]: Simplify (+ (* +nan.0 (pow k 2)) (+ (* +nan.0 k) +nan.0)) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 153.778 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k) 153.778 * [approximate]: Taking taylor expansion of (sqrt k) in (k) around 0 153.778 * [taylor]: Taking taylor expansion of (sqrt k) in k 153.778 * [taylor]: Taking taylor expansion of k in k 153.778 * [backup-simplify]: Simplify 0 into 0 153.778 * [backup-simplify]: Simplify 1 into 1 153.778 * [backup-simplify]: Simplify (sqrt 0) into 0 153.779 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 153.779 * [taylor]: Taking taylor expansion of (sqrt k) in k 153.779 * [taylor]: Taking taylor expansion of k in k 153.779 * [backup-simplify]: Simplify 0 into 0 153.779 * [backup-simplify]: Simplify 1 into 1 153.779 * [backup-simplify]: Simplify (sqrt 0) into 0 153.780 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 153.780 * [backup-simplify]: Simplify 0 into 0 153.780 * [backup-simplify]: Simplify +nan.0 into +nan.0 153.782 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 153.782 * [backup-simplify]: Simplify +nan.0 into +nan.0 153.784 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 153.784 * [backup-simplify]: Simplify +nan.0 into +nan.0 153.785 * [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)))))))) 153.785 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 (- k)))) into (/ 1 (sqrt (/ -1 k))) 153.785 * [approximate]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in (k) around 0 153.785 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 153.785 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 153.785 * [taylor]: Taking taylor expansion of (/ -1 k) in k 153.785 * [taylor]: Taking taylor expansion of -1 in k 153.785 * [backup-simplify]: Simplify -1 into -1 153.785 * [taylor]: Taking taylor expansion of k in k 153.785 * [backup-simplify]: Simplify 0 into 0 153.785 * [backup-simplify]: Simplify 1 into 1 153.785 * [backup-simplify]: Simplify (/ -1 1) into -1 153.785 * [backup-simplify]: Simplify (sqrt 0) into 0 153.786 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 153.786 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 153.786 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 153.787 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 153.787 * [taylor]: Taking taylor expansion of (/ -1 k) in k 153.787 * [taylor]: Taking taylor expansion of -1 in k 153.787 * [backup-simplify]: Simplify -1 into -1 153.787 * [taylor]: Taking taylor expansion of k in k 153.787 * [backup-simplify]: Simplify 0 into 0 153.787 * [backup-simplify]: Simplify 1 into 1 153.787 * [backup-simplify]: Simplify (/ -1 1) into -1 153.787 * [backup-simplify]: Simplify (sqrt 0) into 0 153.788 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 153.788 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 153.788 * [backup-simplify]: Simplify +nan.0 into +nan.0 153.789 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 153.790 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 153.792 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 153.792 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 153.792 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 153.796 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 153.800 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 153.800 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 153.801 * [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))))) 153.801 * * * * [progress]: [ 4 / 4 ] generating series at (2 2) 153.802 * [backup-simplify]: Simplify (* (/ 1 (sqrt k)) (pow (* 2 n) (- 1/2 (/ k 2)))) into (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) 153.802 * [approximate]: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in (k n) around 0 153.802 * [taylor]: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n 153.802 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 153.802 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 153.802 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 153.802 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 153.802 * [taylor]: Taking taylor expansion of 1/2 in n 153.802 * [backup-simplify]: Simplify 1/2 into 1/2 153.802 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 153.802 * [taylor]: Taking taylor expansion of 1/2 in n 153.802 * [backup-simplify]: Simplify 1/2 into 1/2 153.802 * [taylor]: Taking taylor expansion of k in n 153.802 * [backup-simplify]: Simplify k into k 153.802 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 153.802 * [taylor]: Taking taylor expansion of (* 2 n) in n 153.802 * [taylor]: Taking taylor expansion of 2 in n 153.802 * [backup-simplify]: Simplify 2 into 2 153.802 * [taylor]: Taking taylor expansion of n in n 153.802 * [backup-simplify]: Simplify 0 into 0 153.802 * [backup-simplify]: Simplify 1 into 1 153.803 * [backup-simplify]: Simplify (* 2 0) into 0 153.803 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 153.804 * [backup-simplify]: Simplify (log 2) into (log 2) 153.804 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 153.804 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 153.804 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 153.805 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 153.805 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 153.806 * [backup-simplify]: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 153.806 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 153.806 * [taylor]: Taking taylor expansion of (/ 1 k) in n 153.806 * [taylor]: Taking taylor expansion of k in n 153.806 * [backup-simplify]: Simplify k into k 153.806 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 153.806 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 153.806 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 153.806 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 153.806 * [taylor]: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in k 153.806 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 153.806 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 153.806 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 153.806 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 153.806 * [taylor]: Taking taylor expansion of 1/2 in k 153.807 * [backup-simplify]: Simplify 1/2 into 1/2 153.807 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 153.807 * [taylor]: Taking taylor expansion of 1/2 in k 153.807 * [backup-simplify]: Simplify 1/2 into 1/2 153.807 * [taylor]: Taking taylor expansion of k in k 153.807 * [backup-simplify]: Simplify 0 into 0 153.807 * [backup-simplify]: Simplify 1 into 1 153.807 * [taylor]: Taking taylor expansion of (log (* 2 n)) in k 153.807 * [taylor]: Taking taylor expansion of (* 2 n) in k 153.807 * [taylor]: Taking taylor expansion of 2 in k 153.807 * [backup-simplify]: Simplify 2 into 2 153.807 * [taylor]: Taking taylor expansion of n in k 153.807 * [backup-simplify]: Simplify n into n 153.807 * [backup-simplify]: Simplify (* 2 n) into (* 2 n) 153.807 * [backup-simplify]: Simplify (log (* 2 n)) into (log (* 2 n)) 153.807 * [backup-simplify]: Simplify (* 1/2 0) into 0 153.808 * [backup-simplify]: Simplify (- 0) into 0 153.808 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 153.808 * [backup-simplify]: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 153.808 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 153.808 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 153.808 * [taylor]: Taking taylor expansion of (/ 1 k) in k 153.808 * [taylor]: Taking taylor expansion of k in k 153.808 * [backup-simplify]: Simplify 0 into 0 153.808 * [backup-simplify]: Simplify 1 into 1 153.809 * [backup-simplify]: Simplify (/ 1 1) into 1 153.809 * [backup-simplify]: Simplify (sqrt 0) into 0 153.811 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 153.811 * [taylor]: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in k 153.811 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 153.811 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 153.811 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 153.811 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 153.811 * [taylor]: Taking taylor expansion of 1/2 in k 153.811 * [backup-simplify]: Simplify 1/2 into 1/2 153.811 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 153.811 * [taylor]: Taking taylor expansion of 1/2 in k 153.811 * [backup-simplify]: Simplify 1/2 into 1/2 153.811 * [taylor]: Taking taylor expansion of k in k 153.811 * [backup-simplify]: Simplify 0 into 0 153.811 * [backup-simplify]: Simplify 1 into 1 153.811 * [taylor]: Taking taylor expansion of (log (* 2 n)) in k 153.811 * [taylor]: Taking taylor expansion of (* 2 n) in k 153.811 * [taylor]: Taking taylor expansion of 2 in k 153.811 * [backup-simplify]: Simplify 2 into 2 153.811 * [taylor]: Taking taylor expansion of n in k 153.811 * [backup-simplify]: Simplify n into n 153.811 * [backup-simplify]: Simplify (* 2 n) into (* 2 n) 153.811 * [backup-simplify]: Simplify (log (* 2 n)) into (log (* 2 n)) 153.812 * [backup-simplify]: Simplify (* 1/2 0) into 0 153.812 * [backup-simplify]: Simplify (- 0) into 0 153.813 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 153.813 * [backup-simplify]: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 153.813 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 153.813 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 153.813 * [taylor]: Taking taylor expansion of (/ 1 k) in k 153.813 * [taylor]: Taking taylor expansion of k in k 153.813 * [backup-simplify]: Simplify 0 into 0 153.813 * [backup-simplify]: Simplify 1 into 1 153.813 * [backup-simplify]: Simplify (/ 1 1) into 1 153.814 * [backup-simplify]: Simplify (sqrt 0) into 0 153.815 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 153.815 * [backup-simplify]: Simplify (* (pow (* 2 n) 1/2) 0) into 0 153.815 * [taylor]: Taking taylor expansion of 0 in n 153.815 * [backup-simplify]: Simplify 0 into 0 153.815 * [backup-simplify]: Simplify 0 into 0 153.816 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 n)) into 0 153.817 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 n) 1)))) 1) into 0 153.817 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 153.818 * [backup-simplify]: Simplify (- 1/2) into -1/2 153.818 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 153.819 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 n)))) into (- (* 1/2 (log (* 2 n)))) 153.819 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 n)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 n)))) 1) 1)))) into (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) 153.819 * [backup-simplify]: Simplify (+ (* (pow (* 2 n) 1/2) +nan.0) (* (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt n)))) 153.820 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt n)))) in n 153.820 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt n))) in n 153.820 * [taylor]: Taking taylor expansion of +nan.0 in n 153.820 * [backup-simplify]: Simplify +nan.0 into +nan.0 153.820 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt n)) in n 153.820 * [taylor]: Taking taylor expansion of (sqrt 2) in n 153.820 * [taylor]: Taking taylor expansion of 2 in n 153.820 * [backup-simplify]: Simplify 2 into 2 153.820 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 153.821 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 153.821 * [taylor]: Taking taylor expansion of (sqrt n) in n 153.821 * [taylor]: Taking taylor expansion of n in n 153.821 * [backup-simplify]: Simplify 0 into 0 153.821 * [backup-simplify]: Simplify 1 into 1 153.821 * [backup-simplify]: Simplify (sqrt 0) into 0 153.831 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 153.831 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 153.832 * [backup-simplify]: Simplify (* +nan.0 0) into 0 153.833 * [backup-simplify]: Simplify (- 0) into 0 153.833 * [backup-simplify]: Simplify 0 into 0 153.833 * [backup-simplify]: Simplify 0 into 0 153.833 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 153.836 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 153.837 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 n))) into 0 153.839 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 n) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 n) 1)))) 2) into 0 153.840 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 153.840 * [backup-simplify]: Simplify (- 0) into 0 153.841 * [backup-simplify]: Simplify (+ 0 0) into 0 153.842 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 n))))) into 0 153.843 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 n)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* n 2)) (pow (log (* 2 n)) 2))) 153.843 * [backup-simplify]: Simplify (+ (* (pow (* 2 n) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) +nan.0) (* (* 1/8 (* (sqrt (* n 2)) (pow (log (* 2 n)) 2))) 0))) into (- (+ (* +nan.0 (* (sqrt 2) (sqrt n))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt n)))))) 153.844 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt n))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt n)))))) in n 153.844 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt n))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt n))))) in n 153.844 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt n))) in n 153.844 * [taylor]: Taking taylor expansion of +nan.0 in n 153.844 * [backup-simplify]: Simplify +nan.0 into +nan.0 153.844 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt n)) in n 153.844 * [taylor]: Taking taylor expansion of (sqrt 2) in n 153.844 * [taylor]: Taking taylor expansion of 2 in n 153.844 * [backup-simplify]: Simplify 2 into 2 153.844 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 153.845 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 153.845 * [taylor]: Taking taylor expansion of (sqrt n) in n 153.845 * [taylor]: Taking taylor expansion of n in n 153.845 * [backup-simplify]: Simplify 0 into 0 153.845 * [backup-simplify]: Simplify 1 into 1 153.845 * [backup-simplify]: Simplify (sqrt 0) into 0 153.846 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 153.846 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt n)))) in n 153.846 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt n))) in n 153.846 * [taylor]: Taking taylor expansion of +nan.0 in n 153.846 * [backup-simplify]: Simplify +nan.0 into +nan.0 153.846 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 n))) (sqrt n)) in n 153.846 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 n))) in n 153.846 * [taylor]: Taking taylor expansion of (sqrt 2) in n 153.846 * [taylor]: Taking taylor expansion of 2 in n 153.846 * [backup-simplify]: Simplify 2 into 2 153.846 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 153.847 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 153.847 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 153.847 * [taylor]: Taking taylor expansion of (* 2 n) in n 153.847 * [taylor]: Taking taylor expansion of 2 in n 153.847 * [backup-simplify]: Simplify 2 into 2 153.847 * [taylor]: Taking taylor expansion of n in n 153.847 * [backup-simplify]: Simplify 0 into 0 153.847 * [backup-simplify]: Simplify 1 into 1 153.847 * [backup-simplify]: Simplify (* 2 0) into 0 153.848 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 153.848 * [backup-simplify]: Simplify (log 2) into (log 2) 153.848 * [taylor]: Taking taylor expansion of (sqrt n) in n 153.848 * [taylor]: Taking taylor expansion of n in n 153.848 * [backup-simplify]: Simplify 0 into 0 153.848 * [backup-simplify]: Simplify 1 into 1 153.848 * [backup-simplify]: Simplify (sqrt 0) into 0 153.849 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 153.849 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 153.849 * [backup-simplify]: Simplify (* +nan.0 0) into 0 153.850 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 153.850 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (sqrt 2)) 153.851 * [backup-simplify]: Simplify (* (* (+ (log 2) (log n)) (sqrt 2)) 0) into 0 153.851 * [backup-simplify]: Simplify (* +nan.0 0) into 0 153.851 * [backup-simplify]: Simplify (- 0) into 0 153.852 * [backup-simplify]: Simplify (+ 0 0) into 0 153.852 * [backup-simplify]: Simplify (- 0) into 0 153.852 * [backup-simplify]: Simplify 0 into 0 153.853 * [backup-simplify]: Simplify (+ (* (sqrt 2) +nan.0) (* 0 0)) into (- (* +nan.0 (sqrt 2))) 153.856 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (sqrt 2)))) (* 0 0)) into (- (* +nan.0 (sqrt 2))) 153.857 * [backup-simplify]: Simplify (- (- (* +nan.0 (sqrt 2)))) into (- (* +nan.0 (sqrt 2))) 153.858 * [backup-simplify]: Simplify (- (* +nan.0 (sqrt 2))) into (- (* +nan.0 (sqrt 2))) 153.858 * [backup-simplify]: Simplify 0 into 0 153.859 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 153.861 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 153.862 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 n)))) into 0 153.863 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 n) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 n) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 n) 1)))) 6) into 0 153.864 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 153.864 * [backup-simplify]: Simplify (- 0) into 0 153.865 * [backup-simplify]: Simplify (+ 0 0) into 0 153.865 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 n)))))) into 0 153.866 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 n)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 n)))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* n 2)) (pow (log (* 2 n)) 3))) 153.867 * [backup-simplify]: Simplify (+ (* (pow (* 2 n) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) +nan.0) (+ (* (* 1/8 (* (sqrt (* n 2)) (pow (log (* 2 n)) 2))) +nan.0) (* (* -1/48 (* (sqrt (* n 2)) (pow (log (* 2 n)) 3))) 0)))) into (- (+ (* +nan.0 (* (sqrt 2) (sqrt n))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt n))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt n)))))))) 153.867 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt n))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt n))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt n)))))))) in n 153.867 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt n))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt n))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt n))))))) in n 153.867 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt n))) in n 153.867 * [taylor]: Taking taylor expansion of +nan.0 in n 153.867 * [backup-simplify]: Simplify +nan.0 into +nan.0 153.867 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt n)) in n 153.867 * [taylor]: Taking taylor expansion of (sqrt 2) in n 153.867 * [taylor]: Taking taylor expansion of 2 in n 153.867 * [backup-simplify]: Simplify 2 into 2 153.868 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 153.868 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 153.868 * [taylor]: Taking taylor expansion of (sqrt n) in n 153.868 * [taylor]: Taking taylor expansion of n in n 153.868 * [backup-simplify]: Simplify 0 into 0 153.868 * [backup-simplify]: Simplify 1 into 1 153.868 * [backup-simplify]: Simplify (sqrt 0) into 0 153.869 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 153.869 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt n))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt n)))))) in n 153.869 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt n))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt n))))) in n 153.869 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt n))) in n 153.869 * [taylor]: Taking taylor expansion of +nan.0 in n 153.869 * [backup-simplify]: Simplify +nan.0 into +nan.0 153.869 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 n))) (sqrt n)) in n 153.869 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 n))) in n 153.869 * [taylor]: Taking taylor expansion of (sqrt 2) in n 153.869 * [taylor]: Taking taylor expansion of 2 in n 153.869 * [backup-simplify]: Simplify 2 into 2 153.870 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 153.870 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 153.870 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 153.870 * [taylor]: Taking taylor expansion of (* 2 n) in n 153.870 * [taylor]: Taking taylor expansion of 2 in n 153.870 * [backup-simplify]: Simplify 2 into 2 153.870 * [taylor]: Taking taylor expansion of n in n 153.870 * [backup-simplify]: Simplify 0 into 0 153.870 * [backup-simplify]: Simplify 1 into 1 153.870 * [backup-simplify]: Simplify (* 2 0) into 0 153.871 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 153.871 * [backup-simplify]: Simplify (log 2) into (log 2) 153.871 * [taylor]: Taking taylor expansion of (sqrt n) in n 153.871 * [taylor]: Taking taylor expansion of n in n 153.871 * [backup-simplify]: Simplify 0 into 0 153.871 * [backup-simplify]: Simplify 1 into 1 153.871 * [backup-simplify]: Simplify (sqrt 0) into 0 153.872 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 153.872 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt n)))) in n 153.872 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt n))) in n 153.872 * [taylor]: Taking taylor expansion of +nan.0 in n 153.872 * [backup-simplify]: Simplify +nan.0 into +nan.0 153.872 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt n)) in n 153.872 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 n)) 2)) in n 153.872 * [taylor]: Taking taylor expansion of (sqrt 2) in n 153.873 * [taylor]: Taking taylor expansion of 2 in n 153.873 * [backup-simplify]: Simplify 2 into 2 153.873 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 153.873 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 153.873 * [taylor]: Taking taylor expansion of (pow (log (* 2 n)) 2) in n 153.873 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 153.873 * [taylor]: Taking taylor expansion of (* 2 n) in n 153.873 * [taylor]: Taking taylor expansion of 2 in n 153.873 * [backup-simplify]: Simplify 2 into 2 153.873 * [taylor]: Taking taylor expansion of n in n 153.873 * [backup-simplify]: Simplify 0 into 0 153.873 * [backup-simplify]: Simplify 1 into 1 153.874 * [backup-simplify]: Simplify (* 2 0) into 0 153.874 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 153.874 * [backup-simplify]: Simplify (log 2) into (log 2) 153.876 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 153.876 * [taylor]: Taking taylor expansion of (sqrt n) in n 153.876 * [taylor]: Taking taylor expansion of n in n 153.876 * [backup-simplify]: Simplify 0 into 0 153.876 * [backup-simplify]: Simplify 1 into 1 153.876 * [backup-simplify]: Simplify (sqrt 0) into 0 153.877 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 153.878 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 153.879 * [backup-simplify]: Simplify (* +nan.0 0) into 0 153.879 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 153.880 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (sqrt 2)) 153.881 * [backup-simplify]: Simplify (* (* (+ (log 2) (log n)) (sqrt 2)) 0) into 0 153.881 * [backup-simplify]: Simplify (* +nan.0 0) into 0 153.882 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 153.883 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 153.884 * [backup-simplify]: Simplify (* (+ (log 2) (log n)) (+ (log 2) (log n))) into (pow (+ (log 2) (log n)) 2) 153.885 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log 2) (log n)) 2)) into (* (pow (+ (log 2) (log n)) 2) (sqrt 2)) 153.886 * [backup-simplify]: Simplify (* (* (pow (+ (log 2) (log n)) 2) (sqrt 2)) 0) into 0 153.886 * [backup-simplify]: Simplify (* +nan.0 0) into 0 153.886 * [backup-simplify]: Simplify (- 0) into 0 153.887 * [backup-simplify]: Simplify (+ 0 0) into 0 153.887 * [backup-simplify]: Simplify (- 0) into 0 153.888 * [backup-simplify]: Simplify (+ 0 0) into 0 153.888 * [backup-simplify]: Simplify (- 0) into 0 153.888 * [backup-simplify]: Simplify 0 into 0 153.890 * [backup-simplify]: Simplify (+ (* (sqrt 2) +nan.0) (* 0 0)) into (- (* +nan.0 (sqrt 2))) 153.894 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (sqrt 2)))) (* 0 0)) into (- (* +nan.0 (sqrt 2))) 153.894 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0 153.895 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 153.895 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 153.896 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log 2) (log n)))) into 0 153.897 * [backup-simplify]: Simplify (+ (* (* (+ (log 2) (log n)) (sqrt 2)) +nan.0) (* 0 0)) into (- (+ (* +nan.0 (* (log 2) (sqrt 2))) (- (* +nan.0 (* (sqrt 2) (log n)))))) 153.899 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (log 2) (sqrt 2))) (- (* +nan.0 (* (sqrt 2) (log n))))))) (* 0 0)) into (- (+ (* +nan.0 (* (log 2) (sqrt 2))) (- (* +nan.0 (* (sqrt 2) (log n)))))) 153.900 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (log 2) (sqrt 2))) (- (* +nan.0 (* (sqrt 2) (log n))))))) into (- (+ (* +nan.0 (* (log 2) (sqrt 2))) (- (* +nan.0 (* (sqrt 2) (log n)))))) 153.903 * [backup-simplify]: Simplify (+ (- (* +nan.0 (sqrt 2))) (- (+ (* +nan.0 (* (log 2) (sqrt 2))) (- (* +nan.0 (* (sqrt 2) (log n))))))) into (- (+ (* +nan.0 (sqrt 2)) (- (+ (* +nan.0 (* (log 2) (sqrt 2))) (- (* +nan.0 (* (sqrt 2) (log n)))))))) 153.905 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (sqrt 2)) (- (+ (* +nan.0 (* (log 2) (sqrt 2))) (- (* +nan.0 (* (sqrt 2) (log n))))))))) into (- (+ (* +nan.0 (sqrt 2)) (- (+ (* +nan.0 (* (log 2) (sqrt 2))) (- (* +nan.0 (* (sqrt 2) (log n)))))))) 153.907 * [backup-simplify]: Simplify (- (+ (* +nan.0 (sqrt 2)) (- (+ (* +nan.0 (* (log 2) (sqrt 2))) (- (* +nan.0 (* (sqrt 2) (log n)))))))) into (- (+ (* +nan.0 (sqrt 2)) (- (+ (* +nan.0 (* (log 2) (sqrt 2))) (- (* +nan.0 (* (sqrt 2) (log n)))))))) 153.909 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 153.909 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 153.911 * [backup-simplify]: Simplify (+ (* (sqrt 2) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (sqrt 2))) 153.914 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (sqrt 2)))) (+ (* 0 (- (* +nan.0 (sqrt 2)))) (* 0 0))) into (- (* +nan.0 (sqrt 2))) 153.915 * [backup-simplify]: Simplify (- (- (* +nan.0 (sqrt 2)))) into (- (* +nan.0 (sqrt 2))) 153.916 * [backup-simplify]: Simplify (- (* +nan.0 (sqrt 2))) into (- (* +nan.0 (sqrt 2))) 153.920 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (sqrt 2))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (sqrt 2)) (- (+ (* +nan.0 (* (log 2) (sqrt 2))) (- (* +nan.0 (* (sqrt 2) (log n)))))))) (* n k)) (* (- (* +nan.0 (sqrt 2))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n k))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* (log n) k)))) (- (+ (* +nan.0 (* (sqrt 2) n)) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n k)))) (- (* +nan.0 (* (sqrt 2) (pow n 2)))))))))))) 153.920 * [backup-simplify]: Simplify (* (/ 1 (sqrt (/ 1 k))) (pow (* 2 (/ 1 n)) (- 1/2 (/ (/ 1 k) 2)))) into (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) 153.920 * [approximate]: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in (k n) around 0 153.920 * [taylor]: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n 153.920 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 153.920 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 153.920 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 153.920 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 153.920 * [taylor]: Taking taylor expansion of 1/2 in n 153.920 * [backup-simplify]: Simplify 1/2 into 1/2 153.920 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 153.920 * [taylor]: Taking taylor expansion of 1/2 in n 153.920 * [backup-simplify]: Simplify 1/2 into 1/2 153.920 * [taylor]: Taking taylor expansion of (/ 1 k) in n 153.920 * [taylor]: Taking taylor expansion of k in n 153.920 * [backup-simplify]: Simplify k into k 153.920 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 153.921 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 153.921 * [taylor]: Taking taylor expansion of (/ 2 n) in n 153.921 * [taylor]: Taking taylor expansion of 2 in n 153.921 * [backup-simplify]: Simplify 2 into 2 153.921 * [taylor]: Taking taylor expansion of n in n 153.921 * [backup-simplify]: Simplify 0 into 0 153.921 * [backup-simplify]: Simplify 1 into 1 153.921 * [backup-simplify]: Simplify (/ 2 1) into 2 153.921 * [backup-simplify]: Simplify (log 2) into (log 2) 153.921 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 153.921 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 153.922 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 153.922 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 153.923 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 153.923 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 153.923 * [taylor]: Taking taylor expansion of (sqrt k) in n 153.924 * [taylor]: Taking taylor expansion of k in n 153.924 * [backup-simplify]: Simplify k into k 153.924 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 153.924 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 153.924 * [taylor]: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 153.924 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 153.924 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 153.924 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 153.924 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 153.924 * [taylor]: Taking taylor expansion of 1/2 in k 153.924 * [backup-simplify]: Simplify 1/2 into 1/2 153.924 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 153.924 * [taylor]: Taking taylor expansion of 1/2 in k 153.924 * [backup-simplify]: Simplify 1/2 into 1/2 153.924 * [taylor]: Taking taylor expansion of (/ 1 k) in k 153.924 * [taylor]: Taking taylor expansion of k in k 153.924 * [backup-simplify]: Simplify 0 into 0 153.924 * [backup-simplify]: Simplify 1 into 1 153.924 * [backup-simplify]: Simplify (/ 1 1) into 1 153.924 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in k 153.924 * [taylor]: Taking taylor expansion of (/ 2 n) in k 153.925 * [taylor]: Taking taylor expansion of 2 in k 153.925 * [backup-simplify]: Simplify 2 into 2 153.925 * [taylor]: Taking taylor expansion of n in k 153.925 * [backup-simplify]: Simplify n into n 153.925 * [backup-simplify]: Simplify (/ 2 n) into (/ 2 n) 153.925 * [backup-simplify]: Simplify (log (/ 2 n)) into (log (/ 2 n)) 153.925 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 153.926 * [backup-simplify]: Simplify (- 1/2) into -1/2 153.926 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 153.926 * [backup-simplify]: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 153.926 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 153.926 * [taylor]: Taking taylor expansion of (sqrt k) in k 153.926 * [taylor]: Taking taylor expansion of k in k 153.926 * [backup-simplify]: Simplify 0 into 0 153.926 * [backup-simplify]: Simplify 1 into 1 153.927 * [backup-simplify]: Simplify (sqrt 0) into 0 153.928 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 153.928 * [taylor]: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 153.928 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 153.928 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 153.928 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 153.928 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 153.928 * [taylor]: Taking taylor expansion of 1/2 in k 153.928 * [backup-simplify]: Simplify 1/2 into 1/2 153.928 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 153.928 * [taylor]: Taking taylor expansion of 1/2 in k 153.928 * [backup-simplify]: Simplify 1/2 into 1/2 153.928 * [taylor]: Taking taylor expansion of (/ 1 k) in k 153.928 * [taylor]: Taking taylor expansion of k in k 153.928 * [backup-simplify]: Simplify 0 into 0 153.928 * [backup-simplify]: Simplify 1 into 1 153.929 * [backup-simplify]: Simplify (/ 1 1) into 1 153.929 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in k 153.929 * [taylor]: Taking taylor expansion of (/ 2 n) in k 153.929 * [taylor]: Taking taylor expansion of 2 in k 153.929 * [backup-simplify]: Simplify 2 into 2 153.929 * [taylor]: Taking taylor expansion of n in k 153.929 * [backup-simplify]: Simplify n into n 153.929 * [backup-simplify]: Simplify (/ 2 n) into (/ 2 n) 153.929 * [backup-simplify]: Simplify (log (/ 2 n)) into (log (/ 2 n)) 153.930 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 153.930 * [backup-simplify]: Simplify (- 1/2) into -1/2 153.931 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 153.931 * [backup-simplify]: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 153.931 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 153.931 * [taylor]: Taking taylor expansion of (sqrt k) in k 153.931 * [taylor]: Taking taylor expansion of k in k 153.931 * [backup-simplify]: Simplify 0 into 0 153.931 * [backup-simplify]: Simplify 1 into 1 153.938 * [backup-simplify]: Simplify (sqrt 0) into 0 153.940 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 153.941 * [backup-simplify]: Simplify (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 0) into 0 153.941 * [taylor]: Taking taylor expansion of 0 in n 153.941 * [backup-simplify]: Simplify 0 into 0 153.941 * [backup-simplify]: Simplify 0 into 0 153.941 * [backup-simplify]: Simplify (+ (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) (* 0 0)) into (- (* +nan.0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) 153.941 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 153.941 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 153.941 * [taylor]: Taking taylor expansion of +nan.0 in n 153.941 * [backup-simplify]: Simplify +nan.0 into +nan.0 153.941 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 153.941 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 153.941 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 153.942 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 153.942 * [taylor]: Taking taylor expansion of 1/2 in n 153.942 * [backup-simplify]: Simplify 1/2 into 1/2 153.942 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 153.942 * [taylor]: Taking taylor expansion of 1/2 in n 153.942 * [backup-simplify]: Simplify 1/2 into 1/2 153.942 * [taylor]: Taking taylor expansion of (/ 1 k) in n 153.942 * [taylor]: Taking taylor expansion of k in n 153.942 * [backup-simplify]: Simplify k into k 153.942 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 153.942 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 153.942 * [taylor]: Taking taylor expansion of (/ 2 n) in n 153.942 * [taylor]: Taking taylor expansion of 2 in n 153.942 * [backup-simplify]: Simplify 2 into 2 153.942 * [taylor]: Taking taylor expansion of n in n 153.942 * [backup-simplify]: Simplify 0 into 0 153.942 * [backup-simplify]: Simplify 1 into 1 153.942 * [backup-simplify]: Simplify (/ 2 1) into 2 153.943 * [backup-simplify]: Simplify (log 2) into (log 2) 153.943 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 153.943 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 153.943 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 153.944 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 153.945 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 153.945 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 153.946 * [backup-simplify]: Simplify (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 153.946 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 153.947 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 153.947 * [backup-simplify]: Simplify 0 into 0 153.950 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 153.951 * [backup-simplify]: Simplify (+ (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) 153.951 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 153.951 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 153.951 * [taylor]: Taking taylor expansion of +nan.0 in n 153.951 * [backup-simplify]: Simplify +nan.0 into +nan.0 153.951 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 153.951 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 153.951 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 153.951 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 153.951 * [taylor]: Taking taylor expansion of 1/2 in n 153.952 * [backup-simplify]: Simplify 1/2 into 1/2 153.952 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 153.952 * [taylor]: Taking taylor expansion of 1/2 in n 153.952 * [backup-simplify]: Simplify 1/2 into 1/2 153.952 * [taylor]: Taking taylor expansion of (/ 1 k) in n 153.952 * [taylor]: Taking taylor expansion of k in n 153.952 * [backup-simplify]: Simplify k into k 153.952 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 153.952 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 153.952 * [taylor]: Taking taylor expansion of (/ 2 n) in n 153.952 * [taylor]: Taking taylor expansion of 2 in n 153.952 * [backup-simplify]: Simplify 2 into 2 153.952 * [taylor]: Taking taylor expansion of n in n 153.952 * [backup-simplify]: Simplify 0 into 0 153.952 * [backup-simplify]: Simplify 1 into 1 153.953 * [backup-simplify]: Simplify (/ 2 1) into 2 153.953 * [backup-simplify]: Simplify (log 2) into (log 2) 153.953 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 153.953 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 153.953 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 153.954 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 153.955 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 153.955 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 153.956 * [backup-simplify]: Simplify (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 153.956 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 153.957 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 153.958 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0 153.959 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 153.960 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 153.960 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 153.960 * [backup-simplify]: Simplify (- 0) into 0 153.961 * [backup-simplify]: Simplify (+ 0 0) into 0 153.962 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 153.962 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 153.963 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 153.964 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into 0 153.965 * [backup-simplify]: Simplify (- 0) into 0 153.965 * [backup-simplify]: Simplify 0 into 0 153.965 * [backup-simplify]: Simplify 0 into 0 153.969 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 153.970 * [backup-simplify]: Simplify (+ (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) 153.970 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 153.970 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 153.970 * [taylor]: Taking taylor expansion of +nan.0 in n 153.970 * [backup-simplify]: Simplify +nan.0 into +nan.0 153.970 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 153.970 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 153.970 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 153.970 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 153.970 * [taylor]: Taking taylor expansion of 1/2 in n 153.970 * [backup-simplify]: Simplify 1/2 into 1/2 153.970 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 153.970 * [taylor]: Taking taylor expansion of 1/2 in n 153.970 * [backup-simplify]: Simplify 1/2 into 1/2 153.970 * [taylor]: Taking taylor expansion of (/ 1 k) in n 153.970 * [taylor]: Taking taylor expansion of k in n 153.971 * [backup-simplify]: Simplify k into k 153.971 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 153.971 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 153.971 * [taylor]: Taking taylor expansion of (/ 2 n) in n 153.971 * [taylor]: Taking taylor expansion of 2 in n 153.971 * [backup-simplify]: Simplify 2 into 2 153.971 * [taylor]: Taking taylor expansion of n in n 153.971 * [backup-simplify]: Simplify 0 into 0 153.971 * [backup-simplify]: Simplify 1 into 1 153.971 * [backup-simplify]: Simplify (/ 2 1) into 2 153.972 * [backup-simplify]: Simplify (log 2) into (log 2) 153.972 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 153.972 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 153.972 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 153.973 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 153.973 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 153.973 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 153.974 * [backup-simplify]: Simplify (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 153.974 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 153.975 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 153.976 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow k 2)))))))) 153.976 * [backup-simplify]: Simplify (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* 2 (/ 1 (- n))) (- 1/2 (/ (/ 1 (- k)) 2)))) into (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 153.976 * [approximate]: Taking taylor expansion of (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (k n) around 0 153.976 * [taylor]: Taking taylor expansion of (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 153.976 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 153.976 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 153.976 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 153.976 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 153.976 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 153.976 * [taylor]: Taking taylor expansion of 1/2 in n 153.976 * [backup-simplify]: Simplify 1/2 into 1/2 153.976 * [taylor]: Taking taylor expansion of (/ 1 k) in n 153.976 * [taylor]: Taking taylor expansion of k in n 153.976 * [backup-simplify]: Simplify k into k 153.976 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 153.976 * [taylor]: Taking taylor expansion of 1/2 in n 153.976 * [backup-simplify]: Simplify 1/2 into 1/2 153.976 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 153.976 * [taylor]: Taking taylor expansion of (/ -2 n) in n 153.976 * [taylor]: Taking taylor expansion of -2 in n 153.976 * [backup-simplify]: Simplify -2 into -2 153.976 * [taylor]: Taking taylor expansion of n in n 153.976 * [backup-simplify]: Simplify 0 into 0 153.976 * [backup-simplify]: Simplify 1 into 1 153.977 * [backup-simplify]: Simplify (/ -2 1) into -2 153.977 * [backup-simplify]: Simplify (log -2) into (log -2) 153.977 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 153.977 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 153.978 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 153.978 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 153.978 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 153.978 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 153.978 * [taylor]: Taking taylor expansion of (/ -1 k) in n 153.978 * [taylor]: Taking taylor expansion of -1 in n 153.978 * [backup-simplify]: Simplify -1 into -1 153.978 * [taylor]: Taking taylor expansion of k in n 153.978 * [backup-simplify]: Simplify k into k 153.978 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 153.978 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 153.979 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 153.979 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 153.979 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) 153.979 * [taylor]: Taking taylor expansion of (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 153.979 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 153.979 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 153.979 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 153.979 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 153.979 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 153.979 * [taylor]: Taking taylor expansion of 1/2 in k 153.979 * [backup-simplify]: Simplify 1/2 into 1/2 153.979 * [taylor]: Taking taylor expansion of (/ 1 k) in k 153.979 * [taylor]: Taking taylor expansion of k in k 153.979 * [backup-simplify]: Simplify 0 into 0 153.979 * [backup-simplify]: Simplify 1 into 1 153.979 * [backup-simplify]: Simplify (/ 1 1) into 1 153.979 * [taylor]: Taking taylor expansion of 1/2 in k 153.979 * [backup-simplify]: Simplify 1/2 into 1/2 153.979 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in k 153.980 * [taylor]: Taking taylor expansion of (/ -2 n) in k 153.980 * [taylor]: Taking taylor expansion of -2 in k 153.980 * [backup-simplify]: Simplify -2 into -2 153.980 * [taylor]: Taking taylor expansion of n in k 153.980 * [backup-simplify]: Simplify n into n 153.980 * [backup-simplify]: Simplify (/ -2 n) into (/ -2 n) 153.980 * [backup-simplify]: Simplify (log (/ -2 n)) into (log (/ -2 n)) 153.980 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 153.980 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 153.980 * [backup-simplify]: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 153.980 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 153.980 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 153.980 * [taylor]: Taking taylor expansion of (/ -1 k) in k 153.980 * [taylor]: Taking taylor expansion of -1 in k 153.980 * [backup-simplify]: Simplify -1 into -1 153.980 * [taylor]: Taking taylor expansion of k in k 153.981 * [backup-simplify]: Simplify 0 into 0 153.981 * [backup-simplify]: Simplify 1 into 1 153.981 * [backup-simplify]: Simplify (/ -1 1) into -1 153.981 * [backup-simplify]: Simplify (sqrt 0) into 0 153.982 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 153.982 * [backup-simplify]: Simplify (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) 153.982 * [taylor]: Taking taylor expansion of (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 153.982 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 153.982 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 153.982 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 153.982 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 153.982 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 153.982 * [taylor]: Taking taylor expansion of 1/2 in k 153.982 * [backup-simplify]: Simplify 1/2 into 1/2 153.982 * [taylor]: Taking taylor expansion of (/ 1 k) in k 153.982 * [taylor]: Taking taylor expansion of k in k 153.982 * [backup-simplify]: Simplify 0 into 0 153.982 * [backup-simplify]: Simplify 1 into 1 153.982 * [backup-simplify]: Simplify (/ 1 1) into 1 153.982 * [taylor]: Taking taylor expansion of 1/2 in k 153.982 * [backup-simplify]: Simplify 1/2 into 1/2 153.982 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in k 153.982 * [taylor]: Taking taylor expansion of (/ -2 n) in k 153.982 * [taylor]: Taking taylor expansion of -2 in k 153.983 * [backup-simplify]: Simplify -2 into -2 153.983 * [taylor]: Taking taylor expansion of n in k 153.983 * [backup-simplify]: Simplify n into n 153.983 * [backup-simplify]: Simplify (/ -2 n) into (/ -2 n) 153.983 * [backup-simplify]: Simplify (log (/ -2 n)) into (log (/ -2 n)) 153.983 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 153.983 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 153.983 * [backup-simplify]: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 153.983 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 153.983 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 153.983 * [taylor]: Taking taylor expansion of (/ -1 k) in k 153.983 * [taylor]: Taking taylor expansion of -1 in k 153.983 * [backup-simplify]: Simplify -1 into -1 153.983 * [taylor]: Taking taylor expansion of k in k 153.983 * [backup-simplify]: Simplify 0 into 0 153.983 * [backup-simplify]: Simplify 1 into 1 153.984 * [backup-simplify]: Simplify (/ -1 1) into -1 153.984 * [backup-simplify]: Simplify (sqrt 0) into 0 153.985 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 153.985 * [backup-simplify]: Simplify (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) 153.985 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) in n 153.985 * [taylor]: Taking taylor expansion of +nan.0 in n 153.985 * [backup-simplify]: Simplify +nan.0 into +nan.0 153.985 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 153.985 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 153.985 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 153.985 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 153.985 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 153.985 * [taylor]: Taking taylor expansion of 1/2 in n 153.985 * [backup-simplify]: Simplify 1/2 into 1/2 153.985 * [taylor]: Taking taylor expansion of (/ 1 k) in n 153.985 * [taylor]: Taking taylor expansion of k in n 153.985 * [backup-simplify]: Simplify k into k 153.985 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 153.985 * [taylor]: Taking taylor expansion of 1/2 in n 153.985 * [backup-simplify]: Simplify 1/2 into 1/2 153.985 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 153.985 * [taylor]: Taking taylor expansion of (/ -2 n) in n 153.985 * [taylor]: Taking taylor expansion of -2 in n 153.985 * [backup-simplify]: Simplify -2 into -2 153.985 * [taylor]: Taking taylor expansion of n in n 153.985 * [backup-simplify]: Simplify 0 into 0 153.985 * [backup-simplify]: Simplify 1 into 1 153.986 * [backup-simplify]: Simplify (/ -2 1) into -2 153.986 * [backup-simplify]: Simplify (log -2) into (log -2) 153.986 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 153.986 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 153.986 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 153.987 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 153.987 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 153.987 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) 153.988 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) 153.988 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 153.990 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 153.991 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)))) 153.991 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 153.991 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) in n 153.991 * [taylor]: Taking taylor expansion of +nan.0 in n 153.991 * [backup-simplify]: Simplify +nan.0 into +nan.0 153.991 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 153.991 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 153.991 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 153.991 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 153.991 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 153.991 * [taylor]: Taking taylor expansion of 1/2 in n 153.991 * [backup-simplify]: Simplify 1/2 into 1/2 153.991 * [taylor]: Taking taylor expansion of (/ 1 k) in n 153.991 * [taylor]: Taking taylor expansion of k in n 153.991 * [backup-simplify]: Simplify k into k 153.991 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 153.991 * [taylor]: Taking taylor expansion of 1/2 in n 153.991 * [backup-simplify]: Simplify 1/2 into 1/2 153.991 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 153.991 * [taylor]: Taking taylor expansion of (/ -2 n) in n 153.991 * [taylor]: Taking taylor expansion of -2 in n 153.991 * [backup-simplify]: Simplify -2 into -2 153.991 * [taylor]: Taking taylor expansion of n in n 153.991 * [backup-simplify]: Simplify 0 into 0 153.991 * [backup-simplify]: Simplify 1 into 1 153.992 * [backup-simplify]: Simplify (/ -2 1) into -2 153.992 * [backup-simplify]: Simplify (log -2) into (log -2) 153.992 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 153.992 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 153.992 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 153.993 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 153.993 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 153.993 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) 153.994 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) 153.994 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) 153.995 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0 153.996 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 153.996 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 153.996 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 153.996 * [backup-simplify]: Simplify (+ 0 0) into 0 153.997 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 153.997 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -2) (log n)))) into 0 153.998 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 153.998 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) into 0 153.998 * [backup-simplify]: Simplify 0 into 0 153.999 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 154.001 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 154.002 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)))) 154.002 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 154.002 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) in n 154.002 * [taylor]: Taking taylor expansion of +nan.0 in n 154.002 * [backup-simplify]: Simplify +nan.0 into +nan.0 154.002 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 154.002 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 154.002 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 154.002 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 154.002 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 154.002 * [taylor]: Taking taylor expansion of 1/2 in n 154.002 * [backup-simplify]: Simplify 1/2 into 1/2 154.002 * [taylor]: Taking taylor expansion of (/ 1 k) in n 154.002 * [taylor]: Taking taylor expansion of k in n 154.002 * [backup-simplify]: Simplify k into k 154.002 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 154.002 * [taylor]: Taking taylor expansion of 1/2 in n 154.003 * [backup-simplify]: Simplify 1/2 into 1/2 154.003 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 154.003 * [taylor]: Taking taylor expansion of (/ -2 n) in n 154.003 * [taylor]: Taking taylor expansion of -2 in n 154.003 * [backup-simplify]: Simplify -2 into -2 154.003 * [taylor]: Taking taylor expansion of n in n 154.003 * [backup-simplify]: Simplify 0 into 0 154.003 * [backup-simplify]: Simplify 1 into 1 154.003 * [backup-simplify]: Simplify (/ -2 1) into -2 154.003 * [backup-simplify]: Simplify (log -2) into (log -2) 154.003 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 154.003 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 154.004 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 154.004 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 154.005 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 154.005 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) 154.006 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) 154.006 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) 154.008 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow k 2))) (- (+ (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n)))))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) k))))))) 154.009 * * * [progress]: 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candidate # 154.031 * * * * [progress]: [ 285 / 296 ] simplifiying candidate # 154.031 * * * * [progress]: [ 286 / 296 ] simplifiying candidate # 154.031 * * * * [progress]: [ 287 / 296 ] simplifiying candidate # 154.031 * * * * [progress]: [ 288 / 296 ] simplifiying candidate # 154.031 * * * * [progress]: [ 289 / 296 ] simplifiying candidate # 154.031 * * * * [progress]: [ 290 / 296 ] simplifiying candidate # 154.032 * * * * [progress]: [ 291 / 296 ] simplifiying candidate # 154.032 * * * * [progress]: [ 292 / 296 ] simplifiying candidate # 154.032 * * * * [progress]: [ 293 / 296 ] simplifiying candidate # 154.032 * * * * [progress]: [ 294 / 296 ] simplifiying candidate # 154.032 * * * * [progress]: [ 295 / 296 ] simplifiying candidate # 154.032 * * * * [progress]: [ 296 / 296 ] simplifiying candidate # 154.039 * [simplify]: Simplifying: (expm1 (pow PI (- 1/2 (/ k 2)))) (log1p (pow PI (- 1/2 (/ k 2)))) (* (log PI) (- 1/2 (/ k 2))) (* (log PI) (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) 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(* +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 (* (sqrt 2) (* n k))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* (log n) k)))) (- (+ (* +nan.0 (* (sqrt 2) n)) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n k)))) (- (* +nan.0 (* (sqrt 2) (pow n 2)))))))))))) (- (+ (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow k 2))) (- (+ (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n)))))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) k))))))) 154.047 * * [simplify]: iteration 1: (564 enodes) 154.465 * * [simplify]: iteration 2: (1699 enodes) 155.927 * * [simplify]: Extracting #0: cost 163 inf + 0 155.930 * * [simplify]: Extracting #1: cost 635 inf + 4 155.937 * * [simplify]: Extracting #2: cost 1195 inf + 1662 155.951 * * [simplify]: Extracting #3: cost 1519 inf + 27853 155.973 * * [simplify]: Extracting #4: cost 1058 inf + 161698 156.064 * * [simplify]: Extracting #5: cost 468 inf + 361787 156.160 * * [simplify]: Extracting #6: cost 235 inf + 470690 156.265 * * [simplify]: Extracting #7: cost 43 inf + 573260 156.383 * * [simplify]: Extracting #8: cost 0 inf + 592935 156.523 * * [simplify]: Extracting #9: cost 0 inf + 592134 156.645 * * [simplify]: Extracting #10: cost 0 inf + 591974 156.764 * [simplify]: Simplified to: (expm1 (pow PI (+ 1/2 (* -1/2 k)))) (log1p (pow PI (+ 1/2 (* -1/2 k)))) (* (log PI) (+ 1/2 (* -1/2 k))) (* (log PI) (+ 1/2 (* -1/2 k))) (+ 1/2 (* -1/2 k)) (sqrt PI) (pow PI (/ k 2)) (pow PI (* (cbrt (+ 1/2 (* -1/2 k))) (cbrt (+ 1/2 (* -1/2 k))))) (pow PI (sqrt (+ 1/2 (* -1/2 k)))) PI (pow PI (+ (sqrt (/ k 2)) (sqrt 1/2))) (pow PI 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(* (* n (* (sqrt 2) k)) +nan.0) (fma (* (* (log n) k) (* n (sqrt 2))) +nan.0 (+ (- (* +nan.0 (* (sqrt 2) n))) (* +nan.0 (- (* (log 2) (* n (* (sqrt 2) k))) (* n (* n (sqrt 2))))))))) (+ (* (/ (/ (exp (* (+ 1/2 (* -1/2 k)) (log (* 2 n)))) (* k k)) k) (- +nan.0)) (* +nan.0 (- (/ (exp (* (+ 1/2 (* -1/2 k)) (log (* 2 n)))) k) (/ (exp (* (+ 1/2 (* -1/2 k)) (log (* 2 n)))) (* k k))))) (- (- (* +nan.0 (/ (exp (* (+ 1/2 (* -1/2 k)) (- (log -2) (log (/ -1 n))))) (* k k))) (* +nan.0 (- (exp (* (+ 1/2 (* -1/2 k)) (- (log -2) (log (/ -1 n))))) (/ (exp (* (+ 1/2 (* -1/2 k)) (- (log -2) (log (/ -1 n))))) k))))) 156.804 * * * [progress]: adding candidates to table 161.233 * [progress]: [Phase 3 of 3] Extracting. 161.233 * * [regime]: Finding splitpoints for: (# # # # # # # #) 161.234 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2 PI) n) n k) 161.234 * * * * [regimes]: Trying to branch on (* (* 2 PI) n) from (# # # # # # # #) 161.284 * * * * [regimes]: Trying to branch on n from (# # # # # # # #) 161.342 * * * * [regimes]: Trying to branch on k from (# # # # # # # #) 161.408 * * * [regime]: Found split indices: #